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Maslowich
3 years ago
14

A board 180 cm long is cut into two pieces such that 3 times the length of the larger piece is 85 cm longer than 4 times the len

gth of the smaller piece. How long are the two pieces of board?
Mathematics
1 answer:
zaharov [31]3 years ago
8 0

Answer:

smaller piece is 65cm

larger piece is 115cm

Step-by-step explanation:

let 's' = smaller piece

let '180-s' = larger piece

3(180-s) = 85 + 4s

540 - 3s = 85 + 4s

540 = 85 + 7s

455 = 7s

s = 455/7 which is 65cm

larger piece = 180-65 or 115cm

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no

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A cylindrical can, open at the top, is to hold 840 cm3 of liquid. Find the height and radius that minimize the amount of materia
ycow [4]

Answer:

the radius of the base is equal to x=2\sqrt[3]{\frac{105}{\pi } }

And the height is equal to:

y=\frac{840}{\pi(2\sqrt[3]{\frac{105}{\pi}})^{2} }

Step-by-step explanation:

We write the volume function

f(x,y)=840=\pi x^{2} y where x is the radius of the base and y is the height of the cylinder

y=\frac{840}{\pi x^{2} }

The surface of a cylinder is given by

S(x)=\pi x^{2} +2\pi xy=\pi x^{2} +\frac{1680}{x} on the interval from 0 to infinity

We now determine the critical values by differentiating and making the equation equal to 0

f'(x)=2\pi*x- \frac{1680}{x^{2}} =\frac{2\pi x^{3}-1680}{x^{2} } =0

This equation have 2 complex solutions and one real solution

x=2\sqrt[3]{\frac{105}{\pi } }

For x=0 and infinity the equation goes to infinity also so the radius of the base is equal to x=2\sqrt[3]{\frac{105}{\pi } }

And the height is equal to:

y=\frac{840}{\pi (2\sqrt[3]{\frac{105}{\pi } })^{2} }

y=\frac{840}{\pi(2\sqrt[3]{\frac{105}{\pi}})^{2} }

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3 years ago
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Answer:

-1/9

Step-by-step explanation:

-7/9 + 2/3 also equals to 2/3 - 7/9

Now make the denominator same

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3 years ago
Write the name for the decimal value of point M on the number line.
riadik2000 [5.3K]

The decimal value of point M on the number line is 5.644.

<h3>What is a number line?</h3>

Number line is a straight line divided with numbers placed at equal intervals or segments along its length.

From the question:

Point M = 5.6 + (4/9) * (5.7 - 5.6) = 5.644

The decimal value of point M on the number line is 5.644.

Find out more on number line at: brainly.com/question/24644930

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