The angle between the planes is the same as the angle between their normal vectors, which are
<em>n</em><em>₁</em> = ⟨1, 1, 1⟩
<em>n</em><em>₂</em> = ⟨4, 3, 1⟩
The angle <em>θ</em> between the vectors is such that
⟨1, 1, 1⟩ • ⟨4, 3, 1⟩ = ||⟨1, 1, 1⟩|| ||⟨4, 3, 1⟩|| cos(<em>θ</em>)
Solve for cos(<em>θ</em>) :
4 + 3 + 1 = √(1² + 1² + 1²) √(4² + 3² + 1²) cos(<em>θ</em>)
8 = √3 √26 cos(<em>θ</em>)
cos(<em>θ</em>) = 8/√78
Take .50 and multiply it by 2 because it doubled. then multiply that by 6 or 12 to get your answer
Answer:
80 questions
Step-by-step explanation:
- 35/100 = 28/x
- 35x = 28(100)
- 35x = 2800
- x = 2800/35
- x = 80
Answer:
I get 20
Step-by-step explanation:
While there probably is some logical way to go about this I just did it in excel
screenshot below
For Part A, what to do first is to equate the given equation to zero in order to find your x intercepts (zeroes)
0=-250n^2+3,250n-9,000 after factoring out, we get
-250(n-4)(n-9) and these are your zero values.
For Part B, you need to square the function from the general equation Ax^2+Bx+C=0. So to do that, we use the equated form of the equation 0=-250n^2+3,250n-9,000 and in order to have a positive value of 250n^2, we divide both sides by -1
250n^2-3,250n+9,000=0
to simplify, we divide it by 250 to get n^2-13n+36=0 or n^2-13n = -36 (this form is easier in order to complete the square, ax^2+bx=c)
in squaring, we need to apply <span><span><span>(<span>b/2</span>)^2 to both sides where our b is -13 so,
(-13/2)^2 is 169/4
so the equation now becomes n^2-13n+169/4 = 25/4 or to simplify, we apply the concept of a perfect square binomial, so the equation turns out like this
(n-13/2)^2 = 25/4 then to find the value of n, we apply the square root to both sides to obtain n-13/2 = 5/2 and n is 9. This gives us the confirmation from Part A.
For Part C, since the function is a binomial so the graph is a parabola. The axis of symmetry would be x=5.
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