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loris [4]
3 years ago
14

An ethanol plant added a new tank that holds 350 barrels of ethanol gasoline more than its old tank. Together, they hold 3,650 b

arrels of gasoline. How much gasoline does each tank hold?
Mathematics
1 answer:
Alexeev081 [22]3 years ago
5 0
I RAGE QUIT! This problem is hard.


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A right triangle has a perimeter of 24 cm and a hypotenuse of 10 cm. Find the length of the other two sides.
jekas [21]

Answer:

One of the sides is 6 cm and the other is 8 cm

Step-by-step explanation:

Let's call the unknown sides a and b. From the perimeter information (24 cm) we have:

a + b + hypotenuse = 24

a + b + 10 = 24

a + b = 14

b = 14 - a

So now we can right the Pythagorean theorem as follows:

a^2 + b^2 = hypotenuse^2\\a^2 + (14-a)^2=10^2\\a^2+ 14^2-28\,a+a^2=100\\2\,a^2-28\,a +96=0\\2\,(a^2-14\,a+48)=0\\2\,(a^2-6\,a-8\,a+48)=0\\2(a\,(a-6)-8\,(a-6))=0\\2\,(a-6)\,(a-8)=0

and from this expression in factor form to be zero a must be 6 or a must be 8.

Therefore the solutions are a = 6 (and therefore b = 14 - 6 = 8)

or a = 8 (and therefore b = 14 - 8 = 6)

7 0
3 years ago
Read 2 more answers
A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material for the sides of the can costs
LenKa [72]

Answer:

The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

Step-by-step explanation:

Volume of the Cylinder=400 cm³

Volume of a Cylinder=πr²h

Therefore: πr²h=400

h=\frac{400}{\pi r^2}

Total Surface Area of a Cylinder=2πr²+2πrh

Cost of the materials for the Top and Bottom=0.06 cents per square centimeter

Cost of the materials for the sides=0.03 cents per square centimeter

Cost of the Cylinder=0.06(2πr²)+0.03(2πrh)

C=0.12πr²+0.06πrh

Recall: h=\frac{400}{\pi r^2}

Therefore:

C(r)=0.12\pi r^2+0.06 \pi r(\frac{400}{\pi r^2})

C(r)=0.12\pi r^2+\frac{24}{r}

C(r)=\frac{0.12\pi r^3+24}{r}

The minimum cost occurs when the derivative of the Cost =0.

C^{'}(r)=\frac{6\pi r^3-600}{25r^2}

6\pi r^3-600=0

6\pi r^3=600

\pi r^3=100

r^3=\frac{100}{\pi}

r^3=31.83

r=3.17 cm

Recall that:

h=\frac{400}{\pi r^2}

h=\frac{400}{\pi *3.17^2}

h=12.67cm

The dimensions of the can that will minimize the cost are a Radius of 3.17cm and a Height of 12.67cm.

3 0
3 years ago
A theater has 33 seats in the first row, 37 seats in the second row. 41 seats in the third row, and so on. How many seats are th
Jlenok [28]

Answer:

90 seats are in row 19

Step-by-step explanation:

The pattern is adding 4 seats so 3 x 19 is 57 so 33 + 57 is 90 seats

Hope this helps

5 0
1 year ago
HELP HELP HELP!!!!!!!
erma4kov [3.2K]

Answer:

b = 77

Step-by-step explanation:

a² + b² = c²

36² + b² = 85²

1296 + b² = 7225

b² = 7225 - 1296

b² = 5929

\sqrt{b^2} =\sqrt{5929}

b = 77

3 0
2 years ago
Which statement about 307° is correct?
77julia77 [94]

Answer:

a hope help you stay happy and safe

4 0
3 years ago
Read 2 more answers
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