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Artyom0805 [142]
3 years ago
15

Write the equation of the line parallel to y=1/2x−6 that passes through (−10,4).

Mathematics
1 answer:
Talja [164]3 years ago
5 0

Answer:

y = 1/2 x + 9

Step-by-step explanation:

y = 1/2 x + b

4 = (1/2)(-10) + b

4 = -5 + b

b = 9

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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
What is the equation of the line in slope-intercept form?
kondor19780726 [428]

Answer:

The answer would be C because b=+16 which means that it intercepts line y at 16, which is shown in the graph.

Step-by-step explanation:

5 0
2 years ago
What is the solution to this expression<img src="https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7Bx%5E%7B2%7D%20%5Ccdot%20t%7D%20%20%5Cf
ankoles [38]

Answer:

4/xt 3 sqaured

Step-by-step explanation:

6 0
3 years ago
Find the area of a parallelogram with a base of 5 cm and a height of 15 cm.
amid [387]

Answer:

75cm²

Step-by-step explanation:

area of parallelogram= base*height

area=15*5=75cm²

4 0
3 years ago
4 1/3 divided 5 1/6<br> Please help me!
Effectus [21]

Answer:

6/31

Step-by-step explanation:

4 1/3 ➡ 13/3

5 1/6 ➡ 31/6

to divide two rational expression you should turn the second number upside-down(finding its reciprocal) then multiply them :

13/3 × 6/31 = 26/31

8 0
3 years ago
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