All categories

3 years ago

A line passes through points (0,k) and (2,0) and has a slope of -1.5.

Mathematics

1 answer:

Contact [7]3 years ago

4 0

Answer:

The equation of the line is y = -1.5x + 3

The y-intercept is (0,3)

The value of k is 3.

Step-by-step explanation:

y - 0 = -1.5 (x - 2)

y = -1.5x + 3

You might be interested in

Solve the following differential equation: y" + y' = 8x^2

PtichkaEL [24]

Answer:

$y=y_p+y_h = \frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$

Step-by-step explanation:

Let's find a particular solution. We need a function of the form $y= ax^3+bx^2+cx+d$ such that

$y'= 3ax^2+2bx+c$ and

$y''= 6ax+2b$

$y'+y''= 3ax^2+2bx+c+6ax+2b = 3ax^2+x(2b+6a)+(c+2b) = 8x^2$

then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain

a = 8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.

So, our particular solution is $y_p= \frac{8}{3}x^3-8x^2+16x$ .

Now, let's find the solution $y_p$ of the homogeneus equation $y''+y'=0$ with the method of constants coefficients. Let $y=e^{\lambda x}$

$y'=\lambda e^{\lambda x}$

$y''=\lambda^2e^{\lambda x}$

then $\lambda e^{\lambda x}+\lambda^2 e^{\lambda x} = 0$

$e^{\lambda x}(\lambda +\lambda^2)= 0$

$(\lambda +\lambda^2)= 0$

$\lambda (1+\lambda)= 0$

$\lambda =0$ and $\lambda)= -1$ .

So, $y_h = C_1 + C_2e^{-x}$ and the solution is

$y=y_p+y_h =\frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$ .

5 0

2 years ago

Simplify the imaginary number using the properties of exponents.<br> ¡102

olya-2409 [2.1K]

Answer: Explanation: 102=2⋅51. i102=(i2)51=(−1)51=−1.

Step-by-step explanation:

3 0

2 years ago

I need help finding X please

Vedmedyk [2.9K]

Hello

This is a right angle as you can see by the small square at the bottom. So this means that it is 90 degrees.

Because we already know part of the 90 degrees, we can do 90-50 degree which leave us with 40 degrees.

So as we look at 8x, it needs to equal 40

- 8x=40 divide both sides by 8

- x=5

Hope this helps!

7 0

3 years ago

The graph of f(x) was vertically translated down by a value of k to get the function g(x) = 5x + k. What is the value of k? A -7

Nadya [2.5K]

Answer:

${\boxed{\text{A. }\math{k = -7}}$

Step-by-step explanation:

The general rule for vertical translation of a function ƒ(x) ⟶ ƒ(x) + k .

A positive value of k means that the graph is shifted up by k units.

The graph of ƒ(x) was shifted from (0, 1) to (0, -6).

$\text{The graph was shifted down by seven units, so }{\boxed{\mathbf{k = -7}}$

4 0

3 years ago

Read 2 more answers

find the value of solid figure not including hole cutout. Round to two decimal places. Cube figure is 12 feet long with 4 ft cut

Artemon [7]

Answer:

1577.20 ft³

Step-by-step explanation:

Cube of length = 12 ft = a

Hole diameter which is cutout = 4 ft = d

Hole radius which is cutout = 4/2 =2 ft = r

Volume of the cube = a³

⇒Volume of the cube = a×a×a

⇒Volume of the cube = 12×12×12

⇒Volume of the cube = 1728 ft³

The hole cut out will be in the shape of a cylinder

Volume of cylinder = πr²h

⇒Volume of cylinder = π×2²×12

⇒Volume of cylinder = 150.79 ft³

Now volume of the solid figure with hole cut out is

Volume of the cube - Volume of cylinder

=1728 - 150.79

=1577.20 ft³

∴ Volume of solid figure not including hole cutout is 1577.20 ft³

5 0

3 years ago