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3 years ago

Which set is a function?

Mathematics

2 answers:

7nadin3 [17]3 years ago

6 0

An input can have two outputs but, an output cannot have two inputs. So, D is right.

seraphim [82]3 years ago

5 0

It has to be "D" :)

hope it helped1

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If a punch bottle says 20% fruit juice,and it is a 200 milliliter bottle, how many milliliters of fruit juice is in the bottle?

padilas [110]

Answer:

There are 40 milliliters of fruit juice in the bottle

Step-by-step explanation:

we know taht

20%=20/100=0.20

To find out the milliliters of fruit juice, multiply the volume of the bottle by the percentage of fruit juice in decimal form

$200(0.20)=40\ ml$

therefore

There are 40 milliliters of fruit juice in the bottle

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 a separable differential equation. 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

This is problem six of the homework that you ask for

Marina86 [1]

This equation could represent the relationship e=8.75h

8 0

3 years ago

A colony of bacteria is growing exponentially according to the function below, where t is in hours. How many bacteria are there

pychu [463]

The growth of the bacteria is expressed as:

B(t) = 4 e^0.8t

where t is the time in units of hours. If the bacteria is allowed to grow for 8 hours then the number of bacteria present would be,

B(t) = 4 e^0.8(8)
B(t) = 2407

5 0

3 years ago

Read 2 more answers

Help me out pleaseeee

Kryger [21]

Answer:

The correct option is (b).

Step-by-step explanation:

The solution of the given polynomial is :

$(-\dfrac{1}{3},4)$