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3 years ago

What is the slope of a line that passes through the following points (-2,-5) and (2, 5)?

Mathematics

1 answer:

Jet001 [13]3 years ago

8 0

The correct answer is D! Y2-Y2/X2-X1

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What function is the inverse of the exponential function y = (1.5)x?

vagabundo [1.1K]

Correct question is;

What function is the inverse of the exponential function y = 1.5^(x)?

Answer:

y = log_1.5_x

Step-by-step explanation:

The inverse of exponential functions is usually written in form of logarithm.

For example inverse of y = p^(x) will be written as; y = log_p_(x)

Similarly applying this same pattern to our exponential function y = 1.5^(x), we have the inverse as;

y = log_1.5_x

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2 years ago

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2 years ago

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2 years ago

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Dahasolnce [82]

Answer:

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Step-by-step explanation:

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2 years ago

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