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Anika [276]
3 years ago
14

To find the amount of interest Jesse will pay to borrow money, you can use the formula I = PRT. I = interest; P = principal; R =

Rate; and T=time. How much interest will Jesse pay if he borrows $5,000 for 5 years with an interest rate of 8%? A. $2,000.00 B. $20,000.00 C. $200.00 D. $2,500.00
Mathematics
1 answer:
Cerrena [4.2K]3 years ago
5 0

Answer: A $2000

Step-by-step explanation:

Interest = prt / 100

= 5000 x .08 x 5

= 2000

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One number is 11 more than 3 times another number. Their sum is 75. Find the smaller number.
Musya8 [376]
X = larger number, y = smaller number

x + y = 75
x = 3y + 11

3y + 11 + y = 75
4y + 11 = 75
4y = 75 - 11
4y = 64
y = 64/4
y = 16 <=== ur smaller number

x = 3y + 11
x = 3(16) + 11
x = 48 + 11
x = 59...ur larger number
5 0
3 years ago
A mass weighing 16 pounds stretches a spring (8/3) feet. The mass is initially released from rest from a point 2 feet below the
mezya [45]

Answer with Step-by-step explanation:

Let a mass weighing 16 pounds stretches a spring \frac{8}{3} feet.

Mass=m=\frac{W}{g}

Mass=m=\frac{16}{32}

g=32 ft/s^2

Mass,m=\frac{1}{2} Slug

By hook's law

w=kx

16=\frac{8}{3} k

k=\frac{16\times 3}{8}=6 lb/ft

f(t)=10cos(3t)

A damping force is numerically equal to 1/2 the instantaneous velocity

\beta=\frac{1}{2}

Equation of motion :

m\frac{d^2x}{dt^2}=-kx-\beta \frac{dx}{dt}+f(t)

Using this equation

\frac{1}{2}\frac{d^2x}{dt^2}=-6x-\frac{1}{2}\frac{dx}{dt}+10cos(3t)

\frac{1}{2}\frac{d^2x}{dt^2}+\frac{1}{2}\frac{dx}{dt}+6x=10cos(3t)

\frac{d^2x}{dt^2}+\frac{dx}{dt}+12x=20cos(3t)

Auxillary equation

m^2+m+12=0

m=\frac{-1\pm\sqrt{1-4(1)(12)}}{2}

m=\frac{-1\pmi\sqrt{47}}{2}

m_1=\frac{-1+i\sqrt{47}}{2}

m_2=\frac{-1-i\sqrt{47}}{2}

Complementary function

e^{\frac{-t}{2}}(c_1cos\frac{\sqrt{47}}{2}+c_2sin\frac{\sqrt{47}}{2})

To find the particular solution using undetermined coefficient method

x_p(t)=Acos(3t)+Bsin(3t)

x'_p(t)=-3Asin(3t)+3Bcos(3t)

x''_p(t)=-9Acos(3t)-9sin(3t)

This solution satisfied the equation therefore, substitute the values in the differential equation

-9Acos(3t)-9Bsin(3t)-3Asin(3t)+3Bcos(3t)+12(Acos(3t)+Bsin(3t))=20cos(3t)

(3B+3A)cos(3t)+(3B-3A)sin(3t)=20cso(3t)

Comparing on both sides

3B+3A=20

3B-3A=0

Adding both equation then, we get

6B=20

B=\frac{20}{6}=\frac{10}{3}

Substitute the value of B in any equation

3A+10=20

3A=20-10=10

A=\frac{10}{3}

Particular solution, x_p(t)=\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

Now, the general solution

x(t)=e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

From initial condition

x(0)=2 ft

x'(0)=0

Substitute the values t=0 and x(0)=2

2=c_1+\frac{10}{3}

2-\frac{10}{3}=c_1

c_1=\frac{-4}{3}

x'(t)=-\frac{1}{2}e^{-\frac{t}{2}}(c_1cos(\frac{\sqrt{47}t}{2})+c_2sin(\frac{\sqrt{47}t}{2})+e^{-\frac{t}{2}}(-c_1\frac{\sqrt{47}}{2}sin(\frac{\sqrt{47}t}{2})+\frac{\sqrt{47}}{2}c_2cos(\frac{\sqrt{47}t}{2})-10sin(3t)+10cos(3t)

Substitute x'(0)=0

0=-\frac{1}{2}\times c_1+10+\frac{\sqrt{47}}{2}c_2

\frac{\sqrt{47}}{2}c_2-\frac{1}{2}\times \frac{-4}{3}+10=0

\frac{\sqrt{47}}{2}c_2=-\frac{2}{3}-10=-\frac{32}{3}

c_2==-\frac{64}{3\sqrt{47}}

Substitute the values then we get

x(t)=e^{-\frac{t}{2}}(-\frac{4}{3}cos(\frac{\sqrt{47}t}{2})-\frac{64}{3\sqrt{47}}sin(\frac{\sqrt{47}t}{2})+\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

8 0
3 years ago
Question 10(Multiple Choice Worth 1 points) (06.01 LC) Choose the polynomial that is written in standard form.
Svetach [21]

Answer:

  −3x^8 + 9x^2 + 10x

Step-by-step explanation:

A polynomial is in standard form when the exponents of the variable decrease left to right. The only given expression in that form is ...

  −3x^8 + 9x^2 + 10x

7 0
2 years ago
The sum of two numbers is 25. Their difference is 9. What are the two numbers?
Lynna [10]
Using x and y as the numbers

x+y=25 -------#1
x-y=9  -------#2

Using addition of #1 and #2
x+y+x-y= 25+9
2x+0y=34
2x=34
x=17

Using the value of x and plugging said value into #1 or #2, we can find y
x=17

x+y=25
17+y=25
y=8

OR

x-y=9
17-y=9
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The numbers are 8 and 17
5 0
3 years ago
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Add the fractions simplify your answer 2 7/8 + 2 3/8
Mashutka [201]

Answer:

5 1/4 or 21/4

7 0
3 years ago
Read 2 more answers
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