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3 years ago

How do you write an equation in slope intercept when given the slope and a point?

Mathematics

1 answer:

Vlad1618 [11]3 years ago

8 0

To write an equation in slope intercept form given the slope and a point, plug into point-slope form.

(y - y1) = m(x - x1)

In this equation, m is your slope and (x1, y1) is your point. If you follow this and solve for y, you will get your equation in slope intercept form.

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Can you ever use a calculator to determine if a number is rational or irrational?explain.

AysviL [449]

Yes, for fractions you can multiply the denominator by the numerator. For square roots you can use the square root button.

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3 years ago

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Find the volume of the solid formed by revolving the region bounded by LaTeX: y = \sqrt{x} y = x and the lines LaTeX: y = 1 y =

Strike441 [17]

Answer:

The volume is:

$\displaystyle\frac{37\pi}{10}$

Step-by-step explanation:

See the sketch of the region in the attached graph.

We set the integral using washer method:

$\displaystyle\int_a^b\pi r^2dx$

Notice here the radius of the washer is the difference of the given curves:

$x-\sqrt{x}$

So the integral becomes:

$\displaystyle\int_1^4\pi(x-\sqrt{x})^2dx$

We solve it:

Factor $\pi$ out and distribute the exponent (you can use FOIL):

$\displaystyle\pi\int_1^4x^2-2x\sqrt{x}+x\,dx$

Notice: $x\sqrt{x}=x\cdot x^{1/2}=x^{3/2}$

So the integral becomes:

$\displaystyle\pi\int_1^4x^2-2x^{3/2}+x\,dx$

Then using the basic rule to evaluate the integral:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{2x^{5/2}}{5/2}+\frac{x^2}{2}\right|_1^4$

Simplifying a bit:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{4x^{5/2}}{5}+\frac{x^2}{2}\right|_1^4$

Then plugging the limits of the integral:

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Taking the root (rational exponents):

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Then doing those arithmetic computations we get:

$\displaystyle\frac{37\pi}{10}$

6 0

3 years ago

How to find The point midway

Vadim26 [7]

Step-by-step explanation:

The Midpoint Formula works exactly the same way. If you need to find the point that is exactly halfway between two given points, just average the x-values and the y-values.

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3 years ago

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Numero mixto de 16 -- 5

stealth61 [152]

Answer:

La respuesta correcta es 3 1/5

Step-by-step explanation:

Espero que esto ayude a marcar el MÁS CEREBRAL !!!

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3 years ago

Ericka decided to compare her observation to the average annual trend, which shows the water rising 1.8 mm/year. Remember, she u

Alex787 [66]

Answer with explanation:

Presume that, initial water level to be, 0 mm, at a time t=0.

And water level is rising at the rate of $1.8 \frac{\text{mm}}{\text{year}}$ .

After 6.2 years level of water will be =1.8 × 6.2

=11.16 mm

→Averge, that is increase in water level after 6.2 years is given by

$=\frac{W_{2}-W_{1}}{t_{2}-t_{1}}\\\\=\frac{11.16-0}{6.2-0}\\\\=\frac{11.16}{6.2}\\\\=1.8 \frac{\text{mm}}{\text{year}}$

→→Rate of Depreciating of water level is given by = Negative of Increase of water level= $-1.8 \frac{\text{mm}}{\text{year}}$

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3 years ago

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