A website sells sweaters. The amount of sales p(c) varies directly with the number of customers c.
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Volume of a figure is measure of the space it occupies. The volume of the larger rectangular prism is given as: Option C: 1620 cm³
If a rectangular prism has dimensions <u>a</u> unit, <u>b</u> unit, and <u>c</u> units, then its volume is given as
They are scaled. It means, if two figures are similar, then we can get one figure from another by multiplying some constant value(same for one pair of similar figure) to its dimensions.
For example,
if for given case, one rectangular prism has got dimensions a, b, and c centimetres, then
the second rectangular prism, which is similar, let the scale factor is 'd',t then second prism's dimensions will be a x d units, b x d units, and c x d units.
For first prism(smaller), its one side is given to be 5 cm, let its other two sides be 'b' cm, and 'c' cm, then,
Now, the larger prism has 15 cm corresponding side, thus, scale factor was 3 (since 15 is 3 times 5).
Thus, its dimensions would be 15, 3 x b, 3 x c
Thus, its volume would be
Thus,
The volume of the larger rectangular prism is given as: Option C: 1620 cm³
Learn more about volume of rectangular prism here:
Cos(x) = sin(x + 20o) Use the double cos angle formula
Cos(x) = sin(x)*cos(20) + cos(x)*sin(20) Divide through by cos(x). Tanx = sin(x)/cos(x)
1 = tan(x)*cos(20) + sin(20) Subtract sin(20) from both sides.
1 - sin(20) = tan(x)*cos(20) Calculate the value of 1 - sin(20)
0.65798 = tan(x) * 0.939692 Divide by cos(20)
tan(x) = 0.65795/0.939692
tan(x) = 0.70021 Take the inverse of 0.7) = tan(x)
x = tan-1(0.70021)
x = 35 degrees as expected.
Problem Two
The easiest way to do this is to pick random values and try it. The two acute angles are complementary. So 25 and 65 are random enough.
Let A = 25
Let C = 65
A
Tan(25) = sin(25)/sin(65) ; tan(25) = 0.4663.
sin(25)/sin(65) = 0.4663 Answer
B
Sin(90 - C) = Sin(A)
Tan(90 - A) = Tan(C)
So the question becomes Cos(A) = Tan(C) / sin(A)
Cos(25) = Tan(65)/Sin(25)
0.906 = ? 5.07 This statement isn't true.
C
Sin(65) = Cos(25)/Tan(65)
.906 = 0.4226 C is not the correct answer.
D
D isn't true. The tan does not relate that away. You can find it for yourself.
Cos(A) = Tan(C) You should get 0.906 = 2.14
E
Sin(C) = Cos(A) / Tan(A) I'll leave you to show this is wrong.
Problem 3
The diagram below is for this problem. Cos(x) = 50/100 = 0.5
x = cos-1(0.5)
x = 60 degrees.
Part 2
Sin(60) = opposite / hypotenuse
opposite = sin(60) * hypotenuse
opposite = 86.61 Be sure and round this to whatever the question says to round it to.
