Multiply eq(1) by 2 and eq(2) by 1
Now
Put in eq(1)
-10 + 65 = -5m
55. = -5m
----- -----
-5 -5
-11. = m
There are two ways to solve the problem: using calculus and algebra. For this, I'll be using the algebraic way. The function is parabolic, thus the minimum value is the ordinate of the vertex. Using completing the square, we could get the vertex of the parabola.
y = x^2 + 4x - 5y = x^2 + 4x + 4 - 5 - 4y = (x + 2)^2 - 9Vertex is (-2, -9).
Therefore, the minimum value is -9.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Let's define variables:
x1: gear 1
x2: gear 2
The relationship between gears is:
x1 / x2 = (1 1/2) / (1/2)
Rewriting:
x1 / x2 = (3/2) / (1/2)
x1 / x2 = (3 * (1/2)) / (1/2)
x1 / x2 = 3
Another unit rate is:
x2 / x1 = (1/2) / (1 1/2)
x2 / x1 = (1/2) / (3/2)
x2 / x1 = (1/2) / (3 * (1/2))
x2 / x1 = 1/3
Answer:
two unit rates to represent the gear ratio are:
x1 / x2 = 3
x2 / x1 = 1/3
<u>2x - 3</u> = <u>2x - 4</u>
2 - x 1 - x
(2x - 3)(1 - x) = (2x - 4)(2 - x)
2x(1 - x) - 3(1 - x) = 2x(2 - x) - 4(2 - x)
2x(1) - 2x(x) - 3(1) + 3(x) = 2x(2) - 2x(x) - 4(2) + 4(x)
2x - 2x² - 3 + 3x = 4x - 2x² - 8 + 4x
-2x² + 2x - 3 + 3x = -2x² + 4x - 8 + 4x
-2x² + 2x + 3x - 3 = -2x² + 4x + 4x - 8
-2x² + 5x - 3 = -2x² + 8x - 8
<u>+ 2x² + 2x² </u>
5x - 3 = 8x - 8
<u> - 5x - 5x </u>
-3 = 3x - 8
<u>+ 8 + 8</u>
<u>-5</u> = <u>3x</u>
3 3
-1²/₃ = x
