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3 years ago

1. Jane saved up 20 coins, all nickels and

Mathematics

1 answer:

kompoz [17]3 years ago

6 0

Answer:

10 nickels and 10 quarters

Step-by-step explanation:

Given

Number of coins: 20

Vaiue of coins = $3.00

Required

Number of Nickels and Quarters;

<em>Let N =Nickels and Q =Quarters</em>

The total coins is represented as:

$N + Q = 20$

1 nickel is equivalent to $0.05 and 1 quarter is equivalent to $0.25; So

$0.05N + 0.25Q = 3$

Make N the subject of formula in the first equation

$N = 20 - Q$

Substitute this in the second equation

$0.05(20 - Q) + 0.25Q = 3$

$1 - 0.05Q + 0.25Q = 3$

Collect like terms

$-0.05Q + 0.25Q = 3 - 1$

$0.2Q = 2$

Multiply both sides by 5

$5 * 0.2Q = 2 * 5$

$Q = 10$

Recall that N = 20 - Q

$N = 20 - 10$

$N = 10$

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3 years ago

4x^2 y+8xy'+y=x, y(1)= 9, y'(1)=25

jarptica [38.1K]

Answer with explanation:

$\rightarrow 4x^2y+8x y'+y=x\\\\\rightarrow 8xy'+y(1+4x^2)=x\\\\\rightarrow y'+y\times\frac{1+4x^2}{8x}=\frac{1}{8}$

--------------------------------------------------------Dividing both sides by 8 x

This Integration is of the form ⇒y'+p y=q,which is Linear differential equation.

Integrating Factor

$=e^{\int \frac{1+4x^2}{8x} dx}\\\\e^{\log x^{\frac{1}{8}+\frac{x^2}{2}}\\\\=x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}$

Multiplying both sides by Integrating Factor

$x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}\times [y'+y\times\frac{1+4x^2}{8x}]=\frac{1}{8}\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}\\\\ \text{Integrating both sides}\\\\y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=\frac{1}{8}\int {x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}} \, dx \\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=\int {x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}} \, dx\\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=-[x^{\frac{9}{8}}]\times\frac{ \Gamma(0.5625, -x^2)}{(-x^2)^{\frac{9}{16}}}\\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=(-1)^{\frac{-1}{8}}[ \Gamma(0.5625, -x^2)]+C-----(1)$

When , x=1, gives , y=9.

Evaluate the value of C and substitute in the equation 1.

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3 years ago

A 7th-grade class has 14 girls and 10 boys. An 8th-grade class has 11 girls and 13 boys. What is the probability of picking a st

melomori [17]

Answer:

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Step-by-step explanation:

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3 years ago

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zysi [14]

Answer:

The answer is y=-1x+8 or you can write it this way y=-x+8 either way will work fine.

Step-by-step explanation:

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+1 +1

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I hope this helps:)

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2 years ago