29+18=47 17-8=9+47=56÷8=7 so its 7
Answer:
Side lengths = 1.68 ft and width = 3.36 ft.
Step-by-step explanation:
Let the side lengths of the window be L and the width = 2r ( r is also the radius of the semi-circle).
So we have
Perimeter = 2L + 2r + πr = 12
Area = 2rL + 0.5πr^2
From the first equation
2L = 12 - 2r - πr
Substitute for 2L in the equation for the area:
A = r(12 - 2r - πr) + 0.5πr^2
A = 12r - 2r^2 - πr^2 + 0.5πr^2
A = 12r - 2r^2 - 0.5πr^2
We need to find r for the maximum area:
Finding the derivative and equating to zero:
A' = 12 - 4r - πr = 0=
4r + πr = 12
r = 12 / ( 4 + π)
r = 1.68 ft.
So the width of the window = 2 * 1.68 = 3.36 ft.
Now 2L = 12 - 2r - πr
= 12 - 2*1.68 - 1.68π
= 3.36
L = 1.68.
Answer:
Step-by-step explanation:
The dominant term of this function is x^4. The graph of x^4 starts in Quadrant II and continues in Quadrant I.
If we have y = -x^4, the graph starts in Quadrant III and continues in Quadrant IV. This is the end behavior for f(x)=-x^4+5x^3-3.
Answer:
(5x = 2 = 3 +8a
Step-by-step explanation:
Answer:
Step-by-step explanation:
A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E.
Displacement in vector form
= 28 cos43 i + 28sin43j
= 20.47 i + 19.1 j
The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E
Displacement
= 15 cos47 i - 15 sin47 j
= 10.22 i - 10.97 j
Total displacement
= 20.47 i + 19.1 j + 10.22 i - 10.97 j
= 30.69 i - 8.13 j
Magnitude of displacement
= 31.75 miles
Angle with east direction
TanФ = - 8.13 / 30.69
Ф = 15 degree south of east.
