27
You can find the area of a triangle with base b and height h using this formula.
A=
1
2
bh
The triangle has base b=6miles and height h=9miles.
Find the area.
A
=
1
2
bh
=
1
2
(6)(9)
= (3)(9)
= 27
The area of the triangle is 27 square miles.
Answer:
40b
Step-by-step explanation:
25 + 15 = 40
Factor the following:
5 x^2 + 20 x + 15
Factor 5 out of 5 x^2 + 20 x + 15:
5 (x^2 + 4 x + 3)
The factors of 3 that sum to 4 are 3 and 1. So, x^2 + 4 x + 3 = (x + 3) (x + 1):
Answer: 5 (x + 3) (x + 1)
Problem 9
r+h = 9
SA = 2*pi*r^2 + 2*pi*r*h = 54pi
2*pi*r^2 + 2*pi*r*h = 54pi
2pi*r(r + h) = 54pi
r(r+h) = 27
r(9) = 27
9r = 27
r = 27/9
r = 3
r+h = 9
h = 9-r
h = 9-3
h = 6
Answers: r = 3 and h = 6 are the radius and height respectively.
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Problem 10
d = diameter = 68 mm
r = radius = d/2 = 68/2 = 34 mm
SA = surface area of a sphere
SA = 4*pi*r^2
SA = 4*pi*34^2
SA = 4264pi
Answer: 4264pi square mm
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Problem 11
Plug V = 3000 into the sphere volume formula and isolate r.
V = (4/3)pi*r^3
3000 = (4/3)pi*r^3
(4/3)pi*r^3 = 3000
4pi*r^3 = 3*3000
4pi*r^3 = 9000
r^3 = 9000/(4pi)
r = cube root( 9000/(4pi) )
r = ( 9000/(4pi) )^(1/3)
r = 8.947002 approximately
Now we can determine the surface area of this sphere.
SA = 4pi*r^2
SA = 4*pi*( 8.947002 )^2
SA = 1005.923451
Answer: 1005.923451 square feet approximately
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Problem 12
We'll follow the same idea as problem 11, but in reverse.
SA = 4*pi*r^2
400pi = 4pi*r^2
r^2 = (400pi)/(4pi)
r^2 = 100
r = sqrt(100)
r = 10
Luckily we get a nice whole number for the radius r. Use it to find the volume.
V = (4/3)*pi*r^3
V = (4/3)*pi*10^3
V = (4000/3)pi
Answer: (4000/3)pi cubic inches exactly
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Problem 13
The diagram is missing. I don't have enough info to be able to answer.
Consider we need to find the equation of the circle.
Given:
The Center at (-4,-1), radius = 2.
To find:
The equation of the circle.
Solution:
The standard form of a circle is
Where, (h,k) is the center of the circle and r is the radius of the circle.
Putting h=-4, k=-1 and r=2, we get
Therefore, the equation of the circle is .
