Answer:
(k ∘ p)(x) = 2x^2 − 12x + 13
Step-by-step explanation:
k(x) = 2x^2 − 5 and p(x) = x − 3,
(k ∘ p)(x).= k(p(x))
This means put the function p(x) in for x in the function k(x)
(k ∘ p)(x) = 2(p(x)^2) -5
= 2(x-3)^2 -5
= 2 (x-3)(x-3) -5
FOIL
=2(x^2 -3x -3x+9) -5
=2 (x^2 -6x+9) -5
= 2x^2 -12x +18 -5
Combine like terms
= 2x^2 -12x +13
If the value of cos(θ) is negative, this angle (θ) can only be in one of two quadrants; the sine quadrant or the tan quadrant. In the sine quadrant, tan(θ) must be negative, but since tan(θ) > 0, we can safely say that the angle (<span>θ) is based in the tan quadrant.
We know that cos(</span><span>θ) = - Adjacent / Hypotenuse, and in this case Adjacent = 2 and Hypotenuse = 5. Using Pythagoras' theorem, we can find the opposite side of the right angled triangle situated in the tan quadrant...
</span>Adjacent² + Opposite² = Hypotenuse²
Therefore:
2² + Opposite² = 5²
Opposite² = 5² - 2²
Opposite² = 21
Opposite = √(21)
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Now, sin(θ) must be negative, as the right angled triangle is in the tan quadrant. We also know that sin(<span>θ) = Opposite / Hypotenuse, therefore:
sin(</span><span>θ) = - [</span>√(21)]/[5]
Answer: b. number of trees
Step-by-step explanation:
The concept of geometric probability is basically use when we have continuous data .
Since it is impossible to count continuous data , but geometrically ( in form of length, area etc) we can count the outcomes in general to calculate the required probability.
Therefore, from the given options , Option b. "number of trees" would not be used for geometric probability because among all it is the only discrete case which is countable.
Rest of items ( a. area of a rug , c. length of time , d. length of a field) would be used for geometric probability,
Answer:7 is 433.5
9 is 104
10 is 165.92
Step-by-step explanation: