Answer:
Step-by-step explanation:
To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.
a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:
we can substitute the value of sec(θ) in this equation:
and solve for for cos(θ)
side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by 
b) since right triangle is mentioned in the question. We can use:
we know the value of cos(θ)=1\52. and by comparing the two. we can say that:
- length of the adjacent side = 1
- length of the hypotenuse = 52
we can find the third side using the Pythagoras theorem.
- length of the opposite side = √(2703) ≈ 51.9904
we can find the sin(θ) using this side:
and since 
We know that
[volume of a sphere]=(4/3)*pi*r³
length of a circumference=42 ft
[length of a circumference]=2*pi*r-------> r=[length of a circumference]/(2*pi)
r=[42]/(2*pi)---------> r=6.6845 ft
[volume of a sphere]=(4/3)*pi*6.6845³-----------> 1251.11 ft³
the answer is 1251.11 ft³
9514 1404 393
Answer:
r = 2
Step-by-step explanation:
The first differences between successive terms are ...
10 -5 = 5
20 -10 = 10
The differences are not constant, so the sequence is NOT arithmetic.
__
The ratios of successive terms are ...
10/5 = 2
20/10 = 2
The ratios are constant, so the sequence is ...
geometric with a common ratio of 2.
Answer:
2 sides of the patio are 9ft and another 2 sides are 15ft
Step-by-step explanation:
To solve this problem we have to know thata rectangle has 4 sides and 2 of them are equal to each other
This is the formula to calculate perimeter
p = perimeter 48 ft
a = side a = 9 ft
b = side b
p = 2a + 2b
we replace the known values
48ft = 2*9ft + 2b
48ft = 18ft + 2b
48ft - 18ft = 2b
30 / 2 = b
15 = b
2 sides of the patio are 9ft and another 2 sides are 15ft
Answer:
the answer is 2827.4
Step-by-step explanation:
