Path z is the longest path that leads to the lake.
Describe Algebraic Expression?An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It is a mathematical phrase that can contain one or more terms separated by mathematical operators.
For example, 3x + 4y - 2z is an algebraic expression that contains three terms: 3x, 4y, and -2z. Each term is made up of a coefficient and a variable, where the coefficient is the numerical value that multiplies the variable.
In algebraic expressions, variables are used to represent unknown values, and the expression can be evaluated by substituting known values for the variables. For instance, if x = 2, y = 3, and z = 1, then the expression 3x + 4y - 2z can be evaluated as 3(2) + 4(3) - 2(1) = 12.
Algebraic expressions can also include exponentiation, roots, and other advanced mathematical operations. They are widely used in mathematics and other fields, such as physics and engineering, to represent relationships between variables and to model real-world situations.
Let's start by assigning variables to each path:
Let x be the length of path x (in meters).
Then path y is 116 meters longer than path x, so its length is x + 116.
Path w is 51 meters shorter than path y, so its length is x + 116 - 51 = x + 65.
Path z is 85 meters longer than path w, so its length is x + 65 + 85 = x + 150.
To find the longest path, we need to compare the lengths of all four paths. We can do this by looking at the expressions we just derived:
Path x has length x.
Path y has length x + 116.
Path w has length x + 65.
Path z has length x + 150.
Since all four paths have a common component of x, the lengths of the paths can be compared by comparing the values of the expressions that add to x. We can see that x + 150 is the largest expression, which means that path z is the longest.
Therefore, path z is the longest path that leads to the lake.
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Solve the system of equations. Write the solution as an ordered pair. 4x + 3y = 36 and y = -1/3x + 6
Substitute the expression for y in the second equation into the first equation and solve for x:
4x + 3(-1/3x + 6) = 36
4x - x + 18 = 36
3x = 18
x = 6
Now substitute x = 6 into the second equation to solve for y:
y = (-1/3)(6) + 6
y = 4
Therefore, the solution to the system of equations is the ordered pair (6, 4).
Find the value of each variable, help pls??
Answer:
x = 145
Step-by-step explanation:
We are given a polygon that has 7 sides. We can use the formula [tex]S=(n-2) * 180[/tex] which allows us to write an algebraic expression to solve for x where n = number of sides.
[tex]S=(7-2) * 180[/tex]
Evaluate
[tex]S=5*180[/tex]
[tex]S=900[/tex]
Now that we have our number, lets write an algebraic expression that will help us find the value of x.
[tex]x+116+129+120+130+135+125=900[/tex]
Add like terms
[tex]x+755=900[/tex]
Subtract 755 on both sides
[tex]x=145[/tex]
We can check our work by adding all the angle measures together
[tex]145+116+129+120+130+135+125=900[/tex]
Thus we know 145 is the correct answer.
b-3. which of the following statements is most accurate with respect to outliers in this example? multiple choice 3 the boxplot and z-scores provide consistent results. the boxplot is more reliable because the distribution is not symmetric. the z-scores are more reliable because the distribution is not symmetric. the z-scores are more reliable because the distribution is symmetric.
The correct statements are -
the boxplot and z-scores provide consistent resultsthe z-scores are more reliable because the distribution is symmetric.What are outliers?In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set.
Given is to identify which of the following statements is most accurate with respect to outliers in this example.
The correct statements are -
the boxplot and z-scores provide consistent resultsthe z-scores are more reliable because the distribution is symmetric.Therefore, the correct statements are -
the boxplot and z-scores provide consistent resultsthe z-scores are more reliable because the distribution is symmetric.To solve more questions on outliers, visit the link -
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Explain a right triangle to a group of 6th graders. What do
they need to know? Is there one kind- or more? What makes
them unique? Are there any special kind of right triangles?
Use vocabulary from Geometry and Pre-Cal/Trig. Use
complete sentences trying your best to make things clear to
the younger student.
Answer:
A right triangle is a type of triangle that has one angle measuring 90 degrees and two acute angles. It has a hypotenuse and two legs, and it is the only type of triangle that the Pythagorean theorem can be applied to. There are different types of right triangles, including isosceles right triangles, 45-45-90 triangles, and 30-60-90 triangles, each with its own unique properties.
Step-by-step explanation:
A right triangle is a type of triangle that has one angle which measures exactly 90 degrees, which we call the right angle. The other two angles are called acute angles and they are always less than 90 degrees.
A right triangle has a special property: the side opposite the right angle is called the hypotenuse. This is the longest side of the triangle and it is always opposite to the right angle. The other two sides are called legs.
One important thing to note is that the Pythagorean theorem only works for right triangles. This theorem tells us that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. This formula is often written as a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse.
There are actually several different types of right triangles. For example, if the two legs have the same length, we call it an isosceles right triangle. If one of the acute angles measures exactly 45 degrees, we call it a 45-45-90 triangle, and if one of the acute angles measures exactly 30 degrees and the other measures 60 degrees, we call it a 30-60-90 triangle. These triangles have special properties that make them useful in many different areas of math and science.
In summary, a right triangle is a type of triangle that has one angle measuring 90 degrees and two acute angles. It has a hypotenuse and two legs, and it is the only type of triangle that the Pythagorean theorem can be applied to. There are different types of right triangles, including isosceles right triangles, 45-45-90 triangles, and 30-60-90 triangles, each with its own unique properties.
Kristina paid mortgage interest of $6,320.00 and Medical Expenses of $$19,500.00 during 2022. Her GROSS INCOME was $32,500.
19. How much did she save by
itemizing her deductions?
Answer:
$448.25
Step-by-step explanation:
For her medical expenses, it has to be more than 7.5% of her gross income of $32,500 => 7.5% of $32,500 = $2437.5.
so her deduction for medical expenses is $19,500 - $2437.50 = $17,062.5
so her total itemized deduction is $6,320.00 + $17,062.50 = $23,382.50
Given Kristina will file a single so her standard deduction for 2022 is $12,950.
If she uses standard deduction, her taxable income is 32,500 - 19,500 = 13,000
For the first 10,000 taxed at 10% so it is 10,000 x 10% = $1,000
The next $3000 taxed at 12% = $360
Her total tax is $1,000 + $360 = $1,360
If she uses itemized deduction, her taxable income is 32,500 - 23,382.50 = 9117.5
For the first 10,000 taxed at 10% so it is 9117.5 x 10% = $911.75
The tax saved is $1,360 - $911.75 = $448.25
Hope this helps.
Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place. PLEASE EXPLAIN WELL THANK YOU
Answer:
68.1 square units
Step-by-step explanation:
l = Length of rectangle
= 9 units
w = Width of rectangle
= 6 units
The dashed lines represent the diameter of the circle. Semi-circle is exact half of a circle. This diameter is parallel to the width of the rectangle and is equal in measurement:
r = Radius of semi-circle
= [tex]\frac{Diameter}{2}[/tex]
= [tex]\frac{6}{2}[/tex] units
= 3 units
∴Area of composite solid = Area of rectangle + Area of semi-circle
= [(l × w) + [tex]\frac{1}{2}(\pi r^{2})[/tex]] [tex]units^{2}[/tex]
= {[9 × 6] + [tex]\frac{1}{2}[\pi (3)^{2}][/tex]} [tex]units^{2}[/tex]
= [54 + [tex]\frac{9}{2}\pi[/tex]] [tex]units^{2}[/tex]
= 68.137 [tex]units^{2}[/tex]
= 68.1 square units (Rounded to the nearest tenths place)
PLSS ANSWER THE QUESTION QUICKLY
Answer:
C
The value of the variables in answer C satisfies both of the equations
Sylvia buys a snack pack of nuts as an after lunch treat.she notices that there are twice as many cashews as almonds,so she eats ten cashews and seed there a still five more cashews than almonds.how many almonds were in the snack pack?
45. 30. 15. 5.
Answer:
there were 15 almonds in the snack pack.
Step-by-step explanation:
Let's use variables to represent the unknown quantities. Let's call the number of almonds in the snack pack "a", and the number of cashews in the snack pack "c".
we can use the following equations to represent the problem:
c = 2a (the number of cashews is twice the number of almonds)
c - 10 = a + 5 (there are 5 more cashews than almonds after Sylvia eats 10 cashews)
Substituting the first equation into the second equation, we get:
2a - 10 = a + 5
Solving for "a", we get:
a = 15
So there were 15 almonds in the snack pack.
A 16ft pipe has been cut into two parts, one 3 times as long as the other. How long (in ft) is each part?
Answer:
12 feet
Step-by-step explanation:
Let x be the length of the shorter part of the pipe.
According to the problem, the longer part is three times as long as the shorter part. Therefore, the length of the longer part is 3x.
We also know that the sum of the lengths of the two parts is equal to the original length of the pipe, which is 16 feet.
So we can write an equation:
x + 3x = 16
Simplifying this equation, we get:
4x = 16
Dividing both sides by 4, we get:
x = 4
So the length of the shorter part is 4 feet, and the length of the longer part is 3 times as long, or 3 × 4 = 12 feet.
Using the digits 0-9 once, create accurate number line
The digits are arranged in increasing order from left to right, and that each digit is used exactly once.
What is a number line?
A number line is a visual representation of numbers arranged in a straight line from left to right or from right to left. It is a tool commonly used in mathematics to help visualize numerical relationships, such as addition, subtraction, multiplication, and division.
A typical number line starts at zero in the middle and extends infinitely in both directions, with positive numbers increasing to the right and negative numbers decreasing to the left. The distance between any two points on the number line represents the absolute difference between the corresponding numbers.
Here's a number line using the digits 0-9 exactly once:
-9 --- -8 --- -7 --- -6 --- -5 --- -4 --- -3 --- -2 --- -1 --- 0 --- 1 --- 2 --- 3 --- 4 --- 5 --- 6 --- 7 --- 8 --- 9
Note that the digits are arranged in increasing order from left to right, and that each digit is used exactly once.
Therefore, the digits are arranged in increasing order from left to right, and that each digit is used exactly once.
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-95 times a number -14 is equal to -70 one less thing the number
The equation for the given statement can be written as:
-95x - 14 = -70 - x
To solve for x, we can rearrange the equation and combine like terms:
-95x + x = -70 + 14
-94x = -56
Next, we can divide both sides by -94 to isolate x:
x = -56/-94
Finally, we can simplify the fraction to get our answer:
x = 28/47
Therefore, the solution to the equation is x = 28/47.
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grogg draws the following figure. it so happens that $\angle sap$ is $174^\circ$ less than 4 times $\angle sop$. find the degree measure of $\angle sap.$
The degree measure of [tex]$\angle sap$ is $726^\circ - 4 \times \angle sop$.[/tex]
What is angle?Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.
We can use the following formula to calculate the degree measure of $\angle sap$:
[tex]$\angle sap = 4 \times \angle sop - 174^\circ$[/tex]
Therefore, [tex]$\angle sap = 4 \times \angle sop - 174^\circ = 4 \times (180^\circ - \angle sop) - 174^\circ = 726^\circ - 4 \times \angle sop$[/tex]
Therefore, the degree measure of [tex]$\angle sap$ is $726^\circ - 4 \times \angle sop$.[/tex]
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The figure shows the graph of the function.
f(x)=
The domain are the possible input while the range are the possible output of a function.
(a) The domain = [-√2, √2], the range = [0, 2]
(b) The domain = [-1, 1], the range = [0, 1]
(c) The domain = [-1, 1], the range = [0, -1]
(d) The domain = [0, 2], the range = [0, 1]
(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]
Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
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my son is having trouble with this problem he (6) can you tell him the answer 9+10
Answer:
19
Step-by-step explanation:
111111111
+
1111111111
count how many 1ns are there.
ans is 19
Sorry about the bad quality of the pic, can i get an explanation with answer, thanks. :)
Answer:
3. Initial cost = 99 dollars. Each hour (h) is 19 dollars. The total value will be initial cost + hours*(cost per hour)=> t=99+19h.
4. She will be using the car for 3 days. Each day costs 29.99. There is no initial cost, so her total cost will be 29.99*3=89.97 dollars.
find the coordinates of all points where the lines x + y = 8, y = 5, and x = 1 intersect
Intersection points for the lines are,
⇒ (3, 5) (1, 7) and (1, 5)
What is Line segment?Line segment is the part of line which have two endpoint and bounded by two distinct end points and it contain every point on the line which is between its endpoint.
Given that;
The equation of lines are,
x + y = 8 .. (i)
y = 5 .. (ii)
x = 1 .. (iii)
Now, Intersect point for equation (i) and (ii);
x + y = 8 .. (i)
y = 5 .. (ii)
⇒ x + 5 = 8
⇒ x = 3
Hence, The intersection point = (3, 5)
And, Intersect point for equation (i) and (iii);
x + y = 8 .. (i)
x = 1 .. (iii)
⇒ x + y = 8
⇒ y = 8 - 1
⇒ y = 7
Hence, The intersection point = (1, 7)
And, Intersect point for equation (ii) and (iii);
⇒ (1, 5)
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What is the total number of pencils that Mr. Moretti gives to his students if he puts 3 mechanical pencils in each bag?
Answer:
it depends on how many students?
Step-by-step explanation:
Classify the triangle by its angles , x, 102, x a right,acute or obtuse triangle
The solution is, x = 39. Since we have a 102 degree angle it is a obtuse triangle.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
given that,
its angles , x, 102, x
now, we know,
The sum of the angles in a triangle add to 180
i.e.
x+ 102+x = 180
Combine like terms
so, we get,
102 + 2x = 180
Subtract 102 from each side
2x = 78
divide by 2, both sides,
x =39
Since we have a 102 degree angle it is a obtuse triangle.
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x=-2/3t find the value of t .if x=-1/6
Answer:t= 1/4
Step-by-step explanation:
Divide both sides by -2/3, and simplify which would leave u with 1/4.
Please help me answer this question ASAP!!
The solution to the equation 17(4 + 15) is 323
What is an equation?
An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
Given the equation:
17(4 + 15)
= 17(19)
= 323
OR
17(4 + 15)
= 17(4) + 17(15)
= 68 + 255
= 323
The solution to 17(4 + 15) can be gotten by determining the product of 17 and 19; or adding the product of 17 and 4 to the product of 17 and 15
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3 three sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 5?
The probability that the sum of numbers we will get will be 6 is 7/27.
What is probability?Probability is simply the possibility that something will happen.
Since we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.
The study of events that fit into a probability distribution is known as statistics.
Probability, or the likelihood that an event will occur, is calculated by dividing the number of favorable outcomes by the total number of potential possibilities.
A coin toss serves as the most simple illustration.
When you flip a coin, there are only two possible outcomes: heads or tails.
So, the probability formula:
P(E) = Favourable events/Total events
We need to get the probability of getting the sum of 6.
Then, calculate as follows:
P(E) = Favourable events/Total events
P(E) = 7/27
Therefore, the probability that the sum of numbers we will get will be 6 is 7/27.
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Correct question:
3 three-sided dice (with sides labeled 1, 2, and 3) are rolled and their sum is recorded. What is the probability of rolling a sum of 6?
find the volume of a sphere vd(r) of radius r in d dimensions. in order to accomplish this task, first find the surface area ad of a sphere of unit radius in d dimensions by considering the integral
The formula for the volume of a d-dimensional sphere of radius r is:
V_d(r) = (π^(d/2) / Γ(d/2 + 1)) * r^d
How to explain the volumeIt should be noted that in the formula, Γ is the gamma function.
Let's break down the formula:
π^(d/2) is pi raised to the power of d/2.
Γ(d/2 + 1) is the gamma function evaluated at d/2 + 1.
r^d is the radius raised to the power of d.
Putting it all together, we get the formula above.
For a 2-dimensional sphere (a circle) of radius r, we have d=2, so:
V_2(r) = (π^(2/2) / Γ(2/2 + 1)) * r^2
= (π / Γ(3/2)) * r^2
= (π / (1/2) * √π) * r^2
= 2πr^2
For a 3-dimensional sphere of radius r, we have d=3, so:
V_3(r) = (π^(3/2) / Γ(3/2 + 1)) * r^3
= (4/3) * π * r^3
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Need help solving problem
The equations that determine the cost of each hamburger and each fries is 4x + 5y = 20 and 10x + 7y = 41.20
What is an equation?
An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
Let x represent the cost of each hamburger and y represent the cost of each fries.
She purchased 4 hamburgers and 5 fries for $20.00, hence:
4x + 5y = 20 (1)
She purchased 10 hamburgers and 7 fries for $41.20, hence:
10x + 7y = 41.20 (2)
From both equations, solving simultaneously:
x = 3; y = 1.6
The cost of each hamburger is $3 while the cost of each fries is $1.6
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Susan Marciano invested part of her $19000 bonus in a fund that paid a 12% profit and invested the rest in stock that suffered a %4 loss. Find the amount of each investment if her overall net profit was $520
Answer:
The investment in the fund was $19000 x 0.12 = $2280
The investment in the stock was $19000 - $2280 = $16720
The net profit was $520, so the amount of the profit from the fund was $520 x (2280/16720) = $136
The amount of the loss from the stock was $520 - $136 = $384
graph translation of (x,y) (x, y-2)
Answer:
can you explain a bit better what the problem is?
find the exact value using formulas from geometry. ∫ (1+3x) with upper bound as 3 and lower bound as 1.
The value of the integral ∫(1+3x) dx is equal to 14.
What is integration?Integration is a process of adding up small elemental volumes to find the larger volume.
Given is to find the integral -
∫(1+3x)
We can find the equivalent values as -
∫(1+3x) dx = ∫1 dx + ∫3x dx
∫(1+3x) dx = x + 3x²/2
For the limit x = 1 to x = 3, we can write -
∫(1+3x) dx = (3 + 27/2) - (1 + 3/2)
∫(1+3x) dx = 33/2 - 5/2 = 14
Therefore, the value of the integral ∫(1+3x) dx is equal to 14.
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ricky took out a $258,000, 20-year mortgage at an APR of 3.84%.
what is the monthly payment?
what will be his total interest charges after 20 years?
The total monthly payment of Ricky with an APR of 3.84 % is given by the equation M = $ 1,208.0523
What is Annual Percentage Yield?The annual percentage yield (APY) is the real rate of return earned on an investment, taking into account the effect of compounding interest. An APR is a number that represents the total yearly cost of borrowing money, expressed as a percentage of the principal loan amount.
The monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]
where
M = Total monthly payment
P = The total amount of your loan
I = Your interest rate, as a monthly percentage
N = number of months for paying off your mortgage
Given data ,
Let the monthly payment be represented as M
Now , the number of years n = 20 years
The annual interest rate i = 3.84 %
The total loan amount P = $ 258,000
Now , the monthly payment [tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1][/tex]
On simplifying , we get
[tex]M = 258,000 [ ( \frac{ 0.0384}{12} ) ( 1 + \frac{ 0.0384}{12} )^{12*30} ] / [ ( 1 + \frac{ 0.0384}{12} )^{12*30} - 1 ][/tex]
[tex]M = 258,000 [ (0.0032 ) ( 1.0032 )^{360} ] / [ ( 1.0032 )^{360} - 1 ][/tex]
On further simplification , we get
M = 258,000 [ 0.0101078417 ] / [ 2.158700543922579 ]
M = 258,000 ( 0.00468237327729 )
M = $ 1,208.0523
Hence , the monthly payment of Ricky is $ 1,208.0523
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The stem and leaf plot shows the number of laps around a track
that several teams walked as part of a fund-raiser for the library.
The teams that walked more than 50 laps raised an extra $100 for
the library.
What fraction of the teams raised this extra money?
The fraction of the teams which walked as part of the fundraiser for the library, that raised extra money, is D. 1 / 3.
What fraction of the teams raised extra funds ?You must count the number of teams that were able to walk more than 50 laps in order to determine the percentage of teams that raised the additional funds. The distance walked by teams more than 50 laps were :
5363 6365 miles.There are 12 teams overall, which is equal to the number of leaves.
The fraction of teams that raised additional funds is:
= 4 teams / 12 total teams
= ( 4 ÷ 4 ) / ( 12 ÷ 4 )
= 1 / 3
In conclusion, the fraction of teams which raised extra money was 1 / 3.
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If a rock is thrown upward on an exoplanet of a nearby star with initial velocity of 20 m/s , its height in meters t seconds later is given by y = 20t - 1.87t².
The rock has an instantaneous velocity of 16 meters per second.
How to determine the average velocity and instantaneous velocity of a rock thrown upward
In this problem we need to determine the average velocity of the rock, represented by a secant line, and estimate its instantaneous velocity, represented by a tangent line. The average speed is defined by the following expression:
u = [y(t + Δt) - y(t)] / Δt
Where:
y(t) - Initial position, in meters. y(t + Δt) - Final position, in meters. Δt - Time interval, in seconds. u - Average speed, in meters per second.The instantaneous speed is the average speed when Δt ⇒ 0.
Part A
Case I
y(1) = 20 · 1 - 1.87 · 1²
y(1) = 20 - 1.87
y(1) = 18.13 m
y(2) = 20 · 2 - 1.87 · 2²
y(2) = 40 - 7.48
y(2) = 32.52 m
u = (32.52 m - 18.13 m) / 1 s
u = 14.39 m / s
Case II
y(1.1) = 20 · 1.1 - 1.87 · 1.1²
y(1.1) = 19.737 m
u = (19.737 m - 18.13 m) / 0.1 s
u = 16.07 m / s
Case III
y(1.01) = 20 · 1.01 - 1.87 · 1.01²
y(1.01) = 18.292 m
u = (18.292 m - 18.13 m) / 0.01 s
u = 16.2 m / s
Case IV
y(1.001) = 20 · 1.001 - 1.87 · 1.001²
y(1.001) = 18.146 m
u = (18.146 m - 18.13 m) / 0.001 s
u = 16 m / s
And the instantaneous velocity of the rock is approximately 16 meters per second.
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Which of the following is the best linear approximation for f(x) = cos(x) near x equals pi divided by 2 ?
y equals x minus pi over 2
y equals negative x plus pi over 2
y equals negative x plus pi over 2 plus 1
y equals x minus pi over 2 plus 1
Answer:
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Step-by-step explanation:
The best linear approximation for f(x) = cos(x) near x = pi/2 is given by the equation:
y = -(x - pi/2) + 1
This is because the linear approximation should have the same value and slope as the original function at x = pi/2.
At x = pi/2, the value of f(x) = cos(pi/2) = 0. The value of the linear approximation at x = pi/2 is:
y = -(pi/2 - pi/2) + 1 = 1
So, the value of the linear approximation matches the value of the original function at x = pi/2.
The slope of the original function at x = pi/2 is -sin(pi/2) = -1. The slope of the linear approximation is:
y' = -1
So, the slope of the linear approximation also matches the slope of the original function at x = pi/2.
Therefore, the best linear approximation for f(x) = cos(x) near x = pi/2 is:
y = -(x - pi/2) + 1
Hence, the correct option is "y equals negative x plus pi over 2 plus 1".
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