All categories

3 years ago

What is the slope intercept equation of the line (0,4) and (2.-2)

Mathematics

2 answers:

atroni [7]3 years ago

8 0

Answer:

$slope=-3\\b=4\\$

Equation of the line

$y=-3x+4$

Step-by-step explanation:

To find the slope we need two points, $(x_1,y_1)$ and $(x_2,y_2)$ In this case we have the points $(0,4)$ and $(2, -2)$

$slope=\frac{y_2-y_1}{x_2-x_1}$ (1)

We replace the points in the equation (1)

$\frac{y_2-y_1}{x_2-x_1}$

$\frac{-2-4}{2-0} =\frac{-6}{2} =-3$

We know the equation of the line:

$y=mx+b$ (2)

To find b we replace the slope, x and y with one of the points in the equation (2)

$4=-3*0+b\\4=0+b\\b=4$

We substitute m and b in the general equation of the line

$y=-3x+4$

KonstantinChe [14]3 years ago

3 0

Answer:

y= -3x + 4

Step-by-step explanation:

You might be interested in

Please answer this and will marked as brainlist

xeze [42]

<h3>Answer: 1</h3>

where x is nonzero

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

Explanation:

We'll use two rules here

(a^b)^c = a^(b*c) ... multiply exponents
a^b*a^c = a^(b+c) ... add exponents

------------------------------

The portion [ x^(a-b) ]^(a+b) would turn into x^[ (a-b)(a+b) ] after using the first rule shown above. That turns into x^(a^2 - b^2) after using the difference of squares rule.

Similarly, the second portion turns into x^(b^2-c^2) and the third part becomes x^(c^2-a^2)

-------------------------------

After applying rule 1 to each of the three pieces, we will have 3 bases of x with the exponents of (a^2-b^2), (b^2-c^2) and (c^2-a^2)

Add up those exponents (using rule 2 above) and we get

(a^2-b^2)+(b^2-c^2)+(c^2-a^2)

a^2-b^2+b^2-c^2+c^2-a^2

(a^2-a^2) + (-b^2+b^2) + (-c^2+c^2)

0a^2 + 0b^2 + 0c^2

0+0+0

All three exponents add to 0. As long as x is nonzero, then x^0 = 1

4 0

3 years ago

Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.04 cm thick to a hemispherical dome

pogonyaev

The amount of paint is the volume of paint needed.

The amount of paint needed is 0.065312 cubic meters

<h3>How to determine the amount of paint needed</h3>

The volume of a hemisphere is:

$V = \frac 23\pi r^3$

Differentiate the above equation

$V' = 2\pi r^2 r'$

The above equation represents the estimate of the amount of paint needed.

Where:

r represents the radius (r = 52/2 m)
r' represents the thickness (r' = 0.04 cm)

So, we have:

$V' = 2\pi r^2 r'$

$V' = 2 * 3.14 * (52/2\ m)^2 * (0.04cm)$

$V' = 2 * 3.14 * (26\ m)^2 * (0.04cm)$

Express cm as m

$V' = 2 * 3.14 * (26\ m)^2 * (0.0004m)$

$V' = 0.065312 m^3$

Hence, the amount of paint needed is 0.065312 cubic meters