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
Which function has the least value for the y-intercept?
diamong [38]

Answer:

y-intercept is the value of y when x is equal to zero. Because the y intercept is a point on a graph, you'll usually write it in point/ coordinate form.

Step-by-step explanation:

The y-intercept is where the parabola of a function crosses (or intercepts) the y axis.

6 0
3 years ago
At which points does the graph of f(x)=2x−4 cross the x-axis and y-axis?
blagie [28]

crosses x-axis at (2, 0 ) and y-axis at (0, - 4 )

To find where the graph crosses the x and y axes ( intercepts )

• let x = 0, in the equation for y- intercept

• let y = 0, in the equation for x- intercept

x = 0 : y = 0 - 4 = - 4 ⇒ (0, - 4 )

y = 0 : 2x - 4 = 0 ⇒ 2x = 4 ⇒ x = 2 ⇒ (2, 0 )


6 0
3 years ago
here is the histogram of a data distribution. which of the following numbers is closest to the mean of this distribution
gogolik [260]

Answer:

D

Step-by-step explanation:

1+2+2+3+3+3+4+5+6+6+7+7+7+8+9=73

73/15≈5

4 0
3 years ago
Read 2 more answers
Need help answering this math problem <br> X-5/4=-9/5 then x =
Mrac [35]
I’m pretty sure the answer is -1
5 0
3 years ago
Read 2 more answers
Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different
N76 [4]

Answer:

(a)  As time increases, the amount of water in the pool increases.

     11 gallons per minute

(b)  65 gallons

Step-by-step explanation:

From inspection of the table, we can see that <u>as time increases, the amount of water in the pool increases</u>.

We are told that Ann adds water at a constant rate.  Therefore, this can be modeled as a linear function.  

The rate at which the water is increasing is the <em>rate of change</em> (which is also the <em>slope </em>of a linear function).

Choose 2 ordered pairs from the table:

\textsf{let}\:(x_1,y_1)=(8, 153)

\textsf{let}\:(x_2,y_2)=(12,197)

Input these into the slope formula:

\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11

Therefore, the rate at which the water in the pool is increasing is:

<u>11 gallons per minute</u>

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

y-y_1=m(x-x_1)

\implies y-153=11(x-8)

\implies y-153=11x-88

\implies y=11x-88+153

\implies y=11x+65

When Ann had added no water, x = 0.  Therefore,

y=11(0)+65

y=65

So there was <u>65 gallons</u> of water in the pool before Ann starting adding water.

3 0
2 years ago
Read 2 more answers
Other questions:
  • In AVWX, V X is extended through point X to point Y, mZXVW = (3x + 13)°,
    6·1 answer
  • To make 3 dozen cookies, a recipe calls for 4 eggs and 1/2 cup of chocolate chips. Ben wants to make 12 dozen cookies for a clas
    13·2 answers
  • S is between Band C.<br> True<br> False
    13·1 answer
  • PLEASE HELP GIVING 40 POINTS!!!!! −2.5x−9&lt;16
    5·2 answers
  • The vertical _____ of a function secant are determined by the points that are not in the domain.
    12·2 answers
  • Omg bet you don't know this pt2
    10·1 answer
  • As part of a holf-marathon route, Charlie
    7·1 answer
  • Lee will buy 3 notebooks for $1.29 each, 2 dozen pencils at $3.45 a dozen, and a box of pens for $14.85 a box. How much will Lee
    5·1 answer
  • 20 points and 5 stars..........
    15·2 answers
  • Solve x^2 – 3x = –8 using the quadratic formula.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!