A carpenter is making a wooden window frame that has a width of 1 inch. How much wood does the carpenter need to build the frame
1 answer:
Diagram attached
Answer:
5.5+106 square inches
Step-by-step explanation:
The wooden frame has different shapes- semi circle, rectangles and we would have to calculate area of all the shapes to get the wood required.
To get area of the circle, we use the formula π(R²-r²)/2. Subtract the inner radius from the outer radius =
π(6²-5²)/2= 11π/2
=5.5π square inches
We add area of the semi circle to area of the 3 rectangles from the diagram:
2×1×48×10×1=106 square inches
The rectangle with 10 inches is because we subtracted one inch from both sides of the 12 inches rectangle to avoid repetition and overvaluing the area
Total area =5.5π +106 square inches
Options must have ommitted the "π"
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Answer:
vertex = (0, -4)
equation of the parabola:
Step-by-step explanation:
Given:
- y-intercept of parabola: -4
- parabola passes through points: (-2, 8) and (1, -1)
Vertex form of a parabola:
(where (h, k) is the vertex and is some constant)
Substitute point (0, -4) into the equation:
Substitute point (-2, 8) and into the equation:
Substitute point (1, -1) and into the equation:
Equate to find h:
Substitute found value of h into one of the equations to find a:
Substitute found values of h and a to find k:
Therefore, the equation of the parabola in vertex form is:
So the vertex of the parabola is (0, -4)
Answer:
6.667 ft/s
Step-by-step explanation:
Given
Height of street light = 15ft
Height of man = 6ft
Speed away from pole = 4ft/s
Let x represents the distance between the man and the pole, and Let y represents the distance between the tip of the man's shadow to the pole.
This forms a similar triangle (see attachment below).
From similar triangles, we have
(y - x)/6 = y/15 ----- Solve equation
15(y - x) = 6 * y
15y - 15x = 6y ---- Collect Like Terms
15y - 6y = 15x
9y = 15x --- divide through by 9
y = 15x/9
y = 5x/3 ---- differentiate with respect to time, t
dy/dt = 5/3 dx/dt
dx/dt represents rate of change of distance per time = 4ft/s
while dy/dt represents rate of movement of his shadow tips
dy/dt = 5/3 * 4
dy/dt = 20/3 = 6.667 ft/s
