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Eduardwww [97]
3 years ago
9

A student received a coupon for ​19% off the total purchase price at a clothing store. Let y be the original price of the purcha

se. Use the expression below for the new price of the purchase. Write an equivalent expression by combining like terms.
Mathematics
2 answers:
Oksi-84 [34.3K]3 years ago
8 0

Answer:

y- .19y=x

Step-by-step explanation:

x=price after discount

Illusion [34]3 years ago
3 0

Answer:

y- .19y=x

Step-by-step explanation:

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Prove that 1³+2³+....n³=n²(n+1)²/4. principle of mathematics induction​
alex41 [277]
<h3>The Simplified Question:-</h3>

\sf 1^3+2^3\dots n^3=\dfrac{n^2(n+1)^2}{2}

\\ \sf\longmapsto 1^3+2^3+\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2

<h3>Solution:-</h3>

Let

\\ \sf\longmapsto P(n)=1^3+2^3\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2

For n=1

\\ \sf\longmapsto P(1)=\left(\dfrac{1(1+1)}{2}\right)^2

\\ \sf\longmapsto P(1)=\left(\dfrac{1(2)}{2}\right)^2

\\ \sf\longmapsto P(1)=\left(\dfrac{2}{2}\right)^2

\\ \sf\longmapsto P(1)=(1)^2

\\ \bf\longmapsto P(1)=1=1^3

Let k be any positive integer.

\\ \sf\longmapsto P(k)= 1^3+2^3\dots k^3=\left(\dfrac{k(k+1)}{2}\right)^2

We have to prove that p(k+1) is true.

consider

\sf 1^3+2^3\dots k^3+(k+1)^3

\\ \sf\longmapsto \left(\dfrac{k(k+1)}{2}\right)^2+(k+1)^3

\\ \sf\longmapsto \dfrac{k^2(k+1)^2}{4}+(k+1)^3

\\ \sf\longmapsto \dfrac{k^2(k+1)^2+4(k+1)^3}{4}

\\ \sf\longmapsto \dfrac{k+1)^2\left\{k^2+4k+4\right\}}{4}

\\ \sf\longmapsto \dfrac{(k+1)^2(k+2)^2}{4}

\\ \sf\longmapsto \dfrac{(k+1)^2(k+1+1)^2}{4}

\\ \sf\longmapsto \left(\dfrac{(k+1)(k+1+1)}{2}\right)^2

\\ \sf\longmapsto (1^3+2^3+3^3\dots k^3)+(k+1)^3

Thus P(k+1) is true whenever P(k) is true.

Hence by the Principal of mathematical induction statement P(n) is true for \bf n\epsilon N.

Note:-

We can solve without simplifying the Question .I did it for clear steps and understanding .

<h3>Learn More:-</h3>

brainly.com/question/13253046?

brainly.com/question/13347635?

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Answer:

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