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2 years ago

10

Asia is a chef in a restaurant. To prepare for dinner service, she chops 7 1/2 onions in 1/6 of an hour. What is Asia's rate of

chopping in onions per hour?

1 answer:

Monica [59]2 years ago

3 0

Answer:

135 onions

Step-by-step explanation:

bc

7 1/2 = 15/2

15/2 x 3 = 45/2

45/2 = 22.5

bc its only 1 of 6 pieces, you have to multiply 22.5 by 6

22.6 x 6 = 135

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Integrala x la a treia ori ln la a doua dx va rog

Studentka2010 [4]

I don't speak Romanian, but the closest translation for this suggests you're trying to compute

$\displaystyle \int x^3 \ln(x)^2 \, dx$

Integrate by parts:

$\displaystyle \int x^3 \ln(x)^2 \, dx = uv - \int v \, du$

where

u = ln(x)² ⇒ du = 2 ln(x)/x dx

dv = x³ dx ⇒ v = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \int x^3 \ln(x) \, dx$

Integrate by parts again:

$\displaystyle \int x^3 \ln(x) \, dx = u'v' - \int v' du'$

where

u' = ln(x) ⇒ du' = dx/x

dv' = x³ dx ⇒ v' = 1/4 x⁴

$\implies \displaystyle \int x^3 \ln(x) \, dx = \frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx$

So, we have

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac12 \left(\frac14 x^4 \ln(x) - \frac14 \int x^3 \, dx \right)$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \int x^3 \, dx$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac18 \left(\frac14 x^4\right) + C$

$\displaystyle \int x^3 \ln(x)^2 \, dx = \frac14 x^4 \ln(x)^2 - \frac18 x^4 \ln(x) + \frac1{32} x^4 + C$

$\boxed{\displaystyle \int x^3 \ln(x)^2 \, dx = \frac1{32} x^4 \left(8\ln(x)^2 - 4\ln(x) + 1\right) + C}$

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2 years ago

Which values from the set {−6,−4,−3,−1,0,2} satisfy this inequality?

Vladimir [108]

-12x+3 greater than or equal to 5
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To turn the negative sign of -12x into positive, we multiply both sides by minus, which shifts the inequality sign.
So, 12x less than or equal to 2
x is less than or equal to 1/6
Therefore, 0, -1, -3, -4 and -6 satisfy this inequality.

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3 years ago

What is the y-intercept of y=-3x + 6?<br> O 6<br> -3<br> 3<br> 0 6

Bezzdna [24]

Answer:

6

Step-by-step explanation:

Slope intercept form is y=mx+b, with m being the slope and be being the y intercept, so when you look for what b is in the equation for y=-3x+6 then 6 is b.

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2 years ago

What word describes the equal shares of the shape?

timurjin [86]

<span>Partition describes the equal shares of a shape.
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3 years ago

The ratio of 4:8 is equivalent to x:6, what is the value of x?

Dimas [21]

Answer:

x = 3

Step-by-step explanation:

Given

4 : 8 = x : 6, expressing in ratio form, that is

$\frac{4}{8}$ = $\frac{x}{6}$ ( cross- multiply )

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x = 3

Thus 4 : 8 = 3 : 6

6 0

3 years ago

Read 2 more answers