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zavuch27 [327]
3 years ago
13

Pls help me with these questions

Mathematics
1 answer:
KIM [24]3 years ago
5 0

Answer:

bald black man

Step-by-step explanation:

bald+black man, y=bbcx

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Let r be the region bounded by y = x 2 and y = 9. find a and b so that the horizontal lines y = a and y = b split the region r i
Arturiano [62]

y = x² has a lower bound at the vertex (0, 0); <em> y = 0</em>

y = 9 has an upper bound at y = 9

x² = 9   ⇒  x = +/- 3  the region is bounded on the left at x = -3 and on the right at x = 3

Solve the integral from -3 to 3 to find the area under the curve, then multiply by 1/3 to calculate 1/3 of the area.

\int\limits^3_3 (9 - {x^{2}}) \, dx = (9x - x³/3) | from -3 to 3

= (9(3) - 3³/3) - (9(-3) - (-3)³/3)

= (27 - 9) - (- 27 - (-9))

= 16 - (-16)

= 32

*** 32/3 is 1/3 of the area ****

Now that we know what 1/3 of the area is, we can find the height <em>at y = a</em> which will satisfy 1/3 of the area. We do this by solving the integral from "0 to a" and setting it equal to 1/3 of the area (32/3).

\int\limits^a_0 (9 - {x^{2}}) \, dx - a(9 - a²)

=  (9x - x³/3) | from 0 to a   - (9a - a³)

= (9a - a³/3) - (9(0) - (0)³/3) - 9a + a³

= 9a - a³/3 - 9a + a³

= a³ - a³/3

= 2a³/3

32/3 = 2a³/3

32 = 2a³

16 = a³

∛16 = a  

2∛2 = a  (This is the distance from the upper bound (y = 9)

Answer: y = 9 - 2∛2

Follow the same steps using 2/3 of the area (64/3) to find "b".

64 = 2b³

32 = b³

∛32 = b   3.17

2∛4 = b  (This is the distance from the upper bound (y = 9)

Answer: y = 9 - 2∛4


8 0
3 years ago
suppose y varies directly with x, and y = 8 when x = -6. what direct variation equation relates x and y? what is the value of y
Kisachek [45]
\bf \qquad \qquad \textit{direct proportional variation}\\\\&#10;\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad  y=kx\impliedby &#10;\begin{array}{llll}&#10;k=constant\ of\\&#10;\qquad  variation&#10;\end{array}\\\\&#10;-------------------------------\\\\&#10;\textit{we also know that }&#10;\begin{cases}&#10;y=8\\&#10;x=-6&#10;\end{cases}\implies 8=k(-6)\implies \cfrac{8}{-6}=k&#10;\\\\\\&#10;-\cfrac{4}{3}=k\qquad therefore\qquad \boxed{y=-\cfrac{4}{3}x}&#10;\\\\\\&#10;\textit{when x = -2, what is \underline{y}?}\qquad y=-\cfrac{4}{3}(-2)
8 0
3 years ago
(0, -19), (20, 15)<br> I am having trouble
FinnZ [79.3K]

Answer:

-38285

Step-by-step explanation:

this is what my calculator told me

sorry but ask someone else

I don´t know what slopes are

so sorry

7 0
3 years ago
Can you help me with this problems
k0ka [10]
To find y = mx + b you need to determine the slope. To find slope use the formula
m = y2 - y1 / x2 - x1

Use two points on the graph such as (4, 100) and (12, 300)

Now plug it into the formula

m = 300 - 100 / 12 - 4

m = 200 / 8

m = 25

Now we know the slope, but we need to find the y-intercept.

y = mx + b

y = 25x + b

Substitute one of the points (4, 100) as the y value and x value to find b, the y intercept

100 = 25(4) + b

100 = 100+ b

100 - 100 = b

0 = b

Now plug in your formula

Y = 25x + 0

y = 25x



7 0
3 years ago
Zacarías and Paz together have $756.80 if Zacarías has $489.59, how much does Paz have? Write and solve an addition equation to
Assoli18 [71]
Pat has $267.21. All you had to do was subtract the 2 numbers
3 0
3 years ago
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