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3 years ago

Please explain how you got the answer!

Mathematics

2 answers:

ValentinkaMS [17]3 years ago

6 0

Definition of additional: MORE, more, and more.
Not a definition of additional: SAME, same, and same.

We are given that EF is parallel to GH.
Remember, the definition of additional.

We wouldn't want the same piece of information, would we?

That's why we want a new piece of information:
Answer Choice B; FG parallel to EH.

worty [1.4K]3 years ago

4 0

The correct answer is side EF is congruent to side GH

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How much will it cost to ride if the cab travels 13.5 miles?

MrMuchimi

Please provide more information. This question is not able to be answered with the information provided. Try giving the full problem!

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3 years ago

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Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

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2 years ago

Write two numbers that multiply to the value on top and add to the value on bottom.

Svet_ta [14]

8 and 1

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3 years ago

In a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning. Estimate the prob

umka2103 [35]

Answer:

$\frac{19}{18,750,000}=0.0000010133333333$

Step-by-step explanation:

We have been given that in a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning.

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$

$\text{P( A randomly selected person in the United States will be struck by lightning this year)}=\frac{304}{300,000,000}$

$\text{P( A randomly selected person in the United States will be struck by lightning this year)}=\frac{19}{18,750,000}$

$\text{P( A randomly selected person in the United States will be struck by lightning this year)}=0.0000010133333333$

Therefore, the probability that a randomly selected person in the United States will be struck by lightning this year is $\frac{19}{18,750,000}=0.0000010133333333$ .

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4 years ago

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Use the point and the slope to graph each line. Write the equation of the line. The line passes through point (2,-2) and is para

elixir [45]

Answer:

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Step-by-step explanation:

slope- intercept form

y= mx +c, where m is the slope and c is the y-intercept.

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Substitute m= -1 into the equation:

y= -x +c

To find the value of c, substitute a pair of coordinates into the equation.

When x= 2, y= -2,

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c= -2 +2

c= 0

Thus, the equation of the line is y= -x.

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3 years ago