BC is tangent to circle A at B and to circle D at C. AB= 10 BC= 21 DC= 8 find AD to the nearest tenth
1 answer:
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9514 1404 393
Answer:
Step-by-step explanation:
A lot of math is about matching patterns.
For example, ...
g(x) = f(x -h) +k
means g(x) is the function f(x) translated right by h units and up by k units. This will be true for any expression of f(x).
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In this problem, f(x) = √x. We want to translate it left 6 units (h=-6)*, and up 4 units (k=4).
The notation above means that we will replace x with (x-h) = x+6. and we will add k = 4 to the result.
f(x) = √x
g(x) = f(x+6) +4
g(x) = √(x+6) +4 . . . . . . matches choice D
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* Left is the opposite of right, so left 6 units is the opposite of right 6 units. h=6 for <em>right 6 units</em>, so h=-6 for <em>left 6 units</em>. Then x-h = x-(-6) = x+6.
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<em>Comment on the graph</em>
I find it useful to see a picture with these things. In the attached graphing calculator output, the blue curve is left 6 and up 4 from the red curve. The blue curve is g(x); the red one is f(x).
Answer:
b = 15.75
Step-by-step explanation:
Lets find the interception points of the curves
36 x² = 25
x² = 25/36 = 0.69444
|x| = √(25/36) = 5/6
thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).
The area of the bounded region is given by the integral
The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.
125/18 = b^{1.5}/9
b = (62.5²)^{1/3} = 15.75