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3 years ago

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