Ask question

Ask question

All categories

3 years ago

15

A gas tank can hold 12 gallons of gas. The equation p(g) = 3.5g gives the amount of money it costs when filling the tank with ga

s. What is the range for this situation?

1 answer:

erica [24]3 years ago

3 0

Answer: 12/4=3 so it would be 12(6)=3.5

Step-by-step explanation:

You might be interested in

What is six times the difference of a number is 9 and 18

AVprozaik [17]

Answer: 6 x (18-9) = 54

Step-by-step explanation: 18-9 is 9 and 6 times 9 is 54

6 0

3 years ago

Please Help me this is the first part of 4 in this question. I will be posting the other 3 shortly. I need the answer. This is v

Ket [755]

Answer:

y = 1/6x + 5

Step-by-step explanation:

-x + 6y = 30

6y = x + 30

y = 1/6x + 5

6 0

2 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

3 years ago

The chemistry class was making 300 gallons of 30% isopropyl alcohol. They mixed 12% with 42%. How much of each did they use?

alexgriva [62]

Answer:

<u>The chemistry class mixed 120 gallons of 12% isopropyl alcohol and 180 gallons of 42% isopropyl alcohol.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount of isopropyl alcohol made by the chemistry class = 300 of 30%

Amount of 12% isopropyl alcohol mixed by the chemistry class = x

Amount of 42% isopropyl alcohol mixed by the chemistry class = 300 - x

2. How much of each did they use?

Let's write our equation to solve for x, this way:

30% = 0.3, 12% = 0.12, 42% = 0.42

0.12x + 0.42 (300 - x) = 0.3 * 300

0.12x + 126 - 0.42x = 90

-0.3x = 90 - 126

-0.3x = -36

x = -36/-0.3

<u>x = 120 ⇒ 300 - x = 180</u>

<u>Let's prove x = 120 is correct</u>

0.12x + 0.42 (300 - x) = 0.3 * 300

0.12 * 120 + 0.42 (300 - 120) = 0.3 * 300

14.4 + 75.6 = 90

90 = 90

<u>We proved x = 120 is correct</u>

5 0

3 years ago

Which of the following equations represents a graph that decreases?

almond37 [142]

D because it is a decimal (lower than 0)

7 0

3 years ago