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2 years ago

11

Pls help me it is urgent

1 answer:

Anna007 [38]2 years ago

4 0

Answer: C

Step-by-step explanation:

The area of a rectangle is just the length multiplied by its height. The length of this rectangle is (x+5), while the height is just 3. Therefore the answer is:

$3(x+5)$

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

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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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A car initially traveling at 20 kilometers per hour takes 10 seconds to speed up to 70 km/hour. At what rate is it changing spee

Snezhnost [94]

Initial velocity=u=20km/h
Final velocity=v=70km/h
Time=10s=t

Convert speeds to m/s

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$\\ \rm\longmapsto v=70\times \dfrac{5}{18}=19.4m/s$

$\boxed{\sf Acceleration=\dfrac{v-u}{t}}$

$\\ \rm\longmapsto Acceleration=\dfrac{19.4-5.05}{10}$

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3 years ago

dmitriy555 [2]

Answer:

A.

Step-by-step explanation:

The slope of the line parallel to the original line is the same. And you don't add x after the slope.

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2 years ago