Ask question

Ask question

All categories

3 years ago

10

Larry saves 15% of his annual salary for retirement. This year his salary was $2000 more than last year and he saved $3300. What

was his salary last year

1 answer:

Vlad1618 [11]3 years ago

7 0

Answer:

I think the answer is 28695.65

Step-by-step explanation:

You might be interested in

Simplify the expression.<br> 2x³y +7x³y-xy³

jek_recluse [69]

Answer:

xy*(2x^2 + 7x^2 - y^2)

Step-by-step explanation:

You can get xy out of the expression since all have xy

7 0

1 year ago

Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

1 year ago

What is an equation of the line that passes through th (3,-1) and has a slope of 2?

dezoksy [38]

The given point to us is (3,-1) and the slope of the line is 2 . We can use the <u>point</u><u> </u><u>slope </u>form of the line as ,

$\sf\longrightarrow m ( x - x_1) = y - y_1$

Substitute the values ,

$\sf\longrightarrow 2( x - 3 ) = y - (-1)$

Simplify LHS and RHS ,

$\sf\longrightarrow 2x - 6 = y +1$

Put all terms on one side ,

$\sf\longrightarrow \boxed{\bf 2x - y -7=0}$

4 0

2 years ago

What is the lateral area of the pyramid

Mkey [24]

Answer:

43.75 ft²

Step-by-step explanation:

$s_l$ = (l√(w/2)² + h²) + (w√(l/2)² + h²)

l & w become 3.5, and h becomes 6.

<em /> $s_l$ <em> </em>= (3.5√(3.5/2)² + 6²) + (3.5√(3.5/2)² + 6²)

<em>Step 1:Because this is a square pyramid, what you see above essentially becomes what you see below.</em>

<em /> $s_l$ = 2(3.5√(3.5/2)² + 6²)

<em>Step 2: Divide 3.5 by 2 to get 1.75.</em>

<em /> $s_l$ <em> </em>= 2(3.5√1.75² + 6²)

<em>Step 3: Square both 1.75 and 6 to get 3.0625 and 36 respectively.</em>

$s_l$ = 2(3.5√3.0625 + 36)

<em>Step 4: Add 3.0625 and 36 to get 39.0625.</em>

<em /> $s_l$ = 2(3.5√39.0625)

<em>Step 5: The square root of 39.0625 is 6.25.</em>

<em /> $s_l$ <em> </em>= 2(3.5 * 6.25)

<em>Step 6: Multiply 3.5 by 6.25 to get 21.875.</em>

<em /> $s_l$ = 2(21.875)

<em>Step 7: Multiply 2 by 21.875 to get 43.75.</em>

<em /> $s_l$ = 43.75 ft²

The lateral area of this pyramid is 43.75 ft².

<em />

<em />

3 0

2 years ago

Find the value of the trigonometric ratio. Simplify the ratio if possible.

sweet [91]

Step-by-step explanation:

Given that,

BC = 8

Ac = 15

We can find AB using the pythagoas theorem.

$AB=\sqrt{AC^2+BC^2}\\\\=\sqrt{15^2+8^2}\\\\AB=17$

We know that,

$\cos\theta=\dfrac{B}{H}$ , B is base and H is Hypotenuse

$\cosB=\dfrac{8}{17}$

Hence, this is the required solution.

3 0

2 years ago