The derivative of ∫ₓ² cos⁽⁵ˣ⁾ f(t) dt with respect to x is -5cos⁽⁵ˣ⁾f(x)ln(cos⁽⁵ˣ⁾).
To find the derivative of the integral ∫ₓ² cos⁽⁵ˣ⁾ f(t) dt with respect to x, we can apply the Fundamental Theorem of Calculus and the Chain Rule.
Let F(x) = ∫ₓ² cos⁽⁵ˣ⁾ f(t) dt be the antiderivative of the integrand. Then, by the Fundamental Theorem of Calculus, we have d/dx ∫ₓ² cos⁽⁵ˣ⁾ f(t) dt = d/dx F(x).
Next, we apply the Chain Rule. Since the upper limit of integration is a function of x, we need to differentiate it with respect to x as well. The derivative of x² with respect to x is 2x.
Therefore, by the Chain Rule, we have d/dx F(x) = F'(x) * (2x) = 2x * cos⁽⁵ˣ⁾ f(x), where F'(x) represents the derivative of F(x).
Now, to simplify further, we notice that the derivative of cos⁽⁵ˣ⁾ with respect to x is -5sin⁽⁵ˣ⁾. Thus, we have d/dx F(x) = -5cos⁽⁵ˣ⁾f(x)sin⁽⁵ˣ⁾ * (2x).
Using the identity sin⁽²x⁾ = 1 - cos⁽²x⁾, we can rewrite sin⁽⁵ˣ⁾ as sin⁽²x⁾ * sin⁽³x⁾ = (1 - cos⁽²x⁾) * sin⁽³x⁾ = sin⁽³x⁾ - cos⁽²x⁾sin⁽³x⁾.
Since sin⁽³x⁾ and cos⁽²x⁾ are both functions of x, we can differentiate them as well. The derivative of sin⁽³x⁾ with respect to x is 3cos⁽²x⁾sin⁽³x⁾, and the derivative of cos⁽²x⁾ with respect to x is -2sin⁽²x⁾cos⁽²x⁾.
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Complete Question
Find d/dx ∫ₓ² cos⁽⁵ˣ⁾ f(t) dt
Angela compro un terreno rectangular que tiene un perimetro de
10x - 28a
Si el ancho del terreno es 2x - 4a
¿Cual es la expresión que muestra la medida del largo del terreno?
The expression that shows the measurement of the length of the land is L = 3x - 10a.
Let L be the length of the rectangular plot.
We know that the perimeter of a rectangle is given by the sum of the lengths of all its sides. In this case, the perimeter is 10x - 28a, so we can write:
Perimeter = 2L + 2W
10x - 28a = 2L + 2(2x - 4a)
10x - 28a = 2L + 4x - 8a
2L = 6x - 20a
L = 3x - 10a
In other words, the length of the land is equal to three times the width minus ten times the value of 'a'.
To explain this equation in a little more detail, we can say that the length of the rectangular plot is dependent on both the width of the land and the value of 'a'.
The expression tells us that as the value of 'a' increases, the length of the land decreases, and as the width of the land increases, the length of the land also increases. This equation is useful because it allows us to calculate the length of the land without having to measure it directly, as long as we know the value of 'a' and the width of the land.
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Please help I’ll give brainiest! Fill in the missing exponent !
Answer:
Answer is .............3.
Answer:
It's 3
So whenever u see a power outside the bracket u times it with the inner brackets
In the final answer a is with the power of 8 because 2 times 4 is 8
U do the opposite to find the power of b u divide 12 with 4 which will be 3 ☺️
Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australia. While booking her family's plane tickets, she notices on the itinerary that the airline is offering a sixteen hour straight flight from Los Angeles to Melbourne on a Boeing 747-8 Intercontinental Jet. In an effort to learn more about the capabilities of the Jet, Sheleah does a little research and stumbles upon the following graph and facts about the Jet's fuel consumption.
The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel.
Use a linear model to predict the amount of jet fuel that is present on the Jet after it has been in flight for 18 hours without stopping to refuel. In two or more complete sentences, explain your answer. i need the slope formula and how u got it this is due in 10 min please help
Answer:
4455555
treduiyg
ggcsss
Sabia and arlan bougth 45 book for r 30 each old all ok them at the rote of 24 find the different the money pent and return
If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,
Rs 30 = 45 book
Rs 30 = 45
Rs 1 = 45 / 30
Rs 24 = 3/2 × 24
Rs 24 = 34 books
Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.
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What is the ratio of 185:370
Answer: .5
hope thisi helps
plz mark brainliset
Step-by-step explanation:
185:370
divide both sides by185
you get the ratio is 1:2
plssssssss helpppppp meeeee
The harbor at Green Top Lake has a lot of green algae at the end of the summer. However, as the weather gets colder, the algae begins to die. At the beginning of the fall, the harbor has 150,000 square feet of algae. Half of the algae dies per month.
Answer:
Step-by-step explanation:
5)))
Which two points would a line of fit go through to best fit the data? (6, 4) and (9, 1) (3, 5) and (10, 1) (1, 8) and (10, 1) (1, 5) and (7, 3)
The two points that a line of fit would go through to best fit the data are (3, 5) and (10, 1).
We need to find which pair of points have a line passing through them that best fits the data. One way to do this is to calculate the slope of the line passing through each pair of points and choose the pair of points with the slope closest to the average slope.
The slope of a line passing through two points \((x_1, y_1)\) \((x_2, y_2)\) is given by the formula:
slope = \(\frac{(y_2 - y_1)}{ (x_2 - x_1)}\)
Using this formula, we can calculate the slopes of the lines passing through each pair of points:
Pair 1: slope = \(\frac{(1 - 4)}{(9-6)}\) = -1
Pair 2: slope = \(\frac{(1 - 5)}{(10-3)}\) = -0.67
Pair 3: slope = \(\frac{(1 - 8) }{(10-1)}\) = -0.88
Pair 4: slope =\(\frac{ (3 - 5)}{(7-1)}\) = -0.33
The average slope is:
average slope = \(\frac{(-1 + (-0.67) + (-0.88) + (-0.33))}{4}\) = -0.72
The pair of points with the slope closest to the average slope is pair 2, with a slope of -0.67. Therefore, the two points that a line of fit would go through to best fit the data are (3, 5) and (10, 1).
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how do I solve the value of the n
A concave shaving mirror has a radius of curvature of +31.5 cm. It is positioned so that the (upright) image of a man's face is 3.40 times the size of the face. How far is the mirror from the face? Number i Units
The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.
Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40
We know that the formula for magnification is given by:
m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :
f = r/2where,f = focal length of the mirror
Using the mirror formula:1/f = 1/v - 1/u
We know that a concave mirror has a positive focal length, so we can replace f with r/2.
We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u
Also, from the given data, we have :m = v/u
Substituting the value of v/u in terms of m, we get: u/v = 1/m
So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u
Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm
Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.
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Suppose that, in a probability experiment, there are three independent events A, B and C. Furthermore, P(A) = 0.2, P(B) = 0.24, and P(C) = 0.32.
What is the probability that all three events will happen?
The probability that all three events will happen is 0.01536.
Let A, B and C be the three independent events, such that
P(A) = 0.2
P(B) = 0.24
P(C) = 0.32
The probability that all three events will happen can be calculated using the formula:
P(A ∩ B ∩ C) = P(A) × P(B) × P(C)
Now, substituting the values, we get:
P(A ∩ B ∩ C) = 0.2 × 0.24 × 0.32
= 0.01536
Therefore, the probability that all three events will happen is 0.01536.
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in a class of 36 students, 12 are boys the percentage of girls in the class is?
what can be the maximum number of digits in the repeating block of digits in the decimal expansion 5/7
Answer: To find the decimal expansion of 5/7, we can perform long division as follows:
0.7│5.0
4 2
────
8 │ 30
28
───
20 │ 200
196
────
4
Hence, 5/7 = 0.714285... where the digits 714285 repeat indefinitely. To find the maximum number of digits in the repeating block of digits, we can observe that the repeating block will be at most 6 digits long because 7 has a factor of 2 and 5, and therefore 7 divides 10^6 - 1 = 999999.
In fact, we can see that the repeating block in this case has 6 digits, since the digits 714285 repeat indefinitely, and there are 6 digits in this repeating block. Therefore, the maximum number of digits in the repeating block of digits in the decimal expansion of 5/7 is 6.
Step-by-step explanation:
2 1/3 - 1/3
Easy question
Answer:
the answer is 2
Step-by-step explanation:
just subtract 2 -
the proportion of dental procedures that are extractions is 0.16. which of the following exemplifies a type i error in this situation? a. we reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually different from 0.16. b. we reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually 0.16. c. we fail to reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually different from 0.16. d. we fail to reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually 0.16.
The following exemplifies a type of error in this situation, we fail to reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually different from 0.16.
What is dental extraction?
An extraction is a process used to remove a tooth from its socket in the gum. A regular dentist, an oral surgeon, or a periodontist typically performs it. Normal teeth might look different, especially the molars.
Here, we have
The proportion of dental procedures that are extractions is 0.16.
We have to find errors in this situation,
we concluded that we fail to reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually different from 0.16.
Hence, the following exemplifies a type of error in this situation, we fail to reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually different from 0.16.
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I need help with this practiceThe subject is complex numbers and vectors*It asks to fill in the four boxes, *enter the roots in order of increasing angle measure
ANSWER:
\(\begin{gathered} \:\sqrt[4]{4}cis\left(-\frac{\pi }{24}\right)\: \\ \\ \:\sqrt[4]{4}cis\left(\frac{11\pi}{24}\right)\: \\ \\ \:\sqrt[4]{4}cis\left(\frac{23\pi}{24}\right)\: \\ \\ \:\sqrt[4]{4}cis\left(\frac{35\pi}{24}\right)\: \end{gathered}\)STEP-BY-STEP EXPLANATION:
We have the following expression:
\(2\sqrt{3}-2i\)To calculate the 4 roots we must match the equation with x raised to 4, just like this:
\(x^4=2\sqrt{3}-2i\)For this case the roots are given as follows:
\(\begin{gathered} \:z_k=\sqrt[n]{\left|a\right|}\left(\cos\left(\frac{\arctan\left(\alpha\right)+2k\pi}{n}\right)+i\sin\left(\frac{\arctan\left(\alpha\right)+2k\pi}{n}\right)\right) \\ \\ \text{ In this case:} \\ \\ n=4 \\ \\ |a|=\sqrt{\left(2\sqrt{3}\right)^2+\left(-2\right)^2}=\sqrt{12+4}=\sqrt{16} \\ \\ a=4 \\ \\ \alpha=\left(\frac{-2}{2\sqrt{3}}\right) \\ \\ \text{ Therefore:} \\ \\ \arctan\left(\frac{-2}{2\sqrt{3}}\right)=-\frac{\pi}{6} \end{gathered}\)Taking into account the above, we calculate for each x,
when k = 0,1, 2 3, just like this:
\(\begin{gathered} x_1=\sqrt[4]{4}\left(\cos\left(\frac{-\frac{\pi}{6}+2\cdot\:0\pi}{4}\right)+i\sin\left(\frac{-\frac{\pi}{6}+2\cdot\:0\pi}{4}\right)\right)=\sqrt[4]{4}\left(\cos\left(-\frac{\pi}{24}\frac{}{}\right)+i\sin\left(-\frac{\pi}{24}\right)\right)=\sqrt[4]{4}cis\left(-\frac{\pi}{24}\right) \\ \\ x_2=\sqrt[4]{4}\left(\cos\left(\frac{-\frac{\pi}{6}+2\cdot\:1\pi}{4}\right)+i\sin\left(\frac{-\frac{\pi}{6}+2\cdot\:1\pi}{4}\right)\right)=\sqrt[4]{4}\left(\cos\left(\frac{11\pi\:}{24}\right)+i\sin\left(\frac{11\pi\:}{24}\right)\right)=\:\sqrt[4]{4}cis\left(\frac{11\pi\:}{24}\right)\: \\ \\ x_3=\sqrt[4]{4}\left(\cos\left(\frac{-\frac{\pi}{6}+2\cdot\:2\pi}{4}\right)+i\sin\left(\frac{-\frac{\pi}{6}+2\cdot\:2\pi}{4}\right)\right)=\sqrt[4]{4}\left(\cos\left(\frac{23\pi\:}{24}\right)+i\sin\left(\frac{23\pi\:}{24}\right)\right)=\sqrt[4]{4}cis\left(\frac{23\pi\:}{24}\right)\: \\ \\ x_4=\sqrt[4]{4}\left(\cos\left(\frac{-\frac{\pi}{6}+2\cdot\:3\pi}{4}\right)+i\sin\left(\frac{-\frac{\pi}{6}+2\cdot\:3\pi}{4}\right)\right)=\sqrt[4]{4}\left(\cos\left(\frac{35\pi\:}{24}\right)+i\sin\left(\frac{35\pi\:}{24}\right)\right)=\:\sqrt[4]{4}cis\left(\frac{35\pi\:}{24}\right)\: \end{gathered}\)Find m<1 and m<2. Justify your answer.
Answer:
M<1 80 by the corresponding angles postulate
Step-by-step explanation:
Please show me the steps of solving this and the answer 2n² +3n-9
Answer: n=-3 and n=3/2
Step-by-step explanation:
To solve the expression, we want to find the values of n. Since there are no common factors in 2, 3, -9, we directly multiply the "a" and "c" values.
2×(-9)=-18
This means, we want to find two numbers that multiply to -18 and adds to 3. This can also be known as the cross method.
We will find that 6 and -3 multiply to -18, and adds to 3.
In our box method, we want to find the common factors.
|2n²|6n|
|-3n|-9|
Note: Just pretend the lines line up and form a square box, with a term in each box.
After finding that is in common between the boxes, we get (n+3)(2n-3)=0
To solve, we set each factor equal to 0.
n+3=0
n=-3
2n-3=0
2n=3
n=3/2
the region r in the first quadrant is bounded by the graph of y = tan(x), the x-axis, and the vertical line x = 1. what is the volume of the solid formed by revolving r around the vertical line x = 1?
The volume of the solid is approximately V ≈ 1.062 cubic units.
We have,
To find the volume of the solid formed by revolving region R around the vertical line x = 1, we can use the method of cylindrical shells.
The volume of the solid can be obtained by integrating the area of each cylindrical shell.
Each shell is formed by taking a thin vertical strip of width dx from region R and rotating it around the line x = 1.
Let's denote the radius of each cylindrical shell as r(x), where r(x) is the distance from the line x = 1 to the curve y = tan(x).
Since the shell is formed by revolving the strip around x = 1, the radius of the shell is given by r(x) = 1 - x.
The height of each cylindrical shell is the difference in y-values between the curve y = tan(x) and the x-axis, which is given by y(x) = tan(x).
The differential volume of each cylindrical shell is given by
dV = 2π r(x) y(x) dx.
To find the total volume of the solid, we integrate the differential volume over the interval where region R exists, which is from x = 0 to x = 1.
Therefore, volume V is given by the integral:
V = ∫[0,1] 2π x (1 - x) x tan(x) dx
To solve this integral, we can use integration techniques or numerical methods.
Using numerical approximation, the volume is approximately V ≈ 1.062 cubic units.
Thus,
The volume of the solid is approximately V ≈ 1.062 cubic units.
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-40, -47, -54, -61, ...
Find a 29
Answer:
Step-by-step explanation:
It is an arithmetic sequence with common difference d = -7
a₂₉ = a₄ + (29-4)d = -61 + 25(-7) = -236
theta with hat on top subscript 1 and theta with hat on top subscript 2 are unbiased estimators of the same parameter theta. what condition must be imposed on the constants k subscript 1 and k subscript 2 so that the quantity 10 k subscript 1 theta with hat on top subscript 1 plus 10 k subscript 2 theta with hat on top subscript 2 is also an unbiased estimator of theta?
The scaled values sum up to 1/10.
How to find unbiased estimator?For a linear combination of unbiased estimators to be unbiased, the coefficients must add up to 1. That is:k subscript 1 + k subscript 2 = 1
E[10 k subscript 1 theta with hat on top subscript 1 + 10 k subscript 2 theta with hat on top subscript 2] = 10 k subscript 1 E[theta with hat on top subscript 1] + 10 k subscript 2 E[theta with hat on top subscript 2]
Since both estimators are unbiased, we have:E[theta with hat on top subscript 1] = theta
E[theta with hat on top subscript 2] = theta
Substituting these values into the above equation, :E[10 k subscript 1 theta with hat on top subscript 1 + 10 k subscript 2 theta with hat on top subscript 2] = 10 k subscript 1 theta + 10 k subscript 2 theta = theta (10 k subscript 1 + 10 k subscript 2) = theta
k subscript 1 + k subscript 2 = 1
10 k subscript 1 + 10 k subscript 2 = 10
Dividing both sides by 10:k subscript 1 + k subscript 2 = 1
k subscript 1/10 + k subscript 2/10 = 1/10
Therefore, their sum is equal to 1, and their scaled values sum up to 1/10.
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What is the value of the expression - 7 x 3.67
Blank 1:
Answer:
-25.69
Step-by-step explanation:
-7 x 3.67 = -25.69
Answer:
use a calculator
Step-by-step explanation:
pull out phone, go to calculator, enter problem, get answer.
Traingle ABC below has a rigth angle C and a hieght CD. If AC is 3 units long, and BC is 4, what is the lengtyh of CD
Answer:
5 units
Step-by-step explanation:
the length of CD can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
3² + 4²
= 9 + 16
= 25
the square root of 25 is 5
Find the average of first six multiples of 2.
Answer:
7
Step-by-step explanation:
2+4+6+8+10+2
=42÷6(coz 6 multiples)
=7
if a scarf is 25 percent off and normally cost 20 dollars how much will it cost after 6.5 percent sales tax is paid?
Answer:
$15.98
Step-by-step explanation:
25% off means it is 75% of its normal cost
0.75 x 20 = 15
The scarf is $15 after 25% discount. Then we calculate its final cost after tax:
6.5% = 0.065
1.065 x 15 = 15.975 which rounds to $15.98
Answer: 15.98
Step-by-step explanation: 25% off 20 is 15. 6.5% times 15 is .98 so the answer is 15.98
Pedro ordered a pizza. The pizza place charges $12 for a large pizza plus an additional $2.50 per topping. The total cost of Pedro's pizza was $22. Write and solve an equation to determine many toppings Pedro ordered.
Answer:
4 toppings
Step-by-step explanation:
22-12=10
2.50*?=10
2.50*4=10
4 toppings
Answer:
12+(2.50x)
12+(2.50*4)
12+(10)
22
Step-by-step explanation:
x stands for number of toppings
The following arithmetic sequence models an installment purchase. Give the down payment , monthly payment , and length of the plan. 400, 510, 620, 730, 840, 950, 1,060.
The down payment is 400, the monthly payment is 65 and the length of the plan is 7 months. An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive numbers is constant.
Arithmetic refers to the branch of mathematics that deals with numbers and the basic operations of addition, subtraction, multiplication, and division. An arithmetic sequence is a specific type of mathematical pattern where each term is obtained by adding a constant value to the previous term.
Here is the way to determine the monthly payment:
(1,060 - 400) / 7 = (660) / 7 = 65
As you can see the down payment is 400 and the last value in the sequence is 1060, so the total amount of the plan is 1060.
Also, the difference between any two consecutive terms is 110, as we can see that from the sequence:
510 - 400 = 110
620 - 510 = 110
730 - 620 = 110
840 - 730 = 110
950 - 840 = 110
1060 - 950 = 110
So the length of the plan is 7 months as the sequence contains 7 terms.
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1. While raking leaves, a woman applies an input force of 32 N to a rake. The rake has an output force of 16 N. What is the mechanical advantage of the rake?
2. A carpenter turns a handle to adjust a saw blade. The input work is 55 J and the output work is 51 J. What is the efficiency of the blade adjuster?
1. the mechanical advantage of the rake is 0.5. 2. the efficiency of the blade adjuster is approximately 92.73%.
1. The mechanical advantage of a simple machine is determined by the ratio of the output force to the input force. In this case, the woman applies an input force of 32 N to the rake, and the rake exerts an output force of 16 N.
The mechanical advantage (MA) can be calculated as MA = Output Force / Input Force.
Using the given values, we can substitute them into the formula:
MA = 16 N / 32 N = 0.5.
Therefore, the mechanical advantage of the rake is 0.5.
Explanation:
The mechanical advantage represents the amplification of force achieved by using a machine. In this case, the mechanical advantage of 0.5 means that the rake reduces the input force by half to produce the output force. It indicates that for every 1 unit of input force applied by the woman, the rake generates 0.5 units of output force.
2. Efficiency is a measure of how effectively a machine converts input work to output work. It is calculated as the ratio of output work to input work, expressed as a percentage.
The efficiency (η) can be calculated using the formula: Efficiency = (Output Work / Input Work) * 100%.
Given that the input work is 55 J and the output work is 51 J, we can substitute these values into the formula:
Efficiency = (51 J / 55 J) * 100% ≈ 92.73%.
Therefore, the efficiency of the blade adjuster is approximately 92.73%.
Explanation:
Efficiency quantifies the effectiveness of a machine in converting the input energy into useful output energy. In this case, the blade adjuster converts 51 J of input work into 51 J of output work. The efficiency of approximately 92.73% indicates that the blade adjuster is relatively efficient, as a high percentage of the input work is effectively converted into useful output work.
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What is the circumference of the following circle?
Answer:
C = 2pi(r)
= 2pi(5)
≈ 31.416
≈ 31.4
Answer:
Hello! answer: 31.4
Step-by-step explanation:
I'm using 3.14 for pi and
To find circumference you just have to do diameter × pi or radius × 2 × pi since we have the radius we can just do radius × 2 × pi so
5 × 2 × 3.14 = 31.4 so our circumfrence is 31.4 Hope that helps!!
What is the coefficient of x² in 5x²y?
The coefficient of the variable x squared is number 5.
What are the coefficients?
The coefficients are the numbers on the left side or before each variable.
What is an algebraic expression?Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
In this problem we have an expression given by:
5x²y
And we want to know what is the coefficient of x²
5 is the coefficient
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