Answer:
200
Step-by-step explanation:
the formula for working out the area is to multiply the length by the width.
so for this you would multiply 100 by 2 which gives you 200 cm squared
What is the product?
1 answer:
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The dimensions of the box are 10 ft and 5 ft
The maximum volume is 500 ft³
Step-by-step explanation:
A rectangle box with
- A square base and no top
- It needs to be made using 300 ft² of material
- It has greatest volume
Surface area of a box without top (SA) = perimeter of base × height + area of the base
Volume of a box (V) = base area × height
Assume that the length of the side of the square base is x and the height of the box is y
∵ It needs to be made using 300 ft² of material
∴ The surface area of the box is 300 ft²
∵ Its base is a square of side length x ft
∴ Perimeter of the base = 4 × x = 4 x
∴ Area of the base = x²
∵ The height of the box = y ft
∵ SA = perimeter of base × height + area of the base
∵ SA = (4x)(y) + x²
∴ SA = 4xy + x²
∵ SA of the box = 300 ft²
- Equate the two expressions of SA
∴ 4xy + x² = 300
Now let us find y in terms of x
- Subtract x² from both sides
∴ 4xy = 300 - x²
- Divide each term by 4x to find y
∴
∵ V = area of the base × height
∴ V = x² × y = x²y
- Substitute y by the equation of it above
∴
∴
∵ The volume of the box is greatest
- That means differentiate V and equate it by 0
∵
∵ ⇒ greatest volume
∴
- Subtract 75 from both sides
∴
- Divide both sides by
∴ x² = 100
- Take √ for both sides
∴ x = 10
Substitute the value of x in the equation of y
∵
∴ y = 5
The dimensions of the box are 10 ft and 5 ft
∵
∵ x = 10
∴
∴
∴ V = 750 - 250
∴ V = 500 ft³
The maximum volume is 500 ft³
Learn more:
You can learn more about the volume in brainly.com/question/6443737
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Answer:
For this case we define the dependent variable as Y and the independent variable X. We assume that we have n observations and that means the following pairs:
For this case we assume that we want to find a linear regression model given by:
Where:
represent the estimated slope for the model
represent the estimated intercept for the model
And for any estimation of the dependent variable is given by this model.
The difference between the observed value of the dependnet variable and the value predicted using the estimated regression equation is known as residual, and the residual is given by this formula:
So the best option for this case is:
d. residual
Step-by-step explanation:
For this case we define the dependent variable as Y and the independent variable X. We assume that we have n observations and that means the following pairs:
For this case we assume that we want to find a linear regression model given by:
Where:
represent the estimated slope for the model
represent the estimated intercept for the model
And for any estimation of the dependent variable is given by this model.
The difference between the observed value of the dependnet variable and the value predicted using the estimated regression equation is known as residual, and the residual is given by this formula:
So the best option for this case is:
d. residual