To solve, set an equation:
472=0.8x
Divide both sides by 0.8
472/0.8=0.8x/0.8
x=590
Answer: The original price was $590
Answer:
5 feet & 15 feet
Step-by-step explanation:
<em>The question is to find the lengths of 2 sides of the rectangle</em>.
<u>Solution:</u>
Let shorter side be "x"
Let longer side be "y"
From the question, we can write:
y = 3x
also
y - x = 10
Now, putting the first on second equation, we get:
y - x = 10
3x - x = 10
2x = 10
x = 10/2 = 5
Now, y = 3x, y = 3(5) = 15
So we can say the lengths of 2 sides of the rectangle is 5 feet & 15 feet
So, I came up with something like this. I didn't find the final equation algebraically, but simply "figured it out". And I'm not sure how much "correct" this solution is, but it seems to work.
![f(x)=\sin(\omega(x))\\\\f(\pi^n)=\sin(\omega(\pi^n))=0, n\in\mathbb{N}\\\\\\\sin x=0 \implies x=k\pi,k\in\mathbb{Z}\\\Downarrow\\\omega(\pi^n)=k\pi\\\\\boxed{\omega(x)=k\sqrt[\log_{\pi} x]{x},k\in\mathbb{Z}}](https://tex.z-dn.net/?f=f%28x%29%3D%5Csin%28%5Comega%28x%29%29%5C%5C%5C%5Cf%28%5Cpi%5En%29%3D%5Csin%28%5Comega%28%5Cpi%5En%29%29%3D0%2C%20n%5Cin%5Cmathbb%7BN%7D%5C%5C%5C%5C%5C%5C%5Csin%20x%3D0%20%5Cimplies%20x%3Dk%5Cpi%2Ck%5Cin%5Cmathbb%7BZ%7D%5C%5C%5CDownarrow%5C%5C%5Comega%28%5Cpi%5En%29%3Dk%5Cpi%5C%5C%5C%5C%5Cboxed%7B%5Comega%28x%29%3Dk%5Csqrt%5B%5Clog_%7B%5Cpi%7D%20x%5D%7Bx%7D%2Ck%5Cin%5Cmathbb%7BZ%7D%7D)
We want to see how much the population of goats grows each year. We will see that the correct option is c: 17%.
<h3>
Exponential growth of populations</h3>
We know that:
- The initial number of goats is 1,500.
- After 11 years, the population is 8,400.
The population can be modeled with an exponential equation as:
P(t) = A*(1 + r)^t
Where:
- A is the initial population.
- r is what we want to find, it depends on how much the population increases.
- t is the time in years.
So we have:
P(t) = 1500*(1 + r)^t
And we know that after 11 years the population is 8,400, so we have:
P(11) = 1500*(1 + r)^11 = 8400
Now we can solve this for r:
(1 + r)^11 = 8400/1500 = 5.6
(1 + r) = (5.6)^(1/11) = 1.17
r = 1.17 - 1 = 0.17
r = 0.17
To get it in percentage form, you just need to multiply it by 100%
0.17*100% = 17%
This means that the population increases a 17% each year, so the correct option is c.
If you want to learn more about exponential growth, you can read:
brainly.com/question/13223520
Evaluate the derivative of f(x) at x = 1. I'll use the limit definition:
Then using the point-slope formula, the equation of the tangent line to f(x) at the point (1, 5) is
y - 5 = 9 (x - 1)
y = 9x - 4
