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jenyasd209 [6]
3 years ago
11

There are two formulas that can be used to find the volume of a rectangular prism. Find the volume using both formulas.

Mathematics
1 answer:
Rina8888 [55]3 years ago
4 0

Answer:

Volume = \frac{1}{8} cubic units.

Step-by-step explanation:

The volume of a rectangular prism is given by,

V =  (\textrm {Length}) \times (\textrm {Width}) \times (\textrm {Height})  .......... (1) and

V = (\textrm {Base Area})\times (\textrm {Height}) .......... (2)

Now, the length of the given prism is \frac{1}{2} units, width is \frac{1}{2} units and the height is \frac{1}{2} units.

So. from equation (1) the volume, V = (\frac{1}{2}) \times (\frac{1}{2}) \times (\frac{1}{2}) = \frac{1}{8} cubic units.

Now, base area = B = (\frac{1}{2}) \times (\frac{1}{2}) = \frac{1}{4} sq. units.

So, from equation (2) we get

V = (\frac{1}{4}) \times (\frac{1}{2}) = \frac{1}{8} cubic units. (Answer)

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The arc of the parabola y = x^2 from (3,9) to (4,16) is rotated about the y-axis. Find the area of the resulting surface. Please
Hitman42 [59]

Answer:

156.5

Step-by-step explanation:

Thinking process:

The area can be calculated using the formula:

S = \int\limits^4_3 {2\pi x\sqrt{1+}(2x)^{2} } \, dx

We let the substitution take place.

Therefore, we let u = 1 + 4x^{2}

Thus, du = 8dx.

So,

xdx = \frac{1}{8}du

Also, the interval of the integration changes to [ 37, 65]

Thus,

S = \int\limits^4_3 {2\pi \sqrt{1+4x^{2} } } \, dx \\= \int\limits^65_35 {2\pi \sqrt{\frac{1}{8}u } } \, dx

= \frac{1}{6} [ 65^{\frac{3}{2}-37^{\frac{3}{2} }  }

= 156.5 units²

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3 years ago
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JulsSmile [24]

Answer:

Y = 6

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Step-by-step explanation:

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3 years ago
A wire 6 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the
zhenek [66]

Answer:

Used wire in circle  x = 2.64 m

Used in square   L - x = 3.36 m

Total wire used 6 m

Step-by-step explanation:

We have a wire of 6 meters long.

We will cut it a distance x from one end, to get two pieces

x    and   6 - x

We are going to use the piece x  to get the circle then

So Perimetr of a circle is 2π*r    (r is the radius of the circle) then:

x = 2*π*r    ⇒    r = x/2*π

And area would be  A(c) = π* (x/2*π)²   ⇒ A(c) = x²/4π

From 6 - x we will get a square, and as the perimeter is 4 times the side

we have

( 6 - x )/ 4  is the side of the square

And the area is  A(s) = [( 6 - x ) /4]²

Total area as function of x is

A(t)  = A(c) + A(s)

A(x)  =  x²/4π  + [ ( 6  -  x  ) / 4 ]²

A(x)  =   x²/4π  + (36 + x² - 12x) /16

A(x)  = 1 / 16π [ 4x² + 36π + πx² -  12π x ]

Taking drivatives on both sides of the equation we get:

A´(x) = 1/ 16π [8x +2πx - 12π]

A´(x) = 0    ⇒      1/ 16π [8x +2πx - 12π]  = 0

[8x +2πx - 12π]  = 0

8x + 6.28x -  37.68  = 0

14.28x - 37.68 =  0      ⇒  x  = 37.68 /14.28

x = 2.64 m   length of wire used in the circle

Then the length L  for the side of the square is  

(6 - x )/4    ⇒ ( 6 - 2.64 )/ 4   ⇒ 3.36 / 4    

L = 0.84 m   total length of wire used in the square is

3.36 m

And total length of wire used is 6 m

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Gwar [14]

Step-by-step explanation:

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2 years ago
Find the value: 3/2 ÷ 5/8 (write your answer as a fraction AND as a decimal number)
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Answer:

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Step-by-step explanation:

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