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grin007 [14]
3 years ago
6

Original price $77.00 markdown: 32% sale price

Mathematics
1 answer:
Dvinal [7]3 years ago
4 0
The sale price would be 24.64
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Stars that are medium-sized are: A. about the size of our sun B. about four times the size of our sun C. less than half the size
aliina [53]
C because the sun is like 100 times bigger than our Earth so if its medium well there we go
8 0
3 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
One fifth of the sum of two angles is 24 and half their difference is 14.Calculate the two angles
Brums [2.3K]
Let, the angles = a, b
It is given that, a+b /5 = 24
a + b = 120   --- equation (1)

a-b/2 = 14
a - b = 28  ---- equation (2)
a = 28 + b

Now, substitute this value of b in equation (1), 
28 + b + b = 120
2b = 120 - 28
b = 92/2
b = 46
Now, a = 28 + b = 28 + 46 = 74

In short, Your Angles are 74 and 46

Hope this helps!
4 0
3 years ago
The circle shown below has a diameter of 18 centimeters. What is the area of the shaded sector?
N76 [4]
Area of circle = Pi x r*2

If diameter is 18, radius is 9.

Area = pi (3.14) x r*2 (9*2 = 81) .. 3.14 x 81 = 254.34 sq cen = total area of circle.

A circle is 360 degrees, the shaded area is 270 degrees. the shaded area is 3/4 (270/360) of the area of the circle.

254.34 x 3/4 = 190.755 sq cen

Hope this helps
7 0
3 years ago
Read 2 more answers
Rob is saving to buy a new MP3 player. For every $15 he earns babysitting, he saves $9. On Saturday, Rob earned $60 babysitting.
alexandr402 [8]
$60 ÷ $15 = 4
$9 × 4 = $36
he saved $36 when he earned $60
8 0
3 years ago
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