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3 years ago

A line that passes through (-8,4) and has a slope of -5/4

Mathematics

1 answer:

zhannawk [14.2K]3 years ago

3 0

Answer:

y2-y1, x2-x1

Step-by-step explanation:

4-(-5)= 4-(-8)

4+5=4+8

9=12

9/12

3/4

the slope of line is 3/4

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Describe the trend/correlation<br> shown in the scatter plot below

Mkey [24]

Answer:

Negative correlation.

Step-by-step explanation:

Negative correlation means that as x increases, y decreases

Positive correlation means that as x increases, y also increases.

No correlation means that neither of the two above cases happens.

In the graph, we can see that on the right (when x is negative) the general y values are larger.

As x increases, the y-values decrease.

(Particularly, we could adjust these data with a linear equation with a negative slope)

Then this is a negative correlation.

3 0

3 years ago

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 is 5.25 divided by 15

AveGali [126]

---0.35 is the answer---

7 0

3 years ago

Read 2 more answers

Round 5,600,679 to the nearest thousand

vampirchik [111]

The answer is 5,601,000

4 0

3 years ago

Help me guys. plz no Decimal please. Thank you!

Scrat [10]

Answer: 1,145,375cm^3

Step-by-step explanation:

8 0

3 years ago

A line that passes through (-8,4) and has a slope of -5/4​

A line that passes through (-8,4) and has a slope of -5/4