Cot(-x) = 1 / tan(-x)
Tan(-x) * 1 / tan(-x) = 1
Answer:
B. -1
Step-by-step explanation:
x^3-4x^2+2x+10=x^2-5x-3
We know it has 3 roots since it is a 3rd degree polynomial.
Two of the roots are (3+2i) and (3-2i)
Subtract x^2-5x-3 from both sides
x^3-4x^2+2x+10-(x^2-5x-3)=x^2-5x-3 -(x^2-5x-3)
Distribute the minus sign
x^3-4x^2+2x+10-x^2+5x+3=x^2-5x-3 -x^2+5x+3
x^3 -5x^2+7x +13 =0
Graphing this equation , we see that it crosses the x axis at x=-1
That covers the three roots, 1 real and two complex
P(x) that will be R(x) - C(x):
Note the use of parentheses! Without them we would not realize that both the 21 and the 98 should be subtracted.
Now that we have our profit function, we can see that:<span>Its graph will be a parabola because of the squared term.The parabola will open downward because of the negative coefficient, -2, in front of the squared term.The highest point (which would be the maximum profit) on the downward parabola would be the vertex of the parabola.</span>From the above we now know that we want to find the vertex of the profit parabola.
The x coordinate of the vertex of a parabola will be -b/2a where the "b" is the coefficient of the x term and the "a" is the coefficient of the x squared term. From p(x)= -2^2 + 34x-98
we can see that your "a" is -2 and your "b" is 34. So the x coordinate of the vertex (which is where the maximum profit is) will be: -34/-2=17
Answer: 117cm^2
Step-by-step explanation:
Arectangle = L*W
= 54cm^2
Atrapezoid = 1/2 (a+b) (h)
= 1/2 (15+6) (6)
= 1/2 (21) (6)
= 1/2 (126)
= 63cm^2
Answer:

Step-by-step explanation:
Given.
In a deck, there are:


Required
Determine the probability that a selected card is a spade
This is represented as: P(Spade) and it is calculated using:

Substitute 13 for Spade and 52 for Cards


<em>Hence, the required probability is 0.25</em>