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drek231 [11]
3 years ago
13

Which ratio is equal to 78?

Mathematics
1 answer:
lyudmila [28]3 years ago
5 0

Answer:

78 : 162 = 13 : 27. These two equalities are examples of proportions (equal ratios); it is as simple as that.

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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
The school that Brenda goes to is selling tickets to the annual talent show. On the first day of the ticket sales the school sol
KiRa [710]
A=cost er adult ticket
c=cost per child ticket

2a+14c=96
12a+8c=120

solve

simplify by dividing firs equation by 2 and 2nd by 4

a+7c=48
3a+2c=30

multiply first equaiton by -3 and add to second
-3a-21c=-144
<u>3a+2c=30 +</u>
0a-19c=-114

-19c=-114
divide both sides by -19
x=6

sub back

a+7c=48
6+7c=48
minus 6
7c=42
divide 7
c=6

adult ticket=$6
child ticekt=$6
7 0
3 years ago
Find each percent increase or decrease to the nearest percent:
Svet_ta [14]
From 10 to 15 -> 10 increased with half its size (5), that means increase of 50%
From 16 to 12 -> decrease of 4, which is a quarter of 16, that means a decrease of 25%
4 0
3 years ago
Celeste makes $9.75 an hour and owes $875 how much hours must she work to pay her bills and save $500
lianna [129]
So Celeste makes 9.75 an hour this is very confusing ummm help me come on ree
4 0
3 years ago
What is 5/2x + 2y = 5
Vikentia [17]

Answer:

y= -x+1/2

Step-by-step explanation:

7 0
2 years ago
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