Answer:
vertex = (4, - 8 )
Step-by-step explanation:
The equation of a quadratic in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = (x - 4)² - 8 ← is in vertex form
with (h, k ) = (4, - 8 ) ← coordinates of vertex
Answer:
Time taken by the un powered raft to cover this distance is T = 192.12 hr
Step-by-step explanation:
Let speed of boat = u 
Speed of current = v
Let distance between A & B = 100 km
Time taken in downstream = 32 hours
u + v = 3.125 ------ (1)
Time taken in upstream = 48 hours
u - v = 2.084 ------- (2)
By solving equation (1) & (2)
u = 2.6045
v = 0.5205
Now the time taken by the un powered raft to cover this distance
Because un powered raft travel with the speed of the current.
T = 192.12 hr
Therefore the time taken by the un powered raft to cover this distance is
T = 192.12 hr
1.8, Problem 37: A lidless cardboard box is to be made with a volume of 4 m3
. Find the
dimensions of the box that requires the least amount of cardboard.
Solution: If the dimensions of our box are x, y, and z, then we’re seeking to minimize
A(x, y, z) = xy + 2xz + 2yz subject to the constraint that xyz = 4. Our first step is to make
the first function a function of just 2 variables. From xyz = 4, we see z = 4/xy, and if we substitute
this into A(x, y, z), we obtain a new function A(x, y) = xy + 8/y + 8/x. Since we’re optimizing
something, we want to calculate the critical points, which occur when Ax = Ay = 0 or either Ax
or Ay is undefined. If Ax or Ay is undefined, then x = 0 or y = 0, which means xyz = 4 can’t
hold. So, we calculate when Ax = 0 = Ay. Ax = y − 8/x2 = 0 and Ay = x − 8/y2 = 0. From
these, we obtain x
2y = 8 = xy2
. This forces x = y = 2, which forces z = 1. Calculating second
derivatives and applying the second derivative test, we see that (x, y) = (2, 2) is a local minimum
for A(x, y). To show it’s an absolute minimum, first notice that A(x, y) is defined for all choices
of x and y that are positive (if x and y are arbitrarily large, you can still make z REALLY small
so that xyz = 4 still). Therefore, the domain is NOT a closed and bounded region (it’s neither
closed nor bounded), so you can’t apply the Extreme Value Theorem. However, you can salvage
something: observe what happens to A(x, y) as x → 0, as y → 0, as x → ∞, and y → ∞. In each
of these cases, at least one of the variables must go to ∞, meaning that A(x, y) goes to ∞. Thus,
moving away from (2, 2) forces A(x, y) to increase, and so (2, 2) is an absolute minimum for A(x, y).
Answer:
It takes 3.5 seconds for the ball to hit the ground
Step-by-step explanation:
By finding the x intercepts you can determine when the ball hits the ground.
the second x intercept is (3.5,0), which means the ball hits the ground at 3.5 seconds
Answer:
B (3/4,5/4)
Step-by-step explanation:
y = 2- x
y = 3x - 1
Hope this helps ^-^
