The area of the minor sector is 33.33 cm^2 and the area of minor segment is 53.27 cm^2.
A chord of a circle is a straight line segment that connects any two points on the circumference of the circle.
The area of the major sector can be found by using the formula:
Area of major sector = (Angle of sector / 360) * π * r^2
Where the angle of sector is 120°, and the radius of the circle is 10cm.
So the area of the major sector = (120/360) * π * (10 cm)^2 = (1/3) * π * 100 cm^2 = 33.33 cm^2
To find the area of the minor segment, we need to find the area of the minor sector and then subtract it from the area of the triangle formed by the center of the circle, the midpoint of the chord, and the endpoint of the chord.
The area of the minor segment = area of the triangle - area of the minor sector
As the angle subtended by the chord is 120°, the minor sector will subtend an angle of (360-120) = 240°.
So the area of the minor sector = (120/360) * π * (10 cm)^2 = (2/3) * π * 100 cm^2 = 33.33 cm^2
The area of the triangle can be found by using the formula:
Area of the triangle = (1/2) * b * h
Where b is the distance between the center of the circle and the midpoint of the chord and h is the length of the altitude drawn from the center of the circle to the chord.
So the area of the minor segment = (1/2) * (10cm) * (10cm) * sin(120/2) -33.33 cm^2 = 50*sqrt(3) - 33.33 cm^2=53.27 cm^2
Therefore, the area of the minor sector is 33.33 cm^2 and the area of minor segment is 53.27 cm^2.
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Type the correct answer in each box. Write your answers as fractions, using / as the fraction bar, and write the greater value first.if log3 (8x-3)-log 4 = 2, the value of x is
The value of x 1/2 or 3/2.
The logarithm of any number N if interpreted as an exponential form, is the exponent to which the base of the logarithm should be raised, to obtain the number N. Here we shall aim at knowing more about logarithmic functions, types of logarithms, the graph of the logarithmic function, and the properties of logarithms.
The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log). Logarithmic function properties are helpful to work across complex log functions. All the general arithmetic operations across numbers are transformed into a different set of operations within logarithms. The product of two numbers, when taken within the logarithmic functions is equal to the sum of the logarithmic values of the two functions. Similarly, the operations of division are transformed into the difference of the logarithms of the two numbers.
Here, we use:
1) loga/b = log a - log b
2) logba = (logc a)/(logc b)
Given logarithmic equation:
logₓ(8x-3) - logₓ4 = 2
logₓ (8x-3/4) = 2
(8x-3/4) = x²
8x - 3 = 4x²
4x² - 8x + 3 = 0
x = 1/2 or 3/2
Thus, the value of x 1/2 or 3/2.
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find the area of the parallelogram with vertices a(−3, 0), b(−1, 6), c(8, 5), and d(6, −1).
Applying the area of the parallelogram formula, it can be concluded that the area is 56 square units.
The area of the parallelogram is the magnitude of the cross-product of the adjacent edges (base and height).
Given information:
A parallelogram is made up of 4 vertices: A(−3, 0), B(−1, 6), C(8, 5), and D(6, −1).
So first we find the adjacent edges as follows:
AB = B - A
= ( (-1-(-3)) , (6-0) )
= (2,6)
AD = D - A
= ((6-(-3)) , (-1-0))
= (9,-1)
We want to find the area of the parallelogram, we do the following step:
[tex]AB x AD = \left[\begin{array}{ccc}i&j&k\\2&6&0\\9&-1&0\end{array}\right][/tex]
= i(0 - 0) + j(0 - 0) + k(-2 - 54)
= -56k
The area of the parallelogram = | AB x AD |
= √(-56)²
= 56 square unit
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(8 pts.) in a binomial experiment, the probability of success in any trial of the experiment is 0.7. you will conduct 10 trials of this experiment. a. what is the probability of getting exactly 5 successes? b. what is the probability of getting 6 or more successes?
a) The probability of getting exactly 5 successes is 0.1029.
b)The probability of getting 6 or more successes is 0.8497510126.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Here, p = 0.7, q = 0.3 and n = 10
a) The probability of getting exactly 5 successes
P (x= 5) = C(10, 5) (0.7)⁵ (0.3)⁵
= 10!/ 5! 5! x 0.16807 x 0.00243
= 0.1029
b)The probability of getting 6 or more successes
P(X≥6) = 1 - P(X<6)
= 1 - P(X = 0, 1,2, 3, 4, 5)
= 1 - [ P(0) + P(1) P(2) + P(3) + P(4) + P(5)]
= 1 - [C(10, 0) [tex](0.3)^{10[/tex] + C(10, 1) (0.7) [tex](0.3)^{9[/tex] + C(10, 2) (0.7)² [tex](0.3)^{8[/tex]
+ C(10, 3) (0.7)³ [tex](0.3)^{7[/tex] + C(10, 4) [tex](0.7)^4[/tex][tex](0.3)^{6[/tex] + C(10, 4) [tex](0.7)^5[/tex]
[tex](0.3)^{5[/tex] ]
= 1 - [ 0.0000059049 + 0.000137781 + 0.0014467005 +
0.009001692 + 0.036756909 + 0.1029]
= 1 - 0.1502489874
= 0.8497510126
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4. Algebra The deductions from Emily's monthly pay are FIT of $112,
state income tax of 4% of her gross pay, city income tax (CIT) of 1.5% of
her gross pay, Social Security, and Medicare. Her monthly net pay is
$3,223. Find her monthly gross pay.
Answer:
Let G be Emily's gross pay.
Deductions:
FIT = 112
State Tax = 0.04G
City Tax = 0.015G
Social Security and Medicare
Net pay = Gross pay - Deductions
3,223 = G - 112 - 0.04G - 0.015G - Social Security - Medicare
We can then solve for G by isolating it on one side of the equation:
3,223 + 112 + 0.04G + 0.015G = G - Social Security - Medicare
3,223 + 0.055G = G - (Social Security + Medicare)
Now we can solve for G by dividing both sides by 1.055
G = 3223 / 1.055 + (Social Security + Medicare)
So we can find the gross pay but we don't have the exact amount for Social Security and Medicare that are being deduced.
What are two possible transformations that together could have been used to create the image of (mc022-1 ) ---> A' from A?
(<-- the graph (see picture))
A. a reflection across the x axis followed by a reflection across the y axis
B. a translation of 6 units down followed by a rotation of 90 degrees clockwise about the origin
C. a reflection across the y axis followed by a reflection across the x axis
D. a translation of 6 units down followed by a reflection across the y axis
The only option that represents the two possible transformations that together could have been used to create the image is; D. a translation of 6 units down followed by a reflection across the y axis
What transformation rule was used?In geometry, a transformation is defined as an operation that moves, flips, or changes a shape that is called the preimage in order to create a new shape that is called the image. Some of the types of transformations includes; Translation, Reflection, Dilation e.t.c
Let us analyze each of the options;
A. This is not correct because the transformation rule for a reflection over the x -axis is (x, y) → (x, −y) while the transformation rule for the reflection of point (x, y) across the y-axis is (-x, y). This will not correspond with the final transformation given.
B) This is not correct because it will not produce the complete match as the rotation given will not allow for proper mapping.
C) This is NOT correct just like is seen in option A above.
D) This is correct because after translation by 6 units downwards, when we reflect across the y-axis, it produces the final transformed image.
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Assignt
Describe the coefficients of a cubic polynomial function of that has one rational zero, a, and two irrational zeros, √band -√b, where b is rational.
OA Some are irrational numbers.
O B. They are all complex numbers.
O C. They are all rational numbers.
OD. They are all irrational numbers.
Answer:
234565432344343
a rectangle has its upper two vertices on the graph of and its lower two vertices on the -axis. what is the maximum possible area of the rectangle?
The maximum area of the rectangle is determined by the distance between the two points on the graph and the -axis.
What is rectangle?A rectangle is a four-sided shape with four right angles and two pairs of parallel sides. It is one of the most common shapes in the world, found in everything from building designs to artwork. Rectangles are also used in math, specifically to measure area and perimeter. Rectangles can also be classified according to their sides, with squares being a special type of rectangle with four equal sides.
To calculate the maximum possible area of the rectangle, we can use the formula A = (x2 - x1)(y2 - y1).
In this case, the two points on the graph have the same -coordinate, so the x2 - x1 part of the equation is zero. This means that the y2 - y1 part of the equation gives the maximum possible area of the rectangle. To calculate this, we need to take the difference between the two points on the graph.
For example, if the two points on the graph were (2,4) and (2,6), the maximum area of the rectangle would be (6 - 4) = 2.
Therefore, the maximum possible area of the rectangle is equal to the difference between the two points on the graph.
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a hand of 14 cards is dealt from a well-shuffled standard 52-card deck of cards. what is the probability that the hand contains 4 jacks?
The probability that the hand contains 4 jacks is solved to be
0.003697
How to solve the probabilityProbability is solved using the formula
= required outcome / possible outcome
The required outcome
= number of ways of picking 4 jacks * number of ways of 10 cards from 48
= ⁴C₄ * ⁴⁸C₁₀
= 1 * 6540715896
= 6540715896
The possible outcome
= number of ways of picking 14 card from possible 52 cards
= ⁵²C₁₄
= 1.768966345 * 10¹²
The probability
= required outcome / possible outcome
= 6540715896 / 1.768966345 * 10¹²
= 11 / 2975
= 0.00369747
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The Scale On A Map Is 1 Inch = 60 Miles. If Two Cities Are 2 3/4 Inches Apart On The Map, How Many Miles Are They Apart?
As you answer the following questions, write explanations for why your current answer is correct
A - 58.3 mi
B - 165 mi
C - 120 mi
D - 21.8 mi
The Scale On A Map Is 1 Inch = 60 Miles. If Two Cities Are 2 3/4 Inches Apart On The Map, the number of miles they are apart is, 165 Miles
So, Option B is correct.
What is the scale factor ?Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.
For example, Two spheres look similar but could have different radii.
Given that,
The Scale On A Map Is 1 Inch = 60 Miles
Two Cities Are 2 3/4 Inches Apart On The Map
The number of miles they are apart =?
1 Inch = 60 Miles
11/4 Inch = 60 × 11/4 Miles
= 165 Miles
So, The actual distance is 165 Miles
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Find two monomials whose product equals -20a^4b², and whose sum is a monomial with a coefficient of 1.
Answer:
-4a²b
5a²b
Step-by-step explanation:
A monomial is a polynomial that has one term only but can have multiple variables.
Given monomial:
[tex]-20a^4b^2[/tex]
The coefficient of the given monomial is -20.
Therefore, we need to find two numbers that multiply to -20 and sum to 1.
Factors of -20:
-1 and 20-2 and 10-4 and 5-5 and 4-10 and 2-20 and 1Therefore, the two numbers that multiply to -20 and sum to 1 are:
-4 and 5Rewrite -20 as the product of -4 and 5:
[tex]\implies -4 \cdot 5 \cdot a^4b^2[/tex]
Rewrite the exponents as sums of equal numbers:
[tex]\implies -4 \cdot 5 \cdot a^{2+2} \cdot b^{1+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c[/tex]
[tex]\implies -4 \cdot 5 \cdot a^2 \cdot a^2\cdot b^{1}\cdot b^{1}[/tex]
Rearrange as the product of two monomials with the same variables:
[tex]\implies -4a^2 b^{1}\cdot 5 a^2 b^{1}[/tex]
[tex]\implies -4a^2 b\cdot 5 a^2 b[/tex]
Therefore, the two monomials whose product equals -20a⁴b², and whose sum is a monomial with a coefficient of 1 are:
-4a²b5a²bCheck the sum of the two found monomials:
[tex]\begin{aligned}\implies -4a^2b+5a^2b&=(-4+5)a^2b\\&=(1)a^2b\\&=a^2b\end{aligned}[/tex]
Thus proving that the sum of the monomials has a coefficient of 1.
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer: 25.0
Step-by-step explanation:
[tex]\frac{x}{\sin 65^{\circ}}=\frac{22}{\sin 53^{\circ}}\\\\x=\frac{22 \sin 65^{\circ}}{\sin 53^{\circ}}\\\\x \approx 25.0[/tex]
Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure
x1+4x2 =11
2x1+7x2=18
The equations ( x1+4x2 ) = 11 and ( 2x1+7x2 ) = 18 give the solution as x1 = -5 and x2 = 4.
In order to solve the equation using elementary row operation it is required to multiply the first equation with -2, so that the term with x1 is eliminated from both equations and the value of x2 can be found.
Now
-2. ( x1+4x2 ) = -2 . 11
(-2x1 - 8x2 ) = -22
Now, this equation is added to the second equation (the left-hand sides of both equations are added together and the right-hand side of the equations are added together).
(-2x1 - 8x2 ) + ( 2x1+7x2 ) = ( -22 + 18 )
-2x1 + 2x1 - 8x2 + 7x2 = -4
-x2 = -4
(x2 = 4)
The value of x2 = 4 is now put in equation 1 to get the value of x1,
( x1 + 4x2 ) = 11
x1+ 4 (4) = 11
x1 + 16 = 11
x1 = (11 - 16)
(x1 = - 5)
So solution is x1 = -5 and x2 = 4.
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Is Gunner or Gordon correct?
Answer:
Gordon
Step-by-step explanation:
The domain is the x values and the range is the y values. The y values are the not the same. The y values for function A are all positive and the y values for function B are all negative.
The x values are the same for both functions, so the domain is the same for both functions.
a shipping service restricts the dimensions of the boxes it will ship for a certain type of service. the restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130130130 inches. the perimeter of the base is determined using the width and length of the box. if a box has a height of 606060 inches and its length is 2.52.52, point, 5 times the width, which inequality shows the allowable width xxx, in inches, of the box?
The inequality 60 + 5x ≤ 130 shows the maximum width, in inches, of the box that meets the restrictions of the shipping service, given that the box has a height of 60 inches and a length of 2.5 times the width.
1. Let x = the width of the box, in inches.
2. The perimeter of the base of the box is calculated by the following formula: Perimeter = 2(Width) + 2(Length)
3. Therefore, the equation is: 60 + 5x + 2(2.5x) = 130
4. Simplify the equation by expanding the parentheses and combining like terms: 60 + 5x + 5x = 130
5. Solve for x: 5x = 130 - 60
6. Simplify: 5x = 70
7. Divide both sides by 5 to find x: x = 70/5
8. Simplify: x = 14
9. Therefore, the inequality 60 + 5x ≤ 130 shows the maximum width, in inches, of the box that meets the restrictions of the shipping service is 14 inches
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The time to manufacture a pair of headphones on each assembly line is 1/3 hour. if there are 24 assembly lines and they operate 8 hours a day, how many pairs of headphones can be manufactured in a day?
you get brainliest if you answer!!!!!! i need this right now! +15 points
The number of pais of headphones that can be manufactured in a day = 576
Given that the time to manufacture a pair of headphones on each assembly line is 1/3 hour.
By unitary method the number of pairs of headphones can be manufactured in an hour :
1 ÷ (1/3)
= 1/ (1/3)
= 3
So, 3 pairs of headphones can be manufactured in an hour.
We need to determine the number of pairs of headphones that can be manufactured in a day.
Since we can operate assemply line 8 hours a day.
By unitary method the number of pairs of headphones can be manufactured in 8 hours:
3 × 8 = 24
And there are such 24 assembly lines.
So, the number of pais of headphones that can be manufactured in a day:
24 × 24 = 576
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Solve for X, Leave in simplest radical form.
Hope it helps.
If you have any query, feel free to ask.
suppose the average number of hours worked per week for high-school aged teens in the united states is 17 hours per week with a standard deviation of 4 hours. a high school teacher working at an inner city high school is concerned about the time students spend working at after school jobs. she randomly selects 15 of her students and calculates their average work hours to be 14.3 hours per week. identify the population and sample.
suppose the average number of hours worked per week for high-school aged teens in the united states is 17 hours per week with a standard deviation of 4 hours. So, the number of people selected from the public for a research is known as a sample.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.
For the given details the correct matching will be:
Parameter - 17 hrs per week
Population - All high-school-aged teens in the US
Statistic - 14.4 hours per week
Sample - 15 students
Population is everything that is taken into account for an experiment since parameters reflect population characteristics and statistics state sample parameters.
The number of people selected from the public for a research is known as a sample.
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You are flying a kite with 20 feet of string extended. The angle of elevation from the spool of string to the kite is 67º.
How far off the ground is the kite if you hold the spool 5 feet off the ground? Round your answer to the nearest tenth.
The kite is about
feet off the ground?
The kite is flying 23.4ft far of the ground.
as per the details stated above,
the angle of elevation given is 67 degrees
the length at which the string is extended is 20 feet
the spool is 5ft above the ground
so if d is the height of the spool the the actual length of the kite flying will be ( the length of the kite flying + the height of the spool (d) )
according to the question
the hypotenuse side of the triangle or the length of the string is extended is 20 feet
we have to find the opposite side of the triangle using the sine rule
sin [tex]67^0 = \frac{h}{20}[/tex]
=> 20 sin [tex]67^0[/tex] = h
=> h = 18.4 feet
the kite is flying above the spool 5 feet of the ground that is
the kite flying at
h = 18.4 + d
=> 18.4 + 5
=> 23.4 feet
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I need help with this problem ?
Answer:
398.32
Step-by-step explanation:
647.82 - 249.50 = 398.32
the manager of a garden shop mixes grass seed that is 60% rye grass with 70lb of grass seed that is 80% rye grass tp make a mixture that is 74% rye grass. how much of the 60% mixture is used
The manager of a garden shop wants to make a mixture that contains 74% rye grass. The weight of the 60% mixture used in this composition is 30 lb.
Percentage is used to denote a fraction of a hundred.
Suppose q represents the weight of the mix that contains 60% rye grass, then the weight of rye grass in this mix is:
w1 = 60% q = 0.6 q
Mix 2: 70 lb grass seed that contains 80% rye grass. The weight of rye grass in the second mix is:
w1 = 80% x 70 = 56 lb
The final mixture has 74% rye grass. Total weight of rye grass in the final mixture:
weight of rye grass = w1 + w2
= 0.6 q + 56
Total weight of the final mixture = (q + 70) lb
74% = 0.74 = (0.6 q + 56) / (q + 70)
0.6 q + 56 = 0.74 (q + 70)
0.74 q - 0.6 q = 56 - 0.74 x 70
0.14 q = 4.2
q = 4.2/0.14 = 30
Hence, the weight of 60% mixture is 30 lb.
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Write an equation of the line passing through the point (8, 7) that is perpendicular to the line y 7
The equation of the line would be y = 17/7x + 1.
What is the equation of the line?
The equation of a line is a mathematical expression that describes the position of a line in a coordinate plane. It typically takes the form of "y = mx + b", where "m" is the slope of the line and "b" is the y-intercept, the point where the line crosses the y-axis.
The whole question is:
Write an equation of the line passing through the point (8,7) that is perpendicular to the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex]
To write the equation of a line that is perpendicular to a given line, we can use the slope of the given line and the point the new line passes through.
The slope of the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] can be found by isolating y and then taking the derivative, which gives us: -7/17.
The slope of a line perpendicular to this line is the negative reciprocal of the given line's slope, which is 17/7.
We also know that the new line passes through the point (8,7). Using a point-slope form of a line which is (y-y1) = m(x-x1) where m is the slope, we can write the equation of the line as:
y - 7 = 17/7(x - 8)
So the equation of the line that passes through the point (8,7) and is perpendicular to the line [tex]y + 7 = -\frac{7}{17}(x+8)[/tex] is:
y = 17/7x + 1
Hence, the equation of the line would be y = 17/7x + 1.
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A square with sides 6 inches is shown. If $P$ is a point such that the segment $\overline{PA}$, $\overline{PB}$, $\overline{PC}$ are equal in length, and segment $\overline{PC}$ is perpendicular to segment $\overline{FD}$, what is the area, in square inches, of triangle $APB$
The area of the triangle APB is 6.75 square inches.
We know that PA=PB=PC and that PC is perpendicular to FD. Thus C will be the midpoint of FD.
Draw a perpendicular from P to AB, let the point of intersection be Q.
We know that CQ = DB = 6 inches
That is PC + PQ = 6 inches
PQ = (6 - PC) inches
Consider triangle APQ, it is a right angled triangle, right angled at Q. So using Pythagorean theorem
PA² = PQ² + AQ²
PA² = (6 - PC)² + (AB/2)²
PA² = (6 - PA)² + (6/2)²
PA² = 36 - 12PA + PA² + 9
12PA = 45
PA = 3.75
So PA = PB = PC = 3.75 inches
Also PQ = 6 - PC = 2.25 inches
The area of a triangle can be found by using the formula:
area = (base * height) / 2.
In this case, the base, AB is equal to the length of the side of the square, which is 6 inches, and the height is equal to PQ. So the area of triangle APB is
= (6*2.25)/2
= 6.75 square inches.
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Find the length of the third side, if necessary write in simplest radical form
Answer:
1
Step-by-step explanation:
use Pythagoras as shown
Without using paper and pencil how would you find the sum of 9.8 and 2.6
Answer:
12.4
Step-by-step explanation:
Suppose you know that the amount of time it takes your friend Susan to get from her residence to class averages 50 minutes, with a standard deviation of 5 minutes. What proportion of Susan's trips to class would take less than 40 minutes? What proportion of Susan's trips to class would take more than 50 minutes or less than 40 minutes?
Answer:
To solve this problem, we will use the following steps:
Step 1: We know that the amount of time it takes Susan to get from her residence to class averages 50 minutes, with a standard deviation of 5 minutes. So we can use this information to calculate the proportion of Susan's trips to class that would take less than 40 minutes.
Step 2: To calculate the proportion of Susan's trips to class that would take less than 40 minutes, we need to find the z-score for the value of 40 minutes. We can use the following formula to find the z-score:
z = (x - μ) / σ
Where x is the value we are interested in (40 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).
z = (40 - 50) / 5 = -2
Step 3: We can use a standard normal table or a calculator to find the proportion of Susan's trips to class that would take less than 40 minutes.
The proportion of Susan's trips to class that would take less than 40 minutes is 0.0228 or 2.28%.
Step 4: To calculate the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes, we need to find the proportion of Susan's trips to class that would take more than 50 minutes and add it to the proportion of Susan's trips to class that would take less than 40 minutes.
Step 5: To find the proportion of Susan's trips to class that would take more than 50 minutes, we need to find the z-score for the value of 50 minutes.
z = (50 - 50) / 5 = 0
Using a standard normal table or a calculator, the proportion of Susan's trips to class that would take more than 50 minutes is 0.5 or 50%.
Step 6: Finally, we can add the proportion of Susan's trips to class that would take more than 50 minutes and the proportion of Susan's trips to class that would take less than 40 minutes to find the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes.
0.50 + 0.0228 = 0.5228 or 52.28%
Final Answer: The proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes is 0.5228 or 52.28%.
cos-
4π
3
Find exact value
The exact value of the cosine ( (4π)/3) ] is -0.5.
What is the exact value of cos ( (4π)/3 )?
The exact value of the cosine function [ Cos ( (4π)/3) ] is calculated by resolving the pi radian into degrees as shown below.
π radian = 180 degrees
The exact value of the cosine ( (4π)/3) ] is calculated as
Cos ( ( 4π ) / 3 ) = cos ( 4 x 180 / 3 )
cos ( 4 x 180 / 3 ) = cos ( 4 x 60 )
cos ( 4 x 60 ) = cos ( 240 )
cos ( 240 ) = -0.5
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Burt deposited $100,000 into an account that compounds interest semiannually at a rate of 2.66%. At the end of each 6-month period, a withdrawal of $8000 is made from the account. How long will it take until the account has a balance of $0? round your answer to the nearest year.
step by step formula pls <3
Answer:
Step-by-step explanation:
The formula for calculating the time it will take for an investment to reach a certain amount given a rate of return and regular withdrawals is:
Time = (ln(Final Balance/Initial Balance))/(ln(1 + Rate of Return))
In this case, the Initial Balance is $100,000, the Final Balance is $0, and the Rate of Return is 2.66%.
Time = (ln(0/100000))/(ln(1 + 0.0266))
Time = (-11.51)/(0.026101)
Time = -440.17
Since the time is given in years, we need to round the answer to the nearest year.
Answer: It will take 440 years for the account to have a balance of $0.
This is the question
The equation of the tangent line at x = 4 is:
y = 179*x - 490
(your teacher or the person who wrote this problem made a mistake somewhere, as none of the options is near correct)
How to find the equation of the tangent line?We have:
f(x) = 4x³ - 2x² + 3x - 10
When x = 4 we have:
f(4) = 4*4³ - 2*4² + 3*4 - 10 = 226
So we want a line tangent to the curve at the point (4, 226)
To find the slope of that line, we need to evaluate the derivative of f(x) in x = 4.
The derivative is:
f'(x) = 3*4x² - 2*2x + 3
f'(x) = 12x² - 4x + 3
Then the slope is:
f'(4) = 12*4² - 4*4 + 3 = 179
Then the tangent line is something like:
y = 179*x + b
To find the value of b, we replace the values of the point (4, 226)
226 = 179*4 + b
226 - 179*4 = b = -490
The line is:
y = 179*x - 490
Notice that this is not in the options, meaning that the problem (or the options) are written incorrectly.
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given two points, (3,2) and (7,18), determine both the linear and quadratic equations crossing both points. let f(x) and f(k) be the linear and quadratic equation respectively. write both in standard form. write the function in terms of function notation.
The linear equation passing through both points is:
f(x) = 8x - 14 ,the quadratic equation passing through both points is:
[tex]f(k) = -1/28k^2 + 17/14k - 36/7[/tex]
Linear Equation:
f(x) = mx + b
Where, m is the slope and b is the y-intercept.
Calculation:
By substituting the two points (3,2) and (7,18) in the equation, we get:
2 = 3m + b
18 = 7m + b
Solving the equation we get:
m = 8
b = -14
Therefore, the linear equation passing through both points is:
f(x) = 8x - 14
Quadratic Equation:
f(k) = ax^2 + bx + c
Where, a, b and c are constants.
Calculation:
Substituting the two points (3,2) and (7,18) in the equation, we get:
2 = a(3)^2 + b(3) + c
18 = a(7)^2 + b(7) + c
Solving the equation we get:
a = -1/28
b = 17/14
c = -36/7
Therefore, the quadratic equation passing through both points is:
f(k) = -1/28k^2 + 17/14k - 36/7
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Given the following, where D is the incenter of ABC, DF=6, and DB=10, find EB.
if D is the incenter of ABC, DF=6, and DB=10 then EB is 8.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given that D is the incenter of ABC, DF=6, and DB=10
We need to find EB
As D is the incenter then DF=DG=DE
so DE is 6
We know DB and DE
DBE is a right triangle and we can find EB by pythagoras theorem
EB²+DE²=DB²
EB²+36=100
EB²=100-36
EB²=64
Take square root on both sides
EB=8
Hence, if D is the incenter of ABC, DF=6, and DB=10 then EB is 8.
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