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Ivanshal [37]
3 years ago
6

In the diagram below, p is a ________ .

Mathematics
1 answer:
Nina [5.8K]3 years ago
4 0
In the diagram, p is a plane angle. 
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Consider functions of the form f(x)=a^x for various values of a. In particular, choose a sequence of values of a that converges
sleet_krkn [62]

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):

f(x)=a^{x}\\ f'(x)=a^xln(a)

The process will help us to understand what is happening, at first we rewrite the function:

f(x)=a^x\\ f(x)=e^{ln(a^x)}\\ f(x)=e^{xln(a)}\\

And then, we use the chain rule to differentiate:

f'(x)=e^{xln(a)}ln(a)\\ f'(x)=a^xln(a)

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)

3 0
3 years ago
In parallelogram IFGH, mF = (x + 20° and mi<br> (4x – 10)<br> Find the value of x.
sveta [45]

Answer:

x = 34

Step-by-step explanation:

4x - 10 + x + 20 = 180

5x + 10 = 180

5x = 170

x = 34

6 0
3 years ago
I’m A Triangle, The Sum Of Any Two Side Lenghts, <br><br> Finish The Sentence
Alchen [17]
Equals the third side length
4 0
3 years ago
phyllis invested 66000 dollars, a portion earning simple interest rate of 5% per year and the rest earning a rate of 7% per year
Lelechka [254]

<u>Answer: </u>

Physliis invested 32000 dollar at 5% interest rate and 34000 dollar at 7% interest rate.

<u>Solution:</u>

Let Phyllis invest ‘x’ dollar at 5% per year and (66000-x) dollar at 7% per year.

We know,

\text { Simple interest }=\frac{\text {Principal} \times r a t e \times T i m e}{100}

In the question it is given that Simple interest earned from both the investments at the end of the year is $3980.

Using the given below equation, we will try to find out the investments at each rate.

\begin{array}{l}{\frac{x \times 5 \times 1}{100}+\frac{(66000-x) \times 7 \times 1}{100}=3980} \\\\ {\frac{5 x}{100}+\frac{462000-7 x}{100}=3980} \\\\ {\frac{5 x+462000-7 x}{100}=3980} \\\\ {-2 \mathrm{x}+462000=3980 \times 100} \\\\ {-2 \mathrm{x}=398000-462000} \\\\ {-2 \mathrm{x}=-64000} \\\\ {\mathrm{x}=\frac{-64000}{-2}}\end{array}

x = 32000

We can calculate amount for 7% interest rate by,

(66000-32000) =34000

Thus Phyllis invested 32000 dollar at 5% interest rate and 34000 dollar at 7% interest rate.

8 0
3 years ago
kate takes 48 minutes to get to the park. if she gets to the park at 2:32 what time did she leave for the park
olya-2409 [2.1K]

Answer:

1:44

Step-by-step explanation:

You can subtract 32 minutes from 2:32 to get 2:00.

Since you only subtracted 32, subtract 16 (16+32=48) from 60, since 60 minutes is one hour, to get 1:44

8 0
3 years ago
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