<em>y</em> - 1/<em>z</em> = 1 ==> <em>y</em> = 1 + 1/<em>z</em>
<em>z</em> - 1/<em>x</em> = 1 ==> <em>z</em> = 1 + 1/<em>x</em>
==> <em>y</em> = 1 + 1/(1 + 1/<em>x</em>) = 1 + <em>x</em>/(<em>x</em> + 1) = (2<em>x</em> + 1)/(<em>x</em> + 1)
<em>x</em> - 1/<em>y</em> = <em>x</em> - (<em>x</em> + 1)/(2<em>x</em> + 1) = (2<em>x</em> ² - 1)/(2<em>x</em> + 1) = 1
==> 2<em>x</em> ² - 1 = 2<em>x</em> + 1
==> 2<em>x</em> ² - 2<em>x</em> - 2 = 0
==> <em>x</em> ² - <em>x</em> - 1 = 0
==> <em>x</em> = (1 ± √5)/2
If you start solving for <em>z</em>, then for <em>x</em>, then for <em>y</em>, you would get the same equation as above (with <em>y</em> in place of <em>x</em>), and the same thing happens if you solve for <em>x</em>, then <em>y</em>, then <em>z</em>. So it turns out that <em>x</em> = <em>y</em> = <em>z</em>.
9514 1404 393
Answer:
y = x + 4
Step-by-step explanation:
To find the constant in the equation, look in the table for the value of y when x=0. That value is 4, so ...
y = x + 4
Answer:
x = -11/9
Step-by-step explanation:
7(x+3)=-2(x-5)
Distribute
7x+21 = -2x+10
Add 2x to each side
7x+21 +2x = -2x+10+2x
9x +21 = 10
Subtract 21 from each side
9x +21-21 = 10-21
9x = -11
Divide each side by 9
9x/9 = -11/9
x = -11/9
Step-by-step explanation:
A left Riemann sum approximates a definite integral as:
Given ∫₂⁸ cos(x²) dx:
a = 2, b = 8, and f(x) = cos(x²)
Therefore, Δx = 6/n and x = 2 + (6/n) (k − 1).
Plugging into the sum:
∑₁ⁿ cos((2 + (6/n) (k − 1))²) (6/n)
Therefore, the answer is C. Notice that answer D would be a right Riemann sum rather than a left (uses k instead of k−1).
I think it’s one half 1/2
