Answer:
k = 11.
Step-by-step explanation:
y = x^2 - 5x + k
dy/dx = 2x - 5 = the slope of the tangent to the curve
The slope of the normal = -1/(2x - 5)
The line 3y + x =25 is normal to the curve so finding its slope:
3y = 25 - x
y = -1/3 x + 25/3 <------- Slope is -1/3
So at the point of intersection with the curve, if the line is normal to the curve:
-1/3 = -1 / (2x - 5)
2x - 5 = 3 giving x = 4.
Substituting for x in y = x^2 - 5x + k:
When x = 4, y = (4)^2 - 5*4 + k
y = 16 - 20 + k
so y = k - 4.
From the equation y = -1/3 x + 25/3, at x = 4
y = (-1/3)*4 + 25/3 = 21/3 = 7.
So y = k - 4 = 7
k = 7 + 4 = 11.
0.813 is your answer because 7 is higher than 5 which means you have to round it up and not down
Answer:
Option B.
Step-by-step explanation:
The demand function is

where p is price.
Solve the demand equation for p.


The revenue function is

Substitute the value of p in the above function.


Differentiate with respect to q.

Equate R'(q)=0,


Divide both sides by 2.

Therefore, the correct option is B.
<span>Given:
75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. </span>→ 25% goes to other schools.
<span>
five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. </span>→ 7% of the 5-star recruits don't get full football scholarships.<span>
a. The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
75% * 93% = 69.75%
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?
25% of selected five-star recruit will not select a university from one of the three best conferences. I got the number based on the given data. Since, 75% will go, the remaining percent won't go. Total percentage should be 100% of the population.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive?
These are independent events. One can still go to different school and still be legible for the full football scholarship.
For question 2, pls. see attachment.</span>
Answer:
You can view a kite as 4 triangles
Step-by-step explanation:
A geometric kite can easily be viewed as 4 triangles. The formula to calculate the area of a kite (width x height)/2 is very similar to the one of a triangle (base x height)/2.
According to the formula to calculate the area of a kite, we would get:
(36 x 30)/2 = 540.
If we take the approach of using 4 triangles, we could imagine a shape formed by 4 triangles measuring 18 inches wide with a height of 15.
The area of each triangle would then be: (18 x 15)/2 = 135
If we multiply this 135 by 4... we get 540.