Find the new amount of the original amount is 45 grams and the percent of decrease is 36%.
1 answer:
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Answer:
A. As "a"⇒e, the function f(x)=aˣ tends to be its derivative.
Step-by-step explanation:
A. To show the stretched relation between the fact that "a"⇒e and the derivatives of the function, let´s differentiate f(x) without a value for "a" (leaving it as a constant):
The process will help us to understand what is happening, at first we rewrite the function:
And then, we use the chain rule to differentiate:
Notice the only difference between f(x) and its derivative is the new factor ln(a). But we know that ln(e)=1, this tell us that as "a"⇒e, ln(a)⇒1 (because ln(x) is a continuous function in (0,∞) ) and as a consequence f'(x)⇒f(x).
In the graph that is attached it´s shown that the functions follows this inequality (the segmented lines are the derivatives):
if a<e<b, then aˣln(a) < aˣ < eˣ < bˣ < bˣln(b) (and below we explain why this happen)
Considering that ln(a) is a growing function and ln(e)=1, we have:
if a<e<b, then ln(a)< 1 <ln(b)
if a<e, then aˣln(a)<aˣ
if e<b, then bˣ<bˣln(b)
And because eˣ is defined to be the same as its derivative, the cases above results in the following
if a<e<b, then aˣ < eˣ < bˣ (because this function is also a growing function as "a" and "b" gets closer to e)
if a<e, then aˣln(a)<aˣ<eˣ ( f'(x)<f(x) )
if e<b, then eˣ<bˣ<bˣln(b) ( f(x)<f'(x) )
but as "a"⇒e, the difference between f(x) and f'(x) begin to decrease until it gets zero (when a=e)
Answer:
The area of the shaded region is 148.04 cm².
Step-by-step explanation:
It is provided that a 7 cm × 5 cm rectangle is inside a circle with radius 6 cm.
The sides of the rectangle are:
l = 7 cm
b = 6 cm.
The radius of the circle is, r = 6 cm.
Compute the area of the shaded region as follows:
Area of the shaded region = Area of rectangle - Area of circle
Thus, the area of the shaded region is 148.04 cm².
Answer:
OR 77.78%
Step-by-step explanation:
So, we first need to find out how many numbers fit the "less than 29 or odd" group.
This would be: 1, 2, 3, 5, 15, 21, and 29, which is a total of 7 numbers.
Next, we figure out the total amount of numbers in the population.
This would be: 1, 2, 3, 5, 15, 21, 29, 38, and 500, which is a total of 9 numbers.
Finally, we put the first number (7) over the total (9) =
is now able to be written in a percentage, if you need.
The probability is OR 77.78%