Ask question

Ask question

All categories

3 years ago

14

Two trains leave towns 1490 kilometers apart at the same time and travel toward each other. One train travels 20 km/h slower tha

n the other. If they meet in 5 hours, what is the rate of each train?

1 answer:

Fynjy0 [20]3 years ago

5 0

Answer:

rate 1. 50 2. 56

Step-by-step explanation:

if you graph them all together.

You might be interested in

Solve -5(3n + 4) = 40.

Sveta_85 [38]

N=-4
Distribute the -5
-15n-20=40
-15n=60
n=-4

3 0

2 years ago

Hunter is going to graph the ordered pairs that are represented by this table on a coordinate plane.

valentina_108 [34]

Answer:

1.

Step-by-step explanation:

When x is 0, the point will lie on the x-axis, so we need to find how many times this happens.

There's only 1 0, so the answer is 1.

6 0

3 years ago

Read 2 more answers

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 million people have equal chances of being called by telephone from a broadcasting show. Determine the probability of one pa

Softa [21]

One out of one million

7 0

3 years ago

Read 2 more answers

What is 5/8 + 3/4 using these sticks

uysha [10]

3/4 =6/8 so you have 3/4slices of pizza cut the 3 of them in half

6 0

4 years ago