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3 years ago

what is the y intercept of the line with a slope of - 4/7 that also passes through the point (7 , - 7/2) ?

Mathematics

1 answer:

kondor19780726 [428]3 years ago

8 0

The answer is the last option: $\frac{1}{2}$

Explanation:

1. You have that the equation of the line is:

$y=mx+b$

Where $m$ is the slope of the line and $b$ is the intercept with the y-axis.

2. Therefore, you must find $b$ .

3. Then, you must substitute the points given in the problem and the slope into the equation of the line and solve for $b$ , as following:

$y=mx+b\\-\frac{7}{2}=(-\frac{4}{7})(7)+b\\-\frac{7}{2}=-4+b\\b=\frac{1}{2}$

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den301095 [7]

This angle is "29 degrees 6 minutes 6 seconds".

-- There are 60 minutes in 1 degree.
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-- There are 60 seconds in 1 minute.
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29 6' 6" = (29)° + (6/60)° + (6/3600)°

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3 years ago

Find derivative problem 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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Irina18 [472]

Answer:

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3 years ago

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3 years ago

The equation y = 7x+25 gives the number of minutes it takes to prepare a meal y given the number of people being served x. Which

klemol [59]

Answer- C. For every extra person served, the time it takes to prepare a meal increases by 7 minutes.

Solution-

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Where y = the number of minutes it takes to prepare a meal

x = the number of people being served.

If the number of persons increased by one, so x' = (x+1)

Then y' = 7x' + 25 = 7(x+1) + 25 = 7x + 7 + 25 = 7x + 25 + 7 = y + 7

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3 years ago