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
Dmitrij [34]
3 years ago
13

The measurenicnt of the circumference of a circle is found to be 56 centimeters. The possible error in measuring the circumferen

cc is 1.2 centimeters.
(a) Approximate the percent error in computing the area of the circle.
(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 3%.
Mathematics
1 answer:
BartSMP [9]3 years ago
5 0

Answer:

(a) Approximate the percent error in computing the area of the circle: 4.5%

(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 3%: 0.6 cm

Step-by-step explanation:

(a)

First we need to calculate the radius from the circumference:

c=2\pi r\\r=\frac{c}{2\pi } \\c=8.9 cm

I leave only one decimal as we need to keep significative figures

Now we proceed to calculate the error for the radius:

\Delta r=\frac{dt}{dc} \Delta c\\\\\frac{dt}{dc} =    \frac{1}{2 \pi } \\\\\Delta r=\frac{1}{2 \pi } (1.2)\\\\\Delta r= 0.2 cm

r = 8.9 \pm 0.2 cm

Again only one decimal because the significative figures

Now that we have the radius, we can calculate the area and the error:

A=\pi r^{2}\\A=249 cm^{2}

Then we calculate the error:

\Delta A= (\frac{dA}{dr} ) \Delta r\\\\\Delta A= 2\pi r \Delta r\\\\\Delta A= 11.2 cm^{2}

A=249 \pm 11.2 cm^{2}

Now we proceed to calculate the percent error:

\%e =\frac{\Delta A}{A} *100\\\\\%e =\frac{11.2}{249} *100\\\\\%e =4.5\%

(b)

With the previous values and equations, now we set our error in 3%, so we just go back changing the values:

\%e =\frac{\Delta A}{A} *100\\\\3\%=\frac{\Delta A}{249} *100\\\\\Delta A =7.5 cm^{2}

Now we calculate the error for the radius:

\Delta r= \frac{\Delta A}{2 \pi r}\\\\\Delta r= \frac{7.5}{2 \pi 8.9}\\\\\Delta r= 0.1 cm

Now we proceed with the error for the circumference:

\Delta c= \frac{\Delta r}{\frac{1}{2\pi }} = 2\pi \Delta r\\\\\Delta c= 2\pi 0.1\\\\\Delta c= 0.6 cm

You might be interested in
If f(x) = k where k is a constant, and the points (6,1) and (8,1) lie on the graph of y = f(x), what is the value of f(0)?
Colt1911 [192]

Answer:

The value of f(0)=1

Step-by-step explanation:

We are given that

f(x)=k

y=f(x)

(6,1) and (8,1) lies on the graph of y=f(x)

We have to find the value of f(0).

f(6)=1

f(8)=1

f(x)=k

By comparing ,we get

k=1

Therefore, y=f(x)=1

Now, substitute x=0

f(0)=1

Hence, the value of f(0)=1

7 0
2 years ago
Solve for x<br> 3x + y = 3
d1i1m1o1n [39]

Answer:

isolate the 3x subtract y then divide by 3 both sides and reduce

5 0
3 years ago
Read 2 more answers
18/15 into a mixed number
mamaluj [8]
\frac{18}{15} = \frac{18:3}{15:3} = \frac{6}{5} =1 \frac{1}{5}
3 0
3 years ago
2x²-1<br> what is the evaluation algebraic expression ​
Basile [38]
The answer would be 3 because 2 times 2 is 4 minus -1 would be 3
7 0
3 years ago
Please help!!! : ))) <br> Sorry it's flipped lol
lyudmila [28]

Answer:

20-24

Step-by-step explanation:

you can see that when you find the middle of the total data the data set left is in the 20-24 category

hope this helps! :)

8 0
3 years ago
Other questions:
  • Plz can any1 answer this question asap
    13·2 answers
  • Figure ABCD is translated down by 6 units:
    15·1 answer
  • I need it by morning and I need the work HELP!!!
    15·1 answer
  • The pre-image, ΔSTU, has undergone a type of transformation called a rigid transformation to produce the image, ΔVWX. Compare th
    14·1 answer
  • Need help on this baldy plzz anyone.♥
    10·2 answers
  • The salary at Beth’s company is $32,000 for someone with no experience and increases by $2700 per year of experience. Write a ru
    6·1 answer
  • Avery solves the equation below by first squaring both sides of the equation.
    7·1 answer
  • Pleasseee helppp!!!what is the value of x and y ?
    5·1 answer
  • Challenge Question Sally's bank account balance was $50 on Monday. On Tuesday, she bought a new pair of shoes for $45. On Thursd
    10·1 answer
  • What must happen to make harvesting electricity possible??
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!