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3 years ago

The hypotenuse of a right triangle is 15cm, and the shorter leg is 9cm. Find the length of the other leg

Mathematics

2 answers:

pishuonlain [190]3 years ago

3 0

Hello!

If you add up the squares of the two legs, it will equal the square of the hypotenuse. As we already have the hypotenuse, we will subtract.

225-81=144

Now we find the square root.

√144=12

Therefore, the other leg is 12 cm long.

I hope this helps!

jasenka [17]3 years ago

3 0

Hello,

We apply the theorem of Pythagoras. Let x be the other side, y the hypotenuse and z the smallest side.

x² = y² - z²

x² = 15² - 9²

x² = 225 - 81 = 144

x = √(144) = 12 cm

Bye :)

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4 years ago

Tickets to a movie cost $7.25 for adults and $5.50 for students a group of friends purchased 8 tickets for $52.75 how many adult

irina1246 [14]

Answer:

The number of adults tickets and student tickets purchased is 5 and 3.

Given that,

Tickets to a movie cost $7.25 for adults and $5.50 for students.

A group of friends purchased 8 tickets for $52.75.

Here we assume the no of adult tickets and no of student tickets be x and y.

Based on the above information, the calculation is as follows:

7.25x + 5.50y = 52.75 .............(i)

x + y = 8

x = 8 - y..................(2)

Now put the x value in the equation (1)

So,

7.25(8-y) + 5.50y = 52.75

7.25 × 8 - 7.25y + 5.50y = 52.75

58 - 1.75y = 52.75

5.25 = 1.75y

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So,

x = 8 - 3

= 5

Therefore we can conclude that the number of adults tickets and student tickets purchased is 5 and 3.

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2 years ago

Find the area of the region that lies inside the first curve and outside the second curve.

marishachu [46]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = $\dfrac{1}{2}$

$\theta = -\dfrac{\pi}{3}, \ \ \dfrac{\pi}{3}$

Now, the area of the region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

$A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \ \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ 5^2 d \theta$

$A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \ \theta d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \ d \theta$

$A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} \dfrac{cos \ 2 \theta +1}{2} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}$

$A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix} {cos \ 2 \theta +1} \end {pmatrix} \ \ d \theta - \dfrac{25}{2} \begin {bmatrix} \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}$

$A =25 \begin {bmatrix} \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}} \ \ - \dfrac{25}{2} \begin {bmatrix} \dfrac{2 \pi}{3} \end {bmatrix}$

$A =25 \begin {bmatrix} \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3}) \end {bmatrix} - \dfrac{25 \pi}{3}$

$A = 25 \begin{bmatrix} \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} + \dfrac{\pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}$

$A = 25 \begin{bmatrix} \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3} \end {bmatrix}- \dfrac{ 25 \pi}{3}$

$A = \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}$

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Download docx

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3 years ago

Determine the volume of the rectangular prism.

Flauer [41]

Answer:

Step-by-step explanation:

We know the formula for a rectangular prism is length × width × height

We also know all the sides so we can rewrite the formula replacing variables.

The length is 8, the width is 2 $\frac{1}{2}$ and the height is 2 $\frac{1}{2}$

8 × 2 $\frac{1}{2}$ × 2 $\frac{1}{2}$

Multiply which ever way is easy for you. I am just multiplying from left to right.

8 × 2 $\frac{1}{2}$ = 20

20 × 2 $\frac{1}{2}$ = 50

Now we get 50. Before we put our answer as 50, there are two more steps.

First we need to add the measurement unit which is feet or ft

We also need to add ³ since it is volume

50 ft³ is our final answer

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3 years ago

A bage contains 5 blue marbles, 3 red marbles, and 2 yellow marbles. You select a marble at radom. What is p(yellow)

vodomira [7]

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Answer: 1/5

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4 years ago