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
lions [1.4K]
3 years ago
14

Over the last 50 years, the average cost of a car has increased by a total of 1,094%. If the average cost of a car today is $31,

918, how much was the average cost 50 years ago
Mathematics
1 answer:
krek1111 [17]3 years ago
3 0

Answer:

$2673

Step-by-step explanation:

Let x represent average cost of car 50 years ago.

We have been given that over the last 50 years, the average cost of a car has increased by a total of 1,094%. The average cost of a car today is $31,918. We are asked to find the average cost 50 years ago.

We can represent our given information in an equation as:

x+1,094\%\text{ of } x=\$31,918

x+\frac{1,094}{100}* x=\$31,918

x+10.94x=\$31,918

11.94x=\$31,918

\frac{11.94x}{11.94}=\frac{\$31,918}{11.94}

x=\$2673.1993299

x\approx \$2673

Therefore, the average cost of the car 50 years ago was $2673.

You might be interested in
The following spinner has four sections. There are equal sections for 1, 4, and 3. The section for 2 is twice as large as each o
Airida [17]

Answer:

gorge bush doesn't care

Step-by-step explanation:

about black people ~ ye

6 0
2 years ago
What number line represents the solution to the inequality below<br><br>-6&lt; -2x
aliina [53]

Answer:

The answer is 3 or x<3.

4 0
1 year ago
This is a "water tank" calculus problem that I've been working on and I would really appreciate it if someone could look at my w
Sedaia [141]
Part A

Everything looks good but line 4. You need to put all of the "2h" in parenthesis so the teacher will know you are squaring all of 2h. As you have it right now, you are saying "only square the h, not the 2". Be careful as silly mistakes like this will often cost you points. 

============================================================

Part B

It looks like you have the right answer. Though you'll need to use parenthesis to ensure that all of "75t/(2pi)" is under the cube root. I'm assuming you made a typo or forgot to put the parenthesis. 

dh/dt = (25)/(2pi*h^2)
2pi*h^2*dh = 25*dt
int[ 2pi*h^2*dh ] = int[ 25*dt ] ... applying integral to both sides
(2/3)pi*h^3 = 25t + C
2pi*h^3 = 3(25t + C)
h^3 = (3(25t + C))/(2pi)
h^3 = (75t + 3C)/(2pi)
h^3 = (75t + C)/(2pi)
h = [ (75t + C)/(2pi) ]^(1/3)

Plug in the initial conditions. If the volume is V = 0 then the height is h = 0 at time t = 0
0 = [ (75(0) + C)/(2pi) ]^(1/3)
0 = [ (0 + C)/(2pi) ]^(1/3)
0 = [ (C)/(2pi) ]^(1/3)
0^3 =  (C)/(2pi)
0 = C/(2pi)
C/(2pi) = 0
C = 0*2pi
C = 0 

Therefore the h(t) function is...
h(t) = [ (75t + C)/(2pi) ]^(1/3)
h(t) = [ (75t + 0)/(2pi) ]^(1/3)
h(t) = [ (75t)/(2pi) ]^(1/3)

Answer:
h(t) = [ (75t)/(2pi) ]^(1/3)

============================================================

Part C

Your answer is correct. 
Below is an alternative way to find the same answer

--------------------------------------

Plug in the given height; solve for t
h(t) = [ (75t)/(2pi) ]^(1/3)
8 = [ (75t)/(2pi) ]^(1/3)
8^3 = (75t)/(2pi)
512 = (75t)/(2pi)
(75t)/(2pi) = 512
75t = 512*2pi
75t = 1024pi
t = 1024pi/75
At this time value, the height of the water is 8 feet

Set up the radius r(t) function 
r = 2*h
r = 2*h(t)
r = 2*[ (75t)/(2pi) ]^(1/3) .... using the answer from part B

Differentiate that r(t) function with respect to t
r = 2*[ (75t)/(2pi) ]^(1/3)
dr/dt = 2*(1/3)*[ (75t)/(2pi) ]^(1/3-1)*d/dt[(75t)/(2pi)] 
dr/dt = (2/3)*[ (75t)/(2pi) ]^(-2/3)*(75/(2pi))
dr/dt = (2/3)*(75/(2pi))*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)

Plug in t = 1024pi/75 found earlier above
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75(1024pi/75))/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (1024pi)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*(1/64)
dr/dt = 25/(64pi)
getting the same answer as before

----------------------------

Thinking back as I finish up, your method is definitely shorter and more efficient. So I prefer your method, which is effectively this:
r = 2h, dr/dh = 2
dh/dt = (25)/(2pi*h^2) ... from part A
dr/dt = dr/dh*dh/dt ... chain rule
dr/dt = 2*((25)/(2pi*h^2))
dr/dt = ((25)/(pi*h^2))
dr/dt = ((25)/(pi*8^2)) ... plugging in h = 8
dr/dt = (25)/(64pi)
which is what you stated in your screenshot (though I added on the line dr/dt = dr/dh*dh/dt to show the chain rule in action)
8 0
3 years ago
How to convert ounces into pounds?
Vesna [10]
Hello! Its really simple 16 ounces equal 1 pound!
8 0
3 years ago
Read 2 more answers
Match each verbal description to its equivalent function rule as applied to the given function below.
stepladder [879]
The top-left graph goes with the bottom-right equation, y=90(1/4)^x

The bottom-left graph goes with the top-right equation, y = 120(3/4)^x

The top-right graph goes with the bottom-left equation, y = 120(1/4)^x

The bottom-right graph goes with the top-left equation, y = 90(3/4)^x

y=90(1/4)^x has a larger percent decrease than y = 90(3/4)^x
cause if you multiply a number by 1/4, that's smaller than multiplying number by 3/4. so y=90(1/4)^x decreases really fast

same with the y = 120(3/4)^x ones
5 0
3 years ago
Other questions:
  • A bakery sold 101 cupcakes in one day. The head baker predicted he would sell 81 cupcakes that day. What was the percent error o
    9·1 answer
  • What is the measure of the largest angle of a triangle whose measures are in the ratio 2:3:4
    10·1 answer
  • Need to find Value of x
    5·1 answer
  • One case can hold 3 boxes.Each box can hold 3 binders.How man cases are needed to hold 126 binders?
    14·2 answers
  • 6. (4.11.2) A 500-page book contains 250 sheets of paper. The thickness of the paper used to manufacture the book has mean 0.08
    7·1 answer
  • Find the equation of the line in slope intercept form parallel to 5x−5y=−2 and goes through the point (−10,4) y=?
    12·1 answer
  • In column C, there are too many numbers after the decimal place. Karl does not need this level of detail as it is distracting fr
    14·1 answer
  • True or False: The following set of points could represent a function:
    12·1 answer
  • A planet has a circular orbit around a star. It is a distance of 81,000,000 km from the centre of the star. It orbits at an aver
    15·1 answer
  • Jason wants to plant 66 carrot seeds and 44 onion bulbs. He would like to plant them so
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!