Answer:
16m
Step-by-step explanation:
radius is half of diameter
Answer:
290
Step-by-step explanation:
These are rectangular prisms. The volume formula for a rectangular prism is
l x w x h.
I'll call the bottom cuboid 'Figure A'.
Figure A has a length of 8, a width of 5, and a height of 5. The volume formula is: 8 x 5 x 5. 40 x 5 =200
The volume of Figure A is 200.
I'll call the top cuboid Figure B.
Figure B has a length of 3, a width of 5, and a height of 6. That turns into
3 x 5 x 6.
The volume of Figure B is 90.
The volume of a composite figure is the sum of the figure's volume.
200+90=290
Draw a rectangle. If the length is 3 inches longer than its width, we can write the width as "w" and the length as the width + 3
Area is (width)(Length) = (width)(width+3)
W
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| | L = w+3
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A = (w+3)(w)
A = w2 + 3w = 108.
(Problem states that area is 108 sq in)
Need to solve this quadratic equation
w2 + 3y - 108 = 0
Factor:
(w - 9) (w + 12) = 0
So
w - 9 = 0. or. w + 12 = 0
Solve these and get
w = 9. or. w = -12
Only one that makes sense in real life is the poitive one.
So the dimensions are
Width = 9 inches
Length = 12 inches
Answer:
Let x represent the edge dimension of the square base in feet. Then the area of the base or lid is x², and the height of the box is 5/x². Total cost is then ...
... cost = cost of lid + 4×(cost of one side) + cost of bottom
... cost = 0.2x² + 4×(0.2x(5/x²)) + 0.5x²
... cost = 0.7x² + 4/x
We can differentiate this with respect to x and set that derivative to zero. This will give us the x-value at which the cost is a minimum.
... d(cost)/dx = 1.4x -4/x² = 0
... x³ = 4/1.4
... x = ∛(20/7) ≈ 1.419
Then the height of the box is
... height = 5/x² ≈ 5/2.01351 ≈ 2.483
The box is 1.491 ft square and 2.483 ft high.
______
The average cost of the top and bottom is (0.2 +0.5)/2 = 0.35 per square foot. The overall cost will be minimized when the average cost of each face is the same. That is, the areas of the lateral faces will be equal and must be 0.35/0.2 = 1.75 times the area of the top or bottom to make the average cost of a lateral face equal to that of the top or bottom. Hence, the base will be square, and the box will be 1.75 times as high as it is wide or deep. The base edge dimension is then ∛(5/1.75) ≈ 1.419 ft.
Step-by-step explanation:
You can go 21 days without exceeding your budget.
$19 x 21 (21 representing the days) = $399
Then you take $399 and add $45
$399 + $45 = $444
I hope this answer helped!