Hello from MrBillDoesMath!
Answer:
@ = pi/3 (or 60 degrees) or @ = 7 pi/3 (or 420 degrees)
Discussion:
Let "@' denote the angle "theta". We are asked to find @ in the interval [0, 4 pi)
where
4cos(@) - 2 = 0. Adding 2 to both sides
4 cos(@) - 2 +2 = 2 =>
4 cos(@) = 2 Divide both sides by 4
cos(@) = 2/4 = 0.5
This implies that @ = pi/3 (or 60 degrees) or @ = (pi/3 + 2pi) = 7 pi/3 (or 420 degrees)
Thank you,
MrB
Answer:
You will be paying $41.30 in total.
Step-by-step explanation:
The cost of the meal is $35 and you want to leave 18% tip on the meal.
We want to find the total amount that will be paid.
First, we have to find 18% of $35 and then, add it to the original bill ($35).
18% of 35 is:
18/100 * 35 = $6.30
The tip is $6.30, therefore, the total amount paid will be:
$35 + $6.30 = $41.30
You will be paying $41.30 in total.
Well, I bet you want your answer right away! So here it is.
<span>Given <span>f (x) = 3x + 2</span> and <span>g(x) = 4 – 5x</span>, find <span>(f + g)(x), (f – g)(x), (f × g)(x)</span>, and <span>(f / g)(x)</span>.</span>
To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.
(f + g)(x) = f (x) + g(x)
= [3x + 2] + [4 – 5x]
= 3x + 2 + 4 – 5x
= 3x – 5x + 2 + 4
= –2x + 6
(f – g)(x) = f (x) – g(x)
= [3x + 2] – [4 – 5x]
= 3x + 2 – 4 + 5x
= 3x + 5x + 2 – 4
= 8x – 2
(f × g)(x) = [f (x)][g(x)]
= (3x + 2)(4 – 5x)
= 12x + 8 – 15x2 – 10x
= –15x2 + 2x + 8
<span>\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}<span><span>(<span><span>g</span><span>f</span><span></span></span>)</span>(x)=<span><span><span>g(x)</span></span><span><span>f(x)</span></span><span></span></span></span></span><span>= \small{\dfrac{3x+2}{4-5x}}<span>=<span><span><span>4−5x</span></span><span><span>3x+2</span></span><span></span></span></span></span>
My answer is the neat listing of each of my results, clearly labelled as to which is which.
( f + g ) (x) = –2x + 6
( f – g ) (x) = 8x – 2
( f × g ) (x) = –15x2 + 2x + 8
<span>\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}<span><span>(<span><span>g</span><span>f</span><span></span></span>)</span>(x)=<span><span><span>4−5x</span></span><span><span>3x+2</span></span><span>
Hope I helped! :) If I did not help that's okay.
-Duolingo
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