Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object.
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Answer:
x = theta = 0°
Step-by-step explanation:
Given the trigonometry function
Tan²x/2-2 cos x = 1
Tan²x-4cosx = 2 ... 1
From trigonometry identity
Sec²x = tan²x+1
tan²x = sec²x-1 ... 2
Substituting 2 into 1, we have:
sec²x-1 -4cosx = 2
Note that secx = 1/cosx
1/cos²x - 1 - 4cosx = 2
Let cosx. = P
1/P² - 1 - 4P = 2
1-P²-4P³ = 2P²
4P³+2P²+P²-1 = 0
4P³+3P² = 1
P²(4P+3) = 1
P² = 1 and 4P+3 = 1
P = ±1 and P = -3/4
Since cosx = P
If P = 1
Cosx = 1
x = arccos1
x = 0°
If x = -1
cosx = -1
x = arccos(-1)
x = 180°
Since our angle must be between 0 and 1 therefore x = 0°
Answer:
x = -1 and x = 5
Step-by-step explanation:
<em>What are the solutions of the equation (x – 3)² + 2(x – 3) -8 = 0? Use u substitution to solve.</em>
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(x – 3)² + 2(x – 3) -8 = 0 -------------------------------------------------------(1)
To solve this problem, we will follow the steps below;
let u = x-3
we will replace x-3 by u in the given equation:
(x – 3)² + 2(x – 3) -8 = 0
u² + 2u -8 = 0 ----------------------------------------------------------- --------------(2)
We will now solve the above quadratic equation
find two numbers such that its product gives -8 and its sum gives 2
The two numbers are 4 and -2
That is; 4×-2 = -8 and 4+(-2) = 2
we will replace 2u by (4u -2u) in equation (2)
u² + 2u -8 = 0
u² + 4u - 2u -8 = 0
u(u+4) -2(u+4) = 0
(u+4)(u-2) = 0
Either u + 4 = 0
u = -4
or
u-2 = 0
u = 2
Either u = -4 or u = 2
But u = x-3
x = u +3
when u = -4
x = u + 3
x = -4 + 3
x=-1
when u = 2
x = u + 3
x = 2 + 3
x=5
Therefore, x = -1 and x =5
x
Make sure that you are looking at the right boxes
Ok, there is no need to use a calculator for this.
Try and figure out what are the closest numbers for each one. For example, the first one, π, is lower than 4 but greater than 3. Therefore, it would be between 3 and 4.
