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3 years ago

What is the scale factor of two similar pyramids with volume of 13824 cubic feel and 216 cubic feet?

Mathematics

1 answer:

velikii [3]3 years ago

3 0

Answer: The scale factor is 4

Step-by-step explanation:

We know that the pyramids are similar. The volume of one of these pyramids is 13,824 cubic feet and the volume of the other one is 216 cubic feet. Then:

$V_1=13,824ft^3\\V_2=216ft^3$

By Similar solids theorem, if two similar solids have a scale factor of $\frac{a}{b}$ , then corresponding volumes have a ratio of $\frac{a^3}{b^3}$

Then:

$\frac{V_1}{V_2}=\frac{a^3}{b^3}$

Knowing this, we can find the scale factor. This is:

$\frac{13,824}{216}=\frac{a^3}{b^3}\\\\\frac{13,824}{216}=(\frac{a}{b})^3\\\\\frac{a}{b}=\sqrt[3]{\frac{13,824}{216}}\\\\scale\ factor=\frac{a}{b}=4$

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Why do the functions f(x) = sin−1(x) and g(x) = cos−1(x) have different ranges?

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We Know that
For a function to have an inverse function, it must be one-to-one—that is, it must pass the Horizontal Line Test.

1. On the interval [–pi/2, pi/2], the function y = sin x is increasing
2. On the interval [–pi/2, pi/2], y = sin x takes on its full range of values, [–1, 1]
3. On the interval [–pi/2, pi/2], y = sin x is one-to-one
sin x has an inverse function on this interval [–pi/2, pi/2]

On the restricted domain [–pi/2, pi/2] y = sin x has a unique inverse function called the inverse sine function. f(x) = sin−1(x)
the range of y=sin x in the domain [–pi/2, pi/2] is [-1,1]
the range of y=sin-1 x in the domain [-1,1] is [–pi/2, pi/2]

1. On the interval [0, pi], the function y = cos x is decreasing
2. On the interval [0, pi], y = cos x takes on its full range of values, [–1, 1]
3. On the interval [0, pi], y = cos x is one-to-one
cos x has an inverse function on this interval [0, pi]

On the restricted domain [0, pi] y = cos x has a unique inverse function called the inverse sine function. f(x) = cos−1(x)
the range of y=cos x in the domain [0, pi] is [-1,1]
the range of y=cos-1 x in the domain [-1,1] is [0, pi]

the answer is

the values of the range are different because the domain in which the inverse function exists are different

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3 years ago

Which of the following is NOT a possible value for the correlation coefficient? 1) negative 0.9 2) zero 3) positive 0.15 4) posi

AnnyKZ [126]

Answer:

4) positive 1.05

Step-by-step explanation:

Correlation:-

Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together.

Examples:i) The yield of a crop varies with the amount of rainfall

ii) The price of a commodity increases with the reduction in its supply and so on.

That is when the changes in one variable are associated or followed by changes in the other, is called correlation

positive correlation:- If an increase (or decrease ) in the values of one variable corresponds to an increase(or decrease ) in the other, then correlation is said to be positive.

negative correlation:- If an increase (or decrease ) in the values of one variable corresponds to an decrease(or increase ) in the other, then correlation is said to be negative.

no correlation:-

If there is no relationship indicated between the variables,they are said to be independent or uncorrelated.

uses of correlation:-it is used in presenting the average relationship between any two variables through a single value of co-efficient of correlation. correlation is a statistical technique that can show whether and how strongly pairs of variables are related.

The range of correlation is $-1\leq r\leq 1$

r=-1 is the negative correlation

r=1 is the positive correlation

so the answer is not a possible value for the correlation coefficient is positive 1.05.

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3 years ago