1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jonny [76]
3 years ago
6

Find derivative problem Find B’(6)

Mathematics
1 answer:
dalvyx [7]3 years ago
5 0

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.

You might be interested in
After the first round on a television game show, the three contestants have -$300, $600, -$400. Which of the three dollar amount
Elanso [62]
-400 dollars as it it the lowest amount of money
4 0
3 years ago
Is 8/9 greater than 1
Zanzabum
No because 1 = 9/9 
8/9<9/9
5 0
3 years ago
Read 2 more answers
Find the measures of the interior angles and please tell me all angles
VLD [36.1K]
Angle A = 59
Angle B = 48

4 0
3 years ago
PLZ HELP!! WILL MARK BRANLYIST!!! 30 POINTS!!
V125BC [204]

Answer:

The distance between the light and the actor's face is 29.24 ft

Step-by-step explanation:

In the attached photo, you can see where the hypotenuse, the opposite side, and and adjacent side are located from the given angle measurement which is 70°. Our known side length is 10 ft which is our adjacent side and our variable is the hypotenuse. So, we will use <u>cos</u>.

Cos=\frac{adjacent}{hypotenuse}

Let's plug in our numbers and variable.

(Cos)70=\frac{10}{x}

Since our hypotenuse is a variable, we are going to flip the equation so we can find the value of the hypotenuse which is also our variable.

x=\frac{10}{(cos)70}

Divide 10 by (cos)70.

<em>x = 29.24</em>

So, the hypotenuse is 29.24 feet which shows the distance between the light and the actor's face.

8 0
2 years ago
) a circle with radius 63mm
Jet001 [13]

Answer:

<em>radius: r2 = 3.14 × 632 = 12470 square mm</em>

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • Distance to your brothers house is 552 miles, and the distance to Disneyland is 736 miles. If it took 12 hours to drive to your
    13·1 answer
  • Simplify (5 √2 - 1) ^2
    12·2 answers
  • -9/4 v + 4/5 = 7/8 v=? step by step need help asap please
    14·1 answer
  • When building a house, the number of days required to build is inversely proportional to with the number of workers. One house w
    10·1 answer
  • What ordered pair represents the y-intercept of the graph y = 2x - 3?
    15·1 answer
  • If sin(3x+2)=cos(4x-10), what is the value of x to the nearest tenth?A. 7.6B. 12.0C. 14.0D. 26.9
    14·1 answer
  • 4 – 2( x – 3 ) = 2 4
    15·2 answers
  • Please someone can help me...
    11·2 answers
  • What is the measure of angle WXU?
    14·1 answer
  • What percent of 4c in each expression? <br> *2a
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!