2 years ago

Is the statement “The absolute value of a number is always greater than its opposite” true?

Mathematics

1 answer:

german2 years ago

6 0

Answer:

No; the absolute value of a negative number is equal to its opposite

Step-by-step explanation:

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Given that f(x) = x² + 3x 28 and g(x) = x + 7, find f(x) + g(x) and

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f(x) + g(x) = x^2 + 4x + 35

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A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents t

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Answer:

A) A[p(t)] = 36πt²

B) 7234.56 square units

Step-by-step explanation:

Given functions:

$\begin{cases}p(t)=6t \\ A(p)=\pi p^2 \end{cases}$

Part A

To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):

$\begin{aligned}A(p) & = \pi p^2\\\\ \implies A[p(t)] & = \pi [p(t)]^2\\& = \pi (6t)^2\\& = \pi 6^2 t^2\\& = 36\pi t^2\end{aligned}$

Part B

Given

t = 8 minutes
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Substitute the given values into the equation for A[p(t)} found in part A:

$\begin{aligned}A[p(8)] & = 36\pi t^2\\& = 36 \cdot 3.14 \cdot 8^2\\& = 36 \cdot 3.14 \cdot 64\\& = 113.04 \cdot 64\\& = 7234.56\:\: \sf square\:units\end{aligned}$

Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.

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