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.
Answer:
17.94
Step-by-step explanation:
The formula for a problem like this is
P W/2 -W^2
Multiply the perimeter by half of the width and then subtract the width squared.
7.8/2 This would give us 3.9
Then we multiply this by the perimeter
3.9x20.2 This leads us too 78.78
Then we subtract w^2
7.8X7.8 Is equal too 60.84
Then we subtract
78.78-60.84 This leads us too 17.94
Answer:
s = √(3V/[8 in])
Step-by-step explanation:
Where are "the following functions" that were mentioned in this problem statement? Please share them. Thanks.
The volume of a right square pyramid is V = (1/3)(area of base)(height). In more depth, V = (1/3)(s²)(h). We want to solve this for s.
Multiplying both sides by 3 to eliminate the fractional coefficient, we get:
3V = s²(h), and so s² = 3V/h.
Taking the square root of this, we get:
s = √(3V/h).
Now let's substitute the given numerical value for the height:
s = √(3V/[8 in]). We could also label this as a(V) as is done in the problem statement.
Answer:
the answer is 40 boys
Step-by-step explanation:
Let's say there are x boys who play both cards and carrom.
We setup up an equation that involved all information given and x.
Boys who only play cards = 45-x
Boys who only play carrom = 20-x
Boys who play both = x
Add there together and you should get 60, which is the total number of students in the class.
(45-x)+(20-x)+x=60
65-x=60
x=5
Boys who only play cards=45-x=45–5=40
hope it helps you
Answer:
Perpendicular bisector - A line that bisects another line into two equal halves so that four right angles are created.
Cylinder - A 3D solid with circles as its bases.
Plane - A flat, 2D surface that extends infinitely.
Regular Polygon - A polygon where all angles and all sides are equal (ex. square, pentagon, triangle).