Answer:
Step-by-step explanation:
We are given that:
And we want to find sec(θ).
First, note that both sine and tangent are positive. The only quadrant in which this can occur is QI. Hence, all trig ratios will be positive.
Also, recall that sine is the ratio of the opposite side to the hypotenuse. Using this information and the Pythagorean Theorem, we can determine the adjacent side:
So, with respect to θ, the adjacent side is √(17), the opposite side is 8, and the hypotenuse is 9.
Secant is the ratio of the hypotenuse to the adjacent. Hence:
Again, since θ is in QI, all trig ratios are positive.
Okay, so to make 1.95 a 2 we need to add .05. Now we can just figure out the difference between 2 and 13 and add the .05 later.
13-2=11, so we know the difference between 1.95 and 13 is 11.05.
Answer:
<T = 83
Step-by-step explanation:
In a parallelogram <M = < P and < N = <T (opposite angles are congruent)
We also know that <M + <N = 180 ( consecutive angles are supplementary)
<M + <N = 180
6x+10 + 5x+10.5 = 180
Combine like terms
11x+20.5 = 180
Subtract 20.5 from each side
11x +20.5-20.5 = 180-20.5
11x = 159.5
Divide each side by 11
11x/11 = 159.5/11
x=14.5
We can find <N
<N = 5x+10.5
= 5(14.5)+105
=72.5 +10.5
= 83
<N = <T = 83
Those are vertical angles so must be equal
X+95=90
X= -5°
So that whole angle is 90°
Step-by-step explanation:
Let x = m² and y = 4n.
Then m⁶ - 64n³ = x³ - y³
= (x - y)(x² + xy + y²)
= (m² - 4n)(m⁴ + 4m²n + 16n²).