Answer:
5+2x=23
Step-by-step explanation:
The number of rides you went on is 9.
F(x) = x² - 13x + 30
f(x) = x² - 3x - 10x + 30 = 0
f(x) = x(x - 3) -10(x - 3) = 0
f(x) = (x-3)(x-10) = 0
f(x) = 3 OR 10
In short, Your Answer would be Option B & D
Hope this helps!
21/0.3= 70
there were 70 raisins in the box
Answer:
x = 28 m
y = 14 m
A(max) = 392 m²
Step-by-step explanation:
Rectangular garden A (r ) = x * y
Let´s call x the side of the rectangle to be constructed with a rock wall, then only one x side of the rectangle will be fencing with wire.
the perimeter of the rectangle is p = 2*x + 2*y ( but in this particular case only one side x will be fencing with wire
56 = x + 2*y 56 - 2*y = x
A(r) = ( 56 - 2*y ) * y
A(y ) = 56*y - 2*y²
Tacking derivatives on both sides of the equation we get:
A´(y ) = 56 - 4 * y A´(y) = 0 56 - 4*y = 0 4*y = 56
y = 14 m
and x = 56 - 2*y = 56 - 28 = 28 m
Then dimensions of the garden:
x = 28 m
y = 14 m
A(max) = 392 m²
How do we know that the area we found is a local maximum??
We find the second derivative
A´´(y) = - 4 A´´(y) < 0 then the function A(y) has a local maximum at y = 14 m
Answer:
- C. π(3in)2(12in) − 9(four over threeπ(1.5in)3)
Step-by-step explanation:
Volume of water is the difference of volume of vase at 12 in height and the total volume of marbles.
<u>Volume of cylinder up to water level:</u>
- Vs = πr²h = π(6/2)²(12) = π×(3 in)²×(12 in)
<u>Volume of marbles:</u>
- Vm = 9(4/3πr³) = 9×(4/3×π(3/2)³) = 9×(4/3×π×(1.5 in)³)
<u>Volume of water:</u>
- Vw = Vs - Vm = π×(3 in)²×(12 in) - 9×(4/3×π×(1.5 in)³)
Correct choice is C
