-2x - 7 = 3 need the answer

Jamie wants to borrow $15,000 from South Western Bank. They offered a 4 year loan with an APR of 5.5%. How much will she pay in

Anna [14]

She will pay $825 on the loan she took out

6 0

3 years ago

Read 2 more answers

The cubic polynomial below has a double root at r4 and one root at x = 6 and passes Through the point (2, 36) as shown. Algebrai

qaws [65]

The graph in the question is missing.

Answer:

y = $\frac{-1}{4}( x^3 + 2x^2 - 32x -96)$

Step-by-step explanation:

The function is cubic

It has roots as -4, -4 , 6

this means the value of x = -4, -4 , 6 which makes the entire equation zero

so we have solutions as

x+4 = 0

x- 6 = 0

on forming a cubic equation using these

(x+4)(x+4)(x-6)

the equation passes through (2,36)

put x = 2

(2+4)(2+4)(2-6) = (6)*(6)*(-4)

which exceeds 36 so we product the equation with -1/4 to get 36

Final equation

y = $\frac{-1}{4} (x+4)(x+4)(x-6)$

y = $\frac{-1}{4}( x^3 + 2x^2 - 32x -96)$

3 0

2 years ago

Find a number if: 3/7 of it is 2 1/14

mina [271]

Answer:

49 7/12

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

What’s the value of the 8 in 281480100

luda_lava [24]

We want to find the value of the 8 in 281,480,100

Let's find the place value of each of the numbers:

2 - hundred millions

8 - ten millions

1 - millions

4 - hundred thousands

8 - ten thousands

0 - thousands

1 - hundreds

0 - tens

0 - ones

I see there are two 8's so I wouldn't be too sure of which value to find, but just in case, we have the chart made above for place values.

There is one 8 at the ten millions value.

There is one 8 at the ten thousands value.

7 0

3 years ago

Read 2 more answers

Find a particular solution to the nonhomogeneous differential equation y′′+4y=cos(2x)+sin(2x).

I am Lyosha [343]

Take the homogeneous part and find the roots to the characteristic equation:

$y''+4y=0\implies r^2+4=0\implies r=\pm2i$

This means the characteristic solution is $y_c=C_1\cos2x+C_2\sin2x$ .

Since the characteristic solution already contains both functions on the RHS of the ODE, you could try finding a solution via the method of undetermined coefficients of the form $y_p=ax\cos2x+bx\sin2x$ . Finding the second derivative involves quite a few applications of the product rule, so I'll resort to a different method via variation of parameters.

With $y_1=\cos2x$ and $y_2=\sin2x$ , you're looking for a particular solution of the form $y_p=u_1y_1+u_2y_2$ . The functions $u_i$ satisfy

$u_1=\displaystyle-\int\frac{y_2(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$
$u_2=\displaystyle\int\frac{y_1(\cos2x+\sin2x)}{W(y_1,y_2)}\,\mathrm dx$

where $W(y_1,y_2)$ is the Wronskian determinant of the two characteristic solutions.

$W(\cos2x,\sin2x)=\begin{bmatrix}\cos2x&\sin2x\\-2\cos2x&2\sin2x\end{vmatrix}=2$

So you have

$u_1=\displaystyle-\frac12\int(\sin2x(\cos2x+\sin2x))\,\mathrm dx$
$u_1=-\dfrac x4+\dfrac18\cos^22x+\dfrac1{16}\sin4x$

$u_2=\displaystyle\frac12\int(\cos2x(\cos2x+\sin2x))\,\mathrm dx$
$u_2=\dfrac x4-\dfrac18\cos^22x+\dfrac1{16}\sin4x$

So you end up with a solution

$u_1y_1+u_2y_2=\dfrac18\cos2x-\dfrac14x\cos2x+\dfrac14x\sin2x$

but since $\cos2x$ is already accounted for in the characteristic solution, the particular solution is then

$y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x$

so that the general solution is

$y=C_1\cos2x+C_2\sin2x-\dfrac14x\cos2x+\dfrac14x\sin2x$

7 0

3 years ago