Help, easy math. will mark brainlist!!
2 answers:
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Answer:
The equation for the curve is:
Step-by-step explanation:
We know that for a curve defined as:
y = f(x)
The slope of the curve at the point x is:
y = f'(x)
where f'(x) = df(x)/dx
Here we know that we have a function that passes through the point (0, 7)
We also know that the slope of the curve at every point is twice the value of the y-coordinate. (remember that the y-coordinate is given by f(x))
Then we have two equations:
f(0) = 7
f'(x) = 2*f(x)
From the shape of the equation, we can assume than this is an exponential equation like:
Replacing that in the second equation, we get:
From that equation, we can conclude that k = 2
Then:
Now we can use the first equation:
f(0) = 7
With this, we can find the value of A.
Then we can conclude that the equation for the curve is:
Answer:
a) a = 7.37, b = 15.13, C = 67°
b) 1 triangle
Step-by-step explanation:
<h3>a)</h3>Two angles and one side are given. That means the triangle is uniquely determined, and the remaining sides can be found from the Law of Sines.
The third angle is ...
C = 180° -A -B = 180° -29° -84° = 67°
Then the Law of Sines tells you ...
a/sin(A) = b/sin(B) = c/sin(C)
a = sin(A)/sin(C)·c = sin(29°)/sin(67°)·14 ≈ 7.37
b = sin(B)/sin(C)·c = sin(84°)/sin(67°)·14 ≈ 15.13
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<h3>b)</h3>Ordinarily, when the given angle (B = 30°) is opposite the shorter of the given sides (b = 10 < a = 20), it means there are two possible solutions to the triangle.
However, when the sine of the angle is exactly equal to the ratio of the given sides: sin(30°) = 10/20 = 1/2, the larger angle can only be 90°. That is, the one triangle that can be formed is a right triangle.
The Law of Sines tells you this.
sin(A)/a = sin(B)/b
sin(A) = (a/b)sin(B) . . . . . . multiply by 'a'
A = arcsin(a/b·sin(B)) = arcsin(20/10·sin(π/6)) = arcsin(1)
A = 90°
