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Luda [366]
2 years ago
7

A competitive knitter is knitting a circular place mat. The radius of the mat is given by the formula

Mathematics
1 answer:
Ilia_Sergeevich [38]2 years ago
5 0

Answer: A. A'(t)=\frac{4356\pi}{(t+11)^{3}}-\frac{527076\pi}{(t+11)^{5}}

              B. A'(5) = 1.76 cm/s

Step-by-step explanation: <u>Rate</u> <u>of</u> <u>change</u> measures the slope of a curve at a certain instant, therefore, rate is the derivative.

A. Area of a circle is given by

A=\pi.r^{2}

So to find the rate of the area:

\frac{dA}{dt}=\frac{dA}{dr}.\frac{dr}{dt}

\frac{dA}{dr} =2.\pi.r

Using r(t)=3-\frac{363}{(t+11)^{2}}

\frac{dr}{dt}=\frac{726}{(t+11)^{3}}

Then

\frac{dA}{dt}=2.\pi.r.[\frac{726}{(t+11)^{3}}]

\frac{dA}{dt}=2.\pi.[3-\frac{363}{(t+11)^{2}}].\frac{726}{(t+11)^{3}}

Multipying and simplifying:

\frac{dA}{dt}=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}

The rate at which the area is increasing is given by expression A'(t)=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}.

B. At t = 5, rate is:

A'(5)=\frac{4356\pi}{(5+11)^{3}} -\frac{527076\pi}{(5+11)^{5}}

A'(5)=\frac{4356\pi}{4096} -\frac{527076\pi}{1048576}

A'(5)=\frac{2408693760\pi}{4294967296}

A'(5)=1.76268

At 5 seconds, the area is expanded at a rate of 1.76 cm/s.

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Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet. . . . a. 2 feet. b. 4 feet.
Mademuasel [1]
Volume of Pyramid = (1/3)*(base area) * height.

32 ft³  =  (1/3)*(4*4)* h.        Since Pyramid is square based.

32 = (16/3)*h

16h/3 = 32

h = 32*3/16

h = 6

Height = 6 feet.  Option C. 

4 0
3 years ago
5. Write an equation for a line with a slope of -4 and goes through the point (5, -1). Show all work.​
Artyom0805 [142]

Answer:

y=-4x+19

Step-by-step explanation:

Plug into point-slope formula

y-y1=m(x-x1)

y-(-1)=-4(x-5)

y+1=-4x+20

 -1          -1

y=-4x+19

4 0
2 years ago
GEOMETRY!!!! PLEASE HELP
DaniilM [7]

Answer:

i believe it's 12 but i'm not entirely sure

Step-by-step explanation:

i hope this helps :) please let me know if it was wrong

have a nice day !!

4 0
2 years ago
Given that set A has 48 elements and set B has 21 elements, determine each of the following. (a) The maximum possible number of
yKpoI14uk [10]

Answer:  The required answers are

(a) 69,  (b) 21,  (c) 21  and  (d) 0.

Step-by-step explanation:  We are given that the set A has 48 elements and the set B has 21 elements.

(a) To determine the maximum possible number of elements in A ∪ B.

If the sets A and B are disjoint, that is they do not have any common element. Then, A ∩ B = { }   ⇒   n(A ∩ B) = 0.

From set theory, we have

n(A\cup B)=n(A)+n(B)-n(A\cap B)=48+21-0=69.

So, the maximum possible number of elements in  A ∪ B is 69.

(b) To determine the minimum possible number of elements in A ∪ B.

If the set B is a subset of set A, that is all the elements of set B are present in set A. Then,  n(A ∩ B) = 21.

From set theory, we have

n(A\cup B)=n(A)+n(B)-n(A\cap B)=48+21-21=48.

So, the minimum possible number of elements in  A ∪ B is 21.

(c) To determine the maximum possible number of elements in A ∩ B.

If the set B is a subset of set A, that is all the elements of set B are present in set A. Then, n(A ∩ B) = 21.

So, the maximum possible number of elements in  A ∩ B is 21.

(d) To determine the minimum possible number of elements in A ∩ B.

If the sets A and B are disjoint, that is there is no common element in the sets A and B . Then,  n(A ∩ B) = 0.

So, the maximum possible number of elements in  A ∩ B is 0.

Thus, the required answers are

(a) 69,  (b) 21,  (c) 21  and  (d) 0.

6 0
3 years ago
Corrine bought a coffee and a bagel for $5.35. If the coffee cost $1.95, how much did the bagel cost?
ki77a [65]
5.35 minus 1.95 = 3.40
6 0
3 years ago
Read 2 more answers
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