Solve the proportion17/3 = y/6

1 answer:

7 0

To solve a proportion, you can either use cross products or basic multiplication.

To do cross products, you would multiply 17 (1st numerator) by 6 (2nd denominator).

Do the same with the other diagonal angle, 3 times y.

You'll end up with 3y = 102.

To solve for y, you divide both sides by 3.

102 ÷ 3 = 34

y = 34

The other way you could solve this is to see that 6 is 2 times as large as 3, so you would multiply 17 by 2 to get an equal proportion.

3 × 2 = 6
17 × 2 = 34

Your final answer is y = 34. Hope this helps! :)

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Put the differential equation 9ty+ety′=yt2+81 into the form y′+p(t)y=g(t) and find p(t) and g(t). p(t)= help (formulas) g(t)= he

alexgriva [62]

Answer:

$p(t) = \frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) }$

g(t) = 0

And

The differential equation $9ty + e^{t}y' = \frac{y}{t^{2} + 81 }$ is linear and homogeneous

Step-by-step explanation:

Given that,

The differential equation is -

$9ty + e^{t}y' = \frac{y}{t^{2} + 81 }$

$e^{t}y' + (9t - \frac{1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t(t^{2} + 81 ) - 1}{t^{2} + 81 } )y = 0\\e^{t}y' + (\frac{9t^{3} + 729t - 1}{t^{2} + 81 } )y = 0\\y' + [\frac{9t^{3} + 729t - 1}{e^{t}(t^{2} + 81) } ]y = 0$