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3 years ago

Which rational expression is equal to a positive whole number when evaluated?2 ^1/28 ^1/312 ^1/415 ^1/5

Mathematics

1 answer:

madreJ [45]3 years ago

3 0

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Now Ann is x years old and her sister is eight years younger than her. After five years , Anne's age is twice the age of her sis

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1 year ago

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

The middle school basketball team is selling t-shirts for $12.50 each to raise money for new uniforms. They have already sold 40

adoni [48]

Answer: 28

Step-by-step explanation:

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2 years ago

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Square root of 5 + square root of 3 the whole divided by sqaure root of 5 - square root of 3

xxMikexx [17]

Answer:

The answer is 4 + √15 .

Step-by-step explanation:

You have to get rid of surds in the denorminator by multiplying it with the opposite sign :

$\frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

$= \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} }$

$= \frac{ {( \sqrt{5} + \sqrt{3} ) }^{2} }{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3}) }$

$= \frac{ {( \sqrt{5} )}^{2} + 2( \sqrt{5} )( \sqrt{3}) + {( \sqrt{3}) }^{2} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3} )}^{2} }$

$= \frac{5 + 2 \sqrt{15} + 3 }{5 - 3}$

$= \frac{8 + 2 \sqrt{15} }{2}$

$= 4 + \sqrt{15}$

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3 years ago