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3 years ago

Help help help help

Mathematics

1 answer:

Butoxors [25]3 years ago

5 0

Answer:

g=3

Step-by-step explanation:

f(g) = g^2 +3g

Let f(g) = 18

18 = g^2 +3g

Subtract 18 from each side

18-18 =g^2 +3g-18

0 = g^2 +3g-18

Factor

0 = (g+6) (g-3)

Using the zero product property

g+6 =0 g-3 =0

g = -6 g =3

The only solution listed is g=3

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A box with no top is to be constructed from a piece of cardboard whose length measures 5 in. more than its width. The box is to

ddd [48]

Answer:

$9\text{ inch, }14\text{ inch, }2\text{ inch}$

Step-by-step explanation:

GIVEN: A box with no top is to be constructed from a piece of cardboard whose length measures $5\text{ inch}$ more than its width. The box is to be formed by cutting squares that measure $2\text{ inch}$ on each side from the four corners and then folding up the sides.

TO FIND: If the volume of the box will be $100\text{ inch}^3$ , what are the dimensions of the piece of cardboard.

SOLUTION:

Let the width of cardboard be $x$

length of cardboard $=x+5\text{ inch}$

As box is formed by cutting $2\text{ inch }$ squares from corners of cardboard

length of cardboard $=x+5-4=x+1\text{ inch}$

width of cardboard $=x-4\text{ inch}$

height of cardboard $=2\text{ inch}$

volume of cardboard $=\text{length}\times\text{width}\times\text{height}$

$=2(x+1)(x-4)$

$x^2-3x-54=0$

solving we get

$x=9,-6$

width of cardboard $=9\text{ inch}$

length of cardboard $=x+5=14\text{ inch}$

height of cardboard $=2\text{ inch}$

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Step-by-step explanation:

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$\bf \textit{Amount for Exponential Decay using Half-Life}\\\\
A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
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\end{cases}
\\\\\\
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