1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
chubhunter [2.5K]
3 years ago
11

Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem.

Mathematics
1 answer:
Molodets [167]3 years ago
5 0

Answer:

See verification below

Step-by-step explanation:

Remember that the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M.

Now, to apply the theorem, we have that f(0)=0²+0-1=-1, f(5)=5²+5-1=29, then f(0)=-1<11<29=f(5). Additionally, f is continous since it is a polynomial. Then the IVT applies, and such c exists.

To find, c, solve the quadratic equation f(c)=11. This equation is c²+c-1=11. Rearranging, c²+c-12=0. Factor the expression to get (c+4)(c-3)=0. Then c=-4 or c=3. -4 is not in the interval, then we take c=3. Indeed, f(3)=3²+3-1=9+3-1=11.

You might be interested in
Elisa withdrew $20 at a time from her bank account and withdrew a total of $140.francis withdrew $45 at a time from his bank acc
solmaris [256]
Elisa made more withdrawals because when you divide Elisa's total withdrawal by the amount of cash she withdrew at a time would be 140/20=7. When you compare that to Francis's withdrawal which would be 270/45=6. 7>6 so Elisa made more withdrawals than Francis. 
7 0
3 years ago
Read 2 more answers
Simplify the expression.<br><br><br> Write your answer without negative exponents.
Phoenix [80]

Answer:

-5/ (x^19 * y^12)

Step-by-step explanation:

-15x^-10 * y ^ -3 * x^-9 * y^-9/3 (It's writing it like this.)

15 and 3 have a GCF of 3.

-5x^-10 * y^-3 * x^-9 * y^-9/1

Reduce similar occurrences. *twice in a row*

-5x^(-10 + (-9)) * y^(-3 + (-9))/1

Remove extra signs *twice in a row*

-5x^(-10 - 9) * y^(-3 - 9)/1

Remove extraneous 1.

-5x^(-10 - 9) * y^(-3 - 9)

Add integers.

-5x^-19 * y^-12

Negative powers change multiplication to division.

-5 / (x^19 * y^12) is the final answer.

Even with that, the simplified answer wouldn't have negative exponents because of the negative powers rule.

8 0
2 years ago
What is the solution of the inequality shown below
Eduardwww [97]

Answer:

there is no inequality..

Step-by-step explanation:

5 0
3 years ago
Solve the system of linear equations by graphing.<br> y = x +2<br> y = -x -4<br> The solution is
Mnenie [13.5K]

Answer:

Solution: (-3,-1)

8 0
3 years ago
Read 2 more answers
Find the constant rate of change for each linear function and interpret its meaning
Marina CMI [18]

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

and to get it, we simply need two points off of the straight line, hmm let's use the ones in the picture below.

(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}

3 0
2 years ago
Other questions:
  • Find the area A of triangle JKL with the vertices J(5,8), K(0,7), and L(5,4)
    10·1 answer
  • This question is a fair question: “Which do you think is the most common age group of people who like pop music?” true or false
    13·1 answer
  • HELP!!!!!!!!!!!!!!!!!!!!!!!! ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!
    9·1 answer
  • QUICKEST ANSWER BRAINLIEST CORRECT AND A FOLLOW<br><br>answer the 3 questions ​
    11·2 answers
  • Suppose that Upper X has a discrete uniform distribution f left-parenthesis x right-parenthesis equals StartLayout left-brace1st
    5·1 answer
  • Find the value of x in each case
    5·1 answer
  • a coffee shop sells coffee beans by the pound. A container hold 16 kilograms of coffee beans. For every 1 kilogram, there are ap
    10·1 answer
  • Degree is defined as number of incidents to vertex.<br>Select one:<br> True<br>False​
    5·1 answer
  • The midpoints of the sides of a square of side 6 are joined to form a new square. This procedure is infinitely repeated for each
    13·1 answer
  • In the biblical account, adam lived to be how old? <br> a. 99 <br> b. 122 <br> c. 545 <br> d. 930
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!