so, 2 raised to what power would make 32?? it would be 5 because 2^5=32
2^1=1
2^2=4
2^3=16
2^5=32
Let the length be x and the width be w
The perimeter will be:
2x+3w=1500
thus
3w=(1500-2x)
w=(1500-2x)/3
w=500-2/3x
The area will be:
A=x*w
A=x(500-2/3x)
A=500x-(2/3)x²
The above is a quadratic equation; thus finding the axis of symmetry we will evaluate for the value of x that will give us maximum area.
Axis of symmetry:
x=-b/(2a)
from our equation:
a=(-2/3) and b=500
thus
x=-500/[2(-2/3)]
x=375
the length will be 375 m
The width will be 250 m
Hum, this problem was difficult. You use the next expression to solve this problem. \[\cos (A - B) = \cos A \cos B + \sin A \sin B \] \[\cos (A + B) = \cos A \cos B - \sin A \sin B\] \[\cos (A - B ) - \cos (A +B ) =2 \sin A \sin B\] So \[\sin A \sin B = 0.5 \left( \cos(A - B) - \cos(A + B) \right)\] A = 1.8 x, B = 0.5 x \[\sin (1.8x) \sin (0.5x) = 0.5\left( \cos(1.8-0.5)x - \cos(1.8+0.5)x \right)\]\[= 0.5 \left( \cos(1.3x) - \cos (2.3x) \right)\] It's finish !!
Answer:
c & d
Step-by-step explanation:
Factor x^2 + 3 x − 10 using the AC method
Answer:
x = 4, y = 1
(4, 1)
Step-by-step explanation:
-2x - y = -9
5x -2y = 18
-2x - y = -9
+2x +2x
-y = 2x - 9
/-1 /-1
y = -2x + 9
5x -2y = 18
5x - 2(-2x + 9) = 18
5x + 4x - 18 = 18
9x - 18 = 18
+ 18 + 18
9x = 36
/9 /9
x = 4
Now, we solve for y:
-2(4) - y = -9
-8 - y = -9
+ 8 +8
-y = -1
/-1 /-1
y = 1
(x, y) -> (4, 1)
Hope this helps!
