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

BartSMP [9]

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:

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

5 0

3 years ago

Find the value of x in the picture below.

sveta [45]

The answer is c because

7 0

3 years ago

Describe a way to calculate 304-81 mentally by using reasoning other that the common subtraction algorithm. Then write a coheren

Leno4ka [110]

Answer:

A simple way to mentally subtract is to simplify the numbers, subtract, then subtract or add for the simplified answer.

Step-by-step explanation:

A simple way to mentally subtract is to simplify the numbers, subtract, then subtract or add for the simplified answer. For this 304 - 81 is easier as 300 - 80. Make note that we took away 4 from 304 and 1 from 81. Now we just subtract mentally, and 300 - 80 = 220. If we took 4 from 304, this means that our answer should be 4 less, since 4 less would be 304 - 80 = 216. If we took 1 from 81, then we add 1 back to get the equation 304 - 81 = 217.

304 - 81 = ?

300 - 80 = 220

304 - 80 = 216

304 - 81 = 217

7 0

3 years ago

Read 2 more answers

There are 6 flavors of candy in a bag. The probability of randomly selecting strawberry is 1/4, lime is 3/16, cherry is 1/8, and

Iteru [2.4K]

The answer is 3/8. You can find a common denominator of 64 among all of the fractions. From this, you can find how many orange candies there are. There is 64 candies, and 40 of them are other flavors, so there's 24 orange candies. You can create the fraction 24/64 and simplify it down to 3/8.

3 0

3 years ago

Read 2 more answers

Hi does anyone know how to solve this question if so please show the working out.

tester [92]

Explanation:

The Law of Sines is your friend, as is the Pythagorean theorem.

Label the unmarked slanted segments "a" and "b" with "b" being the hypotenuse of the right triangle, and "a" being the common segment between the 45° and 60° angles.

Then we have from the Pythagorean theorem ...

b² = 4² +(2√2)² = 24

b = √24

From the Law of Sines, we know that ...

b/sin(60°) = a/sin(θ)

y/sin(45°) = a/sin(φ)

Solving the first of these equations for "a" and the second for "y", we get ...

a = b·sin(θ)/sin(60°)

and ...

y = a·sin(45°)/sin(φ)

Substituting for "a" into the second equation, we get ...

y = b·sin(θ)/sin(60°)·sin(45°)/sin(φ) = (b·sin(45°)/sin(60°))·sin(θ)/sin(φ)

So, we need to find the value of the coefficient ...

b·sin(45°)/sin(60°) = (√24·(√2)/2)/((√3)/2)

= √(24·2/3) = √16 = 4

and that completes the development:

y = 4·sin(θ)/sin(φ)

6 0

3 years ago