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3 years ago

1. The distance you travel varies directly with the amount of gas you use. You can travel 300 miles on 12 gallons of gas.

Mathematics

2 answers:

mihalych1998 [28]3 years ago

7 0

y = distance traveled

x = gallons of gas used

k = slope of the graph between distance traveled and gallons of gas used

slope is given as

k = 300 miles / 12 gallons

k = 25 miles/gallon

so the equation can be written as

y = 25 x

given : y = 750 miles

using the equation

y = 25 x

inserting the values

750 = 25 x

x = 30 gallons

c = cost per gallon = $3.75

c = total cost

Total cost is given as

Total cost = Cost per gallon x number of gallons

C = c x

C = $3.75 (30)

C = $112.5

Ratling [72]3 years ago

5 0

Answer is in the attachment

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The family of solutions to the differential equation y ′ = −4xy3 is y = 1 √ C + 4x2 . Find the solution that satisfies the initi

slega [8]

Answer:

The correct option is 4

Step-by-step explanation:

The solution is given as

$y(x)=\frac{1}{\sqrt{C+4x^2}}$

Now for the initial condition the value of C is calculated as

$y(x)=\frac{1}{\sqrt{C+4x^2}}\\y(-2)=\frac{1}{\sqrt{C+4(-2)^2}}\\4=\frac{1}{\sqrt{C+4(4)}}\\4=\frac{1}{\sqrt{C+16}}\\16=\frac{1}{C+16}\\C+16=\frac{1}{16}\\C=\frac{1}{16}-16$

So the solution is given as

$y(x)=\frac{1}{\sqrt{C+4x^2}}\\y(x)=\frac{1}{\sqrt{\frac{1}{16}-16+4x^2}}$

Simplifying the equation as

$y(x)=\frac{1}{\sqrt{\frac{1}{16}-16+4x^2}}\\y(x)=\frac{1}{\sqrt{\frac{1-256+64x^2}{16}}}\\y(x)=\frac{\sqrt{16}}{\sqrt{{1-256+64x^2}}}\\y(x)=\frac{4}{\sqrt{{1+64(x^2-4)}}}$