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fomenos
3 years ago
9

A particular dam contains approximately 1,900,000,000,000 cubic feet of water. for a week long spike flood, the dam released at

a rate of 24,600 cubic feet per second. how much water was released during the flood?
what percentage of the dam was released during the flood?
​
Mathematics
1 answer:
Fantom [35]3 years ago
7 0

Answer:

a) How much water was released during the flood?

14878080000 cubic feet or 14,878,080,000ft³

b) What percentage of the dam was released during the flood?

0.78%

Step-by-step explanation:

a) How much water was released during the flood?

The first step would be to find out how many seconds are in a week

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

7 days = 1 week

Hence, the number of seconds in a week =

1 week × (7 days/1 week)× (24 hours/1 day )×( 60 minutes/1 hour) ×( 60 seconds/1 minute)

= 604800 seconds

Therefore, the quantity of water released per week =

604800 seconds × 24,600 cubic feet per second

= 14,878,080,000 cubic feet or 14,878,080,000ft³

b) What percentage of the dam was released during the flood?

This is calculated as quantity released during the week ÷ Quantity of water in the dam × 100%

Quantity of water released during the flood in a week = 14,878,080,000 cubic feet

Quantity of water in the dam= 1,900,000,000,000 cubic feet of water

Percentage of the dam released during the flood =

14,878,080,000 cubic feet ÷ 1,900,000,000,000 × 100

= 0.7830568421%

Approximately = 0.78%

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Find the area of the triangle with the given vertices. Use the fact that the area of the triangle having u and v as adjacent sid
Gnom [1K]

Answer:

The area of the triangle is A=\sqrt{\frac{4027}{2}}

Step-by-step explanation:

Using the fact that the area of the triangle having u and v as adjacent sides is given by

A=\frac{1}{2}||{\bf u} \times {\bf v} ||

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This is the definition of cross product of two vectors in space:

Let {\bf u} = u_1{\bf i}+u_2{\bf j}+u_3{\bf k} and {\bf v} = v_1{\bf i}+v_2{\bf j}+v_3{\bf k} be vectors in space. The cross product of {\bf u} and {\bf v} is the vector

{\bf u} \times {\bf v}=(u_2v_3-u_3v_2){\bf i}-(u_1v_3-u_3v_1){\bf j}+(u_1v_2-u_2v_1){\bf k}

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\begin{pmatrix}0\cdot \left(-7\right)-\left(-9\left(-5\right)\right)&-9\left(-7\right)-2\left(-7\right)&2\left(-5\right)-0\cdot \left(-7\right)\end{pmatrix}\\\\\begin{pmatrix}-45&77&-10\end{pmatrix}

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A=\frac{1}{2}||{\bf AB} \times {\bf AC} ||=\frac{1}{2}\sqrt{8054}=\sqrt{\frac{4027}{2}}

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