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vazorg [7]
3 years ago
7

A certain cylindrical tank holds 20,000 gallons of water which can be drained from the bottom of the tank in 20 minutes the volu

me tea of water remaining in the tank after T minutes is given by the function (v)= 20,000(1-(t/20)^2 where B is in gallons zero is less than or equal to T which less than or equal to 20 is in a minutes and T equals zero represent the instant the tank starts draining how fast is the water draining 4 1/2 minutes after it begins

Mathematics
1 answer:
zalisa [80]3 years ago
4 0
Given that the volume of water remaining in the tank after t minutes is given by the function

V(t)=20,000\left(1- \frac{t}{20} \right)^2

where V is in gallons, 0 ≤ t ≤ 20 is in minutes, and t = 0 represents the instant the tank starts draining.

The rate at which water is draining four and a half minutes after it begins is given by

\left.
 \frac{dV}{dt} \right|_{t=4 \frac{1}{2} = \frac{9}{2} 
}=\left[40,000\left(1- \frac{t}{20} \right)\left(- \frac{1}{20} 
\right)\right]_{t= \frac{9}{2} } \\  \\ =\left[-2,000\left(1- 
\frac{t}{20} \right)\right]_{t= \frac{9}{2} }=-2,000\left(1- 
\frac{4.5}{20} \right) \\  \\ =-2,000(1-0.225)=-2,000(0.775)=-1,550\, 
gallons\ per\ minute

Therefore, the water is draining at a rate of 1,550 gallons per minute four ans a half minutes after it begins.

Answer option E is the correct answer.
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Plums cost $0.77 per pound Mangoes cost $1.32 per pound Write an expression that can be used to find the cost of buying p pounds
marissa [1.9K]

Answer:

The graphs below show the cost y of buying x pounds of fruit. One graph shows the cost of buying x pounds of peaches, and the other shows the cost of buying x pounds of plums.

Which kind of fruit costs more per pound? Explain.

Bananas cost less per pound than peaches or plums. Draw a line alongside the other graphs that might represent the cost y of buying x pounds of bananas.

IM Commentary

This task allows students to reason about the relative costs per pound of the two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope.

Solutions

Solution: Slope as Unit Rate

The graph that represents the cost of x pounds of peaches is steeper, so it must have a larger slope. The slope can be interpreted as the unit rate; in this case it tells you the cost of a single pound of fruit.

Since the slope for the peach graph is greater than the slope of the plum graph, the cost of a pound of peaches is greater than the cost of a pound of plums.

For b, students should realize that the cost per pound of bananas will be represented by a slope that is less than either of the other two, and draw a line through the origin labeled "Bananas" and lying below both of the other graphs.

Solution: Adding a scale to the graph

Students who prefer to work with specific numbers can approach this problem by sketching in a scale on the x-axis and y-axis. For example, if they decided that a pound of peaches might cost a dollar, then they might plot the point (1,1) on the line labeled "Peaches", then fill out the rest of the scale accordingly. They could then read off the cost of a pound of plums and see that it is less than for peaches.

For the second question, they could choose any price per pound b for bananas that is less than the one they read off for plums, and then draw a line from the origin through the point (b, 1), and label it "Bananas".

4 0
3 years ago
Can anyone help me<br> Please and thankyou? Been struggling for 20minutes
schepotkina [342]

There is an app that will help for these types of questions called, "Showmath."

5 0
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cricket20 [7]
3x^2 + 9x + 6 = 0
3x^2 + 3x + 6x + 6 = 0
3x(x + 1) + 6(x + 1) = 0
(3x + 6)(x + 1) = 0
3x + 6 = 0 and x + 1 = 0
3x = -6 and x = -1
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6 0
3 years ago
Find the values of x and y.
vova2212 [387]

Look at the picture.

We have the equation (1) 12x + 4y = 40.

We know, the sum of the acute angles in a right triangle is 90°.

Therefore we have the equation (2) (12x + 4y) + (17x - y) = 90

Substitute (1) to (2):

40 + 17x - y = 90        <em>subtract 40 from both sides</em>

17x - y = 50   (3)

We have the system of equations:

\left\{\begin{array}{ccc}12x + 4y = 40&|:4\\17x-y=50\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x + y = 10\\17x-y=50\end{array}\right}\ \text{add both side of equations}\\.\qquad20x=60\qquad|:20\\.\qquad x=3

Substitute the value of x to (3)

17(3)-y=50\\51-y=50\qquad|-51\\-y=-1\to y=1

Answer: x = 3 and y = 1.

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Hello :
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