We don't need the answers. Let's do the problems.
In triangle ABC with sides a,b,c labeled in the usual way, the Law of Sines is
Side a is opposite vertex A, etc.
1. A=46, B=29, a=x, b=5
a/sin A = b/sin B
a = b(sin A)/sin B
x = (5) sin 46 / sin 29 = 7.41878636786
Answer: x=7.4
2. We don't have to spell it all out with a, b and c.
x/sin 65 = 22/sin 53
x = 22 (sin 65)/sin 53 = 24.96604654309146
Answer: x=25.0
3. x/sin 15 = 12/sin 128
x = 12 sin 15/sin 128 = 3.941352991713482
Answer: 3.9
4. x = 18 sin 73 / sin 59 = 20.081827192002002 = 20.1
5. Trickier, we need the missing angle 180-19-26=135
x = 32 sin 19 / sin 135 = 14.73353278 = 14.7
6. 180-78-75=27
x = 28 sin 27 / sin 75 = 13.16015541 = 13.2
7. 180-51-70=59
x = 9 sin 59 / sin 70 = 8.20960549830328 = 8.2
8. 180-52-33=95
x/ sin 33 = 16/sin 95
x = 16 sin 33 / sin 95 = 8.747511482 = 8.7
Answer: 0.965
Step-by-step explanation:
Given : Water use in the summer is normally distributed with
Let X be the random variable that represents the quantity of water required on a particular day.
Z-score :
Now, the probability that a day requires more water than is stored in city reservoirs is given by:-
We can see that on comparing the above value to the given P(X > 350)= 1 - P(Z < b) , we get the value of b is 0.965.
Answer:
45.050 or rounded, 45
Step-by-step explanation:
since x is at the bottom then switch
which is 45.050
Answer:
a) See the proof below.
b)
Step-by-step explanation:
Part a
For this case we assume that we have the following series and this series has a finite radius of convergence
and we assume that
for all n, this information is given by the problem.
We assume that the series converges at the point since w eknwo that converges, and since converges we can conclude that:
For this case we need to show that converges also for
So we need to proof that
We can do some algebra and we can rewrite the following expression like this:
and we see that the last series is alternating.
Since we know that converges then the sequence {
} must be positive and we need to have
And then by the alternating series test we can conclude that also converges. And then we conclude that the power series
converges for
,and that complete the proof.
Part b
For this case we need to provide a series whose interval of convergence is exactly (-1,1]
And the best function for this
Because the series converges to
when
using the root test.
But by the properties of the natural log the series diverges at because
and for
we know that converges since
is an alternating series that converges because the expression tends to 0.