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grandymaker [24]
3 years ago
15

Plz help me with this question!! Giving 10 points!

Mathematics
1 answer:
BartSMP [9]3 years ago
8 0
Add the number and that should be your numbers
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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.

5 0
3 years ago
I just need yall help ... {:
KonstantinChe [14]

Answer:C

Step-by-step explanation:

The answer is C because the minimum is 33 and the maximum is 51. The first quartile is 33. THE SECOND QUATILE IS 39 and the 3rd quartile is 47.

4 0
2 years ago
Read 2 more answers
Look at this expression
vladimir2022 [97]

Answer:

OD22264 is the correct answer for that

4 0
2 years ago
For the function f(x)=(1/2)⋅6^x , identify the domain, range, y-intercept, and asymptote.
skelet666 [1.2K]

Answer:

Step-by-step explanation:

f(x) = (1/2) *6^x = 2^-1 * 2^x *3^x

y= 2^ (x-1) * 3^x

Domain represents all values that x can have and is all real numbers

Range all values that y can have and is y > 0 ( all real numbers that are positive)

The y-intercept is the point where the graph intersects the y-axis so x=0 there

y = 2^(0-1) *3^0 = 1/2 *1 = 1/2

the asymptote is at y= 0

6 0
3 years ago
Which word phrases represent the variable expression 7d? Choose all answers that are correct. A. the product of 7 and a number B
amm1812
A and D are correct.
8 0
3 years ago
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