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
sveticcg [70]
3 years ago
6

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 3 − 2x, (0

, 1) The equation ex = 3 − 2x is equivalent to the equation f(x) = ex − 3 + 2x = 0. f(x) is continuous on the interval [0, 1], f(0) = _____, and f(1) = _____. Since f(0) < 0 < f(1) , there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation ex = 3 − 2x, in the interval (0, 1)
Mathematics
1 answer:
laila [671]3 years ago
3 0

Answer:

f(x) is continuous on the interval [0, 1], f(0) = <u>-2</u> , and f(1) = <u>1.718</u> . Since f(0) < 0 < f(1) , there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation ex = 3 − 2x, in the interval (0, 1)

Step-by-step explanation:

From the question we are told that

   The equation is f(x) = e^x - 3-2x  

    The interval is  [0, 1]

Generally f(0) is  

      f(0) = e^0 - 3-2(0)

=>   f(0) = 1 - 3-2(0)  

=>    f(0) = -2  

Generally f(1) is

       f(1) = e^1 - 3-2(1)

       f(1) = e^1 - 1

       f(1) = 1.718

From the value we see that at x =  0  , f(0) =  -2 which is below the x-axis

    and  the  at  x = 1  , f(1) =  1.718  which is above the x-axis

Now  the according to Intermediate Value Theorem , given the condition stated above, there will exist a root c in the interval  such that

    f(c) =  0  

You might be interested in
How is solving inequalities with multiplication and division similar to solving equations with multiplication and division?
bija089 [108]
Because they’re both the opposites of eachothers quantities
5 0
2 years ago
Read 2 more answers
Compute the conditional probabilities from the two-way frequency table.
Natali5045456 [20]

Answer:

The table is show clearly in the figure attached.

P(boy if favourite activity is swimming) = 8/17 = 0.47

P(girl if favourite activity is sport) = 7/27 = 0.26

P(girl if favourite activity is reading) = 4/6 = 0.67

P(boy if favourite activity is sport) = 20/27 = 0.74

P(favourite activity is swimming if a girl) = 9/20 = 0.45

P(favourite activity is reading if a boy) = 2/30 = 0.07

P(favourite activity is swimming if a boy) = 8/30 = 0.27

P(favourite activity is reading if a girl) = 4/20 = 0.2

6 0
3 years ago
When a figure is translated, reflected, or rotated, what's the same about the original igure and its image? What's different?
Liula [17]

Answer:

The image of a translation, reflection, or rotation is congruent to the original figure, and the image of a dilation is similar to the original figure. Two figures are similar when one can be obtained from the other by a sequence of translations, reflections, rotations, and dilations.

7 0
3 years ago
Marking brainliest <br><br> Can someone give me an example on why animal testing is bad?
DENIUS [597]
Wdym by animal testing? Like doing experiments on rats as an example?
4 0
3 years ago
Triangle Numbers are generated by creating trianglesof progressively larger size. Example include pinswhen bowling or balls when
iris [78.8K]

for the first term:

n= 1 there is 1 item

n=2 there are 2+1 = 3 items

n = 3 there are 3+2+1 = 3+2 = 6 items

n = 4 there are 4+3+2+1 = 4+6 = 10 items

We are adding the "n" term each time

n = 5 10+5 = 15

n= 6 15+6 = 21

n = 7 21+7 = 28

n = 8 28+8 = 36

There would be 36 items in the 8th step

4 0
1 year ago
Other questions:
  • How do you solve this the 8 is for the whole base not just the right triangle just so you know
    7·1 answer
  • Write the expression in the simplest form. (-11/2 x +3) -2(- 11/4 x - 5/2)
    14·1 answer
  • Which expression is equivalent to n(3+2n)?<br> a)2n²+3n+5<br> b)5n+5<br> c)2n+8<br> d)11n
    14·2 answers
  • The length of rectangle is represented by x and the width by y. The square of the diagonal of the rectangle is equal to the sum
    13·2 answers
  • Which is equivalent to the expression below?<br><br> 3p+4+p+12+3q
    9·1 answer
  • Kristen gets home from work at 5:34 p.m. Kristen's dinner is ready at 5:51 p.m.
    15·1 answer
  • The angle of a triangle is 30 degrees 60 degrees and 90 degrees Is this a unique triangle
    13·1 answer
  • After multiplying, a calculator screen displays the answer shown below. How would you write this number in standard form? Enter
    15·1 answer
  • Determine the number of solutions for the equation shown below.
    10·2 answers
  • Need help please answer ASAP!<br> 25&amp;26
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!