Prove that the two circles shown below are similar. Circle A is shown with a center at 3, 4 and a radius of 5. Circle C is shown
1 answer:
You might be interested in
ANSWER
Yes, the two expressions are equivalent.
The identity property of multiplication.
EXPLANATION
The identity element for multiplication of real numbers is 1.
This means that, if you multiply any real number by 1, you get the same real number
The given expression is,
These two expressions are equivalent.
The property that is applied is the identity property of multiplication.
Yes, the two expressions are equivalent.
The identity property of multiplication.
EXPLANATION
The identity element for multiplication of real numbers is 1.
This means that, if you multiply any real number by 1, you get the same real number
The given expression is,
These two expressions are equivalent.
The property that is applied is the identity property of multiplication.
Answer:
(a) -69.59 . . . . the approximate slope of the curve at x=2
(b) 26.583 . . . . the value of x where the slope of f(x) is about -25.
Step-by-step explanation:
(a) The slope of a function <em>f </em>over the interval [x, x+h] is given by ...
... slope = (f(x+h) -f(x))/h
The problem statement asks for the value of ...
... (f(2.01) -f(2))/0.01
Matching this expression to the pattern above, we find x = 2, h = 0.01. An appropriate interpretation of the expression is that it gives the approximate slope of f(x) near x=2.
The value of that slope is about ...
... (f(2.01) -f(2))/0.01 ≈ 1850·(0.92122386 -0.9216)/.01 ≈ -69.5857
(b) f(x+1) = 1850·0.96^(x+1) = 0.96·f(x)
Then the equation becomes ...
... 0.96·f(x) = f(x) -25
... 25 = 0.04·f(x) . . . . . . . . add 25-0.96·f(x)
... 625 = f(x) . . . . . . . . . . . multiply by 25
... 625 = 1850·0.96^x . . . substitute definition of f(x)
... 625/1850 = 0.96^x . . . divide by the coefficient of the exponential term
... log(625/1850) = x·log(0.96) . . . . take logs
... x = log(625/1850)/log(0.96) ≈ -0.471292/-0.0177288
... x ≈ 26.583
If you rearrange the equation to ...
... f(x+1) -f(x) = -25
Comparing this to the equation for slope, above, it looks a lot like we're trying to find the interval [x, x+1] over which the average slope is -25.
