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3 years ago

What is the volume??

Mathematics

1 answer:

goldenfox [79]3 years ago

4 0

Answer:

That would be 84.

Step-by-step explanation:

Here it is

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The Johnson family wants to start a college fund for their daughter Gabriella. They put $63, 000 into an account that grows at a

Rainbow [258]

Answer:

It will take approximately 34.13 years

Step-by-step explanation:

The function G(t) below represents the amount of money in some account t years after the account is opened for The Johnson's daughter Gabriella:

$G(t)= 63,000(1+ .0255/4)^ {4t}$

It's required to find the number of years (t) it will take for the account to reach G(t)=150,000. We need to solve the equation:

$63,000(1+ .0255/4)^ {4t}=150,000$

Dividing by 63,000 and simplifying:

$\displaystyle (1+ .0255/4)^ {4t}=\frac{150,000}{63,000}=2.38095$

Taking logarithms:

$\displaystyle \log(1+ .0255/4)^ {4t}=\log 2.38095$

Applying logarithms property:

$\displaystyle (4t) \log(1+ .0255/4)=\log 2.38095$

Solving for t:

$\displaystyle 4t =\frac{\log 2.38095}{\log(1+ .0255/4)}$

$\displaystyle t =\frac{\log 2.38095}{4\log(1+ .0255/4)}$

Calculating:

$\displaystyle t =\frac{0.37675}{0.01104}$

$\boxed{t \approx 34.13}$

It will take approximately 34.13 years

5 0

3 years ago

1. The equation c = 2.95g shows how much it costs to buy gas at a gas station on a

Karolina [17]

Answer:

see the procedure

Step-by-step explanation:

we have

$c=2.95g$

where

c -----> the cost in dollars

g ----> the number gallons of gas purchased

1) For g=1 gal

substitute the value of g in the equation and solve for c

$c=2.95(1)$

$c=\$2.95$

The pair (1,2.95) fit the relationship

2) For g=3 gal

substitute the value of g in the equation and solve for c

$c=2.95(3)$

$c=\$8.85$

The pair (3,8.85) fit the relationship

3) For g=5 gal

substitute the value of g in the equation and solve for c

$c=2.95(5)$

$c=\$14.75$

The pair (5,14.75) fit the relationship

4) For c=$20.65

substitute the value of c in the equation and solve for g

$20.65=2.95g$

$g=20.65/2.95$

$g=7\ gal$

The pair (7,20.65) fit the relationship

7 0

3 years ago

5 Exam-style ABCD is a kite.

Mnenie [13.5K]

let's recall that in a Kite the diagonals meet each other at 90° angles, Check the picture below, so we're looking for the equation of a line that's perpendicular to BD and that passes through (-1 , 3).

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of BD

$y = \stackrel{\stackrel{m}{\downarrow }}{3}x-1\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

$\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{3\implies \cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}$

so we're really looking for the equation of a line whose slope is -1/3 and passes through point A

$(\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{1}{3}}[x-\stackrel{x_1}{(-1)}]\implies y-3=-\cfrac{1}{3}(x+1) \\\\\\ y-3=-\cfrac{1}{3}x-\cfrac{1}{3}\implies y=-\cfrac{1}{3}x-\cfrac{1}{3}+3\implies y=-\cfrac{1}{3}x+\cfrac{8}{3}$