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2 years ago

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Two water tanks release water at the same time. • Water tank A holds 6,000 gallons of water and water is released from this tank

at a rate of 2 gallons per minute, m. • Water tank B holds 8,250 gallons of water and water is released at a rate of 3 gallons per minute, m. After how many minutes will the two tanks hold the same amount of water?
A 450
B 14,250
C 2,250
D None of the above

2 answers:

Ksenya-84 [330]2 years ago

7 0

Answer:

Step-by-step explanation:

its A

serious [3.7K]2 years ago

5 0

Answer:

c

Step-by-step explanation:

answer is c u have to divide

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Quinn returned home one summer's day to find it sweat-inducingly hot! He turned the air conditioner on and fell asleep. The room

Alenkasestr [34]

Answer:

$f(x)=-0.5x+40$

Step-by-step explanation:

To solve this problem, we need to find the linear function. We know that the constant rate of change is -0.5° Celsius per minute. Also, after 60 minutes the temperature was 10° Celsius. So, we have a one point and the slope of the linear function, let's use the point-slope formula

$y-y_{1} =m(x-x_{1} )\\y-10=-0.5(x-60)\\y=-0.5x+30+10\\y=-0.5x+40$

Where the y-intercept is at (0, 40).

Now, we have two points to graph the relation between minutes and Celsius degrees.

Therefore, the room's temperature as a function of time is

$f(x)=-0.5x+40$

Its graph is attached.

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2 years ago

Find 10-3. Write the subtraction fact two ways.

love history [14]

This is a problem of fact families, but <em>what is fact families?</em> Well it is a family of four things. Two of them are additions and two of them are subtractions. So this question asks about fact families by w<span>riting the <em>subtraction fact two ways</em>. So we have:

</span><span> $10-3$

First way. So let's take the number 10 and explain this problem using triangles. Let's say that we have 10 triangles in the beginning:

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So I want to take away 3 triangles, then by taking away 3<em> what is left? </em>Well the answer is 7:

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That is, if we subtract 3 from 10 then the result is:

$10-3=7$

Second way. In this subtraction we take the same 10 triangles:

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Now I want to take away 7 triangles, then by taking away 7 what is left is 3:

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That is, if we subtract 7 from 10 then the result is:

$10-7=3$

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2 years ago

A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

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= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

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2 years ago

On one afternoon in a shoe warehouse, three large shipments of shoes arrived. The weights of the shipments were 1 ton 115 pounds

Goryan [66]

Alright, lets get started.

The weight of first shipment = 1 ton 115 pounds

As we know, 1 ton = 2000 pounds, so

So, the weight of first shipment = $2000 + 115 = 2115$ pounds

The weight of second shipment = 1723 pounds 7 ounces

The weight of third shipment = 957 pounds 11 ounces

So, adding all three weights = $2115 pounds + 1723 pounds 7 ounces + 957 pounds 11 ounces$

So, all three weights = 4795 pounds 18 ounces

As we know, 16 ounces = 1 pound, so

all three weights = 4795 pound 1 pound 2 ounces

All three weights = 4796 pounds 2 ounces

4796 could be wriiten as 4000 + 796

As we know, 2000 pound = 1 ton so

All three weight = 2 tons 796 pounds 2 ounces

So, the total weight of three shipments = 2 tons 796 pounds 2 ounces : Answer

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2 years ago

Chicxulub is a crater on the Yucatán Peninsula of Mexico. It was formed 6.5 × 107 years ago. Vredefort crater in South Africa wa

Rus_ich [418]

Answer: The oldest one is Vredfort Crater.

Step-by-step explanation:

The data is:

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We want to find the oldest, so we need to find the larger number of the 4 we have.

For this, we need to see at the exponents, the larger the exponent the larger the number.

We have two with a 9 in the exponent:

Vredfort and Sudbury.

Now we look at the number, Vredfort has 2x10^9 and Sudbury has 1.8x10^9.

Both have the same exponent, but the scalar of Vredfort is larger (2 is greater than 1.8) so we have that Vredfort is older.

5 0

2 years ago

Read 2 more answers