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4 years ago

If you earn $48 in 4 hours. What is the unit rate per hour?

Mathematics

2 answers:

LiRa [457]4 years ago

5 0

Answer:

$12

Step-by-step explanation:

erma4kov [3.2K]4 years ago

3 0

48/4 = 12. So $12 per hour

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Write down the explicit solution for each of the following: a) x’=t–sin(t); x(0)=1

Kay [80]

Answer:

a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)

Step-by-step explanation:

Let's solve by separating variables:

$x'=\frac{dx}{dt}$

a) x’=t–sin(t), x(0)=1

$dx=(t-sint)dt$

Apply integral both sides:

$\int {} \, dx=\int {(t-sint)} \, dt\\\\x=\frac{t^2}{2}+cost +k$

where k is a constant due to integration. With x(0)=1, substitute:

$1=0+cos0+k\\\\1=1+k\\k=0$

Finally:

$x=\frac{t^2}{2} +cos(t)$

b) x’+2x=4; x(0)=5

$dx=(4-2x)dt\\\\\frac{dx}{4-2x}=dt \\\\\int {\frac{dx}{4-2x}}= \int {dt}\\$

Completing the integral:

$-\frac{1}{2} \int{\frac{(-2)dx}{4-2x}}= \int {dt}$

Solving the operator:

$-\frac{1}{2}ln(4-2x)=t+k$

Using algebra, it becomes explicit:

$x=2+ke^{-2t}$

With x(0)=5, substitute:

$5=2+ke^{-2(0)}=2+k(1)\\\\k=3$

Finally:

$x=2+3e^{-2t}$

c) x’’+4x=0; x(0)=0; x’(0)=1

Let $x=e^{mt}$ be the solution for the equation, then:

$x'=me^{mt}\\x''=m^{2}e^{mt}$

Substituting these equations in c)

$m^{2}e^{mt}+4(e^{mt})=0\\\\m^{2}+4=0\\\\m^{2}=-4\\\\m=2i$

This becomes the solution m=α±βi where α=0 and β=2

$x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)$

Where A and B are constants. With x(0)=0; x’(0)=1:

$x=Asin(2t)+Bcos(2t)\\\\x'=2Acos(2t)-2Bsin(2t)\\\\0=Asin(2(0))+Bcos(2(0))\\\\0=0+B(1)\\\\B=0\\\\1=2Acos(2(0))\\\\1=2A\\\\A=\frac{1}{2}$

Finally:

$x=\frac{1}{2} sin(2t)$

7 0

3 years ago

To determine a student’s overall test score for the semester, Ms. Lopez throws out the lowest test score and takes the average o

Ugo [173]

Answer:

80%

Step-by-step explanation:

I'm assuming you want the average of the class.

62 + 78 + 83 + 84 + 93

= 400

400/5

= 80

Therefore Victor's overall test score is 80%

6 0

3 years ago

IMPORTANT. LOTS OF POINTS. SOLVE NOW. Rays OM , ON , and OP coincide at time t=0. At the same instant in time, OM and OP begin t

Anton [14]

I believe if Socratic is right the answer is -x+4y=8

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3 years ago

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Which is true 0.0093<0.01

Yuliya22 [10]

Step-by-step explanation:

<h2>I dont see other options tell me other options in the comments but this one ahead is not true （⌒▽⌒）Hope my answer helps you plz Mark me brainliest</h2>

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3 years ago

The members of a class voted to visit the zoo, museum, or science center on their next field trip. If the zoo got 33% of the vot

Alenkasestr [34]

Answer:

Step-by-step explanation:

100-33=67

67-29=38

38%

6 0

3 years ago

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If you earn $48 in 4 hours. What is the unit rate per hour?​

If you earn $48 in 4 hours. What is the unit rate per hour?