Find the solution set for this equation -a2+12a=0

Carry out three steps of the Bisection Method for f(x)=3x−x4 as follows: (a) Show that f(x) has a zero in [1,2]. (b) Determine w

ELEN [110]

Answer:

a) There's a zero between [1,2]

b) There's a zero between [1.5,2]

c) There's a zero between [1.5,1.75].

Step-by-step explanation:

We have $f(x)=3^x-x^4$

A)We need to show that f(x) has a zero in the interval [1, 2]. We have to see if the function f is continuous with f(1) and f(2).

$f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(2)=3^2-(2)^4=9-16=(-7)$

We can see that f(1) and f(2) have opposite signs. And f(1)>f(2) and the function is continuous, this means that exists a real number c between the interval [1,2] where f(c)=0.

B)We have to repeat the same steps of A)

For the subinterval [1,1.5]:

$f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13$

f(1) and f(1.5) have the same signs, this means there's no zero in the subinterval [1,1.5].

For the subinterval [1.5,2]:

$f(x)=3^x-x^4\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13\\\\f(2)=3^2-(2)^4=9-16=(-7)$

f(1.5) and f(2) have opposite signs, this means there's a zero between the subinterval [1.5,2].

C)We have to repeat the same steps of A)

For the subinterval [1,1.25]:

$f(x)=3^x-x^4\\\\f(1)=3^1-(1)^4=3-1=2\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5$

f(1) and f(1.25) have the same signs, this means there's no zero in the subinterval [1,1.25].

For the subinterval [1.25,1.5]:

$f(x)=3^x-x^4\\\\f(1.25)=3^1^.^2^5-(1.25)^4=3.94-2.44=1.5\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13$

f(1.25) and f(1.5) have the same signs, this means there's no zero in the subinterval [1.25,1.5].

For the subinterval [1.5,1.75]:

$f(x)=3^x-x^4\\\\f(1.5)=3^1^.^5-(1.5)^4=5.19-5.06=0.13\\\\f(1.75)=3^1^.^7^5-(1.75)^4=6.83-9.37=(-2.54)$

f(1.5) and f(1.75) have opposite signs, this means there's a zero between the subinterval [1.5,1.75].

For the subinterval [1.75,2]:

$f(x)=3^x-x^4\\\\f(1.75)=3^1^.^7^5-(1.75)^4=6.83-9.37=(-2.54)\\\\f(2)=3^2-(2)^4=9-16=(-7)$

f(1.75) and f(2) have the same signs, this means there isn't a zero between the subinterval [1.75,2].

The graph of the function shows that the answers are correct.

6 0

3 years ago

Select the correct answer.

Brums [2.3K]

Answer:

5 4/9

Step-by-step explanation:

Convert a mixed number 2 19

to a improper fraction: 2 1/9 = 2 19 = 2 · 9 + 19 = 18 + 19 = 199

To find new numerator:

a) Multiply the whole number 2 by the denominator 9. Whole number 2 equally 2 * 99 = 189

b) Add the answer from previous step 18 to the numerator 1. New numerator is 18 + 1 = 19

c) Write a previous answer (new numerator 19) over the denominator 9.

Two and one ninth is nineteen ninths

Add: 19

9+ (-29) = 19 + (-2)9= 179

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(9, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 9 = 81. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - nineteen ninths plus minus two ninths = seventeen ninths.

Conversion a mixed number 3 59

to a improper fraction: 3 5/9 = 3 59= 3 · 9 + 59= 27 + 51 = 329

To find new numerator:

a) Multiply the whole number 3 by the denominator 9. Whole number 3 equally 3 * 99 = 279

b) Add the answer from previous step 27 to the numerator 5. New numerator is 27 + 5 = 32

c) Write a previous answer (new numerator 32) over the denominator 9.

Three and five ninths is thirty-two ninths

Add: the result of step No. 2 + 32

9= 179+ 329 = 17 + 329 = 499

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(9, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 9 = 81. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - seventeen ninths plus thirty-two ninths = forty-nine ninths.

7 0

3 years ago

colleen truman earns aa 4.5% commission on all sales. in june, her sales totaled $40,000. how much did she earn in commission?

prisoha [69]

She earned 1,800$ in commission. Total=40,000$ multiply by the percentage which is 4.5% = 0.045
40,000 x 0.045=1,800$

8 0

3 years ago

Read 2 more answers

Bill has a rectangular garden that is 3 1/2 feet by 4 1/2 feet. A bag of fertilizer covers 5 1/4 square feet. What is the minimu

sveta [45]

Answer: