(1/2)(n - 4) - 3 = 3 - (2n + 3
Distribute the (1/2) on the left and the -1 on the right.
(1/2)n - 2 - 3 = 3 - 2n - 3
Combine like terms.
(1/2)n - 5 = -2n
Add 2n to both sides and add 5 to both sides
2.5n = 5
Divide both sides by 2.5
n = 2
Binomial theorem:
The
term corresponds with the term in the sum for which
. For this
, we get
So the coefficient you want to find is
Answer:
<h3>36 and 12</h3>
Step-by-step explanation:
Let the two positive integers be x and y.
If their product is 432, then
xy = 432 ......... 1
Also if the sum of the first plus three times the second is a minimum, then;
p(x) = x + 3y
From 1;
y = 432/x ..... 3
Substitute 3 into 2;
p(x) = x+3y
p(x)= x + 3(432/x)
p(x) = x + 1296/x
Since the expression is at minimum when dp(x)/dx = 0
dp/dx = 1 + (-1296)/x²
dp/dx = 1 -1296/x²
0 = 1 -1296/x²
0 = (x²-1296)/x²
cross multiply
0 = x²-1296
x² = 1296
x = √1296
x = 36
Since xy = 432
36y = 432
y = 432/36
y = 12
Hence the two positive numbers are 36 and 12
The area of the triangle is (1/2)(DE)^2*tan(60°) = (1/2)*2*√3 = √3.
Selection C is appropriate.
The answer is A) P’(5,4)Q’(2,7)
hope this helped .
