(x+1) x (3x-4) is the answer
Drawing a diagram of a triangle may be helpful. The hypotenuse is irrelevant, but the vertical leg and the horizontal leg are useful. Since we know the engineer is looking up at a 45 degree angle from a distance of 200 feet, we can label the vertical leg the "opposite", since it is on the opposite side of the angle we are given. The horizontal leg then becomes the "adjacent". You can then use trigonometry to solve for the opposite.
The options are:
sin(theta)= opposite/hypotenuse
cos(theta)= adjacent/hypotenuse
tan(theta)= opposite/adjacent
Since we don't care about the hypotenuse, the last equation is the one to use. The angle we are given can be substituted in for theta:
tan(45)= x/200
1.61977519= x/200
x= 323.955038 feet
Given:
The radius, r=4x
The height,

To find the volume of the cone:
The volume of the cone formula is,

Substitute the values of r and h in the above formula we get,

Hence, the volume of the cone is

Thus, the correct option is option D.
Answer:
The ages of the four siblings are: 5, 7, 9 and 11 years old.
Step-by-step explanation:
The computation of the age of the four siblings is shown below:
Given that
n = 4
a1 =? a2 =? a3 =? a4 =?
a4 = a1 + 6 years
S4 = 32
Based on the above information
As we know that
Sn = (a1 + a4) × n ÷ 2
S4 = (a1 + a4) × 4 ÷ 2
32 = (a1 + a1 +6) × 2
16 = 2a1 + 6
2a1 = 10
a1 = 10 ÷ 2
= 5
So, a4 = a1 +6
= 5 +6
= 11
a4 = a1 + (4-1) × d
11 = 5 + 3 × d
d = 6 ÷ 3
= 2
So,
a2 = a1 + d
= 5 + 2
= 7
a3 = a2 + d
= 7 + 2
= 9
Hence, The ages of the four siblings are: 5, 7, 9 and 11 years old.
Answer:
1296 cm²
Step-by-step explanation:
36² = 1296 cm²
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