Answer:
center: (0,0)
vertices: (-4,0) and (4,0)
foci: (-10.8,0) and (10.8,0)
asymptotes: y = -5/2*x and y = 5/2*x
Step-by-step explanation:
Hyperbola with center as origin general equation is:
x²/a² - y²/b² = 1
Our equation is:
25x² - 4y² = 400
Dividing each term by 400:
25x²/400 - 4y²/400 = 400/400
x²/16 - y²/100 = 1
which matches the general equation. Then, the center is (0,0)
a² = 16
a = 4
b² = 100
b = 10
c² = a² + b²
c = √(16+100) = 10.8
General vertices formula: (±a,0). Replacing, the vertices are: (-4,0) and (4,0)
General foci formula: (±c,0). Replacing, the foci are: (-10.8,0) and (10.8,0)
General asymptotes formula: y = ±b/a*x. Replacing, the asymptotes are:
y = -10/4*x = -5/2*x
y = 10/4*x = 5/2*x
Answer:
y=-25x+225
Step-by-step explanation:
The slope is -25 and I think the y-intercept is 225.
Hope this helps.
Here is our profit as a function of # of posters
p(x) =-10x² + 200x - 250
Here is our price per poster, as a function of the # of posters:
pr(x) = 20 - x
Since we want to find the optimum price and # of posters, let's plug our price function into our profit function, to find the optimum x, and then use that to find the optimum price:
p(x) = -10 (20-x)² + 200 (20 - x) - 250
p(x) = -10 (400 -40x + x²) + 4000 - 200x - 250
Take a look at our profit function. It is a normal trinomial square, with a negative sign on the squared term. This means the curve is a downward facing parabola, so our profit maximum will be the top of the curve.
By taking the derivative, we can find where p'(x) = 0 (where the slope of p(x) equals 0), to see where the top of profit function is.
p(x) = -4000 +400x -10x² + 4000 -200x -250
p'(x) = 400 - 20x -200
0 = 200 - 20x
20x = 200
x = 10
p'(x) = 0 at x=10. This is the peak of our profit function. To find the price per poster, plug x=10 into our price function:
price = 20 - x
price = 10
Now plug x=10 into our original profit function in order to find our maximum profit:
<span>p(x)= -10x^2 +200x -250
p(x) = -10 (10)</span>² +200 (10) - 250
<span>p(x) = -1000 + 2000 - 250
p(x) = 750
Correct answer is C)</span>
Step-by-step explanation:
I think the answer should be y = 36 ( 3x) as the numbers in the sequence are being divide by 3
<h3>
Answer: D) 130.5 degrees</h3>
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Work Shown:
Note: I used the law of cosines. Make sure your calculator is in degree mode.
