Answer:
The y intercept is 4, or (0,4).
Step-by-step explanation:
You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This point will always have an x coordinate of zero.
Answer:
The sheet should be turned up 7.5cm on each side to obtain maximum volume.
Step-by-step explanation:
If we make a rectangular eavesdrop, by bending the sheet along dotted line, then.
Height of eaves trough = x cm
Length of eaves trough = 600 cm
Width of eaves trough = (30 - 2x) cm
We know that Volume is given by:
V = Length · Width · Height
V = (x)(30 - 2x)(600)
V = -1200x² + 18000x
To maximize the volume, we take the derivative and put it equal to zero.
To be parallel it needs the same slope which is 8x. Now just replace the + 10 with the given y intercept.
Answer y = 8x -5
9514 1404 393
Answer:
60 m
Step-by-step explanation:
The difference in height is the short leg of a right triangle with long leg 35 m and hypotenuse 37 m.
(∆h)² + 35² = 37² . . . . . . . . . . the Pythagorean theorem
(∆h)² = 1369 -1225 = 144
∆h = √144 = 12 . . . meters
The taller building is 48 m + 12 m = 60 m high.
The answer is (2,4,6)
Proof:
Solve the following system:{x + y + z = 12 | (equation 1){2 x - y - z = -6 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Swap equation 1 with equation 2:{2 x - y - z = -6 | (equation 1){x + y + z = 12 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Subtract 1/2 × (equation 1) from equation 2:{2 x - y - z = -6 | (equation 1){0 x+(3 y)/2 + (3 z)/2 = 15 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Multiply equation 2 by 2/3:{2 x - y - z = -6 | (equation 1){0 x+y + z = 10 | (equation 2){x + 3 y + 5 z = 44 | (equation 3)
Subtract 1/2 × (equation 1) from equation 3:{2 x - y - z = -6 | (equation 1){0 x+y + z = 10 | (equation 2){0 x+(7 y)/2 + (11 z)/2 = 47 | (equation 3)
Multiply equation 3 by 2:{2 x - y - z = -6 | (equation 1){0 x+y + z = 10 | (equation 2)v0 x+7 y + 11 z = 94 | (equation 3)
Swap equation 2 with equation 3:{2 x - y - z = -6 | (equation 1){0 x+7 y + 11 z = 94 | (equation 2){0 x+y + z = 10 | (equation 3)
Subtract 1/7 × (equation 2) from equation 3:{2 x - y - z = -6 | (equation 1){0 x+7 y + 11 z = 94 | (equation 2){0 x+0 y - (4 z)/7 = (-24)/7 | (equation 3)Multiply equation 3 by -7/4:{2 x - y - z = -6 | (equation 1){0 x+7 y + 11 z = 94 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Subtract 11 × (equation 3) from equation 2:{2 x - y - z = -6 | (equation 1){0 x+7 y+0 z = 28 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Divide equation 2 by 7:{2 x - y - z = -6 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Add equation 2 to equation 1:{2 x + 0 y - z = -2 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)Add equation 3 to equation 1:{2 x+0 y+0 z = 4 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Divide equation 1 by 2:{x+0 y+0 z = 2 | (equation 1){0 x+y+0 z = 4 | (equation 2){0 x+0 y+z = 6 | (equation 3)
Collect results:
Answer: {x = 2, y = 4 , z = 6
