<span>4 x 362 = 4 x (300 + 60 + 2) = 4 x 300+ 4 x 60 + 4 x 2 = 1200 + 240 + 8 + 1448</span>
The solution to the problem is as follows:
let y = asinx + bcosx
<span>
dy/dx = acosx - bsinx </span>
<span>
= 0 for max/min </span>
<span>
bsinx = acosx </span>
<span>
sinx/cosx = a/b </span>
<span>
tanx = a/b </span>
<span>
then the hypotenuse of the corresponding right-angled triangle is √(a^2 + b^2) </span>
<span>the max/min of y occurs when tanx = a/b </span>
<span>
then sinx = a/√(a^2 + b^2) and cosx = b/√(a^2 + b^2) </span>
<span>
y = a( a/√(a^2 + b^2)) + b( b/√(a^2 + b^2)) </span>
<span>
= (a^2 + b^2)/√(a^2 + b^2) </span>
<span>
= √(a^2 + b^2)</span>
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If the number is 'xy'
Y-x=3
7xy=4yx
y=3+x
7(10x+y) =4(10y+x)
70x+7y=40y+4x
3+x=y
70x+7(3+x) =40(3+x) +4x
70x+21+7x=120+40x+4x
77x+21=120+44x
77x-44x=120-21
33x=99
x=3
y=x+3
y=3+3
y=6
Hence The number is 36....
Answer:
It takes Nick alone 7.5 days to finish painting a house.
Step-by-step explanation:
Let the speed of Brad's painting be B
Let the speed of Nick's painting be N
And let the amount of work required to paint a house be H
Let the time it takes Nick alone to finish painting a house be t
(Speed of painting) = (amount of work to be done)/(total time it takes to finish)
From the question,
B = (H/5) (eqn 1)
N = (H/t) (eqn 2)
But they both paint a house in 3 days
In 3 days, Brad does (3×B) amount of work and Nick does (3×N) amount of work too.
Therefore, H = 3B + 3N (eqn 3)
Recall (eqn 1) and (eqn 2) and substitute for B and N in (eqn 3)
H = 3B + 3N
B = (H/5); N = (H/t)
H = (3H/5) + (3H/t)
1 = (3/5) + (3/t)
Multiply through by 5t
5t = 3t + 15
5t - 3t = 15
2t = 15
t = (15/2) = 7.5 days
8) A. x + 2,
2) B. f(x) = (x -3) (x +9).
Step-by-step explanation:
Step 1; If the function equals 0, we substitute all the separate factors to 0. We keep the variable on the left side while all the other values go to the right side.
If f(x) = (x +3) (x -9) = 0, then x +3 = 0, x -9 = 0. So x = -3 and x = 9.
If f(x) = (x -3) (x +9) = 0, then x -3 = 0, x +9 = 0. So x = 3 and x = -9.
If f(x) = (x -3) (x -9) = 0, then x -3 = 0, x -9 = 0. So x = 3 and x = 9.
If f(x) = (x +3) (x +9) = 0, then x +3 = 0, x +9 = 0. So x = -3 and x = -9.
So if the factors are 3 and -9, option B is an answer.
Step 2; For the given graph, the same applies. The graph passes through the points of (-2, 0) and (4, 0) on the x-axis.
So if x = -2, then x +2 = 0 and if x = 4, x -4 = 0. The first equation is option A while the second equation is not given.
