The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.
<h3>How to find the find the dilation factor</h3>
In this problem we have the following relationship bewteen the two <em>quadratic</em> equations: g(x) = f(k · x), which means that for all y the following relationship between f(x) and g(x):
Let suppose that y = 3, then 
and 
, then the value k is:
k = (- 5.5)/(- 1.8)
k = 3.056
The value k needed for the transformation of f(x) to g(x) = f(k · x) is equal to 3.056.
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X = string section
y = brass section
x = y + 35
y = 29 .....there are 29 in the brass section
x = 29 + 35
x = 64...there are 64 in the string section
for a total of : 64 + 29 = 93 total musicians <==
Answer:
12.1 cm
Step-by-step explanation:
Using the law of sines, we can find angle C. Then from the sum of angles, we can find angle B. The law of sines again will tell us the length AC.
sin(C)/c = sin(A)/a
C = arcsin((c/a)sin(A)) = arcsin(8.2/13.5·sin(81°)) ≈ 36.86°
Then angle B is ...
B = 180° -A -C = 180° -81° -36.86° = 62.14°
and side b is ...
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 13.5·sin(62.14°)/sin(81°) ≈ 12.0835
The length of AC is about 12.1 cm.
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<em>Comment on the solution</em>
The problem can also be solved using the law of cosines. The equation is ...
13.5² = 8.2² +b² -2·8.2·b·cos(81°)
This is a quadratic in b. Its solution can be found using the quadratic formula or by completing the square.
b = 8.2·cos(81°) +√(13.5² -8.2² +(8.2·cos(81°))²)
b = 8.2·cos(81°) +√(13.5² -(8.2·sin(81°))²) . . . . . simplified a bit
