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3 years ago

15

In Colorado, the temperature was 17.2° below zero. if the temperature continues to drop 4° every hour, what is the new temperatu

re after 5.5 hours? Please explain !!

1 answer:

katovenus [111]3 years ago

4 0

Answer:

-4.8°

Step-by-step explanation:

5.5 x 4

= 22

17.2 - 22

=4.8

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Neko [114]

31-(-5) = 155
the square root of 155 is 12.45

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3 years ago

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Aleah enjoys swimming and skating with her friends. She has a budget where she spends no more than $80 a month for her activitie

kari74 [83]

<span>a) define the variables
The variables are x and y ; x can represent the number of times Aleah goes swimming ; while y can represents the number of times Aleah goes skating.

b) are there any restrictions on the variables?
The total sum of both activities must be equal or less than $80 a month

c) write a linear inequality to represent this situation
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12 5
8 10
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3 years ago

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Kaylis [27]

Step-by-step explanation:

Use photo math in the AppStore

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2 years ago

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A conical water tank with vertex down has a radius of 13 feet at the top and is 21 feet high. If water flows into the tank at a

VLD [36.1K]

Answer:

$\frac{dh}{dt}\approx0.08622\text{ ft/min}$

Step-by-step explanation:

We know that the conical water tank has a radius of 13 feet and is 21 feet high.

We also know that water is flowing into the tank at a rate of 30ft³/min. In other words, our derivative of the volume with respect to time t is:

$\frac{dV}{dt}=\frac{30\text{ ft}^3}{\text{min}}$

We want to find how fast the depth of the water is increasing when the water is 17 feet deep. So, we want to find dh/dt.

First, remember that the volume for a cone is given by the formula:

$V=\frac{1}{3}\pi r^2h$

We want to find dh/dt. So, let's take the derivative of both sides with respect to the time t. However, first, let's put the equation in terms of h.

We can see that we have two similar triangles. So, we can write the following proportion:

$\frac{r}{h}=\frac{13}{21}$

Multiply both sides by h:

$r=\frac{13}{21}h$

So, let's substitute this in r:

$V=\frac{1}{3}\pi (\frac{13}{21}h)^2h$

Square:

$V=\frac{1}{3}\pi (\frac{169}{441}h^2)h$

Simplify:

$V=\frac{169}{1323}\pi h^3$

Now, let's take the derivative of both sides with respect to t:

$\frac{d}{dt}[V]=\frac{d}{dt}[\frac{169}{1323}\pi h^3}]$

Simplify:

$\frac{dV}{dt}=\frac{169}{1323}\pi \frac{d}{dt}[h^3}]$

Differentiate implicitly. This yields:

$\frac{dV}{dt}=\frac{169}{1323}\pi (3h^2)\frac{dh}{dt}$

We want to find dh/dt when the water is 17 feet deep. So, let's substitute 17 for h. Also, let's substitute 30 for dV/dt. This yields:

$30=\frac{169}{1323}\pi (3(17)^2)\frac{dh}{dt}$

Evaluate:

$30=\frac{146523}{1323}\pi( \frac{dh}{dt})$

Multiply both sides by 1323:

$39690=146523\pi\frac{dh}{dt}$

Solve for dh/dt:

$\frac{dh}{dt}=\frac{39690}{146523}\pi$

Use a calculator. So:

$\frac{dh}{dt}\approx0.08622\text{ ft/min}$

The water is rising at a rate of approximately 0.086 feet per minute.

And we're done!

Edit: Forgot the picture :)

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3 years ago

Suppose that IQ scores in one region are normally distributed with a standard deviation of 16. Suppose also that exactly 52% of

dimulka [17.4K]

Answer: 100.8

Step-by-step explanation:

Given that:

Standard deviation (σ) = 16

X > 100

From the z table :

Zscore = P(X > 100) = - 0.05

Zscore = - 0.05

Thus ;

Zscore = (x - m) / σ

x = 100

-0.05 = ( 100 - m) / 16

-0.05 * 16 = 100 - m

- 0.8 = 100 - m

m = 100 + 0.8

Mean = 100. 8

Mean score = 100.8

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3 years ago