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3 years ago

11

The Big Bike Shop has in line skates in sale for 15% off the regular price. A pair of in line skates usually cost $89. Find the

amount of the discount and the sales price?

1 answer:

Paul [167]3 years ago

8 0

89*0.85=75.65

89-75.65=13.35

Discount: 13.35
Sale price: 75.65

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On his bookshelf, Adam has the difference between two-thirds of Brett's books and two-thirds of Charlie's books. If Brett has 84

Gala2k [10]

Answer:

30 books

Step-by-step explanation:

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2 years ago

Does the set {t, t Int} form a fundamental set of solutions for t^2y" -- ty' +y = 0?

Ivanshal [37]

Answer:

yes

Step-by-step explanation:

We are given that a Cauchy Euler's equation

$t^2y''-ty'+y=0$ where t is not equal to zero

We are given that two solutions of given Cauchy Euler's equation are t,t ln t

We have to find the solutions are independent or dependent.

To find the solutions are independent or dependent we use wronskain

$w(x)=\begin{vmatrix}y_1&y_2\\y'_1&y'_2\end{vmatrix}$

If wrosnkian is not equal to zero then solutions are dependent and if wronskian is zero then the set of solution is independent.

Let $y_1=t,y_2=t ln t$

$y'_1=1,y'_2=lnt+1$

$w(x)=\begin{vmatrix}t&t lnt\\1&lnt+1\end{vmatrix}$

$w(x)=t(lnt+1)-tlnt=tlnt+t-tlnt=t$ where t is not equal to zero.

Hence,the wronskian is not equal to zero .Therefore, the set of solutions is independent.

Hence, the set {t , tln t} form a fundamental set of solutions for given equation.

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3 years ago

What two numbers have a product of -2 and a sum of 7

Citrus2011 [14]

<em>Greetings from Brasil...</em>

According to the statement of the question, we can assemble the following system of equation:

X · Y = - 2 i

X + Y = 7 ii

isolating X from i and replacing in ii:

X · Y = - 2

X = - 2/Y

X + Y = 7

(- 2/Y) + Y = 7 <em>multiplying everything by Y</em>

(- 2Y/Y) + Y·Y = 7·Y

- 2 + Y² = 7X <em> rearranging everything</em>

Y² - 7X - 2 = 0 <em>2nd degree equation</em>

Δ = b² - 4·a·c

Δ = (- 7)² - 4·1·(- 2)

Δ = 49 + 8

Δ = 57

X = (- b ± √Δ)/2a

X' = (- (- 7) ± √57)/2·1

X' = (7 + √57)/2

X' = (7 - √57)/2

So, the numbers are:

<h2>(7 + √57)/2</h2>

and

<h2>(7 - √57)/2</h2>

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Step-by-step explanation:

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2 years ago

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I hope this helps.

Have a awesome day. :)

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2 years ago

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