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2 years ago

What fraction is equivilent to 0.997

Mathematics

1 answer:

LekaFEV [45]2 years ago

4 0

Answer: 997/1000

Step-by-step explanation: on removing the decimal the number of digits after decimal points comes in the numerator

hence 0.997=997/1000

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Use the general slicing method to find the volume of the following solids. The solid whose base is the region bounded by the cur

Y_Kistochka [10]

Answer:

The volume is $V=\frac{64}{15}$

Step-by-step explanation:

The General Slicing Method is given by

Suppose a solid object extends from x = a to x = b and the cross section of the solid perpendicular to the x-axis has an area given by a function A that is integrable on [a, b]. The volume of the solid is

$V=\int\limits^b_a {A(x)} \, dx$

Because a typical cross section perpendicular to the x-axis is a square disk (according with the graph below), the area of a cross section is

The key observation is that the width is the distance between the upper bounding curve $y = 2 - x^2$ and the lower bounding curve $y = x^2$

The width of each square is given by

$w=(2-x^2)-x^2=2-2x^2$

This means that the area of the square cross section at the point x is

$A(x)=(2-2x^2)^2$

The intersection points of the two bounding curves satisfy $2 - x^2=x^2$ , which has solutions x = ±1.

$2-x^2=x^2\\-2x^2=-2\\\frac{-2x^2}{-2}=\frac{-2}{-2}\\x^2=1\\\\x=\sqrt{1},\:x=-\sqrt{1}$

Therefore, the cross sections lie between x = -1 and x = 1. Integrating the cross-sectional areas, the volume of the solid is

$V=\int\limits^{1}_{-1} {(2-2x^2)^2} \, dx\\\\V=\int _{-1}^14-8x^2+4x^4dx\\\\V=\int _{-1}^14dx-\int _{-1}^18x^2dx+\int _{-1}^14x^4dx\\\\V=\left[4x\right]^1_{-1}-8\left[\frac{x^3}{3}\right]^1_{-1}+4\left[\frac{x^5}{5}\right]^1_{-1}\\\\V=8-\frac{16}{3}+\frac{8}{5}\\\\V=\frac{64}{15}$

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2 years ago

Based on the graphic, which three-dimensional figure has the greatest volume?

dedylja [7]

Answer:c) they have the same volume

Step-by-step explanation: same height equals same volume

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Find the value of x and y? A) x=15 y=12 B) x=14 y=11 C) x=14 y=12 D) x=15 y=11

Alina [70]

im pretty sure the answer is c.

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2 years ago

Define the polynomial by the number of terms.

Lera25 [3.4K]

If the number of terms is one then it is called a mono-nomial
if number of terms is two then it is called binomial.
if the number of terms is three or more than three then it is called poly-nomial.

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2 years ago

Karina needs a total of $45 to buy her mother a birthday present. She has saved 20% of the amount so far. How much has she saved

professor190 [17]

Answer:

$9.00

Step-by-step explanation:

$45.00x20%=9

7 0

2 years ago

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