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(3.5)/(3p^(3))+(7)/(4p)
Which expression is equivalent to the sum for all
p > 7 ?
Choose 1 answer:
(A)
(24.5)/(12p^(4))
(B)
(21p^(2)+14)/(12p^(3))
(C)
(21p^(2)-14)/(12p^(3))
(D)
(10.5p^(2)-28)/(12p^(3))

$\frac{3.5}{3 p^{3}}+\frac{7}{4 p}$ $\newline$ Which expression is equivalent to the sum for all p>7 ? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{24.5}{12 p^{4}}$ $\newline$ (B) $\frac{21 p^{2}+14}{12 p^{3}}$ $\newline$ (C) $\frac{21 p^{2}-14}{12 p^{3}}$ $\newline$ (D) $\frac{10.5 p^{2}-28}{12 p^{3}}$

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Compare linear and exponential growth

Full solution

Q.

\frac{3.5}{3 p^{3}}+\frac{7}{4 p}

\newline

Which expression is equivalent to the sum for all

p>7

?

\newline

Choose

1

answer:

\newline

(A)

\frac{24.5}{12 p^{4}}

\newline

(B)

\frac{21 p^{2}+14}{12 p^{3}}

\newline

(C)

\frac{21 p^{2}-14}{12 p^{3}}

\newline

(D)

\frac{10.5 p^{2}-28}{12 p^{3}}

Find Common Denominator: Combine the fractions by finding a common denominator. $\frac{3.5}{3p^{3}} + \frac{7}{4p}$ Common denominator is $12p^{3}$ .
Rewrite with Common Denominator: Rewrite each fraction with the common denominator. $\frac{3.5 \cdot 4}{12p^3} + \frac{7 \cdot 3p^2}{12p^3}$ = $\frac{14}{12p^3} + \frac{21p^2}{12p^3}$
Combine Numerators: Combine the numerators over the common denominator. $\frac{14 + 21p^2}{12p^3}$
Simplify Expression: Simplify the expression. $\frac{21p^2 + 14}{12p^3}$

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