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3 years ago

Emma started babysitting her neighbor. After babysitting for 5 hours, she made $37.50. What is her babysitting pay rate?

Mathematics

1 answer:

LUCKY_DIMON [66]3 years ago

5 0

Answer:

$7.50

Step-by-step explanation:

Hourly Pay * 5 = 37.5

Rearrange to find the hourly pay

Hourly pay = 37.5 / 5 = 7.5

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Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$

Thus, the required solution is

$y(t)=(-2+1\times t)e^{-5t}\\\\\Rightarrow y(t)=(-2+t)e^{-5t}.$

6 0

3 years ago

-/2 points

Rom4ik [11]

Answer:

Part 1) The domain of the quadratic function is the interval (-∞,∞)

Part 2) The range is the interval (-∞,1]

Step-by-step explanation:

we have

$f(x)=-x^2+14x-48$

This is a quadratic equation (vertical parabola) open downward (the leading coefficient is negative)

step 1

Find the domain

The domain of a function is the set of all possible values of x

The domain of the quadratic function is the interval

(-∞,∞)

All real numbers

step 2

Find the range

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

we have a vertical parabola open downward

The vertex is a maximum

Let

(h,k) the vertex of the parabola

The range is the interval

(-∞,k]

Find the vertex

$f(x)=-x^2+14x-48$

Factor -1 the leading coefficient

$f(x)=-(x^2-14x)-48$

Complete the square

$f(x)=-(x^2-14x+49)-48+49$

$f(x)=-(x^2-14x+49)+1$

Rewrite as perfect squares

$f(x)=-(x-7)^2+1$

The vertex is the point (7,1)

therefore

The range is the interval

(-∞,1]

6 0

3 years ago

Factor completely. 2x^4+4x^3-30x^2

kramer

Answer:

Step-by-step explanation:

2x⁴ + 4x³ - 30x² = 2x²*(x² + 2x - 15)

x² + 2x - 15

Sum = 2

Product = -15

Factors = 5 ; (-3)

x² + 2x - 15 = x² + 5x - 3x - 3 *5

= x(x + 5) - 3(x + 5)

= (x + 5)(x - 3)

2x⁴ + 4x³ - 30x² = (2x²) (x + 5)(x - 3)

7 0

4 years ago

Solve any evens for 20 points apiece

Vlad1618 [11]

? what do you mean. do you have questions that need to be solved?

5 0

3 years ago

Which of the following options have the same value as 20% of 45 (choose 3 answer)

11Alexandr11 [23.1K]

Answer:

20% of 45 is 9,

Step-by-step explanation:

So the answer must be 9 for an example 50% of 18 is 9 because to find 50% of something simply divide by 2 .10% of 90 is 9 because to find 10% of something divide by 10. 25% of 36 is 9 because you divide by 4 to get 25% of anything.

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3 years ago