First hour: 3 = 3¹
Second hour: (3) x 3 = 3²
Third hour: (3 x 3) x 3 = 3³
Fourth hour: (3 x 3 x 3) x 3 = 3⁴
Do you see the pattern? <em>
where n is the number of hours</em>
Answer: 3³,
Your income is the money you receive or acquire it's the inflow and your total expenses are the money you spent it's the outflow
Answer:
A) y = -1/2x + 1/2
Step-by-step explanation:
Find the y-intercept(when x = 0), which is 1/2.
Find the slope: m = y2-y1 / x2-x1
I used points: (3, -1), (-3,2)
m = 2 - (-1) / -3 - 3
m = 3 / - 6
m = -1/2
plug this into the slope intercept form equation: y = mx + b
y = -1/2x + 1/2
Answer:
a) 3C1 * 12 C1 / 15 C2
b) 1 - 12C2 / 15C2
Step-by-step explanation:
Được
Viên bi đỏ = 3
Viên bi trắng = 5
Viên bi xanh = 7
Hai quả bóng được rút ra một cách ngẫu nhiên
a) Có 1 bi đỏ
3C1 * 12 C1 / 15 C2
b) Có ít nhất 1 viên bi đỏ trong số 2 viên lấy ra.
Số kết quả của việc chọn hai quả bóng trong số 15 quả bóng = 15 C2
Số kết quả của việc chọn 0 quả bóng đỏ = 15C12
Xác suất chọn được ít nhất 1 viên bi đỏ = 1 - 12C2 / 15C2
Answer:
A) A[p(t)] = 36πt²
B) 7234.56 square units
Step-by-step explanation:
<u>Given functions</u>:
<u>Part A</u>
To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):
![\begin{aligned}A(p) & = \pi p^2\\\\ \implies A[p(t)] & = \pi [p(t)]^2\\& = \pi (6t)^2\\& = \pi 6^2 t^2\\& = 36\pi t^2\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%28p%29%20%26%20%3D%20%5Cpi%20p%5E2%5C%5C%5C%5C%20%5Cimplies%20A%5Bp%28t%29%5D%20%26%20%3D%20%5Cpi%20%5Bp%28t%29%5D%5E2%5C%5C%26%20%3D%20%5Cpi%20%286t%29%5E2%5C%5C%26%20%3D%20%5Cpi%206%5E2%20t%5E2%5C%5C%26%20%3D%2036%5Cpi%20t%5E2%5Cend%7Baligned%7D)
<u>Part B</u>
Given
Substitute the given values into the equation for A[p(t)} found in part A:
![\begin{aligned}A[p(8)] & = 36\pi t^2\\& = 36 \cdot 3.14 \cdot 8^2\\& = 36 \cdot 3.14 \cdot 64\\& = 113.04 \cdot 64\\& = 7234.56\:\: \sf square\:units\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%5Bp%288%29%5D%20%26%20%3D%2036%5Cpi%20t%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%208%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%2064%5C%5C%26%20%3D%20113.04%20%5Ccdot%2064%5C%5C%26%20%3D%207234.56%5C%3A%5C%3A%20%5Csf%20square%5C%3Aunits%5Cend%7Baligned%7D)
Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.
