Answer:
{4, - 1}
Step-by-step explanation:
Given
2y² - 6y - 8 = 0 ← in standard form
with a = 2, b = - 6, c = - 8
Using the quadratic formula to solve for y
y = ( - (- 6) ±
) / (2 × 2)
= ( 6 ±
) / 4
= ( 6 ±
) / 4
= ( 6 ± 10 ) / 4
x =
=
= 4
OR
x =
=
= - 1
Solution is { 4, - 1 }
Alright, lets get started.
Please take a look at the diagram attached.
The reference angle of 75 will be 75
As it is mentioned that the angle intersects the unit circle means r = 1
So, finding cos
cos 75 = ![\frac{X}{r}](https://tex.z-dn.net/?f=%5Cfrac%7BX%7D%7Br%7D)
cos 75 = ![\frac{0.259}{1}](https://tex.z-dn.net/?f=%5Cfrac%7B0.259%7D%7B1%7D)
cos 75 = 0.259 is the Answer
Hope it will help :)
Well, <T+<S will equal 11x +2
so the equation will be 5x+10 + 58 = 11x +2
5x + 68 = 11x +2
66 = 6x (subtract 2, subtract 5x)
x = 11 (division)
To check,
<T = 5 (11) +10
<T = 65
11(11)+2 = 123
<T+<S = 123
65+58 = 123
Answer:
![\text{1. } v=16t+\frac{h-c}{t},\\\text{2. }90\:\mathrm{ft/s}, \\\text{3. Cannot be determined}](https://tex.z-dn.net/?f=%5Ctext%7B1.%20%7D%20v%3D16t%2B%5Cfrac%7Bh-c%7D%7Bt%7D%2C%5C%5C%5Ctext%7B2.%20%7D90%5C%3A%5Cmathrm%7Bft%2Fs%7D%2C%20%5C%5C%5Ctext%7B3.%20Cannot%20be%20determined%7D)
Step-by-step explanation:
1. The initial equation given to us is
. Rearranging the equation to isolate
, we have:
![vt=16t^2+h-c,\\\boxed{v=16t+\frac{h-c}{t}}](https://tex.z-dn.net/?f=vt%3D16t%5E2%2Bh-c%2C%5C%5C%5Cboxed%7Bv%3D16t%2B%5Cfrac%7Bh-c%7D%7Bt%7D%7D)
2. Using the equation we rearranged in part 1, we can substitute given values:
![v=16(3)+\frac{131-5}{3},\\v=48+42=\boxed{90\:\mathrm{ft/s}}](https://tex.z-dn.net/?f=v%3D16%283%29%2B%5Cfrac%7B131-5%7D%7B3%7D%2C%5C%5Cv%3D48%2B42%3D%5Cboxed%7B90%5C%3A%5Cmathrm%7Bft%2Fs%7D%7D)
3. We see from our equation in part 1 (
) that when
, the denominator of our fraction will be equal to 0. Since we cannot divide by 0, the velocity remains undefined and cannot be determined.
The remainder from the division of the algebraic equation is -53/8.
<h3>What is the remainder of the algebraic expression?</h3>
The remainder of the algebraic expression can be determined by using the long division method.
Given that:
![\mathbf{f(x) = \dfrac{x^3 - 6x^2 + 3x - 1}{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%20%3D%20%5Cdfrac%7Bx%5E3%20-%206x%5E2%20%2B%203x%20-%201%7D%7B2x-3%7D%7D)
where:
Using the long division method, we have:
![\mathbf{= \dfrac{x^2}{2} +\dfrac{-\dfrac{9x^2}{2}+3x -1 }{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D%20%2B%5Cdfrac%7B-%5Cdfrac%7B9x%5E2%7D%7B2%7D%2B3x%20-1%20%7D%7B2x-3%7D%7D)
![\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} +\dfrac{-\dfrac{-15x}{4}-1 }{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D-%5Cdfrac%7B9x%7D%7B4%7D%20%2B%5Cdfrac%7B-%5Cdfrac%7B-15x%7D%7B4%7D-1%20%7D%7B2x-3%7D%7D)
![\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}+\dfrac{-\dfrac{53}{8} }{2x-3}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D-%5Cdfrac%7B9x%7D%7B4%7D%20-%5Cdfrac%7B15%7D%7B8%7D%2B%5Cdfrac%7B-%5Cdfrac%7B53%7D%7B8%7D%20%7D%7B2x-3%7D%7D)
![\mathbf{= \dfrac{x^2}{2}-\dfrac{9x}{4} -\dfrac{15}{8}-\dfrac{53 }{8(2x-3)}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%3D%20%5Cdfrac%7Bx%5E2%7D%7B2%7D-%5Cdfrac%7B9x%7D%7B4%7D%20-%5Cdfrac%7B15%7D%7B8%7D-%5Cdfrac%7B53%20%7D%7B8%282x-3%29%7D%7D)
Therefore, we can conclude that the remainder is -53/8.
Learn more about the division of algebraic equations here:
brainly.com/question/4541471
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