PLEASE HELP WITH MATH
2 answers:
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a ) The domain:
x^4 - 16 x² ≥ 0
x² ( x² - 16 ) ≥ 0
x² - 16 ≥ 0
x² ≥ 16
x ∈ ( - ∞, - 4 ] ∪ [ 4 , + ∞ )
b ) f ` ( x ) =
= ( 2 x³ - 16 x ) / √(x^4 - 16 x²)
c ) The slope of the tangent line at x = 5:
f ` ( 5 ) = ( 2 * 125 - 16 * 5 ) / √ ( 625 - 400 ) = 170 / 15 = 34 / 3
The slope of the line normal to the graph at x = 5:
m = - 3 / 34
Answer:
Hardy has 470 more tennis balls than Kerns.
Step-by-step explanation:
Given that:
Total number of tennis balls = 940
Let,
x represents the number of tennis balls Hardy has.
y represents the number of tennis balls Kerns has.
According to given statement,
x+y=940 Eqn 1
x = 3y Eqn 2
Putting x = 3y in Eqn 1
3y+y=940
4y=940
Dividing both sides by 4
Putting y=235 in Eqn 2
x = 3(235)
x = 705
Difference = Hardy's tennis balls - Kerns' tennis balls
Difference = 705 - 235 = 470
Hence,
Hardy has 470 more tennis balls than Kerns.