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Anna007 [38]
2 years ago
12

A) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 4 to each of the follo

wing.
(i) 4 to 5 _______

(ii) 4 to 4.5 _______

(iii) 4 to 4.1 _______


(b) Find the instantaneous rate of change when r = 4.

A'(4) = ______
Mathematics
2 answers:
nata0808 [166]2 years ago
7 0
So the question wants to calculate the change of the area among the circles in respect to its radius changes and the best answer would be the following:
A. 50.27 to 78.54
B.50.27 to 63.62
C.50.27 to 52. 81

The rate of change are the following:
A. 56.24%
B. 26.56%
C. 5.05%
goldenfox [79]2 years ago
7 0

Answer:

a)1. 28.26

2. 26.70

3. 25.44

b) 25.13

Step-by-step explanation:

We are given the following information in the question:

Area of circle

A(r) = \pi r^2, where r is the radius of circle.

a) Formula:

Rate of change of area of circle = \displaystyle\frac{A(r_2) - A(r_1)}{r_2-r_1}

Putting the given values we get:

1. Rate of change of circle when radius changes from 4 to 5

\displaystyle\frac{\pi (5)^2- \pi (4)^2}{5-4} = 9\pi = 28.26

2. Rate of change of circle when radius changes from 4 to 4.5

\displaystyle\frac{\pi (4.5)^2- \pi (4)^2}{4.5-4} =26.70

3. Rate of change of circle when radius changes from 4 to 4.1

\displaystyle\frac{\pi (4.1)^2- \pi (4)^2}{4.1-4} =25.44

b) Instantaneous rate of change

\displaystyle\frac{d(A(r))}{dr} = \frac{d(\pi r^2)}{dr} = 2\pi r

When r = 4

A'(4) = 2\times \pi \times 4 = 25.13

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3x^2-17x- 20 and 100=3x^2-17x-20 needed to simplify and find the X if its equal to 100
Vesnalui [34]

Answer:

Factor 3x^2-17x-20, and you get (x + 1)(3 x - 20)

x = 17/6 + sqrt(1729)/6, x = 17/6 - sqrt(1729)/6

Step-by-step explanation:

Factor 3x^2-17x-20, and you get (x + 1)(3 x - 20)

When 3x^2-17x-20 is equal 100

3x^2-17x-20=100

Subtract both sides by 100

3x^2-17x-120=0

Use the quadratic formula

x = 17/6 + sqrt(1729)/6, x = 17/6 - sqrt(1729)/6

4 0
2 years ago
Square root of 10 plus the square root of 5<br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B10%7D%20%20%2B%20%20%5Csqrt%7B5%20
9966 [12]
Hello Harrisonkaden13, the <span>square root of 10 plus the square root of 5 is,

</span>
<span>Answer:
</span>The principal, real, root of:
<span>^2√10</span><span> = 3.16227766 </span>All roots:
3.16227766 or <span>−3.16227766</span>

10 is not a perfect square.

The principal, real, root of:
^2<span>√5 </span><span>= 2.23606798</span>All roots:
2.23606798 or <span>−2.23606798

</span>5 is not a perfect square

We add them and we get 5.39834564 or -5.39834564.
3 0
2 years ago
I really really really need help in a rush
GaryK [48]
16 because there are four fruits and four combinations. 4×4=16
4 0
2 years ago
What is 26^4 +x)=65??
Lunna [17]

I'm not sure if this is correct but here is the answer:

Exact form:

x=-3/2

decimal form:

x=-1.5

mixed number form:

x=-1 1/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

4 0
3 years ago
Gina has a spinner with five equal parts numbered one thru five. If Gina spins the spinner one time, what is the probability tha
olga55 [171]

Answer: The answer is D

Step-by-step explanation: So, we have five parts on it equaling 1, 2, 3, 4 and 5. The top number is our chance, and the bottom number is how many there are in total, so our answer is D, 1/5.

Hope this helps :)

4 0
2 years ago
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