Using four different numerators, write an equation in which four fractions, when added, have a sum of 1.

Mathematics

1 answer:

valentinak56 [21]3 years ago

8 0

Answer:

1/2 + 1/4 + 1/12 + 8333/10000

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Section 5.2 Problem 17:

Elina [12.6K]

This DE has characteristic equation

$4r^2 - 12r + 9r = (2r - 3)^2 = 0$

with a repeated root at r = 3/2. Then the characteristic solution is

$y_c = C_1 e^{\frac32 x} + C_2 x e^{\frac32 x}$

which has derivative

${y_c}' = \dfrac{3C_1}2 e^{\frac32 x} + \dfrac{3C_2}2 x e^{\frac32x} + C_2 e^{\frac32 x}$

Use the given initial conditions to solve for the constants:

$y(0) = 3 \implies 3 = C_1$

$y'(0) = \dfrac52 \implies \dfrac52 = \dfrac{3C_1}2 + C_2 \implies C_2 = -2$

and so the particular solution to the IVP is

$\boxed{y(x) = 3 e^{\frac32 x} - 2 x e^{\frac32 x}}$

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2 years ago

How to subtract percentages that are fractions

natali 33 [55]

"you can convert the percent to a fraction or decimal. While you might need to subtract a percent from a percent when working in finance, if you are working on homework you more likely will come across problems where you need to subtract a percent from a whole number."

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3 years ago

What is the slope of the line that passes through the points (-4, -1) and (4, 5)?

andreyandreev [35.5K]

Answer:

3/4

Step-by-step explanation:

Since we have two points, we can use the slope formula

m = ( y2-y1)/(x2-x1)

= ( 5 - -1)/( 4 - -4)

= ( 5+1)/(4+4)

= 6/8