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3 years ago

Need help with two questions!!

Mathematics

2 answers:

eimsori [14]3 years ago

5 0

Couple things to note:

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Slope can be calculated using any two points on a line and the formula y₁ - y₂ / x₁ - x₂.

For the first problem, we know the slope of Function A is 6 (refer to slope-intercept form above). To compare the slopes of Function A and Function B, first find the slope of Function B.

Use y₁ - y₂ / x₁ - x₂. Two points on the line are (0, 1) and (-1, -2). Plug these into the formula accordingly and solve for slope.

y₁ - y₂ / x₁ - x₂

1 - (-2) / 0 - (-1)

1 + 2 / 0 + 1

3 / 1

The slope of Function B is 3. This is half of 6 (the slope of Function A), so the correct answer to question 1 is the first option: Slope of Function B = 2 × Slope of Function A.

For the second problem, substitute m and b in y = mx + b according to the graph. b is the y-intercept (the point at which the line intersects the y-axis); it is (0, -4), or -4. This gives us

y = mx - 4

We must now find m. Follow the same steps above to find slope. Our two points are (-2, 0) and (0, -4).

y₁ - y₂ / x₁ - x₂

0 - (-4) / -2 - 0

0 + 4 / -2

4 / -2

-2

Substitute.

y = -2x - 4

The first option is the correct answer.

Marrrta [24]3 years ago

5 0

Answer:

the slope of A is twice the slope of B

y =-2x -4

Step-by-step explanation:

function A = 6x-1

m=6

b=-1

Function B

(0,1) ( 1,4)

slope = (y2-y1)/(x2-x1)

= (4-1)/(1-0)

= 3/1

= 3

slope intercept form the y intercept is 1

y=mx+b

y = 3x+1

compare the slopes

ma = 6

mb = 3

ma is 2 times mb

(-2,0)

(0,-4)

slope = (y2-y1)/(x2-x1)

= (-4-0)/(0--2)

= (-4-0)/(0+2)

= -4/2

m=-2

the y intercept is -4

slope intercept form is y = mx+b

y =-2x -4

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MariettaO [177]

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3 years ago

How do you do this question?

Ksivusya [100]

Answer:

V = (About) 22.2, Graph = First graph/Graph in the attachment

Step-by-step explanation:

Remember that in all these cases, we have a specified method to use, the washer method, disk method, and the cylindrical shell method. Keep in mind that the washer and disk method are one in the same, but I feel that the disk method is better as it avoids splitting the integral into two, and rewriting the curves. Here we will go with the disk method.

$\mathrm{V\:=\:\pi \int _a^b\left(r\right)^2dy\:},\\\mathrm{V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy}$

The plus 1 in '1 + 2/x' is shifting this graph up from where it is rotating, but the negative 1 is subtracting the area between the y-axis and the shaded region, so that when it's flipped around, it becomes a washer.

$V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=\pi \cdot \int _1^3\left(1+\frac{2}{y}\right)^2-1dy\\\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\= \pi \left(\int _1^3\left(1+\frac{2}{y}\right)^2dy-\int _1^31dy\right)\\\\$

$\int _1^3\left(1+\frac{2}{y}\right)^2dy=4\ln \left(3\right)+\frac{14}{3}, \int _1^31dy=2\\\\=> \pi \left(4\ln \left(3\right)+\frac{14}{3}-2\right)\\=> \pi \left(4\ln \left(3\right)+\frac{8}{3}\right)$

Our exact solution will be V = π(4In(3) + 8/3). In decimal form it will be about 22.2 however. Try both solution if you like, but it would be better to use 22.2. Your graph will just be a plot under the curve y = 2/x, the first graph.

5 0

3 years ago

9x+y=28<br> 3x+3y=(-12)<br> Solve using elimination

Rzqust [24]

Answer:

(x, y)=(4,-8)

Step-by-step explanation:

9x+y=28

3x+3y=-12 /:(-3)

9x+y=28.......(1)

-x-y=4......(2)

9x+y=28

(1)+(2): 8x=32

9x+y=28

x=32/8

9x+y=28

x=4

9*4+y=28

x=4

36+y=28

x=4

y=28-36

x=4

y=-8

x=4

(x, y) =(4,-8)

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3 years ago

100 POINT HELP PLEASE !!!!!!!!!!! NO LINKS

NikAS [45]

y = log(3x + 4) + 2

__________________________________________________________

Y-INTERCEPT: set x = 0

y = log(3(0) + 4) + 2

y = log(0 + 4) + 2

y = log( 4) + 2

Using calculator,

y = log( 4) + 2

y ≈ 2.60 when x = 0

__________________________________________________________

X-INTERCEPT: set y = 0

y = log(3x + 4) + 2

0 = log(3x + 4) + 2

-2 = log(3x + 4)

(it's simple. Always remember that the base is 10, even though there seems to be no "smaller number" next to log)

= 3x + 4

$10^{-2}$ - 4 = 3x

[ $10^{-2}$ - 4 ] /3 = x

x = -1.33 when y = 0

__________________________________________________________

<h3>ANSWER: y-intercept is 2.60 and x-intercept is -1.33</h3>

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3 years ago

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Paraphin [41]

Answer:

72 cm3

Step-by-step explanation:

area of triangle is 1/2 base x height

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6 x 12 (height) = 72

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3 years ago

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