Answer:
- y = 81-x
- the domain of P(x) is [0, 81]
- P is maximized at (x, y) = (54, 27)
Step-by-step explanation:
<u>Given</u>
- x plus y equals 81
- x and y are non-negative
<u>Find</u>
- P equals x squared y is maximized
<u>Solution</u>
a. Solve x plus y equals 81 for y.
y equals 81 minus x
__
b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.
P equals x squared left parenthesis 81 minus x right parenthesis
__
c. Find the domain of the function P found in part b.
left bracket 0 comma 81 right bracket
__
d. Find dP/dx. Solve the equation dP/dx = 0.
P = 81x² -x³
dP/dx = 162x -3x² = 3x(54 -x) = 0
The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...
P is maximized at (x, y) = (54, 27).
Theres only 3 shapes that can form such regualr tessellations triangle square and regular hexagon so that being said triangle is your answer
K, so here we go:
1. 3/4 + 3/4. When adding fractions, you only add the numerator or whole numbers (doesn't have a whole number, but the numerator's are the top numbers) NOT the denominator (bottom number) Add 3+3, and this gives you 6. Keep the 4 the same, and you get 6/4. The answer is 6/4, but you can make this a proper fraction, and say it's 1 and 2/4 (one is the whole number, it's like the 4 in number 3)
2. 2- 1 and 1/8. This is just subtraction, subtract the whole numbers first. 2-1=1. now, assume the 2 is 2 and 0/8, and you just took away 1. Now, it's 1 and 0/8. Now, take away another 1/8 and you get 7/8
3. Just division. The Answer is 3/2, or 1 and 1/2
4. Simple division again. Divide 15 by 3. You get 5. This is 1/3 of 15, because 5*3=15.
5. An 8 sided polygon is known as an octagon.
6. A=B*H (Area= base times height.)
7. A quarter is 4. It takes 4 quarter pounds to make a pound (think like money. a quarter is 25 cents. it takes 4 quarters to make a dollar. If you want 60 dollars, how many quarters would you need?) Well, take 60*4, and you get 240. You can make 240 quarter pounders from 60 pounds of meat.
___________________________________________________________
TO CLARIFY:
1= 6/4 OR 1 and 2/4
2= 7/8
3=3/2 OR 1 and 1/2
4=5
5=Octagon.
6: A=B*H
7. 240 quarter pounders
Answer:
8b
Step-by-step explanation:
'8 times b' symbolizes 8 being multiplied by 'b'.
Times is a word associated with multiplying.
8 times b can be 8 * b or most ideally, 8b.
Hope this helps!