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Nimfa-mama [501]
2 years ago
5

There are 3 cans that store 9 tennis balls. Consider the number of balls per can a.find the constant of proportionality for this

situation
b.Write an equation to represent the relationship
Mathematics
1 answer:
sergeinik [125]2 years ago
5 0

Answer:

Write an equation that will model the proportional relationship given in each real world situation.

1. There are 3 cans that store 9 tennis balls. Consider the number of balls per can.

a. Find the constant of proportionality for this situation.

9 balls (B)

_________ = 3

3 cans (C)

b. Write an equation to represent the relationship.

b = 3c

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3 years ago
Find the solution of the given initial value problem in explicit form. y′=(1−5x)y2, y(0)=−12 Enclose numerators and denominators
Nata [24]

Answer:

The solution is y=-\frac{12}{12x-30x^2+1}.

Step-by-step explanation:

A first order differential equation y'=f(x,y) is called a separable equation if the function f(x,y) can be factored into the product of two functions of x and y:

f(x,y)=p(x)h(y)

where p(x) and h(y) are continuous functions.

We have the following differential equation

y'=(1-5x)y^2, \quad y(0)=-12

In the given case p(x)=1-5x and h(y)=y^2.

We divide the equation by h(y) and move dx to the right side:

\frac{1}{y^2}dy\:=(1-5x)dx

Next, integrate both sides:

\int \frac{1}{y^2}dy\:=\int(1-5x)dx\\\\-\frac{1}{y}=x-\frac{5x^2}{2}+C

Now, we solve for y

-\frac{1}{y}=x-\frac{5x^2}{2}+C\\-\frac{1}{y}\cdot \:2y=x\cdot \:2y-\frac{5x^2}{2}\cdot \:2y+C\cdot \:2y\\-2=2yx-5yx^2+2Cy\\y\left(2x-5x^2+2C\right)=-2\\\\y=-\frac{2}{2x-5x^2+2C}

We use the initial condition y(0)=-12 to find the value of C.

-12=-\frac{2}{2\left(0\right)-5\left(0\right)^2+2C}\\-12=-\frac{1}{c}\\c=\frac{1}{12}

Therefore,

y=-\frac{2}{2x-5x^2+2(\frac{1}{12})}\\y=-\frac{12}{12x-30x^2+1}

4 0
3 years ago
Select the correct answer.
andrew-mc [135]

Answer:

v=\sqrt{\frac{E}{m}}

Step-by-step explanation:

The formula is given as:

E=mv^2

We need to solve this formula for v, that means that v to one side and let it be solved in terms of the other variables (E and m). First, we isolate v:

E=mv^2\\\frac{E}{m}=\frac{mv^2}{m}\\\frac{E}{m}=v^2

To isolate v, and eliminate the "square", we need to take square roots of both sides, that will give us v in terms of the other variables:

\frac{E}{m}=v^2\\\sqrt{\frac{E}{m}}=\sqrt{v^2}\\\sqrt{\frac{E}{m}}=v

Putting v to left side (convention), we finally have:

v=\sqrt{\frac{E}{m}}

7 0
3 years ago
6[ 5x (41-36) - (8+14)]
IgorLugansk [536]

Answer:

=18

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
The GCF of 18 and 30 is ____.
hammer [34]

The GCF of 18 and 30 is 6

4 0
3 years ago
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