All categories

3 years ago

The circumference of a circle is 78π cm. Find the diameter, the radius, and the length of an arc of 140°.

1 answer:

5 0

The correct answer is the option D, which is: D. 78 cm; 39 cm; 30.3π cm
The explanation is shown above:
1-The formula for calculate the circumference of a circle is:
C=2πr
78π=2πr
2- The radius is:
r=78π/2π
r=39 cm
3- The diameter is:
D=39 cm x 2
D=78 cm
4- The arc length is:
arc length=(140°π/180°)(39 cm)
arc length=30.3π cm

You might be interested in

Suppose you take the Medical College Admission Test (MCAT) and your score is the 32nd percentile. How do you interpret this resu

ExtremeBDS [4]

In Statistics, percentiles are a representation of the relative position of a particular value within a data set. For example, if your exam score is better than k% of the rest of the class. That means your exam score is at the kth percentile.

If your test score is at the 32nd percentile it can be interpreted as follows:

-Your test score is better than only 32 percent of the other scores recorded for the test.

-32 percent of the people who took the admission test have scores which are lower than yours.

7 0

2 years ago

Which fraction has the same value as 0.6

Zinaida [17]

Using the place value chart we can see that the decimal 0.6 is six tenths, so we can write 0.6 as the fraction $\frac{6}{10}$ . Notice however that $\frac{6}{10}$ is not in lowest terms so we need to divide the numerator and the denominator by the greatest common factor of 6 and 10 which is 2.

-Image Provided-

4 0

2 years ago

Read 2 more answers

Is 6.3 > 6.04 reasonable yes or no Explain

Brums [2.3K]

Answer:

Yes

Step-by-step explanation:

By rounding to the 10ths place, we can easily see that 6.3 is greater than 6.04. 6.3 is already rounded to the 10ths place, but 6.04 rounded to the 10ths place is 6.0.

6.3 is clearly more than 6.0, therefore 6.3 is greater than 6.04.

3 0

1 year ago

What is the volume of the right triangular prism shown?

ollegr [7]

Given:

The sides of the base of the triangle are 8, 15 and 17.

The height of the prism is 15 units.

We need to determine the volume of the right triangular prism.

Area of the base of the triangle:

The area of the base of the triangle can be determined using the Heron's formula.

$S=\frac{a+b+c}{2}$

Substituting a = 8, b = 15 and c = 17. Thus, we have;

$S=\frac{8+15+17}{2}$

$S=\frac{40}{2}=20$

Using Heron's formula, we have;

$Area = \sqrt{S(S-a)(S-b)(S-c)}$

$Area = \sqrt{20(20-8)(20-15)(20-17)}$

$Area = \sqrt{20(12)(5)(3)}$

$Area = \sqrt{3600}$

$Area = 36$

Thus, the area of the base of the right triangular prism is 36 square units.

Volume of the right triangular prism:

The volume of the right triangular prism can be determined using the formula,

$V=\frac{1}{2}A_b h$

where $A_b$ is the area of the base of the prism and h is the height of the prism.

Substituting the values, we have;

$V=\frac{1}{2}(60\times 15)$

$V=450$

Thus, the volume of the right triangular prism is 450 cubic units.

8 0

2 years ago

Find the interval(s) of upward concavity on this accumulation function.

maxonik [38]

$\displaystylef(x)=\int_{0}^{x^2}\sec^2(\sqrt{x})dx \\=\int_{0}^{\sqrt{x^2}}\sec^2(u)\cdot2udu \\=2\int_{0}^{\sqrt{x^2}}\sec^2(u)du \\=2\Big[u\tan(u)-\int\tan(u)du\Big]_{0}^{\sqrt{x^2}} \\=2\Big[u\tan(u)+\ln\Big(\mathrm{abs}(\cos(u))\Big)\Big]_0^x \\=2\Big(x\tan(x)+\dfrac{1}{2}\ln\Big(\cos^2(x)\Big)\Big) \\=2x\tan(x)+\ln(\cos^2(x))$

Hope this helps.

6 0

2 years ago