Answer:
See below.
Step-by-step explanation:
((sinA.cosB+cosA.sinB)^2)+(cosA.cosB-sinA.sinB)^2=1
The 2 halves of this expression are the identities for [sin(A + B)]^2 and
[(cos (A + B)] ^2 respectively , therefore:
((sinA.cosB+cosA.sinB)^2)+(cosA.cosB-sinA.sinB)^2 = [sin(A + B)]^2 +
[(cos (A + B)] ^2
Using the identity sin^2Ф + cos^2Ф = 1 we see that if we put Ф = (A + B) we have
[sin(A + B)]^2 + [(cos (A + B)] ^2 = 1 so the identity
((sinA.cosB+cosA.sinB)^2)+(cosA.cosB-sinA.sinB)^2 = 1 must be true also.
Answer: 81
To get this answer, you do two things
1) Take half of the x coefficient 18 to get 9
2) Square the result from the previous step to get 9^2 = 9*9 = 81
This value is added on to get x^2+18x+81 which factors to (x+9)^2 confirming we have a perfect square trinomial
Answer: it will take 9 hours to empty the pool.
Step-by-step explanation:
The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is
30 × 18 × 4 = 2160 ft³
If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + d(n - 1)
Where
a represents the first term of the sequence(initial amount of water in the pool when completely full).
d represents the common difference(rate at which it is being pumped out)
n represents the number of terms(hours) in the sequence.
From the information given,
a = 2160 degrees
d = - 216 ft3
Tn = 0(the final volume would be zero)
We want to determine the number of terms(hours) for which Tn would be zero. Therefore,
0 = 2160 - 216 (n - 1)
2160 = 216(n - 1) = 216n + 216
216n = 2160 - 216
216n = 1944
n = 1944/216
n = 9
Because a line always goes past the y-intercept and x-intercept. It's not always both, it can sometimes just be the x-intercept or the y-intercept.
When a line intersects these points, for example if a line was to intersect the x-axis then y would be equal to 0, and the opposite for the y-axis. If a line was to intersect the y-axis x would be equal to 0.
Therefore by using that knowledge, and the equation of the line [ y=mx+c or y-y1=m(x-x1) ], we can find the equation of our line. Of course you would need the gradient of that line (the value "m").
