Step-by-step explanation:
Notice that tan (75) can be written as sin(75)/cos(75) = sin(30 + 45) / cos(30 + 45)
And using a couple of trig identities, we have
[sin 30 cos 45 + sin 45 cos 30 ] / [cos 30 cos 45 -sin 30 sin 45] =
[ (1/2)(1/√2) +(1/√2))(√3/2)] / [ (√3/2) (1/√2) -(1/2) (1/√2) ] =
([1 + √3)] / [2 √2]) / ([√3 - 1] / [2 √2]) =
[ 1 + √3] / [√3 - 1] rationalizing the denominator, we have
[ 1 + √3] * [√3 + 1] / 2 =
[ 1 + √3 ] [ 1 + √3 ] / 2 =
[1 + 2√3 + 3] / 2 =
[4 + 2√3 ] / 2 =
2 + √3 so this is the exact value
Answer:
About 4.8
Step-by-step explanation:
The formula for the area is pi(r^2).
Plugging the area in to the equation, you get 72.382=pi(r^2).
Dividing both sides by pi, you get about 23.04=r^2.
Taking the square root of both sides you get about r=4.8
For f(x)=1/x^2-3
Find
A) f(3)
B) f(2-h)
If f(x)=1/x^2-3, then f(3) = 1 / 3^2 - 3. The exponentiation here must be carried out first: f(3) = 1/9 - 3. Then f(3) = 1/9 - 27/9 = -26/9
If f(x)=1/x^2-3, then f(2-h) = 1 / [2-h]^2 - 3. This result may be left as is or expanded. In expanded form, we have:
1
f(2-h) = ------------------ - 3
4-4h +h^2
We can solve the inequality first:
13x+2<4
13x<2 (subtract 2 from both sides)
x<2/13 or 0.15
So the only answer that falls in that range is 0
Hope this helps