Answer:
129.996 cubic feet
Step-by-step explanation:
Assuming that the barrel is a perfect cylinder, we can use the formula to find the volume:

First, we have to find the radius, which is:
D = 2r
So the radius is 3 feet, since it is half of the diameter. Then, we plug in the values.

Now, we solve. Exponents are first...
3.14(9)(4.6)
Now multiply left to right.
28.26(4.6)
129.996 cubic feet
Therefore, the barrel can hold 129.996 cubic feet of oil. Hope this helps you!
Answer:
1.5 seconds
Step-by-step explanation:
Since f(x) represents the distance from the ground to the rock (in feet), we just need to find the values of x for which f(x) = 340. Substituting f(x) = 340 into f(x) = -16x² - 4x + 382 gives us:
340 = -16x² - 4x + 382
0 = -16x² - 4x + 42 (Subtract 340 from both sides)
16x² + 4x - 42 = 0 (Multiply entire equation by -1, "flip" equation)
8x² + 2x - 21 = 0 (Divide entire equation by 2)
(4x + 7)(2x - 3) = 0 (Factor LHS)
4x + 7 = 0 or 2x - 3 = 0 (Zero Product Property)
4x = -7 or 2x = 3 (Subtract -7 and add 3 from/to both sides, respectively)
or 
x = -1.75 is an extraneous solution because in the context of the question, you can't have negative seconds so therefore, the final answer is 1.5 seconds.
Hope this helps!
Answer:
x = 7.5
y = 14
m<1 = 87°
m<7 = 93°
Step-by-step explanation:
Given:
m<2 = (14x - 12),
m<6 = (5y + 23),
m<8 = (8x + 27)
m<2 + m<8 = 180° (consecutive exterior angles are supplementary)
(14x - 12) + (8x + 27) = 180 (substitution)
Solve for x
14x - 12 + 8x + 27 = 180
Collect like terms
22x + 15 = 180
Subtract 15 from each side
22x = 180 - 15
22x = 165
Divide both sides by 22
x = 7.5
m<2 = m<6 (corresponding angles are congruent)
(14x - 12) = (5y + 23) (substitution)
Plug in the value of x
14(7.5) - 12 = 5y + 23
105 - 12 = 5y + 23
93 = 5y + 23
Subtract 23 from each side
93 - 23 = 5y
70 = 5y
Divide both sides by 5
14 = y
y = 14
✅m<1 = m<8 (alternate exterior angles are congruent)
m<1 = (8x + 27) (substitution)
Plug in the value of x
m<1 = 8(7.5) + 27 = 87°
m<7 = m<2 (alternate exterior angles are congruent)
m<7 = (14x - 12) (substitution)
Plug in the value of x
m<7 = 14(7.5) - 12 = 93°
Answer:
d=107
Step-by-step explanation:
7+5^2 *4
PEMDAS
Since there are no parentheses, we do exponents next
7+25*4
Then we multiply
7+100
Then we add
107