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3 years ago

A drum of oil has a height of 4 ft and a radius of 1.2 ft. The oil cost $22 per ft³.

1 answer:

iogann1982 [59]3 years ago

3 0

Volume of a Cylinder (Drum) = πr²h

Substitute the known values,
v = 3.14 * (1.2)² * 4
v = 18.09 Ft³

Now, price for 1 Ft³ = $22
So, for 18.09 Ft³ would be: 22 * 18.09 = $397.9

In short, Your Answer would be: $397.9

Hope this helps!

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Help with 30 please. thanks.

Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

$\displaystyle y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}$

And we want to show that:

$\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}$

Instead of differentiating directly, we can first square both sides:

$\displaystyle y^2 = 3e^{2x} -4x + 1$

We can find the first derivative through implicit differentiation:

$\displaystyle 2y \frac{dy}{dx} = 6e^{2x} -4$

Hence:

$\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}$

And we can find the second derivative by using the quotient rule:

$\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}$

Substitute:

$\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}$

Combine fractions:

$\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}$

Simplify:

$\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}$

Simplify:

$6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}$

Q.E.D.

6 0

2 years ago

Liz and Rick are squeezing lemons for a lemonade stand. Liz squeezed 18 lemons in 6 minutes. Rick squeezed 24 lemons in 12 minut

qwelly [4]

Liz squeezed lemons faster. Liz squeezed 18 lemons in 6 minutes. To find out how many she squeezed in a minute, you would do 18 / 6, which gives you three. Rick squeezed 24 lemons in 12 minutes. To find out how many lemons he squeezed in a minute, you would do 24/12, which gives you 2. So, Liz squeezed 3 lemons per minute while Rick squeezed 2 lemons per minute.

6 0

2 years ago

Two trains leave towns 474 kilometers apart at the same time and travel toward each other. One train travels13 km/m faster than

guajiro [1.7K]

Answer:

112 km/h

125 km/hr

Step-by-step explanation:

Distance = time * speed

Distance = distance train 1 + distance train 2

474 = 2(s) + 2(s + 13)

Distribute

474 = 2s + 2s + 26

Combine like terms

474 = 4s + 26

Subtract 26 from both sides

448 = 4s

Divide both sides by 4

112 = s

s = 112 km/h

s + 13 = 125 km/hr

3 0

2 years ago

A researcher thinks that a person's mood has an effect on how helpful that person is likely to be. To test this, the researcher

eimsori [14]

Answer:

One possible confound for the experiment is the attitude of the research assistants.

Step-by-step explanation:

A confounder simply means a variable that has impact in influencing both the dependent variable and independent variable, causing a spurious association.

So, we can conclude that the attitudes of the research assistants have positive and negative impacts in determining the reactions of both participants in the experiment.

The rudeness of a research assistant will negatively impact the response of the participant allocated to him/her.

The calmness of the other research assistant will positively impact the response of the participant allocated to him/her.

5 0

2 years ago

A rock is placed in a graduated cylinder to determine its volume. The following data are obtained. What is the volume of the roc

yarga [219]

Easy
when rock is in water, it takes up a certain volume, say x
so
initial+x=final volume
luckily we have final and inital
13.7ml+x=28.9ml
minus 13.7ml both sides
x=15.2ml

the volme of the rock is 15.2ml

7 0

2 years ago

Read 2 more answers