Answer:
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
Step-by-step explanation:
8 cos^2 x + 4 cos x-4 = 0
Divide by 4
2 cos^2 x + cos x-1 = 0
Let u = cos x
2 u^2 +u -1 =0
Factor
(2u -1) ( u+1) = 0
Using the zero product property
2u-1 =0 u+1 =0
u = 1/2 u = -1
Substitute cosx for u
cos x = 1/2 cos x = -1
Take the inverse cos on each side
cos ^-1(cos x) = cos ^-1(1/2) cos ^-1( cos x) =cos ^-1( -1)
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
This is an equation representing the ellipse
Explanation:
- The general equation for an ellipse is
so, when you simplify it according to the characteristics of a and b, you would end up in the similar form of the equation given
- where a represents half the length of the major axis and b represents half the length of the minor axis.
- The easiest method to identify, look at whether both the variables are squared, and also the coefficient of x and y should be positive but different.
<u><em>Answer:</em></u>
<u><em>1. x=4 or x=10</em></u>
<u><em>2. x=-10 or x=10</em></u>
<em>No equivalent</em>
<em />
Step-by-step explanation:
1. |x-3|=7 and x-3=7
<em>Absoulte rules.</em>
<em>x-3=-7 and x-3=7</em>
<em>Add 3 both sides.</em>
<em>x-3+3=-7+3</em>
<em>Simplify.</em>
<em>-7+3=-4</em>
<em>x=-4</em>
<em>x-3=7</em>
<em>Add by 3 both sides.</em>
<em>x-3+3=7+3=10</em>
<em>x=10</em>
<em>X=-4, and X=10 is the correct answer.</em>
<em>________________________________</em>
<em>2. |x|-3=7</em>
<em>Add by 3 both sides.</em>
<em>|x|-3+3=7+3</em>
<em>Simplify.</em>
<em>7+3=10</em>
<em>X=10</em>
<em>X=-10 and X=10 is the correct answer.</em>
<em>______________________________</em>
Answer:
B
Step-by-step explanation:
Answer: 80.5
Step-by-step explanation:
Given that,
Base of Triangle = 23 ft
Height of Triangle = 7 ft
We know,
Area of Triangle
= 0.5 × Base × Height unit^2
=(0.5 × 23 × 7) ft^2
= 80.5
