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3 years ago

A circle has a diameter of 14 ft. What is its circumference?

Mathematics

1 answer:

Akimi4 [234]3 years ago

3 0

Answer:

circumference = pi x diameter

14x3.14 = 43.96 ft^2

Hope that answers your question

Step-by-step explanation:

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Manny is deciding between two packages of yogurt. YoFruit costs $4.48 for 16 ounces. Yummy Yogurt costs $2.64 for 8 ounces. How

Y_Kistochka [10]

Answer:

16 is double 8, so just double the price: 2.64 x 2= $5.28

then, subtract to find the dufference: 5.28 - 4.48= $.80

then, divide that by the oz:

.80/16= 5 cents per ounce

3 0

3 years ago

Read 2 more answers

The circumference of a sphere was measured to be 90 cm with a possible error of 0.5 cm.

Akimi4 [234]

Answer:

Error in the sphere's surface: 29 $cm^2$ and relative error in surface measure: 0.011

Error in the sphere's volume: 205 $cm^3$ and relative error in the volume measure: 0.017

Step-by-step explanation:

(a)

The measured length (l) of the circumference is 90 cm with an error of 0.5 cm, that is:

$l=2\,\pi\,R=90\,cm\\R=\frac{90}{2\,\pi} \,cm=\frac{45}{\pi} \,cm=14.3239\,\,cm$

and with regards to the error:

$dl=0.5 \, cm\\dl=2\,\pi\,dR\\dR=\frac{dl}{2\,\pi} =\frac{1}{4\,\pi} cm = 0.0796\,cm$

then when we use the formula for the sphere's surface, we get:

$S=4\,\pi\,R^2\\dS=4\,\pi\,2\,R\,(dR)\\dS=8\,\,\pi\.(\frac{45}{\pi} \,\,cm)\,(\frac{1}{4\pi}\,cm) =\frac{90}{\pi} \,\,cm^2\approx \,29\,cm^2$

Then the relative error in the surface is:

$\frac{dS}{S} =\frac{90/\pi}{4\,\pi\,R^2} =\frac{1}{90} =0.011$

(b)

Use the formula for the volume of the sphere:

$V=\frac{4\,\pi}{3} R^3\\dV=\frac{4\,\pi}{3}\,3\,R^2\,(dR)=4\,\pi\,R^2\,(\frac{1}{4\pi}) \,cm=(\frac{45}{\pi})^2 \,\,cm^3\approx 205\,\,cm^3$

Then the relative error in the volume is:

$\frac{dV}{V} =\frac{205}{12310.5} \approx 0.017$

3 0

3 years ago

Find the arc length of the given curve between the specified points.

yuradex [85]

Answer:

4.25

Step-by-step explanation:

Given:

$f(x) = \frac{x^3}{12} + \frac{1}{x} \\\\Arc Length = \int\limits^a_b {\sqrt{1 + (f'(x))^2} } \, dx \\f '(x) = \frac{x^2}{6} - \frac{1}{x^2}\\\\f'(x)^2 = (\frac{x^2}{6} - \frac{1}{x^2})^2 = \frac{x^4}{36} + \frac{1}{x^4} - \frac{1}{3}\\\\1 + f'(x)^2 = \frac{x^4}{36} + \frac{1}{x^4} + \frac{2}{3}\\\\\= \frac{x^8 + 36 + 12x^4}{36x^4}\\\\= \frac{(x^4 + 6)^2}{36x^4}\\\\=\sqrt{1 + f'(x)^2} = \sqrt{ \frac{(x^4 + 6)^2}{36x^4}}\\\\= \frac{x^2}{6} + \frac{1}{x^2} \\\\$

$ArcLength = \int\limits^4_1 {\frac{x^2}{6} + \frac{1}{x^2} } \, dx \\= (\frac{x^3}{18} - \frac{1}{x})\limits^4_1\\\\= (\frac{64}{18} - \frac{1}{4}) - (\frac{1}{18} - 1)\\\\= \frac{17}{4}= 4.25$

8 0

3 years ago

Plot the points (-5, 10), (2,

Archy [21]

Answer:

A rectangle.

Step-by-step explanation:

The point are plotted on a coordinate plane, whose outcome is presented in the image enclosed below. The figure resembles a rectangle, as all internal angles are right-angled.

7 0

3 years ago

The average rate of change of f(x) is given by the formula f(7) - f (3) 4. Over what interval does this formula give the average

blagie [28]

The answer would be 4

3 0

3 years ago

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