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Example Question #71 : Algebra
varies inversely as both the square of
and the square root of
. Assuming that
does not depend on any other variable, which statement is true of
concerning its relationship to
?
varies directly as the fourth power of
.
varies inversely as
.
varies directly as the fourth root of
.
varies inversely as the fourth power of
.
varies inversely as the fourth root of
.
varies inversely as the fourth power of
.
varies inversely as both the square of
and the square root of
, meaning that for some constant of variation
,
.
Square both sides, and the expression becomes
takes the role of the new constant of variation here, and we now have
,
meaning that varies inversely as the fourth power of
.
Example Question #1 : Direct And Inverse Variation
varies directly as the square of
and inversely as
;
and
. Assuming that
does not depend on any other variables, which of the following gives the variation relationship of
to
?
varies inversely as the seventh power of
.
varies inversely as
.
varies directly as the fourth power of
.
varies inversely as the fourth power of
.
varies directly as
.
varies directly as
.
varies directly as the square of
and inversely as
; therefore, for some constant of variation
,
Setting and
, the formula becomes
Setting as the new constant of variation, we have a new variation equation
,
meaning that varies directly as
.
Example Question #71 : Algebra
If you have a rectangle with a width of and a length of
, what is the area of the rectangle?
To find the area of a rectangle, multiply the length times the width. Therefore, you must multiply times
. To do that, you must multiply the monomial times each part of the trinomial, like so:
Example Question #722 : Psat Mathematics
Find the product:
Use the distributive property:
Simplify: don't forget to use the rules of multiplying exponents (add them)
Example Question #723 : Psat Mathematics
Find the product:
Find the product:
Use the distributive property:
When multiplying variables with exponents, add the exponents:
Example Question #3 : Monomials
Find the product:
Find the product:
Use the distributive property:
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