In a right triangle, this formula can be used:
a^2 + b^2 = c^2
when a and b are the legs and c is the hypotenuse.
Substitute the numbers from the problem into the formula.
14^2 + b^2 = 18^2
Simplify.
196 + b^2 = 324
b^2 = 128
b = square root of 128 = 11.3137...
When 11.313 is rounded to the nearest tenth, it is 11.3
The length of the other leg is 11.3 centimeters.
Hope this helps!
The car moved 175.84 cm in one revolution
The car has moved 17584 cm in 100 revolutions
<em><u>Solution:</u></em>
Given that car wheel is 56 cm in diameter
diameter = 56 cm
To find: distance traveled in one revolution of wheel
Usually wheel is of circular shape
one revolution of wheel = circumference of circle
<em><u>The circumference of circle is given as:</u></em>
![c = 2 \pi r](https://tex.z-dn.net/?f=c%20%3D%202%20%5Cpi%20r)
We know that,
diameter = 2(radius)
![d = 2r](https://tex.z-dn.net/?f=d%20%3D%202r)
<em><u>So the circumference becomes:</u></em>
![c = \pi d](https://tex.z-dn.net/?f=c%20%3D%20%5Cpi%20d)
substitute
= 3.14 and d = 56 cm
![c = 3.14 \times 56 = 175.84](https://tex.z-dn.net/?f=c%20%3D%203.14%20%5Ctimes%2056%20%3D%20175.84)
Thus the car moved 175.84 cm in one revolution
<em><u>B. How far does it go in 100 revolutions</u></em>
Distance covered in 100 revolutions = 100 x Distance covered in 1 revolution
![\rightarrow 100 \times 175.84 = 17584](https://tex.z-dn.net/?f=%5Crightarrow%20100%20%5Ctimes%20175.84%20%3D%2017584)
Thus the car has moved 17584 cm in 100 revolutions
Answer: The correct option is (C) ![a^5.](https://tex.z-dn.net/?f=a%5E5.)
Step-by-step explanation: We are given to choose the correct simplification for the following expression :
![P=a^2.a^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)](https://tex.z-dn.net/?f=P%3Da%5E2.a%5E3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%28i%29)
We will be using the following property of exponents :
![x^a.x^b=x^{a+b}.](https://tex.z-dn.net/?f=x%5Ea.x%5Eb%3Dx%5E%7Ba%2Bb%7D.)
So, the simplification of expression (i) is as follows :
![P\\\\=a^2.a^3\\\\=a^{2+3}\\\\=a^5.](https://tex.z-dn.net/?f=P%5C%5C%5C%5C%3Da%5E2.a%5E3%5C%5C%5C%5C%3Da%5E%7B2%2B3%7D%5C%5C%5C%5C%3Da%5E5.)
Thus, the correct simplification of the given expression is ![a^5.](https://tex.z-dn.net/?f=a%5E5.)
Option (C) is CORRECT.
y is part of a right angle on line AB
a right angle = 90 degrees
90-47 = 43 degrees
y = 43 degrees
a straight line = 180 degrees
180-47 = 133 degrees
x = 133 degrees