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3 years ago

14

10. A trapezold has a base of x and a helght of 3 units. If there is also a square with sides measuring x,

1 answer:

Nookie1986 [14]3 years ago

6 0

Answer:

I Think 0x2 Or 4x + x3 I'm not 100% Sure

Step-by-step explanation:

I Tried..

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Identify the slope and y intercept of the line having equation y=-8x-15

Harrizon [31]

Answer: the slope would be a negative slope with -15 as the y intercept.

Step-by-step explanation:

3 0

2 years ago

A large corporation starts at time t = 0 to invest part of its receipts continuously at a rate of P dollars per year in a fund f

Andrews [41]

Answer:

$A = \frac{P}{r}\left( e^{rt} -1 \right)$

Step-by-step explanation:

This is <em>a separable differential equation</em>. Rearranging terms in the equation gives

$\frac{dA}{rA+P} = dt$

Integration on both sides gives

$\int \frac{dA}{rA+P} = \int dt$

where $c$ is a constant of integration.

The steps for solving the integral on the right hand side are presented below.

$\int \frac{dA}{rA+P} = \begin{vmatrix} rA+P = m \implies rdA = dm\end{vmatrix} \\\\\phantom{\int \frac{dA}{rA+P} } = \int \frac{1}{m} \frac{1}{r} \, dm \\\\\phantom{\int \frac{dA}{rA+P} } = \frac{1}{r} \int \frac{1}{m} \, dm\\\\\phantom{\int \frac{dA}{rA+P} } = \frac{1}{r} \ln |m| + c \\\\&\phantom{\int \frac{dA}{rA+P} } = \frac{1}{r} \ln |rA+P| +c$

Therefore,

$\frac{1}{r} \ln |rA+P| = t+c$

Multiply both sides by $r.$

$\ln |rA+P| = rt+c_1, \quad c_1 := rc$

By taking exponents, we obtain

$e^{\ln |rA+P|} = e^{rt+c_1} \implies |rA+P| = e^{rt} \cdot e^{c_1} rA+P = Ce^{rt}, \quad C:= \pm e^{c_1}$

Isolate $A$ .

$rA+P = Ce^{rt} \implies rA = Ce^{rt} - P \implies A = \frac{C}{r}e^{rt} - \frac{P}{r}$

Since $A = 0$ when $t=0$ , we obtain an initial condition $A(0) = 0$ .

We can use it to find the numeric value of the constant $c$ .

Substituting $0$ for $A$ and $t$ in the equation gives

$0 = \frac{C}{r}e^{0} - \frac{P}{r} \implies \frac{P}{r} = \frac{C}{r} \implies C=P$

Therefore, the solution of the given differential equation is

$A = \frac{P}{r}e^{rt} - \frac{P}{r} = \frac{P}{r}\left( e^{rt} -1 \right)$

4 0

3 years ago

Estimate the sum. Round each number to the nearest whole number, then add. 9 1/2 + 7 1/8

borishaifa [10]

Answer:

12 1/8

Step-by-step explanation:

4 0

3 years ago

At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the

Ivanshal [37]

The sine function for the given scenario is y = 6sin ( (π / 10) x ) - 10.

<u>Step-by-step explanation:</u>

The standard formula for sine function is Asin(Bx)+C.

A buoy bobs up and down 6 meters. That is the buoy shifts vertically and horizontally for 6 meters which is amplitude.

∴Amplitude A= 6.

Period is the distance in the x-axis that makes one full oscillation.

We know that the time taken buoy to move from its highest point to lowest point (half oscillation) is 10 seconds.

∴The period for full oscillation is 20 seconds.

Also, Period =2π divided by B.

⇒ 20 (B) = 2π.

B=2π /20.

= π/ 10.

Since the buoy is in the depth of the ocean 10 meters C = -10.

Applying all the values in the formula,

⇒y = 6sin ( (π/ 10) x ) - 10.

The first point is the mid line,

The first point is x=0,

⇒y=6sin(0)-10.

y= -10.

∴ The line starts at the point y = -10.

The second point is either maximum or minimum value.

That is (5,-4) and (15, -16.)

7 0

3 years ago

The height of the fence in Bella’s back yard is 2 meters.

nydimaria [60]

Stoopid, its 200 centimeters

5 0

4 years ago