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2 years ago

Help, please! Struggling!

Mathematics

1 answer:

MArishka [77]2 years ago

6 0

Answer:

Step-by-step explanation:

(4-7i)(4+7i) =16 + 28i-28i -49i^2 ➡16 - 49i^2

16 + 49 = 65

the fault here is i^2= -1 and -1 multiplied by -49 is +49 not -49

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The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

$V = \frac{1}{3}\pi r^{2}h$

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

$V = \frac{1}{3}\pi r^{2}h$

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

3 years ago

What function equation is represented by the graph? f(x)=14x+3 f(x)=−4x−3 f(x)=−14x−3 f(x)=14x−3

Vladimir [108]

See the explanation

<h2>Explanation:</h2>

Remember you have to provide complete questions in order to get exact answers. Here I'll provide a general explanation, so:

<h3>First.</h3>

$f(x)=14x+3$

The slope is:

$m=14$

The y-intercept is:

$b=3$

By using graphing tool, we get the first graph shown below.

<h3>Second.</h3>

$f(x)=-4x-3$

The slope is:

$m=-4$

The y-intercept is:

$b=-3$

By using graphing tool, we get the second graph shown below.

<h3>Third.</h3>

$f(x)=-14x-3$

The slope is:

$m=-14$

The y-intercept is:

$b=-3$

By using graphing tool, we get the third graph shown below.

<h3>Fourth.</h3>

$f(x)=14x-3$

The slope is:

$m=14$

The y-intercept is:

$b=-3$

By using graphing tool, we get the fourth graph shown below.

<h2>Learn more:</h2>

Linear inequalities: brainly.com/question/12984296

#LearnWithBrainly

7 0

3 years ago

Read 2 more answers

Volgvan

The arc angle AC is measured as 55 degrees.

<h3>How to find arc angle?</h3>

If two secant intersect in the exterior of a circle, then the measure of the angle formed is half the positive difference of the arcs intercepted.

Therefore, the secants intersect outside the circle at point E.

The arc angle AC can be found as follows:

Therefore,

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

arc angle AC = x

arc angle BD = 23 degrees.

m∠BED = 16 degrees.

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

16 = 1 / 2 (x - 23)

16 = 1 / 2x - 23 / 2

16 + 11.5 = 0.5x

27.5 = 0.5x

x = 27.5 / 0.5

x = 55 degrees.

Therefore,

arc angle AC = 55 degrees.

learn more on arc angle here: hhttps://brainly.com/question/23117081

#SPJ1

7 0

1 year ago

Determine the equation of the line described. Put answer in the slope-intercept form, if possible.

julsineya [31]

Step-by-step explanation:

do you have a picture of your work?

and if you have 9.9 in your graph and you get a point it can be valid otherwise it would not help you at all

6 0

1 year ago

Can someone help me with this problem [-64x(-5)-2x(3)]

galina1969 [7]

The answer is 314
(^o^)

5 0

3 years ago

Read 2 more answers