Answer:
see below
Step-by-step explanation:
sin x 1
------------------- = -----------
sec^2 x - tan ^2 x csc x
Sec = 1/cos and tan = sin/cos
sin x 1
------------------- = -----------
1/ cos ^2 x -sin^2/cos ^2 x csc x
Factor the denominator
sin x 1
------------------- = -----------
(1-sin^2 x)/ cos ^2 x csc x
We know that 1 - sin^2 x = cos ^2
sin x 1
------------------- = -----------
(cos^2 x)/ cos ^2 x csc x
sin x 1
------------------- = -----------
1 csc x
Multiply the top and bottom of the left hand side by 1/ sin x
sin x * 1/ sin x 1
------------------- = -----------
1 * 1 sin x csc x
1 1
------------------- = -----------
1 sin x csc x
We know that 1/sin x = csc
1 1
--------- = -----------
csc (x) csc x
Answer:
198.95 cm²
Step-by-step explanation:
Circumference = 50cm
C = πD
D = C/π
r = D/2
r = 50/π/2
r= 7.957747…..cm
Area = π r²
A = π x 7.957747….²
A = 198.95 cm² (2dp)
Answer:

Step-by-step explanation:
Given



Required
The volume of the remaining cylinder
Before the cut-out, the cylinder has a volume (V) of:

After the cut-out, the cylinder has a volume of:
![V = \pi [R^2 -r^2]h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5BR%5E2%20-r%5E2%5Dh)
So, we have:
![V = 3.14* [6^2 -5^2]*15](https://tex.z-dn.net/?f=V%20%3D%203.14%2A%20%5B6%5E2%20-5%5E2%5D%2A15)
![V = 3.14* [36 -25]*15](https://tex.z-dn.net/?f=V%20%3D%203.14%2A%20%5B36%20-25%5D%2A15)


Answer:
Step-by-step explanation:
Answer:
4 miles/1 day=56 miles/X days
X=56/4=14
Step-by-step explanation: