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Vadim26 [7]
3 years ago
14

use the intermediate value theorem to determine whether the following equation has a solution or not x^3-3x-1

Mathematics
1 answer:
xxTIMURxx [149]3 years ago
3 0

Answer:

Yes, this equation has a solution. According to Intermediate Value Theorem at least one solution for [0,2]

Step-by-step explanation:

Hi there!

1) Remember a definition.

Intermediate Value Theorem:

If f is continuous on a given closed interval [a,b], and f(a)≠f(b) and f(a)<k<f(b) then there has to be at least one number 'c' between 'a' and 'b', such that f(c)=k

----

(Check the first graph as an example)

2) The Intermediate Value Theorem can be applied to determine whether there is a solution on a given interval.

Let's choose the interval [0,2]

f(x)=x^{3}-3x-1\\f(0)=(0)^{3}-3(0)-1\\f(0)=-1\\f(0)

Proceed to the other point: 2

f(x)=x^{3}-3x-1\\f(2)=(2)^{3}-3(2)-1\\f(2)=1\\f(2)>0\\

3) Check the 2nd Graph for a the Visual answer, of it.  And the 3rd graph for all solutions of this equation.

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HELP ME PLEASE!!
LUCKY_DIMON [66]

Using a system of equation, we have that:

a)

  • x, which is the cost of on-site service.
  • y, which is the cost of at-store service.
  • z, which is the cost of by-mail service.

b)

The system is:

x = 3y

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15x + 40y + 5z = 3100

c)

The cost of one on-site repair service is of $90.

Item a:

The variables are:

  • x, which is the cost of on-site service.
  • y, which is the cost of at-store service.
  • z, which is the cost of by-mail service.

Item b:

On-site service costs <u>3 times as much as at-store service</u>, thus:

x = 3y

By mail service costs <u>$10 less than at-store</u>  service, thus:

z = y - 10

Last week, the shop completed <u>15 services on-site, 40 services at-store, and 5 services by mail for total sales of $3100</u>, thus:

15x + 40y + 5z = 3100

The system is:

x = 3y

z = y - 10

15x + 40y + 5z = 3100

Item c:

  • The cost of one on-site repair service is x.
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15(4y) + 40y + 5(y - 10) = 3100

60y + 40y + 5y = 3150

105y = 3150

y = \frac{3150}{105}

y = 30

Then

x = 3y = 3(30) = 90

The cost of one on-site repair service is of $90.

A similar problem is given at brainly.com/question/24823220

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