"<span>Curve passes through the point (0,8) and has the property that the slope of the curve at every point pp is four-times the y-coordinate."
Slope of tangent line at a given point = value of derivative of function at that point.
Thus, dy/dx = derivative = 4y
Thus, dy/dx = 4y. Rearrange this with all y on one side and all x on the other:
dy
--- = 4dx
y
Integrating both sides, we get ln|y| = 4x + ln C, or ln|y| - ln C = 4x
|y|
Then ln -------- =4x. This can be written as an exponential function:
C
|y|
--- = e^(4x). Thus, |y| = C*e^(4x). Given that this curve passes thru (0,8),
C
8 = C*e^0, so C = 8. Then the function question is y = 8e^(4x).</span>
Answer:
.
Step-by-step explanation:
We have been an division problem:
.
We will simplify our division problem using rules of exponents.
Using product rule of exponents
we can write:
![45^{45}=(9*5)^{45}=9^{45}*5^{45}](https://tex.z-dn.net/?f=45%5E%7B45%7D%3D%289%2A5%29%5E%7B45%7D%3D9%5E%7B45%7D%2A5%5E%7B45%7D)
![75^{30}=(15*5)^{30}=15^{30}*5^{30}](https://tex.z-dn.net/?f=75%5E%7B30%7D%3D%2815%2A5%29%5E%7B30%7D%3D15%5E%7B30%7D%2A5%5E%7B30%7D)
Substituting these values in our division problem we will get,
![\frac{9^{45}*5^{45}*3^{15}*5^{15}}{15^{30}*5^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B9%5E%7B45%7D%2A5%5E%7B45%7D%2A3%5E%7B15%7D%2A5%5E%7B15%7D%7D%7B15%5E%7B30%7D%2A5%5E%7B30%7D%7D)
Using power rule of exponents
we will get,
![\frac{9^{45}*5^{(45+15)}*3^{15}}{15^{30}*5^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B9%5E%7B45%7D%2A5%5E%7B%2845%2B15%29%7D%2A3%5E%7B15%7D%7D%7B15%5E%7B30%7D%2A5%5E%7B30%7D%7D)
![\frac{9^{45}*5^{60}*3^{15}}{15^{30}*5^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B9%5E%7B45%7D%2A5%5E%7B60%7D%2A3%5E%7B15%7D%7D%7B15%5E%7B30%7D%2A5%5E%7B30%7D%7D)
Using product rule of exponents
we will get,
![\frac{(3*3)^{45}*5^{60}*3^{15}}{(3*5)^{30}*5^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B%283%2A3%29%5E%7B45%7D%2A5%5E%7B60%7D%2A3%5E%7B15%7D%7D%7B%283%2A5%29%5E%7B30%7D%2A5%5E%7B30%7D%7D)
![\frac{3^{45}*3^{45}*5^{60}*3^{15}}{3^{30}*5^{30}*5^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B45%7D%2A3%5E%7B45%7D%2A5%5E%7B60%7D%2A3%5E%7B15%7D%7D%7B3%5E%7B30%7D%2A5%5E%7B30%7D%2A5%5E%7B30%7D%7D)
Using power rule of exponents
we will get,
![\frac{3^{(45+45+15)}*5^{60}}{3^{30}*5^{(30+30)}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B%2845%2B45%2B15%29%7D%2A5%5E%7B60%7D%7D%7B3%5E%7B30%7D%2A5%5E%7B%2830%2B30%29%7D%7D)
![\frac{3^{105}*5^{60}}{3^{30}*5^{60}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B105%7D%2A5%5E%7B60%7D%7D%7B3%5E%7B30%7D%2A5%5E%7B60%7D%7D)
![\frac{3^{105}}{3^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B105%7D%7D%7B3%5E%7B30%7D%7D)
Using quotient rule of exponent
we will get,
![\frac{3^{105}}{3^{30}}=3^{105-30}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B105%7D%7D%7B3%5E%7B30%7D%7D%3D3%5E%7B105-30%7D)
![3^{105-30}=3^{75}](https://tex.z-dn.net/?f=3%5E%7B105-30%7D%3D3%5E%7B75%7D)
Therefore, our resulting quotient will be
.
Answer:
C. Service
Step-by-step explanation:
Consulting is a type of service that helps businesses make good decisions when it comes to finances and business relationships with business partners and clientele.
Answer:
Step-by-step explanation:
3(8)+2(4)÷2(4)+8 PEDMAS
24+8÷8+8
24+1+8
25+8
33
Answer: 12 friends.
Step-by-step explanation:
the data we have is:
Mei Su had 80 coins.
She gave the coins to her friends, in such a way that every friend got a different number of coins, then we have that:
The maximum number of friends that could have coins is when:
friend 1 got 1 coin
friend 2 got 2 coins
friend 3 got 3 coins
friend N got N coins
in such a way that:
(1 + 2 + 3 + ... + N) ≥ 79
I use 79 because "she gave most of the coins", not all.
We want to find the maximum possible N.
Then let's calculate:
1 + 2 + 3 + 4 + 5 = 15
15 + 6 + 7 + 8 + 9 + 10 = 55
now we are close, lets add by one number:
55 + 11 = 66
66 + 12 = 78
now, we can not add more because we will have a number larger than 80.
Then we have N = 12
This means that the maximum number of friends is 12.