Answer:
The volume is 1386 cm³ and curved surface area is 396 cm².
Step-by-step explanation:
Given that,
The diameter of a cylinder is 14 cm
Height of the cylinder is 9 cm
We need to find the volume and curved surface area .
If r is the radius, r = 14/2 = 7 cm
Volume of a cylinder is given by :
The curved surface area of the cylinder is given by :
So, the volume is 1386 cm³ and curved surface area is 396 cm².
Answer:
1) 2 seconds
2) 70 feet
Step-by-step explanation:
we have the formula h = -16x² + 64x + 6
where h = height of ball and x = time in seconds
for 1 , we want to find how long it will take the ball to reach its maximum height.
if we want to find how long it will take to reach its maximum height , then we want to find the x value of vertex ( vertex = peak point and in this situation represents the maximum height and time ) as x = time in this scenario.
the x value of the vertex can be calculated using the formula x = -b/2a
where a and b derive from the formula put in quadratic form ax² + bx + c
so we have -16x² + 64x + 6 , 16 takes the spot of a so a = -16 and 64 takes the spot of b so b = 64
x = -b/2a
b = -16 and a = 64
hence, x = -(64)/2(-16)
==> remove parenthesis
x = -64/2(-16)
==> multiply 2 and -16
x = -64/-32
==> divide -64 by -32
x = 2
The x value of the vertex is two meaning it will take two second for the ball to reach its maximum height.
For 2) we want to find how high the ball will be when it reaches its maximum height
In other words we want to find the y value of the vertex as y = height of ball and we want to find the height of the ball at its maximum height which is at the vertex.
to find the y value of the vertex we simply plug in the x value into the equation and evaluate
we have -16x² + 64x + 6 and the x value of the vertex is 2
so we get -16(2)² + 64(2) + 6
==> evaluate exponent
y = -16(4) + 64(2) + 6
==> multiply -16 and 4
y = -64 + 64(2) + 6
==> the -64 cancels out the x2 in 64(2)
y = 64 + 6
==> add 64 and 6
y = 70
The y value of the vertex is 70 meaning the ball was at 70 feet at its maximum height
For more validation check the attatched image
we know that
The hallway is painted using equal amounts of white and black paint
so
To know the amount of white paint------> calculate the area of white paint
To know the amount of black paint------> calculate the area of black paint
equate the areas
<u>Find the length of the hallway</u>
therefore
<u>the answer part a) is</u>
The hallway is long
<u>Part b) </u>Can this same hallway be painted with the same pattern, but using twice as much black paint as white paint?
we know that
the amount of white paint is
if the black paint is twice that the white paint
then
amount of black paint is
amount of black paint with the same pattern is
equate
(24+24x)\ ft^{2}=(60x)\ ft^{2}
solve for the new value of x
<u>Find the new length of the hallway</u>
therefore
<u>the answer is</u>
Yes, the same hallway can be painted with the same pattern, using twice as much black paint as white paint, but the hallway decreases in length