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2 years ago

!!!! Which equation represents the graph shown? PLEASE HELP ASAP!!!

Mathematics

2 answers:

Julli [10]2 years ago

8 0

Answer:

y= 2x +1

Step-by-step explanation:

Slope-intercept form

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

Since all the slope in the options are the same, let's focus on the y-intercept. From the graph, the line cuts through the y-axis at y= 1. Thus, the y- intercept is 1.

Hence, y= 2x +1 is the correct option.

Extra notes:

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Alexus [3.1K]2 years ago

3 0

Answer: it’s B 2x+1

Step-by-step explanation:

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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

Daniel wants to buy Five-sixths of a pound of pecans. Pecans cost $7.98 per pound. How much will Daniel spend on pecans?

tigry1 [53]

Answer:

A. $6.65

Step-by-step explanation:

To find how much 1/6 is you divide $7.98 by 6 and so the answer is $1.33. Now multiply $1.33 by 5 to get 5/6 or get the answer $6.65.

6 0

3 years ago

Which number line best shows how to solve −2 − (−10)? A number line from negative 10 to 10 is shown with numbers labeled at inte

Viktor [21]

Answer:

Ur answer is #1 = A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 2. Another arrow points from negative 2 to 8.

Step-by-step explanation:

The arrow from 0 to -2 represents the initial "-2" of the problem. Adding -10 would put an arrow of length 10 from that point to the left to -12. However, you are subtracting -10, so that arrow is reversed and goes from -2 to +8.

7 0

2 years ago

A building casts a shadow that is 36 feet long. At the same time of day, a nearby 9-foot tall tree casts a shadow that is 4 feet

ANTONII [103]

Answer:

16 feet is the correct answer to this problem.

5 0

3 years ago

Algebraic expression of 3x and -4y

makvit [3.9K]

Answer:

3x - 4y

Step-by-step explanation:

This results in the algebraic expression 3x - 4y. Nothing more can be done here.

3 0

3 years ago

!!!! Which equation represents the graph shown? PLEASE HELP ASAP!!!​

!!!! Which equation represents the graph shown? PLEASE HELP ASAP!!!