1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kazeer [188]
3 years ago
9

An item is regularly priced at $51. Amanda bought it on sale for 85% off the regular price. How much did Amanda pay?

Mathematics
1 answer:
siniylev [52]3 years ago
4 0

Answer:

85% off $51 is $43.35 which equals to $7.65

Amanda paid only $7.65 for the 85% off the original price.

Step-by-step explanation:

You might be interested in
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
Estimate each product.Then write whether the estimate is greater than or less than the actual product.There are 62 rows of 9 cha
Westkost [7]
That is 62x9 which is 9x2=18 and 9x60=540 so you then add 540+18=558 chairs
8 0
3 years ago
Evaluate 8 − 12 ÷ 2 + 3. (1 point)
Goryan [66]

Answer:

Using PEMDAS, you should get the answer of 5.

7 0
2 years ago
Read 2 more answers
Solve for x: <br> (X+5)^1/2 = (5-2x)^1/4
Greeley [361]

Answer:

X = Negative 2 (-2)

7 0
3 years ago
Find the slope of the line graphed below.
natulia [17]
Good day ^-^///////////

6 0
3 years ago
Read 2 more answers
Other questions:
  • Helpppp!!! Find the measurement ( ? )
    6·1 answer
  • Ramon rented a sprayer and a generator on his first job he used each piece of equipment for 6 hours at a total cost of $90 on hi
    12·1 answer
  • What are the real or imaginary solutions of the polynomial equation x^4-52x^2+576?
    13·2 answers
  • Suppose you need to know an equation of the tangent plane to a surface S at the point P(4, 1, 3). You don't have an equation for
    15·1 answer
  • Please answer this question now in two minutes
    7·1 answer
  • 2.888x10 to the 5 power Divided by 7.22x10 to the 2 power
    8·2 answers
  • Help me please will give brainlest
    13·1 answer
  • Geometry... Please help and I'll mark brainliest. Triangle proofs &amp; reasons
    11·1 answer
  • What is the least number that is exactly divisible by 9, 12 and 15​
    15·2 answers
  • _____ teaspoon is equivalent to 5 ml.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!