All categories

3 years ago

Inverse of t = (120r)/(r+120)

Mathematics

1 answer:

Orlov [11]3 years ago

7 0

9514 1404 393

Answer:

r = 120t/(120 -t)

Step-by-step explanation:

Given t = f(r), solve for r.

$t(r+120)=120r \qquad\text{multiply by $r+120$}\\\\rt+120t=120r \qquad\text{eliminate parentheses}\\\\rt-120r=-120t \qquad\text{subtract $120t+120r$}\\\\r(t-120)=-120t \qquad\text{factor}\\\\r=\dfrac{-120t}{t-120} \qquad\text{divide by $t-120$}\\\\\boxed{r=\dfrac{120t}{120-t}} \qquad\text{negate numerator and denominator}$

You might be interested in

on a certain hot Summer's Day 613 people use the public swimming pool the daily prices are $1.75 for children $2.25 for adults t

Elodia [21]

389 children and 224 adults were at the pool that day.

Step-by-step explanation:

Cost of one child ticket = $1.75

Cost of one adult ticket = $2.25

Total people = 613

Total receipts worth = $1184.75

Let,

Number of children = x

Number of adults = y

According to given statement;

x+y=613 Eqn 1

1.75x+2.25y=1184.75 Eqn 2

Multiplying Eqn 1 by 1.75

$1.75(x+y=613)\\1.75x+1.75y=1072.75\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(1.75x+2.25y)-(1.75x+1.75y)=1184.75-1072.75\\1.75x+2.25y-1.75x-1.75y=112.00\\0.50y=112.00$

Dividing both sides by 0.50

$\frac{0.50y}{0.50}=\frac{112.00}{0.50}\\y=224$

Putting y=224 in Eqn 1

$x+224=613\\x=613-224\\x=389\\$

389 children and 224 adults were at the pool that day.

Keywords: linear equation, subtraction

Learn more about linear equations at:

#LearnwithBrainly

6 0

4 years ago

The sum of three consecutive even integers is -78, what are the integers ?

Digiron [165]

First, you need to analize and understand the problem, then you must choose and strategy. There is a wide variety of strategies to solve a mathematical problem, in this case, you can use the following, which is based on the information given above:
1. You have that the sum of three consecutive even integers is $-78$ , therefore, you can given the variable $x
$ to the first integer, the second even integer is $x+2$ and the third one is $x+4
$ .
2. Calculate x:
 $x+(x+2)+(x+4)=-78$ 
 $3x+6=-78$
 $x=-28
$ 
 $x+2=-28+2=-26
$ 
 $x+4=-28+4=-24
$ 
Therefore, the answer is: $-28,-26,-24
$

5 0

3 years ago

A rectangular sign has length of 3 and 1/2 ft and a width of 1 and 1/8 ft. Will the area of the sign be greater or less than 3 a

zavuch27 [327]

Answer:

$Area = 3\dfrac{15}{16}\ sq\ ft$

Area is greater than $3\frac{1}{2}$ sq ft.

Step-by-step explanation:

Length of rectangular sign board = $3\frac{1}{2}$ ft

Width of rectangular sign board = $1\frac{1}{8}$ ft

Area of a rectangle is given by the formula:

$A = Length \times Width$

To find the area, we are going to multiply $3\frac{1}{2}$ with $1\frac{1}{8}$ .

$1\frac{1}{8}$ is greater than 1.

Therefore the multiplication will be greater than $3\frac{1}{2}$ .

Hence, we can say that area will be greater than $3\frac{1}{2}$ sq ft.

Area of the sign:

$A = 3\dfrac{1}{2}\times 1\dfrac{1}8\\\Rightarrow A = \dfrac{7}{2}\times \frac{9}8\\\Rightarrow A = \dfrac{63}{16}\\\Rightarrow A = 3\dfrac{15}{16}\ sq\ ft$

8 0

3 years ago

Tiana is on a 25-foot ladder that is leaning against her house. Its base is 7 feet from the base of the house. The ladder slips

Lostsunrise [7]

Answer:

4 ft downwards

Step-by-step explanation:

old height off the ground :

7^2+b^2=25^2

49+b^2=625

b^2=576

b=24

new height off the ground :

7+8=15

15^2+ b^2 =25^2

225+b^2 = 625

b^2 = 400

b=20

difference between heights :

24 - 20 = 4

4 0

4 years ago

If m 1= (7x 19), and m 2 = (x+ 5), find m 2.

solong [7]

Answer: othingat all

Step-by-step explanation:

3 0

4 years ago