2 years ago

Please help with 2 questions. Thank you.

Mathematics

1 answer:

8_murik_8 [283]2 years ago

8 0

${e}^{ln(anything)} = anything$

so here we have:

${e}^{ln1} = 1$

${e}^{ln5x} = 5x$

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Chris’s new car gets 42 miles per gallon. What is the equation that represents y, the total miles driven on x gallons of gas?

Fantom [35]

Answer: I think the answer is B

Step-By-Step Explination:

First you find out what x is by doing 42 multiplying it by 0.1 witch equals 4.2 gallons per mile

Next you figure out what y is by doing 4.2y (witch is 4.2 times y)

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2 years ago

Solve the initial value problem: y'(x)=(4y(x)+25)^(1/2) ,y(1)=6. you can't really tell, but the '1/2' is the exponent

goblinko [34]

Answer:

$y(x)=x^2+5x$

Step-by-step explanation:

Given: $y'=\sqrt{4y+25}$

Initial value: y(1)=6

Let $y'=\dfrac{dy}{dx}$

$\dfrac{dy}{dx}=\sqrt{4y+25}$

Variable separable

$\dfrac{dy}{\sqrt{4y+25}}=dx$

Integrate both sides

$\int \dfrac{dy}{\sqrt{4y+25}}=\int dx$

$\sqrt{4y+25}=2x+C$

Initial condition, y(1)=6

$\sqrt{4\cdot 6+25}=2\cdot 1+C$

$C=5$

Put C into equation

Solution:

$\sqrt{4y+25}=2x+5$

$4y+25=(2x+5)^2$

$y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}$

$y(x)=x^2+5x$

Hence, The solution is $y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}$ or $y(x)=x^2+5x$

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