Answer:
f(x) = -5.1x² +14.6x +3
Step-by-step explanation:
The three given points are obviously not on a line, but can be modeled exactly by a 2nd degree polynomial. (The degree is 1 less than the number of points.) I find it convenient to let a graphing calculator's quadratic regression function tell me the coefficients.
<em>Solving by hand</em>
Since the "y-intercept" is 3, the equation can be written
... f(x) = ax² +bx + 3
Filling in the given numbers, we have 2 equations in the 2 unknowns, <em>a</em> and <em>b</em>.
... f(1) = 12.5 = a·1² +b·1 +3
... f(2) = 11.8 = a·2² +b·2 +3
Simplifying these gives ...
Subtracting the first equation from the second gives ...
... (2a +b) -(a +b) = (4.4) -(9.5)
... a = -5.1
The first equation tells us
... b = 9.5 -a = 9.5 +5.1
... b = 14.6
The equation is f(x) = -5.1x² +14.6x +3.
If (kn)(4f)=9v, then:
(9v)
n= ------
(4f)k
Answer:
6√2
Step-by-step explanation:
The square root of 72 is an irrational number, so we can't make the square root of 72 into an accurate decimal form. However, we can simplify it!
- The factors that have the greatest square are 2 and 36.
-
-
Therefore, the answer is 6√2.
9514 1404 393
Answer:
72.5° ≈ 73°
Step-by-step explanation:
The ladder length is the hypotenuse of the right triangle that has the distance from the building as its base and the height up the building as the height of the triangle. The given dimensions are those of the side adjacent to the angle and the hypotenuse.
The appropriate trig relation is ...
Cos = Adjacent/Hypotenuse
cos(angle) = 6/20
The inverse cosine function (arccos) is used to find the angle from its cosine.
angle = arccos(6/20) ≈ 72.54°
The angle is 72.5° rounded to tenths, or 73° rounded to degrees.
Answer:
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