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VikaD [51]
3 years ago
11

If u(x)=-2x^2+3 and v(x)=1/x what is the range of (u*v)(x) **the picture should help

Mathematics
2 answers:
nasty-shy [4]3 years ago
5 0
We have that
u(x)=-2 x^{2} +3 \\ \\ v(x)= \frac{1}{x}
u(v(x))=u( \frac{1}{x})=-2( \frac{1}{x} )^{2}  +3 \\ u( \frac{1}{x})= \frac{(3 x^{2} -2)}{ x^{2} }

using a graph tool
see the attached figure

The horizontal asymptote of this function is at <span>y=3</span><span>.
So,
the range of this function is from </span><span>(−∞,3<span>)</span></span>

il63 [147K]3 years ago
5 0

Answer:

-OO,3

Step-by-step explanation:


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Find derivative problem<br> Find B’(6)
dalvyx [7]

Answer:

B^\prime(6) \approx -28.17

Step-by-step explanation:

We have:

\displaystyle B(t)=24.6\sin(\frac{\pi t}{10})(8-t)

And we want to find B’(6).

So, we will need to find B(t) first. To do so, we will take the derivative of both sides with respect to x. Hence:

\displaystyle B^\prime(t)=\frac{d}{dt}[24.6\sin(\frac{\pi t}{10})(8-t)]

We can move the constant outside:

\displaystyle B^\prime(t)=24.6\frac{d}{dt}[\sin(\frac{\pi t}{10})(8-t)]

Now, we will utilize the product rule. The product rule is:

(uv)^\prime=u^\prime v+u v^\prime

We will let:

\displaystyle u=\sin(\frac{\pi t}{10})\text{ and } \\ \\ v=8-t

Then:

\displaystyle u^\prime=\frac{\pi}{10}\cos(\frac{\pi t}{10})\text{ and } \\ \\ v^\prime= -1

(The derivative of u was determined using the chain rule.)

Then it follows that:

\displaystyle \begin{aligned} B^\prime(t)&=24.6\frac{d}{dt}[\sin(\frac{\pi t}{10})(8-t)] \\ \\ &=24.6[(\frac{\pi}{10}\cos(\frac{\pi t}{10}))(8-t) - \sin(\frac{\pi t}{10})] \end{aligned}

Therefore:

\displaystyle B^\prime(6) =24.6[(\frac{\pi}{10}\cos(\frac{\pi (6)}{10}))(8-(6))- \sin(\frac{\pi (6)}{10})]

By simplification:

\displaystyle B^\prime(6)=24.6 [\frac{\pi}{10}\cos(\frac{3\pi}{5})(2)-\sin(\frac{3\pi}{5})] \approx -28.17

So, the slope of the tangent line to the point (6, B(6)) is -28.17.

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3 years ago
What is 150% of 20? ​
Galina-37 [17]

Answer:

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Step-by-step explanation:

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Evaluate the expression 2b^3+5 (BTW I did the first part it's 3 but I need the second part)​
andrey2020 [161]

To find the exact answer based on the last step, "2(3)^3+5", you must use PEMDAS (attached image below)

 

          2(3)^3+5=2*27+5=54+5=59

Thus the answer is <u>59</u>.

Hope that helps!

         

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2 years ago
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Answer:

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Step-by-step explanation:

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