Answer:
The rectangular prism has dimensions of 5 inches by 7 inches by 8 inches. The volume can be calculated as follows:
Length of base multiplied by width of base multiplied by height.
Volume = 5 × 7 × 8 = 280 cubic inches
A golf ball is spherical. The volume formula for a sphere is:
Volume of a sphere = 4/3πr^3
Given a golf ball's diameter of 1.7 inches, the radius is 1.7/2 = 0.85 inches.
Thus, the volume for each golf ball is calculated as follows:
Volume of each golf ball = 4/3 × 3.14 × 0.85^3
= 2.57 cubic inches
The number of golf balls fitting into the compartment calculates to:
Volume of compartment divided by volume of each golf ball, resulting in
280/2.57 equals 109 golf balls.
Step-by-step explanation:
Answer:
The height of the rock after 3.2 seconds has passed.
Step-by-step explanation:
To respond to this question, we must examine the provided function:
h(t) = –16t2 + 28t + 500
This function h(t) denotes the height of a rock t seconds after it has been launched by a slingshot.
t signifies time (in seconds)
As t is the independent variable and h is the dependent variable, the height of the rock at 3.2 seconds is expressed as h(3.2).
If you have any further questions or need clarification, feel free to ask.
Answer:
The outcomes are listed below.
Step-by-step explanation:
Only the differential costs will be considered. Therefore, the costs associated with sugar beets and their processing are not relevant to the decision.
Beet fiber:
Sold as is for $25
Continued processing yields = 57 - 16= $41
It is more favorable to further process the beet fiber.
Beet juice:
Sold as is for $39
Continued processing yields = 84 - 22= $62
Continuing the processing of beet juice is also more advantageous.
The expense incurred by a company to create "x"....
This indicates what X represents. (The term expense relates to what the function will convey. In other terms, C(x) = The expense for the company))
Consequently, as we progress, the problem further continues:
.... bracelets
Thus, the quantity of bracelets is X.
The function is: C(x)
Functions operate in an uncomplicated manner. You input a value (x) and obtain a value (y) as a result.
Hence, C(256) = 1536
So, they produced 256 bracelets at a cost of 1536 dollars.
This is analogous to stating the function is:
C(x) = 6x
and then inquiring about the function's value when x = 256. It's effectively identical, so don’t let it confound you!
Result 1: 1536$
Result 2: 256
Response:
Volume of the trapezoidal prism = 15x^2 cubic units
Detailed explanation:
First, let’s calculate the area of the trapezoidal bases.
The lengths of the parallel sides are x and 2x, averaging to 1.5x.
The height stands at x
Consequently, area of the trapezoidal base comes out to be 1.5x * x = 1.5x^2
The volume of this prism is computed as area of the base multiplied by height
(the length is not a factor, but height certainly is)
Thus, 1.5x^2 * 10 yields 15x^2
