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3 years ago

Please select the best answer from the choices provided

Mathematics

1 answer:

Murrr4er [49]3 years ago

4 0

Answer:

it would be b) √5

Step-by-step explanation:

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

Ilia_Sergeevich [38]

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: Rate of change 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.

5 0

2 years ago

Factorize: x²+2+1/x²

andrew-mc [135]

$x^{2}+\frac{1}{x^{2}}+2=\boxed{\left(x+\frac{1}{x} \right)^{2}}$

8 0

2 years ago

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Minchanka [31]

Answer:

POSITIVE

Step-by-step explanation:

Because the product of 2 negative numbers is a positive number

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olga2289 [7]

Answer:

The first choice.

Step-by-step explanation:

The area is multiplied by (1/2)^2 = 1/4.

This is because lengths are one dimensional and areas are 2 dimensional.

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5th grade math. correct answer will be marked brainliest.

damaskus [11]

Answer:

1, 2, 3, 5, 6, 10, 15, 30

Step-by-step explanation:

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