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3 years ago

9

What is the area of the parallelogram shown below?

2 answers:

laiz [17]3 years ago

6 0

Answer:

135 units²

Step-by-step explanation:

height = √17²-8²=√289-64=√225=15

area = 9×15 = 135 units²

geniusboy [140]3 years ago

5 0

The answer is 135 units square

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How many 0.2-liter glasses of water are contained in a 3.6-liter pitcher

jolli1 [7]

18 glasses of water

3.6/.2=18

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4 years ago

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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>

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3 years ago

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svet-max [94.6K]

Answer:

Answer=50

Step-by-step explanation:

hope the picture is good enough for an explanation

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3 years ago

I have a vase that is shaped like a rectangular prism. The height is 10 inches. The length of the base is 6 inches. The width of

Keith_Richards [23]

Answer:

$200in^3$

Step-by-step explanation:

To solve this, we are using the formula for the volume of a rectangular prism:

$V=whl$

where

$w$ is the width of the base

$l$ is the length of the base

$h$ is the height of the prism

We know from our problem that the height is 10 inches. The length of the base is 6 inches. The width of the base is 5 inches.

Replacing values

$V=(5in)(10in)(6in)$

$V=300in^3$

Now, to find 2/3 of that volume, we just need to multiply it by 2/3

$\frac{2}{3} V=\frac{2}{3} 300in^3$

$\frac{2}{3} V=200in^3$

We can conclude that 2/3 of the volume of the vase is 200 cubic inches.

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3 years ago

mr chan has three daughters ,an, lien and tao , aged 7,8 and 10 years respectively. he shares $100 between them in the ratio of

Valentin [98]

Step-by-step explanation:

The money was shared in the ratio of their ages which represents

7:8:10 respectively

Lien = 8
7+8+10=25
8/25 x 100/1
0.32 x 100
= $32

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3 years ago