Answer:
V = (3.14)(4.25)²(6)
Step-by-step explanation:
help please ill give brainliest!! please show work
find x
Answer:
x = 10
Step-by-step explanation:
the figure inscribed in the circle is a cyclic quadrilateral , all 4 vertices lie on the circumference.
the opposite angles in a cyclic quadrilateral sum to 180° , that is
6x + 1 + 10x + 19 = 180
16x + 20 = 180 ( subtract 20 from both sides )
16x = 160 ( divide both sides by 16 )
x = 10
A cell phone company charges an initial price of $500 for a new phone and then $60 each month after the purchase. If C (t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function?
The range of the rational function is the set of all real numbers larger than 60 but less than 560, therefore;
Range; [60, 560]
What is a rational function?A rational function, f(x) is a function that can be expressed in the form f(x) = p(x)/q(x), where the functions p(x) and q(x) are polynomial functions.
The initial fee charged by the cell phone company = $500
The monthly charge after purchase = $60
The total cost of owning the cell phone = $500 + $60·t
The average monthly cost of owning a cell phone is therefore;
C(t) = (500 + 60·t)/t
The range of the function is the set of all possible values o C(t), which can be frond from the limit of the function, as follows;
[tex]\lim\limits_{x\to\infty}C(t) = \lim\limits_{x\to\infty}\frac{500 + 60\cdot t}{t} = \lim\limits_{x\to\infty}(\frac{500 }{t} + 60)[/tex] = 60
The limit of the average monthly cost indicates that the range of the function approaches $60 as t approaches infinity.
When t = 1, we get; C(1) = (500 + 60 × 1)/1 = 560
The range of the function is therefore, the set of all real numbers, larger than $60 but less than $560
The range of the function is therefore; [60, 560]
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A graph represents the perimeter y in units for an equilateral triangle with side length x units the slope of the line is 3 and the y intercept is 0
The slope and intercept in this situation is meant as explained below.
We know that,
The linear equation in slope intercept form is equal to y = mx + b, where m is the slope, b is the y-intercept.
In this problem, y is the perimeter in units, x is the side length of a equilateral triangle.
we have,
m = 3
b = 0
substitute
The linear equation is y = 3x,
It is a proportional relationship because the line passes through the origin.
The slope is, m = 3 units / 1 units
That means, the ratio of perimeter of triangle to side length of triangle is 3:1. The y-intercept is 0. Remember that, the y-intercept is the value of y when the value of x is equal to zero.
In this context, the y-intercept is the value of the perimeter when the value of the side length is equal to zero. So, the value of the perimeter is 0 when the value of side length is 0.
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Although part of your question is missing, you might be referring to thid full question:
“ Explain what the slope and intercept mean in each situation. A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0”.
Which describes the transformations applied in the figure above?
A. a counterclockwise rotation of 180 degrees and move 5 units to the left
B. 7 units right and a clockwise rotation of 90 degrees
C. 7 units left and a reflection about the x-axis
D. 7 units left and 2 units up
The statement that describes the transformations applied in the figure above include the following: C. 7 units left and a reflection about the x-axis.
How to reflect the quadrilateral based on the transformation rule?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).
Based on the graph, the coordinates of point A are located at (-6, 1) in quadrant II.
By applying a translation to the A horizontally right by 7 units, the new coordinate A1 of quadrilateral ABCD include the following:
(x, y) → (x + 7, y)
A (-6, 1) → (-6 + 7, 1) = A1 (1, 1)
By applying a reflection over the x-axis to the coordinates of point A1, we have the following coordinates of the image A';
(x, y) → (x, -y)
Point A1 (1, 1) → A' (1, -(1)) = G' (1, -1)
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-Ready
Algebraic Expressions with Exponents-Instruction-Level F
Amelia is building 3 square garden beds that are all the same size. She arranges them side-
by-side to separate certain plants. Amelia wants to know the total area of the garden beds.
length (ft) of one side of a garden bed
Write an expression to show the total
area of the garden beds.
38²
What is the total area if each garden
bed has a length of 4 feet?
ft²
A = $²
7 8 9
6
3
4
51
1
1 2
X
1
t
X
The correct answer is each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.
To find the total area of the garden beds, we can use the expression:
Total area = (length of one side)^2 * number of garden beds
Given that each garden bed has a length of 4 feet, we substitute 4 for the length of one side in the expression:
Total area = (4)^2 * 3
Simplifying:
Total area = 16 * 3
Total area = 48 square feet
Therefore, if each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.
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Which statement best describes the growth rates of the functions below?
The quadratic function grows faster than the exponential function over the entire interval; 0
The exponential function grows faster than the quadratic function over the entire interval; 0
The exponential function grows faster than the quadratic function over only one interval; 2
The exponential function grows faster than the quadratic function over two intervals; 2
"The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
There are three commonly-used forms of quadratics:
Standard Form: y = a x 2 + b x + c y= [tex]ax^2+bx+c y=ax2+bx+c.[/tex]
Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y= a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)
Vertex Form: y = a ( x − h ) 2 + k y= [tex]a(x-h)^2+k y=a(x−h)2+k.[/tex]
Quadratic functions can be represented symbolically by the equation, y(x) = ax2 + bx + c, where a, b, and c are constants, and a ≠ 0. This form is referred to as standard form.
The statement "The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.
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Find the limit of the difference quotients for f(x) = x2+2x+1 if a= -1
The limit of the difference quotients for f(x) = x^2 + 2x + 1 as x approaches -1 is indeterminate.
To find the limit of the difference quotients for the function f(x) = x^2 + 2x + 1 as x approaches -1, we need to evaluate the following expression:
lim(x→-1) [f(x) - f(-1)] / (x - (-1))
First, let's substitute the values into the expression:
lim(x→-1) [tex][(x^2 + 2x + 1) - (-1^2 + 2(-1) + 1)] / (x + 1)[/tex]
Simplifying further:
lim(x→-1) [tex][(x^2 + 2x + 1) - (1 - 2 + 1)] / (x + 1)[/tex]
lim(x→-1)[tex][x^2 + 2x + 1 - 0] / (x + 1)[/tex]
lim(x→-1) [tex](x^2 + 2x + 1) / (x + 1)[/tex]
Now, we can directly substitute x = -1 into the expression:
[tex](-1^2 + 2(-1) + 1) / (-1 + 1)[/tex]
(1 - 2 + 1) / (0)
0 / 0
We have obtained an indeterminate form of 0/0. This indicates that we need to further simplify the expression or use other techniques, such as L'Hôpital's rule, to evaluate the limit. However, without additional information or simplification, we cannot determine the precise value of the limit at x = -1.
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Assume that Canes customer would buy. A maximum of 82000. Units of Alpha and62000 of beta assume that the raw material availability for production is limited to 162000 pounds how many units of each product should Cane produce to maximize profits
The units of each product that Cane should produce to maximize profits will be 62000 units of Beta and 7600 units of
Alpha.
Contribution margin per poundAlpha Beta
Selling price 130 90
Variable cost 78 48
Contribution margin 52 42
Pound per unit 5 2
Contribution margin per pound 10.4 21
Pound Unit
Beta 62000*2 = 124000 62000
Alpha 38000 38000/5 = 7600
Total 162000
Maximum contribution margin = (38000*10.4+124000*21) = 2999200
Highest price = 10.4+5 = 15.40 per pound
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Ayesha is the marketing manager for Superior Stationery Suppliers, a company that supplies a variety of stationery items to its customers, mostly businesses. Ayesha has started a process to understand the key buying motivations for customers. Ayesha must consider each of the following variables in the process, except...
Select the correct answer from each drop-down menu.
Given: Line segment WU is the perpendicular bisector of line TV.
Prove: Line TU ≠ Line VU
WU is the perpendicular bisector of TV and W is the midpoint of TV.
Statements:
WU is the perpendicular bisector of TV.
W is the midpoint of TV.
TW = VW.
∠ZTWU and ∠ZVWU are right angles.
∠ZTWU ≅ ∠LVWU.
WU = WU.
∠ATWU ≅ ∠AVWU.
TU = VU.
Reasons:
Given.
Definition of the perpendicular bisector: It divides a segment into two congruent parts, and W is the midpoint of TV.
Definition of midpoint: The segment TW is congruent to VW because W is the midpoint of TV.
Given that WU is the perpendicular bisector, it means that ∠ZTWU and ∠ZVWU are right angles.
All right angles are congruent.
Reflexive property of congruence: Any segment or angle is congruent to itself.
Corresponding parts of congruent triangles are congruent (CPCTC): Since ∠ATWU and ∠AVWU are corresponding parts of congruent triangles, they are congruent.
Corresponding parts of congruent triangles are congruent (CPCTC): Since TU and VU are corresponding parts of congruent triangles, they are congruent.
Therefore, the correct statements and reasons are:
Statements:
WU is the perpendicular bisector of TV.
W is the midpoint of TV.
TW = VW.
∠ZTWU and ∠ZVWU are right angles.
∠ZTWU ≅ ∠LVWU.
WU = WU.
∠ATWU ≅ ∠AVWU.
TU = VU.
Reasons:
Given.
Definition of the perpendicular bisector.
Definition of midpoint.
Given.
All right angles are congruent.
Reflexive property of congruence.
CPCTC.
CPCTC.
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Is the expression quadratic 3x+5y-2
No, the expression 3x + 5y - 2200 is not a quadratic expression.
A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.
It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.
"3x + 5y - 2" is a linear expression, not a quadratic expression.
In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.
The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.
It is a first-degree polynomial, meaning that the highest power of the variable is 1.
Linear expressions often have a graph that is a straight line.
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No. The expression, 3x + 5y - 2, is not quadratic.
What are quadratic expressions?The expression "3x+5y-2" is a linear expression, not quadratic.
Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.
The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.
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c) A company is considering expanding its business. The expansion will cost 350million initially for the premises and a further sh150 million to refurbish the premises with new equipment. Cash flow projections from the project show the
following cash flows over the next six years.
Year Net cash flows
Sh 000
1 70000
2 70000
3 80000
4 100000
5 100000
6 120000
The equipment will be depreciated to a zero resale value over the same period and after the sixth year, it is expected that the new business could be sold for sh350 million.
Required:
Calculate:
i. The payback period for the project. (5 marks)
ii. The accounting rate of Return (ARR) , using the average investment method.
(5 marks)
iii. The net present value (NPV) of the project. Assume the relevant cost of capital is 12%.
(5 marks)
iv. The internal Rate of Return (IRR) of the project. (5 marks)
i. The payback period for the project is 6 years.
ii. The accounting rate of return (ARR) using the average investment method is 21.18%.
iii. The net present value (NPV) of the project is -165,143.
iv. The internal rate of return (IRR) of the project is approximately 19.61%.
i. The payback period for the project:
To calculate the payback period, we need to determine how long it takes for the cumulative net cash flows to equal or exceed the initial investment of 350 million + 150 million.
Year 1: 70,000, Year 2: 70,000, Year 3: 80,000, Year 4: 100,000, Year 5: 100,000, Year 6: 120,000.
Cumulative Cash Flow:
Year 1: 70,000
Year 2: 70,000 + 70,000 = 140,000
Year 3: 140,000 + 80,000 = 220,000
Year 4: 220,000 + 100,000 = 320,000
Year 5: 320,000 + 100,000 = 420,000
Year 6: 420,000 + 120,000 = 540,000.
The cumulative cash flows exceed the initial investment of 500 million (350 million + 150 million) in Year 6.
So, the payback period for the project is 6 years.
ii. The accounting rate of return (ARR) using the average investment method:
ARR = Average Annual Profit / Average Investment
Average Annual Profit = Sum of Net Cash Flows / Number of Years
Average Annual Profit = (70,000 + 70,000 + 80,000 + 100,000 + 100,000 + 120,000) / 6
Average Annual Profit = 540,000 / 6
Average Annual Profit = 90,000
Average Investment = (Initial Investment + Residual Value) / 2
Average Investment = (500 million + 350 million) / 2
Average Investment = 425 million.
ARR = 90,000 / 425,000 = 0.2118 or 21.18%
iii. The net present value (NPV) of the project:
To calculate NPV, we discount each cash flow to its present value using the cost of capital of 12%.
NPV = (Net Cash Flow1 / [tex](1 + r)^1)[/tex] + (Net Cash Flow2 / [tex](1 + r)^2)[/tex] + ... + (Net Cash Flow6 / (1 + r)^6) - Initial Investment.
[tex]NPV = (70,000 / (1 + 0.12)^1) + (70,000 / (1 + 0.12)^2) + (80,000 / (1 + 0.12)^3) + (100,000 / (1 + 0.12)^4) + (100,000 / (1 + 0.12)^5) + (120,000 / (1 + 0.12)^6) -[/tex] (350 million + 150 million)
Calculating each term and summing them up:
NPV = 54,017 + 48,234 + 54,497 + 62,313 + 55,631 + 60,165 - 500 million
NPV = -165,143
Therefore, the net present value (NPV) of the project is -165,143.
iv. The internal rate of return (IRR) of the project:
To calculate the IRR, we find the discount rate that makes the NPV equal to zero. Using a financial calculator or Excel, we can determine that the IRR for this project is approximately 19.61%.
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Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)
$1300/semiannual period for 8 years at 4.5%/year compounded semiannually
Answer:
Therefore, the amount (future value) of the ordinary annuity is approximately $19,446.27.
Step-by-step explanation:
We can use the formula:
FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)
where we will consider :
FV is the future value,
P is the periodic payment,
r is the interest rate per period,
n is the number of compounding periods per year, and
t is the number of years.
Now given :
P = $1300 (payment per semiannual period)
r = 4.5% per year (or 0.045 as a decimal)
n = 2 (compounded semiannually)
t = 8 years
Plugging in these values into the formula, we will be getting:
FV = 1300 * [(1 + 0.045/2)^(2*8) - 1] / (0.045/2)
Calculating this expression will give us the future value (amount) of the ordinary annuity:
FV = 1300 * [(1 + 0.0225)^(16) - 1] / 0.0225
FV ≈ $19,446.27 (rounded to the nearest cent)
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Kemani Walker
Law of Sines
Jun 15, 9:29:00 PM
?
In ATUV, t = 820 inches, m/U=132° and m2V=25°. Find the length of u, to the
nearest inch.
Answer: u =
Submit Answer
The length of u, to the nearest inch, is 1818 inches.
To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
In this case, we'll use the following formula:
a/sin(A) = b/sin(B) = c/sin(C)
Let's label the sides and angles of the triangle:
Side a = u (length of u)
Side b = t (820 inches)
Side c = v (length of v)
Angle A = m/U (132°)
Angle B = m2V (25°)
Angle C = 180° - A - B (as the sum of angles in a triangle is 180°)
Now, we can use the Law of Sines to set up the equation:
u/sin(A) = t/sin(B)
Plugging in the given values:
u/sin(132°) = 820/sin(25°)
To find the length of u, we'll solve this equation for u.
u = (820 [tex]\times[/tex] sin(132°)) / sin(25°)
Using a calculator, we can evaluate the right side of the equation to get the approximate value of u:
u ≈ (820 [tex]\times[/tex] 0.9397) / 0.4226
u ≈ 1817.54 inches
Rounding to the nearest inch, we have:
u ≈ 1818 inches
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(7x-9)-(8x-5)
Find an expression which represents the difference when 8x-5 is subtracted from 7x-9
The coefficient of x is -1, indicating that there is one fewer x term compared to the original expression. The constant term is -4, which is the result of subtracting 5 from -9.
To find the difference when subtracting 8x - 5 from 7x - 9, we can use the distributive property to distribute the negative sign to each term in 8x - 5:
(7x - 9) - (8x - 5) = 7x - 9 - 8x + 5
Next, we can combine like terms by adding or subtracting the coefficients of the same variables:
7x - 9 - 8x + 5 = (7x - 8x) + (-9 + 5) = -x - 4
Therefore, the expression that represents the difference when 8x - 5 is subtracted from 7x - 9 is -x - 4.
In this expression, the coefficient of x is -1, indicating that there is one fewer x term compared to the original expression. The constant term is -4, which is the result of subtracting 5 from -9.
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if you borrow $1,000 for 4 years at an annual interest rate of 8% what is the total amount of money you will pay back
Please see my question in the attachment, thanks
As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.
In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;
As x → -1⁻, f(x) → ∞.
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What is the volume of a triangle prism 9cm 8cm 9cm
Answer:
324 cm^3
Step-by-step explanation:
Because this is a triangular prism, we can take the base area times the height. The base area is 9*8/2=36.
The height is 9.
So 36*9=324.
Answer:
324 cm³
Step-by-step explanation:
Area of triangle = 1/2 × base × height
Area of triangle = 1/2 × 9 cm × 8 cm
Area of triangle = 36 cm²
The height of the triangular prism is given as 9 cm.
To find the volume of the triangular prism, we multiply the area of the base triangle by the height of the prism:
Volume of triangular prism = area of base × height
Volume of triangular prism = 36 cm² × 9 cm
Volume of triangular prism = 324 cm³
Therefore, the volume of the triangular prism is 324 cubic centimeters (cm³).
K
The formula for the nth square number is S, -n². Use the formula to find the 19th square number.
The 19th square number is (Simplify your answer.)
The nth square number of the value given is the squared value of 19, which is 361
The nth square number , S is related by the formula :
S = -n²n = nth termGiven that , n = 19
The nth square number , where n = 19 can be calculated thus:
S = -19² = 361
S = (-19) * (-19)
S = 361
Therefore, the 19th square number is 361
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Select the correct answer.
Omar has a gift card for $40.00 at a gift shop. Omar wants to buy a hat for himself for $13.50. For his friends, he would like to buy souvenir bracelets, which are $3.25 each. All prices include taxes.
Which inequality can be used to solve for how many bracelets Omar can buy?
A.
3.25x + 13.50 ≤ 40
B.
3.25x + 13.50 ≥ 40
C.
13.50x + 3.25 ≤ 40
D.
13.50x + 3.25 ≥ 40
Answer:
A.
3.25x + 13.50 ≤ 40
Step-by-step explanation:
Polygon ABCDE is the first in a pattern for a high school art project. The polygon is transformed so that the image of A' is at (−4, 2) and the image of D' is at (−2, 1).
polygon ABCDE is on a coordinate plane with point A at 2, 4 and point B at 4, 3 and point C at 3, 2 and point D at 1, 2 and point E at 0, 3
Which transformation can be used to show that ABCDE and its image are congruent?
The transformation used to show congruence between polygon ABCDE and its image is a translation of 6 units to the left and 1 unit down.
To show that polygon ABCDE and its image are congruent, we need to determine which transformation was used. In this case, the transformation that can be used to show congruence is a translation.
A translation is a transformation that moves every point of a figure by the same distance and in the same direction. Since the image of A' is at (-4, 2) and the image of D' is at (-2, 1), we can see that the polygon was shifted 6 units to the left and 1 unit down.
Therefore, the transformation used is a translation of -6 units in the x-direction and -1 unit in the y-direction. This translation preserves the shape and size of the polygon, making ABCDE congruent to its image.
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El resultado de (6+9i) +(4-5i) es/
?
Answer:
es 362770
Step-by-step explanation:
saque esta imformacion de la calculadora
Answer:
10 + 4i
Step-by-step explanation:
To solve this, just combine the like terms:
[tex]\sf{(6+9i)+(4-5i)}[/tex]
[tex]\sf{6+9i+4-5i}[/tex]
[tex]\sf{6+4+9i-5i}[/tex]
[tex]\sf{10+4i}[/tex]
Hence, the answer is 10 + 4i
Here is Takeshi's work determining a third point on the graph of an exponential function, `h(x)`.
Explain why the work is incorrect.
Answer:
Step-by-step explanation:
Let h(x) = y
The exponentail function is of the form :
[tex]y = ab^x[/tex]
We have :
[tex]y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}[/tex]
Given points : (4, 9) and (5, 34.2)
We have:
[tex]\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b[/tex]
Writing the equation with x, y and b:
[tex]y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043[/tex]
a = 0.043
b = 3.8
When x = 6, y will be:
[tex]y = (0.043)(3.8^6)\\\\y = 128.47[/tex]
This is not the y value in the question y = 59.4
Therefore (6, 59.4) does not lie on the graph h(x)
A marble is rolling up an inclined plane. The distance (in cm) the marble has rolled after t seconds is given by s(t)=100t/t+1
a. What is the initial velocity of the marble?
b. How fast is the marble rolling at time 4 seconds?
c. At what time is the velocity 50 cm/s?
d. How fast is the marble rolling when it is 90 cm from its starting point?
e. Find and interpret lim s(t) t-> infinity and lim v(t) lim t-> infinity. Do you think this model is valid for large values of t?
Explain.
a. The initial velocity of the marble is 0 cm/s.
b. The marble is rolling at a speed of 80 cm/s at 4 seconds.
c. The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.
d. The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point at t = 9 seconds.
e. lim s(t) as t approaches infinity is 100 cm and lim v(t) as t approaches infinity is 0 cm/s; the model may not be valid for large values of t as it assumes the marble is rolling up an inclined plane without considering other factors such as friction.
a. To find the initial velocity of the marble, we need to calculate the limit of the function s(t) as t approaches 0:
lim (t->0) s(t) = lim (t->0) (100t / (t + 1))
By substituting 0 into the expression, we get:
lim (t->0) (0 / (0 + 1)) = 0 / 1 = 0.
Therefore, the initial velocity of the marble is 0 cm/s.
b. To find the speed of the marble at time 4 seconds, we substitute t = 4 into the expression for s(t):
s(4) = 100(4) / (4 + 1) = 400 / 5 = 80 cm/s
The marble is rolling at a speed of 80 cm/s at 4 seconds.
c. To find the time at which the velocity is 50 cm/s, we set s'(t) (the derivative of s(t)) equal to 50 and solve for t:
s'(t) = 50
[tex](100 / (t + 1))^2 = 50[/tex]
100 / (t + 1) = ±√50
100 = ±√50(t + 1)
±√50(t + 1) = 100
t + 1 = 100 / ±√50
t + 1 = ±2√2
Since time cannot be negative, we take t + 1 = 2√2:
t = 2√2 - 1
The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.
d. To find the speed of the marble when it is 90 cm from its starting point, we need to solve the equation s(t) = 90 for t:
100t / (t + 1) = 90
100t = 90(t + 1)
100t = 90t + 90
10t = 90
t = 9
The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point, which occurs at t = 9 seconds.
e. The limit of s(t) as t approaches infinity (lim s(t) as t->∞) is calculated by considering the dominant term in the numerator and denominator:
lim (t->∞) (100t / (t + 1))
≈ lim (t->∞) (100t / t)
= lim (t->∞) 100
= 100
Therefore, lim s(t) as t approaches infinity is 100 cm.
Similarly, the limit of v(t) (velocity) as t approaches infinity (lim v(t) as t->∞) can be found by taking the derivative of s(t) and evaluating the limit:
[tex]v(t) = s'(t) = 100 / (t + 1)^2[/tex]
lim (t->∞) v(t) = lim (t->∞) (100 / [tex](t + 1)^2)[/tex]
≈ lim (t->∞)[tex](100 / t^2)[/tex]
= lim (t->∞) [tex](100 / t^2)[/tex]
= 0.
The limit of v(t) as t approaches infinity is 0 cm/s.
As for the validity of the model for large values of t, it is important to note that the given model assumes that the marble is rolling up an inclined plane.
However, without further information about the nature of the inclined plane (e.g., its slope, frictional forces), it is difficult to determine the accuracy.
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D = {x|x is a whole number} E = {x|x is a perfect square between 1 and 9} F = {x|x is an even number greater than or equal to 2 and less than 9} Which of the following is an element of D ∩ (E ∩ F)? 16 3 6 4
The element 4 is an element of D ∩ (E ∩ F).
To find the intersection of sets D, E, and F, we need to determine the elements that are common to all three sets.
Set D consists of all whole numbers, so any whole number can be an element of set D.
Set E consists of perfect squares between 1 and 9. The perfect squares in this range are 1, 4, and 9.
Set F consists of even numbers greater than or equal to 2 and less than 9.
The even numbers in this range are 2, 4, 6, and 8.
Taking the intersection of sets E and F, we find that the common element is 4, as it is the only number that satisfies both conditions of being a perfect square and an even number in the given range.
Finally, taking the intersection of set D with the intersection of sets E and F, we find that the element 4 is also an element of set D ∩ (E ∩ F).
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A bag consists of 5 marbles. There is 1 yellow, 1 red marble, 1 clear marble, 1 green marble, and 1 blue marble. Which table shows the sample space for choosing 2 marbles from the bag with replacement?
Yellow Red Clear Green Blue
Yellow Yellow Yellow Yellow Yellow Yellow
Red Red Red Red Red Red
Clear Clear Clear Clear Clear Clear
Green Green Green Green Green Green
Blue Blue Blue Blue Blue Blue
Yellow Red Clear Green Blue
Red Red, Yellow Red, Red Red, Clear Red, Green Red, Blue
Red Red, Yellow Red, Red Red, Clear Red, Green Red, Blue
Red Red, Yellow Red, Red Red, Clear Red, Green Red, Blue
Yellow Red Clear Green Blue
Yellow Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow
Red Yellow, Red Red Clear, Red Green, Red Blue, Red
Clear Clear Red, Clear Clear Green, Clear Blue, Clear
Green Green, Yellow Red, Green Clear, Green Green Blue, Green
Blue Blue, Yellow Red, Blue Clear, Blue Green, Blue Blue
Yellow Red Clear Green Blue
Yellow Yellow, Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow
Red Yellow, Red Red, Red Clear, Red Green, Red Blue, Red
Clear Yellow, Clear Red, Clear Clear, Clear Green, Clear Blue, Clear
Green Yellow, Green Red, Green Clear, Green Green, Green Blue, Green
Blue Yellow, Blue Red, Blue Clear, Blue Green, Blue Blue, Blue
The sample space for this experiment is the one in the last option.
Which is the correct sample space?The sample space is the set of the possible outputs that we can have for selecting two marbles.
For example, if first you get a yellow marble, and then a red one, the output will be:
yellow red,
And that is different to the output:
red yellow
Where in the second one you draw the red one first.
From the options, the one that shows the complete sample space is the last one:
"Yellow Yellow, Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow
Red Yellow, Red Red, Red Clear, Red Green, Red Blue, Red
Clear Yellow, Clear Red, Clear Clear, Clear Green, Clear Blue, Clear
Green Yellow, Green Red, Green Clear, Green Green, Green Blue, Green
Blue Yellow, Blue Red, Blue Clear, Blue Green, Blue Blue, Blue"
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2) Looking at your average from question 1, with an expected weight of 4 ounces, what is the % error in actual weights? (Assume you think the answer is 10%. Find 10% of 4 ounces to check to see if that answer is reasonable!) Do not round!
A) 17.5%
B) .128%
C) 10%
D) 0.175%
The calculated percentage error with the assumed answer of 10%
To find the percentage error in actual weights, we can use the formula:
Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%
In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:
Measured Value = Expected Value + (10% of Expected Value)
= 4 ounces + (10/100) * 4 ounces
= 4 ounces + 0.4 ounces
= 4.4 ounces
Now we can calculate the percentage error:
Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%
= [(0.4 ounces) / 4 ounces] * 100%
= (0.4/4) * 100%
= 0.1 * 100%
= 10%
Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.
The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%
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Find the area of the parallelogram
The area of the parallelogram is 189 square units
How to determine the areaFirst, we have the determine the length of the base and height.
The distance between the lines x = 9 and f(x) = 9 + 2x is the height
We have that the line parallel to f(x) passes through (4, 11)
The equation in point-slope form is;
y - 11 = 2(x - 4
y = 2x + 3
Substitute x = 9 in the equation, y = 2x + 3.
y = 2(9) + 3 = 21
The points are then (9, 21) and (9, 0).
The distance between the y-axis and the line x = 9 is the base.
Base = 9 units.
The formula for calculating area of a parallelogram is given by ;
= base × height
= 9 × 21
= 189 square units.
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Please help on question asap if you are correct with answer I'll give brainlie st, a thanks and five stars.
When we have a trapezium and w e are finding out the area , would it be possible to have a radius\diameter in the trapezium or is that just for 3D shapes
Is not possible to define a radius nor a diameter in a trapezium.
Is it possible to have a radius/diameter in the trapezium?Radius and diameter are two measures defined for circles.
Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).
At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.
To get the area use the formula:
Area = (base1 + base2)*height / 2
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Select the correct answer. If function g has the factors (x − 7) and (x + 6), what are the zeros of function g? A. -7 and 6 B. -6 and 7 C. 6 and 7 D. -7 and -6
Answer:
-6 and 7.
Step-by-step explanation:
If we have a function called g, and we know that it has two factors: (x - 7) and (x + 6), then we can find the values of x that make g equal to zero. We call those values the "zeros" of the function g. To find the zeros, we just need to solve the equation (x - 7)(x + 6) = 0. The answer is that the zeros of g are -6 and 7.
