Which of the following is an extraneous solution of (45-3x)^((1)/(2))=x-9

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kiruha [24]

Answer: (1) d, f (2) c, d, f (3) e, f (4) a, b, c, d, f (5) e, f

Step-by-step explanation:

a) Natural Numbers: 1, 2, 3, ...

b) Whole Numbers: 0, 1, 2, 3, ... (add zero to the Natural numbers)

c) Integers: ..., -3, -2, -1, 0, 1, 2, 3, ... (add negatives to the Whole numbers)

d) Rationals: Add terminating and repeating decimals to Integers.

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e) Irrationals: Non-repeating decimals that are non-terminating. This is its own category so cannot be a Rational number or above.

f) Real Numbers: ALL of the above (a - e) are Real numbers.

1) -5.2 has a terminating decimal so it is a RATIONAL number.

2) -4 is below zero so is an INTEGER which means it is also a RATIONAL #

3) -4.3212... is a non-terminating decimal so it is an IRRATIONAL number

4) $\sqrt4$ = 2 is a NATURAL number which means it is also a WHOLE number, INTEGER, and RATIONAL number.

5) $\sqrt7$ is a non-terminating decimal so it is an IRRATIONAL number

6 0

3 years ago

Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = x − ln 8x, [1/2, 2]

insens350 [35]

The given function is
f(x) = x - ln(8x), on the interval [1/2, 2].

The derivative of f is
f'(x) = 1 - 1/x
The second derivative is
f''(x) = 1/x²

A local maximum or minimum occurs when f'(x) = 0.
That is,
1 - 1/x = 0 => 1/x = 1 => x =1.
When x = 1, f'' = 1 (positive).
Therefore f(x) is minimum when x=1.
The minimum value is
f(1) = 1 - ln(8) = -1.079

The maximum value of f occurs either at x = 1/2 or at x = 2.
f(1/2) = 1/2 - ln(4) = -0.886
f(2) = 2 - ln(16) = -0.773
The maximum value of f is
f(2) = 2 - ln(16) = -0.773
A graph of f(x) confirms the results.

Answer:
Minimum value = 1 - ln(8)
Maximum value = 2 - ln(16)

4 0

3 years ago

Lee needs of pieces of wire that are each 2/5.how manypieces can he cut from 6 ft long

Oksanka [162]

6 / 2/5
6 * 5/2
30/2
15
15 pieces of wire

Answer: 15 pieces of wire

4 0

3 years ago

Read 2 more answers

GO.o has 3 orange picks for every 2 green. If there are 25 picks in all, how many picks are orange?

Reika [66]

Given

GO.o has 3 orange picks for every 2 green

there are 25 picks in all

Find out how many picks are orange.

To proof

As given in question

GO.o has 3 orange picks for every 2 green

i.e the ratio of orange to every green becomes

$\frac{Orange}{Green}:\frac{3}{2}$

total number of picks = 25

let the GO.o pick of 3 orange picks for every 2 green =x

than the equation becomes

3x + 2x = 25

5x = 25

x = 5

Than

the number of oranges = 3x

putting the value of x

= 15

the number of green = 2x

= 10

thus the 15 picks are orange.

Hence proved

4 0

3 years ago

Read 2 more answers

The probability distribution of the number of students absent on Mondays, is as follows: X 0 1 2 3 4 5 6 7 f(x) 0.02 0.03 0.26 0

alexgriva [62]

a) Add up all the probabilities $f(x)$ where $x>3$ :

$f(4)+f(5)+f(6)+f(7)=0.35$

b) The expected value is

$E[X]=\displaystyle\sum_xx\,f(x)=3.16$

Since X is the number of absent students on Monday, the expectation E[X] is the number of students you can expect to be absent on average on any given Monday. According to the distribution, you can expect around 3 students to be consistently absent.

c) The variance is

$V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2$