Item 18 You and your friend gather 56 apples. You gather 29 apples. Let a be the number of apples your friend gathers. Write an
1 answer:
You might be interested in
Answer:
The constant of proportionality is option D i.e 5.
Step-by-step explanation:
Variation:
Variation problems involve fairly simple relationships or formulas, involving one variable being equal to one term. There are two types of variation i.e.
- Direct variation
- Inverse variation
Direct Variation:
Mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other.
Example
where, k is constant of proportionality.
The above given example is of Direct Variation
∴ y = 5 x
∴ k = 5 = constant of proportionality.
Inverse Variation:
Mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.
Example
where, k is constant of proportionality.
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.
