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3 years ago

Is 0.0009763 a positive or a negative

Mathematics

2 answers:

andrew11 [14]3 years ago

6 0

Step-by-step explanation:

negative because it's a negative number until it gets a full ratio unit or positive unit

juin [17]3 years ago

4 0

Answer:

negative.

Step-by-step explanation:

That depends on the equation that is used to get that answer

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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

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

7 0

2 years ago

If you are driving at a rate of 55 miles per hour, about how many feet per second are you traveling?

Semenov [28]

$55\ \frac{miles}{hour}\\\\
1\ mile\ =\ 5280\ feet\\
1\ hour=\ 3600\ second\\\\
55*\frac{5280}{3600}=80,7\frac{feet}{second}$

3 0

3 years ago

What are the intercepts of 2x + 3y – 6z = 30?

ycow [4]

Intercept of equation 2x + 3y - 6z = 30 is (15, 0, 0) , (0, 10, 0) and (0, 0, -5)

<h3><u>Solution:</u></h3>

Given equation is:

2x + 3y - 6z = 30

We have to find the intercepts

Intercept are the point where equations cut the x- axis, y- axis and z- axis.

y and z both are zero

So substitute y = 0 and z = 0 in given equation

2x + 3(0) - 6(0) = 30

2x = 30

x = 15

<h3>Thus the intercept is (15, 0, 0)</h3>

x and z both are zero

So substitute x = 0 and z = 0 in given equation

2(0) + 3y -6(0) = 30

0 + 3y + 0 = 30

3y = 30

y = 10

<h3>Thus the intercept is (0, 10, 0)</h3>

x and y are both zero

So substitute x = 0 and y = 0 in given equation

2(0) + 3(0) - 6z = 30

-6z = 30

z = -5

<h3>Thus the intercept is (0, 0, -5)</h3>

Thus, intercept of equation 2x + 3y - 6z = 30 is (15,0,0) ,(0,10,0) and (0,0,-5)

6 0

3 years ago

Martina drove 385 miles in 7 hours. at the same rate, how long would it take her to drive 495 miles?

Anarel [89]

385/7 = 495/x

Answer: 9 hours

5 0

3 years ago

Read 2 more answers

Please help out with some of these.

nikdorinn [45]

Answer:

1. 1/12

2. 1/8

3. 1/6

4. 1/6

5. 1/4

6. 1/8

7. 1/6

8. 1/8

9. 1/12

Step-by-step explanation:

6 0

3 years ago