What is the equation of a line that passes through the points (0,5) and (4,8)? Write your answer in slope intercept form

Mathematics

1 answer:

Sergio [31]3 years ago

3 0

The equation for the slope intercept form is 2,3

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7/2x + 1/2x = 7 + 9/2x

lesya [120]

Answer: x=-14

Step-by-step explanation:

5 0

1 year ago

Can somebody help me show work on this??

CaHeK987 [17]

I would if i had paper:( its hard to explain

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3 years ago

A sphere of radius r is cut by a plane h units above the equator, where

Anika [276]

Consider the top half of a sphere centered at the origin with radius $r$ , which can be described by the equation

$z=\sqrt{r^2-x^2-y^2}$

and consider a plane

$z=h$

with $0$ . Call the region between the two surfaces $R$ . The volume of $R$ is given by the triple integral

$\displaystyle\iiint_R\mathrm dV=\int_{-\sqrt{r^2-h^2}}^{\sqrt{r^2-h^2}}\int_{-\sqrt{r^2-h^2-x^2}}^{\sqrt{r^2-h^2-x^2}}\int_h^{\sqrt{r^2-x^2-y^2}}\mathrm dz\,\mathrm dy\,\mathrm dx$

Converting to polar coordinates will help make this computation easier. Set

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\var\phi\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

Now, the volume can be computed with the integral

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_0^{\arctan\frac{\sqrt{r^2-h^2}}h}\int_{h\sec\varphi}^r\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\varphi\,\mathrm d\theta$

You should get

$\dfrac{2\pi}3\left(r^3\arctan\dfrac{\sqrt{r^2-h^2}}h-\dfrac{h^3}2\left(\dfrac{r\sqrt{r^2-h^2}}{h^2}+\ln\dfrac{r+\sqrt{r^2-h^2}}h\right)\right)$

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3 years ago

Loretta and her family are going on vacation. Their destination is 610 miles from their home. Loretta is going to share some of

alexandr402 [8]

Loretta:
Average driving speed = 55 mph
Time = 4 hours
Distance traveled = 55*4 = 220 miles

Dad:
Average driving speed = 65 mph
Let x = hours driven
Distance traveled = 65x miles

The length of the trip is 610 miles, therefore
65x + 220 = 610
65x = 390
x = 6 hours

Answer: Loretta's dad drove for 6 hours.

7 0

3 years ago

the bottom of a 22-foot ladder must be placed 7 feet from a wall. to the nearest tenth of a foot, how far above the ground does

Kitty [74]

The ladder, the wall and the floor form together a triangle rectangle, where the ladder is the hypotenuse of the triangle and the floor and wall are the cathetus. We know from Pythagoreas theorem that the square of the hypotenuse is equal to the sum of the two cathetus squared added, so we can write an equation with the data we have:
hyp^2 = cath1^2 + cath2^2
<span>hyp^2 = wall^2 + floor^2
</span>so we have the hypotenuse value, the floor value and the unknown is the wall height:
(22)^2 = wall^2 + (7)^2
484 = wall^2 + 49
wall^2 = 484 - 49 = 435
wall = √435
wall = 20.9
therefore the ladder touches the wall 20.9 feet above the ground

5 0

2 years ago