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3 years ago

6

A car traveled at an average rate of 51 miles per hour on one highway. It then traveled at an average rate of 71 miles per hour

on a second highway. If the car traveled a total of 508 miles in 8 hours, how many miles were driven on the first highway?

1 answer:

sergiy2304 [10]3 years ago

3 0

d1 = 51(t)

d2 = 71(8 - t)

d1 + d2 = 508

and now you just have to solve for t.

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What’s the square root of 108 a to the 7th power b to the 5th power

MissTica

Answer:

Step-by-step explanation:

Factor all the factors making up the square root.

108: 2*2*3*3*3

a^7: a*a*a*a*a*a*a

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The rule for taking a square root of this is

For every pair, you get to take one number outside the root sign and throw the other one away.

2*3*a * a * a* b * b√(3*a * b)

6a^3b^2 * √(3*a*b)

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3 years ago

If alpha and beta are the zeroes of the polynomial 6x2+x-2 find the value og alpha/beta + beta/alpha

castortr0y [4]

$6x^2+x-2=6x^2+4x-3x-2=2x(3x+2)-1(3x+2)\\\\=(3x+2)(2x-1)\\\\3x+2=0\to x=-\frac{2}{3}\\\\2x-1=0\to x=\frac{1}{2}\\\\\alpha=-\frac{2}{3};\ \beta=\frac{1}{2}\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{-\frac{2}{3}}{\frac{1}{2}}+\frac{\frac{1}{2}}{-\frac{2}{3}}=-\frac{2}{3}\cdot\frac{2}{1}-\frac{1}{2}\cdot\frac{3}{2}=-\frac{4}{3}-\frac{3}{4}\\\\=-\frac{16}{12}-\frac{9}{12}=-\frac{25}{12}=-2\frac{1}{12}$

$use\ Vieta's\ formula:\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}=\frac{\alpha^2+2\alpha\beta+\beta^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2-2\alpha\beta}{\alpha\beta}=\frac{(\alpha+\beta)^2}{\alpha\beta}-2\\\\\alpha+\beta=\frac{-b}{a};\ \alpha\beta=\frac{c}{a}\\\\\frac{(\alpha+\beta)^2}{\alpha\beta}-2=\frac{\left(\frac{-b}{a}\right)^2}{\frac{c}{a}}-2=\frac{b^2}{a^2}\cdot\frac{a}{c}-2=\frac{b^2}{ac}-2$

$6x^2+x-2\\\\a=6;\ b=1;\ c=-2\\\\\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{1^2}{6\cdot(-2)}-2=\frac{1}{-12}-2=-2\frac{1}{12}$

7 0

3 years ago

Help again please...

xeze [42]

Answer:

b

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

A. Solve the differential equation <img src="https://tex.z-dn.net/?f=y%27%3D2x%20%5Csqrt%7B1-y%5E2%7D%20" id="TexFormula1" title

kirill [66]

$y' = \frac{dy}{dx}$

seperable differential equations will have the form
$\frac{dy}{dx} = F(x) G(y)$

what you do from here is isolate all the y terms on one side and all the X terms on the other
$\frac{dy}{G(y)} = F(x) dx$
just divided G(y) to both sides and multiply dx to both sides

then integrate both sides
$\int \frac{1}{G(y)} dy = \int F(x) dx

$

once you integrate, you will have a constant. use the initial value condition to solve for the constant, then try to isolate x or y if the question asks for it

In your problem,
$G(y) = \sqrt{1-y^2}

F(x) = 2x$

so all you need to integrate is
$\int \frac{1}{\sqrt{1-y^2}} dy = \int 2x dx$

5 0

3 years ago

So would the answer be 5 eighths?

adelina 88 [10]

No, the answer is 3/8 because if 3/4 of the cars are Sudan's, and half of that three quarters are white, you need to divide three quarters into two to get the answer. I did this question by using the equivalent fraction 6/8 and dividing both numbers into two.

3 0

3 years ago