A student taking a Calculus class makes the following statement:
”If f(1) > 0 and f(3) < 0, then there exists a number c, between 1 and 3 such that f(c) = 0.”
Is the statement true? If it’s true, explain why, if it is false, explain why, or give an example that disproves it.

Answers

Answer 1
Answer: True

Explanation:

Imagine that f(x) was a road without any gaps. The road can be straight or it can be curved somehow.

Now imagine that a horizontal line is the border between two countries. The country up north is the positive country and the southern country is negative.

f(1) > 0 means we're in the northern country since f(x) is positive here

then f(3) < 0 means we're now in the southern negative country

Somewhere along the road we must have crossed the border at least one time. This must be the case because the road does not have any gaps in it and we cannot teleport. This is what it means to be a continuous function. To draw a continuous curve, you cannot lift your pencil up.

So because f(x) transitions from positive to negative, this means f(x) = 0 at some point at least once. So that's why there exists a c such that f(c) = 0


Related Questions

Solve: 2/3x-4=-2


a. -3
b.-4
c.-9
d.3​

Answers

Answer:

  d.  3

Step-by-step explanation:

Add 4, then multiply by 3/2.

  2/3x -4 +4 = -2 +4

  2/3x = 2

  (3/2)(2/3)x = (3/2)(2)

  x = 3

Can someone Distribute:
-3(2x-8) -2x+4

Answers

Answer:

-8x+28

Step-by-step explanation:

-3(2x-8)-2x+4

-6x+24-2x+4

-8x+28

Hope this helps!

If sin(x) = -1/3 and cos(x) > 0, what is tan(2x)?

Answers

Answer:

a

Step-by-step explanation:

just took it on edg

If the value of x is 199.47°. Then the value of tan (2x) will be 0.808.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

If sin (x) = -1/3

Then the value of x will be

x = sin⁻¹(-1/3)

x = -19.47°, 199.47°, ….

If the value of x is 199.47°. Then the cos x will be positive.

Then the value of tan (2x) will be

tan 2x = tan (2 x 199.47)

tan 2x = tan (398.94)

tan 2x = 0.808

More about the trigonometry link is given below.

https://brainly.com/question/22698523

#SPJ2

how do i check 8d-25=3d

Answers

Answer:

d=5

Step-by-step explanation:

That is the answer if that is what you were looking for.

your welcome

8d-25=3d

8d-3d=25

5d=25

d=5

d=5

8d-25=3d

8(5)-25=3(5)

40-25=15

15=15 so it’s right

PLZ HELP IM BEGGING U

Answers

Answer:

Since the given relation is proportional, the value of s multiplied by the constant of proportionality will be the value of P

we can write the above statement as:

s * k = P   (where k is the constant of proportionality)

putting some given proportional values of s and P

2 * k = 8

k = 8 / 2

k = 4

Now that we have the constant of proportionality, we can use it in the equation we just made

s * k = P

s (4) = P

4s = P

This is the relationship between s and p, represented by an equation

Answer:

Since the given relation is proportional, the value of s multiplied by the constant of proportionality will be the value of P

we can write the above statement as:

s * k = P   (where k is the constant of proportionality)

putting some given proportional values of s and P

2 * k = 8

k = 8 / 2

k = 4

Now that we have the constant of proportionality, we can use it in the equation we just made

s * k = P

s (4) = P

4s = P

This is the relationship between s and p, represented by an equation

What is the side lengths in square feet

Answers

Step-by-step explanation:

Since each side of a square is the same, it can simply be the length of one side squared. If a square has one side of 4 inches, the area would be 4 inches times 4 inches, or 16 square inches.

Help me ASAP!!pls I don’t get it:(

Answers

Answer:
-9
Explanation:

express 60 As the product
of its prime
factors. Write
the prime factors in assessing
Order
ane give your
Answer index form

Answers

Given parameters:

 Number 60;

Problem;

Express as a product of its prime factors

Solution

Every number known can be expressed as a product of its prime factors. Prime factorization involves finding the prime numbers that when multiplied will give the true number.

Prime numbers are numbers that are products of 1 and itself only.

   For the number 60;

                      60  =   2 x 30

                             = 2 x 2 x 15

                             = 2 x 2 x 3 x 5

In index form;   2² x 3 x 5

 

Find the Perimeter of Polygon JKLMN. Round to the tenth.
Please help! I am having an insanely hard time with this

Answers

9514 1404 393

Answer:

  24.1 units

Step-by-step explanation:

This is done using the Pythagorean theorem (or distance formula) to find the lengths of the sides.

For each side of the figure (except the bottom horizontal), you need to identify the dimensions of the right triangle whose hypotenuse is the side of interest. For example, LM is the hypotenuse of a triangle 4 units high and 1 unit wide. The Pythagorean theorem tells you LM has a length of ...

  LM = √(4^2 +1^2) = √17 ≈ 4.12

Similarly ...

  KL = √(2^2 +2^2) = √8 ≈ 2.83

  JK = √(1^2 +6^2) = √37 ≈ 6.08

  NJ = √(5^2 +1^2) = √26 ≈ 5.10

Of course, the length of MN is found by finding the difference of the x-coordinates:

  MN = 3 -(-3) = 6

Then the perimeter is the sum of side lengths:

  4.12 +2.83 +6.08 +5.10 +6.00 = 23.17 ≈ 24.1 . . . units

Could I please get an answer to this, thank you :)

Answers

Answer:

perimeter is 76

area is 330

hope this helps if you can brainliest plz

What is the constant of proportionality in the equation StartFraction x over y EndFraction = StartFraction 2 over 9 EndFraction?

Answers

Answer:

so you asking what's the startfrsction and endfraction in the equation or ?

6 1/4 ÷ 4

(6th grade math)

Answers

Answer: 1.5625

Step-by-step explanation: just a calculator

Answer:

1.5625

Step-by-step explanation:

Benjamin has 5 baskets. Each basket has 10 berries in it. Explain how you could find how many berries benjamin has

Answers

Answer: You can multiply 5 x 10 which means he has 50 berries

find the product:
(-9)(-4)

Answers

Answer:

36

Step-by-step explanation:

-9*-4=36

Yon buys tickets to a concert for himself and a friend. There is a tax of 8% on the price of the tickets and an additional booking fee of $10 for the transaction. Enter an algebraic expression to represent the price per person. Simplify the expression if possible. Use variable t for the price of the 2 tickets in dollars. The algebraic expression is

Answers

Answer: if this is what you have here you go but lmk if this isnt the right answer

Step-by-step explanation:

Can someone help me please

Answers

Answer:

16 units

Step-by-step explanation:

The perimeter is the sum of the lengths

Add up the lengths as shown

3+2+1+2+3+1+1+3

16 units

Find the missing value
5600 -
140
Type your answer...​

Answers

Answer:

[See Below]

Step-by-step explanation:

[tex]Hey~There![/tex]

__________________________________________________________

[tex]\bold{So~to~solve~this~we~do~the~opposite~of~what~we~see:}[/tex]

÷ changes to ×[tex]5,600[/tex] × [tex]140=784,000[/tex]

[tex]\boxed{So~your~answer~is: 784,000}[/tex]

__________________________________________________________

[tex]Hope~this~helps~Mate.\\-Your~Friendly~Answerer,~Shane[/tex] ^-^

Jose’s school has 426 students. His principal has promised the Student Council that their idea will be carried out if they can get at least 25% of the student population to sign a petition. So far, 82 students have signed the petition. Jose used the following steps to write an inequality that can be used to determine the number of student signatures still needed:
Step 1. Declare the variable: Let x = the number of student signatures still needed.
Step 2. Create a ratio equivalent to StartFraction total number of signatures needed over total number of students in the school EndFraction : StartFraction x + 82 over 426 EndFraction.
Step 3. Convert 25% to a decimal: 25% = 0.25.
Step 4. Write the inequality: StartFraction x + 82 over 426 EndFraction less-than-or-equal-to 0.25.
What is Jose’s error?

Answers

Answer:

D) In Step 4, the inequality should be x+82/426 is at least 0.25

they need 25 more signatures to get their idea carried out

Step-by-step explanation:

Answer:

Step 4

Step-by-step explanation:

I took the test! :D

!~Hope this helped~!

I'm bad at explaining, sorry!

Construct a 2x2 matrix A= aij. whose elements are given by

a = |-3i + j|​

Answers

Answer:

2

Step-by-step explanation:

-3/5 divided by -1 1/10

Answers

Answer:

o.54545454545

Step-by-step explanation:

On calculater showed this answer

The zeros of the function are , 3, and , and the y-intercept of the function is located at .

Answers

Answer:

The zeroes are -1, 3, and -2

The y intercept is located at (0,6)

Step-by-step explanation:

(x+2)=0

x=-2

The easiest way is to use an online graph like desmos and graph the problem there. You can see where the y intercept is.

A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7.

1. What are the side lengths of the scaled copy?

2. Suppose you want to scale the copy back to it's original size. What scale factor should you use?

Answers

Answer:

To get the new scaled copy length and width just multiply by seven (2x7 & 3x7)

New length would be 14 because it's "seven times" the original size

New width would be 21

Step-by-step explanation:

1.) 14 and 21

2.) 14 divided by 7 will give you 2

and 21 divided by 7 will give you 3

The answer for question 2 would be to divide your new answers (21 and 14) by the scaled factor of 7.

Suppose there is a 3.1 temperature drop for every thousand feet that an airplane climbs
into the sky. If the temperature on the ground is 60.1, what will the temperature be
when the plane reaches an altitude of 11,000 feet?

Answers

Answer:

34.1 degrees

Step-by-step explanation:

given that the temperature drops 3.1 degrees for every thousand feet of elevation.

for an altitude of 11,000 feet (i.e 11 x 1000 feet), the temperature (compared to ground level) would drop,

= 3.1 deg / 1000-foot   x   11,000 feet

= 34.1 degrees

what is 20/3 decimal form

Answers

6.66667 rounded on the fifth decimal place


An airplane flying at 24,250 feet is directly over a submarine that is 475 feet below sea level. What is the distance between a person in the plane and a person in the submarine?

Answers

Answer:

23,775 feet apart

Step-by-step explanation:

24250+(-475)=23775

what would the solution be?

Answers

Answer:

C.) y = 9

Step-by-step explanation:

Simply substitute in -2 for x.

y = -4(-2) + 1

y = 8 + 1

y = 9

How would I solve number six?

Answers

Answer:

Angle ABC is equal to 130.4°

Step-by-step explanation:

When an angle is bisected, it is divided into two equal parts, so if BD bisects ∠ABC, then the two angles that add up to it, ∠ABD and  ∠DBC, must be equivalent.

We know that ∠ABD equals 65.2, so that must mean that ∠DBC also equals 65.2.

Here is our equation:

∠ABC=∠ABD+∠DBC

After substituting, we will get

∠ABC=65.2+65.2=130.4

130.4° is the measure of ∠ABC.

140.4 ya ya ya ya what ever the person up said pls mark brainlist I really new to post a question and it won’t let me

8) Two lines intersect as shown.
(2x + 20)
60°
What is the value of x?
A 20
B 40
C 50
D60

Answers

Answer:

  A.  20

Step-by-step explanation:

Vertical angles are congruent, so ...

  2x +20 = 60

  x +10 = 30 . . . . . divide by 2

  x = 20 . . . . . . . . .subtract 10

i really need help on this one.

Answers

The answer is:

a = 20/3 = 6 2/3

Please find the next number in the sequence. "1, -3, 9, -27, ...."

Answers

Answer:

-27, 17, -41 and so now

Step-by-step explanation: 1, -3, 9, -27, 17, -41

Answer:

1,-3,9,-27,(-27×-3=81),(81×-3=-243)

Step-by-step explanation:

here common ratio =-3/1=-3

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