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3 years ago

What is the y-intercept of the graph of the equation 6x-5y=-15

Mathematics

1 answer:

guapka [62]3 years ago

7 0

Answer:

y-intercept = 3

Step-by-step explanation:

The given equation is :

6x-5y=-15

We can rewrite it ib slope-intercept form as follows :

Dividing both sides by 5

$\dfrac{6x}{5}-y=\dfrac{-15}{5}\\\\\dfrac{6x}{5}-y=-3\\\\\dfrac{6x}{5}+3=y$ .....(1)

The general equation of slope-intercept form is:

y = mx +c ....(2)

On comparing equation (1) and (2) we get :

m = 6/5

c = 3

Hence, the y intercept of the graph of the equation is 3.

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A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2

andrey2020 [161]

Answer:

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

Step-by-step explanation:

Consider the provided matrix.

$v_1=\begin{bmatrix}-3\\1 \end{bmatrix}$

$v_2=\begin{bmatrix}-1\\1 \end{bmatrix}$

$\lambda_1=4, \lambda_2=2$

The general solution of the equation $x'=Ax$

$x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}$

Substitute the respective values we get:

$x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}$

Substitute initial condition $x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}$

$\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}$

Reduce matrix to reduced row echelon form.

$\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}$

Therefore, $c_1=2.5,c_2=1.5$

Thus, the general solution of the equation $x'=Ax$

$x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}$

$x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

The required position of the particle at time t is: $x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}$

6 0

3 years ago

"per month" means: ADD

Effectus [21]

Per month means multiply
Total means the amount your ending with but for this you could say add
Final answer f = 4.75 + 10m

3 0

2 years ago

A school assembly had 70 students in attendance, and 90% of them were first-graders. How many first-graders were at the assembly

natulia [17]

Answer:

Step-by-step explanation:

Because, 100% of 70 would be 7. Now we have that number lets multiply it by 9 because of 90%. 9 x 7 = 63 first-graders

4 0

2 years ago

The marine needs 14 boats for the 42 people registered for a boat race. How many boats will they need for 6 people?

Degger [83]

Answer:

Step-by-step explanation:

We can write a proportion to determine

42 people 6 people

---------------- = ----------------

14 boats x boats

Using cross products

42x = 6*14

42x =84

Divide each side by 42

42x/42 = 84/42

x = 2

They will need 2 boats

5 0

3 years ago

(1 point) Find f if f′′(x)=2+cos(x),f(0)=3,f(π/2)=−6.

Kitty [74]

5/8-x=9
Hhhijkddnsmks

7 0

3 years ago