Find the circumference and the area of a circle with radius 5 ft Use the value 3.14 for pi and do not round your answers. Be sur
2 answers:
Answer:
Circumference: 31.4 ft
Area: 78.5
Step-by-step explanation:
To do the circumference of a circle, you have to do 2r, let's do 2x
=6.28. Now we will do 6.28x5= 31.4, So 31.4 ft is the answer.
To do the area of a circle you have to do r² so
x r². First we will do the radius first, 5x5=25, so we will do 3.14x25=78.5. So 78.5ft is the answer!
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Answer:
(1) 256 inches
(2) 5 feet
(3) 400 inches
(4) 10 feet
Step-by-step explanation:
(1) The function that gives the height in inches of the spray of water at a distance <em>x</em> from the sprinkler head is given as follows;
h(x) = 160·x - 16·x²
At x = 2 feet, we have;
h(2) = 160 × 2 - 16 × 2² = 256
Therefore, the height of the spray water at a horizontal distance of 2 feet from the sprinkler head h(2) = 256 inches
(2) The x-coordinate, , of the maximum point of a parabola given in the form, y = a·x² + b·x + c is found using the following formula;
= -b/(2·a)
The x-coordinate, , of the maximum point of the given equation of the parabola, h(x) = 160·x - 16·x², (a = -16, b = 160) is therefore;
= -160/(2 × (-16)) = 5
Therefore, the number of feet along the way, the function will reach maximum height, = 5 feet
(3) The function, h(x) = 160·x - 16·x², will reach maximum height, , at x = 5, therefore;
= h(5) = 160 × 5 - 16 × 5² = 400
The maximum height of the spray, = 400 inches
(4) The water is at ground level where h(x) = 0, therefore;
At ground level, h(x) = 0 = 160·x - 16·x²
160·x - 16·x² = 0
∴ 16·x × (10 - x) = 0
By zero product rule, we 16·x = 0, or (10 - x) = 0, from which we have;
x = 0, or x = 10
The water is at ground level at x = 0 and x = 10 feet, therefore, the water will hit the ground again (the second time after leaving the sprinkler head at x = 0) at x = 10 feet.