All categories

3 years ago

Describe how to graph a line given an equation in standard form.

Mathematics

1 answer:

Archy [21]3 years ago

3 0

This is pretty simple. So a standard form equation is probably something like this: 2x+8y=10.
We have to get that equation right there into a slope intercept, which is just isolating the variable y.
2x+8y=16
-2x -2x Subtract the x value.
------------------
(8y=16-2x)/8 Divide the whole equation by 8 to isolate the y value.
------------------
y=2-1/4x
------------------
The fraction with the variable x is the slope. In this case, the slope is -1/4, so meaning it goes down one unit and goes right 4.
------------------
The 2 is the y-intercept. (0, 2)

You might be interested in

Hello people ~

Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

Using Pythagoras Theorem

(a)

TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

(b)

volume of cone = 1/3 * π * r² * h

===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

(c)

First derivative

$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

apply chain rule

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

Equate the first derivative to zero, that is V'(x) = 0

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$

maximum volume: when h = 40/3

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

minimum volume: when h = 0

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

6 0

1 year ago

Read 2 more answers

I spent 15 percent of my money on food last week. If I had $56 how much money was spent on food

liq [111]

15% of 56 is
0.15 * 56 is 8.4
You spent 8.4 dollars on food

Hope this helps :)

6 0

3 years ago

Using De-Moivre's theorem, prove that i^2= -1.

Novosadov [1.4K]

Write i in trigonometric form. Since |i| = 1 and arg(i) = π/2, we have

i = exp(i π/2) = cos(π/2) + i sin(π/2)

By DeMoivre's theorem,

i² = exp(i π/2)² = exp(i π) = cos(π) + i sin(π)

and it follows that i² = -1 since cos(π) = -1 and sin(π) = 0.

3 0

2 years ago

Karita had $138.72 in her checking account. She wrote checks for $45.23 and $18.00. Then she made a deposit of $75.85 into her a

svetlana [45]

Answer:

The best estimate for the money in Karita's account now is $151.

Step-by-step explanation:

Given:

Karita had $138.72 in her checking account.

She wrote checks for $45.23 and $18.00.

Then she made a deposit of $75.85 into her account.

Now, to find the best estimate for the money in Karita's account now.

Initial account = $138.72.

Deducted amount = $45.23+$18.00=$63.23.

So, the amount after deduction:

$138.72 - $63.23 = $75.49.

Now, the amount after deposit:

$75.49 + $75.85 = $151.34.

Therefore, the best estimate for the money in Karita's account now is $151.

6 0

2 years ago

How Do you Simplify Fractions? For example: 4 over 5 + 3 over 5

vova2212 [387]

If I am not mistaken, you cross multiply then divide.

8 0

2 years ago

Read 2 more answers