(10 elements..........) 2^(10)<span>=<span>1024
</span></span><span>A discrete set with n elements has 2^n subsets. 2^n=1024 implies there are n=10 elements in this set. Any subset with 0 through n-1 elements is a proper subset of the set, as in each of those cases there exists at least one element of the set that is not in the subset, which is the requirement to be a proper subset. Therefore, we have 1023 proper subsets.</span>
Let the width path be x.
Length of the outer rectangle = 26 + 2x.
Width of the outer rectangle = 8 +2x.
Combined Area = (2x + 26)*(2x + 8) = 1008
2x*(2x + 8) + 26*(2x + 8 ) = 1008
4x² + 16x + 52x + 208 = 1008
4x² + 68x + 208 - 1008 = 0
4x² + 68x - 800 = 0. Divide through by 4.
x² + 17x - 200 = 0 . This is a quadratic equation.
Multiply first and last coefficients: 1*-200 = -200
We look for two numbers that multiply to give -200, and add to give +17
Those two numbers are 25 and -8.
Check: 25*-8 = -200 25 + -8 = 17
We replace the middle term of +17x in the quadratic expression with 25x -8x
x² +17x - 200 = 0
x² + 25x - 8x - 200 = 0
x(x + 25) - 8(x + 25) = 0
(x+25)(x -8) = 0
x + 25 = 0 or x - 8 = 0
x = 0 -25 x = 0 + 8
x = -25 x = 8
The width of the path can not be negative.
The only valid solution is x = 8.
The width of the path is 8 meters.
Answer:
7 units
Step-by-step explanation:
These points lie on the same horizontal line.
No vertical distance
Only horizontal distance of:
15-8 = 7 units
Answer:
11.25pi units² or 35.3 units² (3 sf)
Step-by-step explanation:
½×r²×theta
½ × 5² × 0.9pi
11.25pi units²
Or, 35.3 units² (3 sf)
Answer:
29
Step-by-step explanation:
Given the function f(x) = x/10x-3, if x = 0.30103;
substituting the value of x into the function;
f(0.30103) = 0.30103/10(0.30103) - 3
f(0.30103) = 0.30103/(3.0103 - 3)
f(0.30103) = 0.30103/0.0103
f(0.30103) = 29.226
f(0.30103) = 29 (to nearest whole number).
