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2 years ago

PLEASE HELP! I need this to be graphed but I don't know how. y=–3/4x–1

Mathematics

2 answers:

Novay_Z [31]2 years ago

7 0

Answer:

see the attachment below

Step-by-step explanation:

ICE Princess25 [194]2 years ago

7 0

Answer:

Slope: 3/4

Y Intercept: -1

Step-by-step explanation:

Use the slope-intercept form to find the slope and y-intercept.

Any line can be graphed using two points. Select two "x" values, and plug them into the equation to find the corresponding "y" values.

Graph the line using the slope and the y-intercept, or the points.

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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

Complementary angles mean all 3 angles equal how many degrees?

Montano1993 [528]

Answer:

Two Angles are Complementary when they add up to 90 degrees (a Right Angle)

Step-by-step explanation:

Please mark Brainliest :)

3 0

2 years ago

There are 350 members in a swimming club. Of them, 2/7 are new members. Of the new members, 3/10 are females. How many new femal

djyliett [7]

350 / 7 = 50
50 * 2 = 100

100 new members

100 / 10 = 10
10 * 3 = 30

30 are new female members

5 0

3 years ago

Read 2 more answers

In in 10 to the sixth power of the 10 is the what

Svetach [21]

10 to the sixth power is 1,000,000. Any number to the tenth power is the number 1 in front of the number of zeros that is equal to the exponent.

4 0

2 years ago

PLEASEEEEEEEEE HELPPPPPPPPPP 70-100 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!! I NEED ONE MORE ANSWER BC I WANNA SEE WHICH ANSWER IS THE

Zina [86]

Answer and Explanation:

Gina wanted to swim at the pool. She is allowed to spend at most $30. The cost to swim in the pool is 3 dollars per hour plus a flat fee of $3. How many hours can Gina swim without going over her spending limit?

This problem can be represented by $3x+3\leq 30$ .

'x' would be the number of hours. "At most" means less than or equal to. So, the value of x would have to be less than or equal to 30.

$3x+3\leq 30-3\\\\3x\leq 27\\\\3x/3\leq 27/3\\\\\boxed{x\leq9}$

So, Gina would have a maximum of 9 hours to swim in the pool.

Hope this helps.

3 0

2 years ago