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AnnZ [28]
3 years ago
5

g The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm2

/min. At what rate is the base of the triangle changing when the altitude is 20 cm and the area is 160 cm2
Mathematics
1 answer:
horsena [70]3 years ago
5 0

Answer:

  -0.6 cm/min

Step-by-step explanation:

The formula for the area of a triangle is ...

  A = (1/2)bh

Solving for the base, we find ...

  b = 2A/h

Then the rate of change of the base is ...

  b' = 2(A'h -Ah')/h^2

Filling in the given values, we find the rate of change of the base to be ...

  b' = 2((2 cm^2/min)(20 cm) -(160 cm^2)(1 cm/min))/(20 cm)^2

  = 2(40-160)/400 cm/min

  = -0.6 cm/min

The base is decreasing at 0.6 cm/minute.

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to arrive at 2000 liters of 60% saline solution the attendant has to mix a 90% and a 40% saline solution. How many liters of eac
CaHeK987 [17]

Answer:

<u>800 liters</u> of 90% saline solution and <u>1200 liters</u> of 40% saline solution should be used.

Step-by-step explanation:

Given:

At 2000 liters of 60% saline solution the attendant has to mix a 90% and a 40% saline solution.

Now, to find the number of liters of saline solution each should be used.

<u><em>Let the liters of 90% saline solution mix be </em></u>x.<u><em /></u>

<u><em>And let the liters of 40% saline solution mix be</em></u> y.

So, the total number of liters:

x+y=2000.

y=2000-x\ \ \ ....(1)

Now, the total percentage of saline solution:

90\%\ of\ x+40\%\ of\ y=60\%\ of\ 2000

\frac{90}{100}\times x+\frac{40}{100}\times y=\frac{60}{100}\times 2000

0.9x+0.4y=1200

Substituting the value of y from equation (1) we get:

0.9x+0.4(2000-x)=1200

0.9x+800-0.4x=1200

0.5x+800=1200

Subtracting both sides by 800 we get:

0.5x=400

Dividing both sides by 0.5 we get:

x=800.

<u>The liters of 90% saline solution mix = 800.</u>

Now, substituting the value of x in equation (1) to get the liters of 40% saline solution:

y=2000-x

y=2000-800

y=1200.

<u>Thus, the liters of 40% saline solution = 1200.</u>

Therefore, 800 liters of 90% saline solution and 1200 liters of 40% saline solution should be used.

8 0
3 years ago
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