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Svet_ta [14]
3 years ago
8

Hendrick's Honda is having a contest to win a new Honda Civic. To win a chance at the car, you must guess the number of keys in

a jar within 5 of the actual number. The people who are within this range get to try a key in the ignition of the Civic. Suppose there are 697 keys in the jar.
Mathematics
1 answer:
Alona [7]3 years ago
3 0

Answer:

The valid range is 697 to 702

Step-by-step explanation:

<em>The question is incomplete; However, the requirement would likely be to determine the valid range which users can guess</em>

Given

Keys = 697

Difference = 5

First, we need to determine the minimum

Minimum = Keys - Difference

Minimum = 697 - 5

Minimum = 697

Next, we determine the maximum

Maximum = 697 + 5

Maximum = 702

Hence:

<em>The valid range is 697 to 702</em>

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A manufacturer has fixed costs of $16,000 per month and can produce w widgets at a cost of 0.1w^(2) + 20w. How many widgets shou
musickatia [10]
Consider c as the cost of the widget so that our given equation is
c = 0.1w^2 + 20w
Take the derivate of the equation.
d/dt (c = 0.1w^2 + 20w)
dc/dt = 0.2w + 20
Given dc/dt = $16000 per month, the number of widgets would contain:
16000 = 0.2w + 20
-0.2w = 20 - 16000
-0.2w = -15980
w = 79900 widgets
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I think the answer is b -3.

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VladimirAG [237]

Answer:

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Step-by-step explanation:

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3 years ago
Please help me solve this by substitution: <br> y=x+2<br> 3x+3y=6
VikaD [51]

Answer:

x = 0, y = 2

Step-by-step explanation:

  1. solve the equation for x

3x + 3(x + 2) = 6

2. Substitute the given value of x into the simplest equation y= x + 2

y = 0 + 2

3. Solve the equation for y

y= 2

4. The possible solution of the system is the ordered pair ( x, y)

( x, y) = ( 0, 2)

3 0
3 years ago
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
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