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Zarrin [17]
3 years ago
5

Question 1

Mathematics
1 answer:
Semenov [28]3 years ago
4 0

Answer:

The volume of cone A is twice the volume of cone B.

Step-by-step explanation:

The formula that is used to find the volume of a cone is given by :

V=\dfrac{1}{3}\pi r^2 h

Where

r is radius of cone and h is height

ATQ,

The radius of the base of cone A is twice as large as the radius of the base of cone B. The  height of cone B is twice the height of cone A.

r_A=2r_B\ \text{and}\ h_B=2h_A

or

\dfrac{r_A}{r_B}={2}\ \text{and}\ \dfrac{h_A}{h_B}=\dfrac{1}{2}

Taking ratios of their volume,

\dfrac{V_A}{V_B}=\dfrac{1/3\pi r_A^2h_A}{1/3\pi r_B^2h_B}\\\\\dfrac{V_A}{V_B}=(\dfrac{r_A}{r_B})^2\times \dfrac{h_A}{h_B}

So,

\dfrac{V_A}{V_B}=(\dfrac{r_A}{r_B})^2\times \dfrac{h_A}{h_B}\\\\\dfrac{V_A}{V_B}=(2)^2\times \dfrac{1}{2}\\\\\dfrac{V_A}{V_B}=2\\\\V_A=2V_B

The volume of cone A is twice the volume of cone B.

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a variable is like a placeholder, an empty spot on the pans. and the expressions on both sides are kind of the conditions for the things to put in these empty spots so that the status of the scale stays unchanged.

for an equation the scale has to stay balanced all the time.

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yes, the solution (the ONLY solution, actually) is x = 4. no other value of x allows the scale to be balanced.

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well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = 4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. 5 ?

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yes, the solution (the ONLY solution, actually) is x = -4. no other value of x allows the scale to be balanced.

-2x - 5 >= 3

well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = -4 is therefore a valid solution for the inequality too.

but so is every other value of x that makes the left side "heavier". what about e.g. -5 ?

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x <= -4

a multiplication or division by a negative value flips the inequality sign, because such an operation makes a light weight heavy and a heavy weight light.

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