Answer:Graphs of inverse functions have a domain and range just like any other graph of a function. The domain of an inverse function is the range of the original, and the range of an inverse function is the domain of an original.
Step-by-step explanation:
20x = 2*100
x = 10 ml (amt of 30% solution needed)
100-x = 90 ml (amt of 10% solution needed)
Very hard but I hope it helps
Answer:
<h2>472.5 cubic feet.</h2>
Step-by-step explanation:
The dimensions of the tent are 9 by 15 at the base and 7 units of height. So, the voume is defined as
Replacing all given values, we have
Therefore, the right answer is the second choice.
Step-by-step explanation:
sin
2
(
20
°
)
+
sec
2
(
20
°
)
Simplify each term.
Tap for fewer steps...
Rewrite
sec
(
20
°
)
in terms of sines and cosines.
sin
2
(
20
°
)
+
(
1
cos
(
20
°
)
)
2
Apply the product rule to
1
cos
(
20
°
)
.
sin
2
(
20
°
)
+
1
2
cos
2
(
20
°
)
One to any power is one.
sin
2
(
20
°
)
+
1
cos
2
(
20
°
)
Simplify each term.
Tap for fewer steps...
Rewrite
1
as
1
2
.
sin
2
(
20
°
)
+
1
2
cos
2
(
20
°
)
Rewrite
1
2
cos
2
(
20
°
)
as
(
1
cos
(
20
°
)
)
2
.
sin
2
(
20
°
)
+
(
1
cos
(
20
°
)
)
2
Convert from
1
cos
(
20
°
)
to
sec
(
20
°
)
.
sin
2
(
20
°
)
+
sec
2
(
20
°
)
The result can be shown in multiple forms.
Exact Form:
sin
2
(
20
°
)
+
sec
2
(
20
°
)
Decimal Form:
1.24945210
The volume of the cube is base times width times height, or any of these measurements cubed, since they're all the same.
Therefore, the volume of the cube is:
12³ = 1728 in³
The volume of the cylinder is π*r²*h, where r is the radius and h is height
Remember that the diameter is twice the radius, so the radius is 2 in and the height is 5 in.
Therefore, each can has a volume of π * 2² * 5 = 20π
Approximating π as 3.14....
The volume of each can is 62.8 in³
1728 ÷ 62.8 = 27.5
Rounding down, 27 cans can fit in the crate.
This is how I suspect the teach wanted you to solve, since it involves finding the volume of both shapes and using pi. However, this is not actually how many cans can fit, because it does not take into account the fact that not every inch of available space will be used.
Here is another way to solve,taking this fact into account, that gives the more accurate answer:
Each can has a diameter of 4in, which means that they each require a square of 4 x 4 in to accommodate their base.
The base of each can requires 16 in² of space in the crate.
The base of the cube is 12 x 12, so the area of the base is 144 in²
144 ÷ 16 = 9, so the base of the cube, or bottom of the box, can fit 9 cans, arranged 3 by 3.
The cube has a height of 12 inches, and each can is 5 inches tall. Therefore, two of these stacks can fit in the box, for 9 x 2 = 18 cans.
This is a much better answer, as it takes into account the fact that the cans can't occupy every inch of available space in the cube.
