log(x(x^2 + 3)^−1/2)

Answers

Answer 1
The solution of given logarithmic equation is:

          =  [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]

Step-by-step explanation:

Given that

The logarithmic equation

            [tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]

To find

The solution of this given logarithmic equation

So, according to the question

we have,

The logarithmic equation

            [tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]

We know that,

    ∵ log(m.n) = logm + logn

Now using this property to solve that logarithmic equation

          =  [tex]log(x.(x^2 + 3 )^{\frac{-1}{2} })[/tex]

          =  [tex]logx+log(x^2 + 3 )^{\frac{-1}{2} }[/tex]

We know that,

    ∵ log(mⁿ) = nlogm

Now using this property to solve that logarithmic equation

          =  [tex]logx+log(x^2 + 3 )^{\frac{-1}{2} }[/tex]

          =  [tex]logx+({\frac{-1}{2} )log(x^2 + 3 )[/tex]

          =  [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]

This is the the solution of given logarithmic equation.

Logarithmic equation.

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number. The logarithm, in its most basic form, counts the number of times the same factor appears when multiplied repeatedly; for instance, since 1000 = 10 x 10 x 10 = 103, its "logarithm base 10" is 3, or log10 (1000) = 3. When there is no possibility of confusion or when the base is irrelevant, as in big O notation, the logarithm of x to base a is written as logₐ (x), logₐ x, or even without the explicit base, log x.

Answer:

          =  [tex]logx-{\frac{1}{2} log(x^2 + 3 )[/tex]

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Related Questions

LeAnn wants to gift wrap a present she got for her little brother. How many square inches of gift wrap will be needed to cover a box that is 4 in x 6 in x 2 in ? In your final answer, include all of your calculations.

Answers

All calculations for answer in picture form

Answer:

There are 88 square inches needed to cover a box that is 4 in • 6 in • 2 in

Step-by-step explanation:

In order to cover the box you need to find the surface area of it. The formula for finding the surface area of a rectangular prism is 2 ((wl) + (hl) + (hw)). The dimensions of the box is 4 inches in length, 6 inches in width, and 2 inches in height.

Apply the dimensions into the formula of the rectangular prism when the numbers are plugged in it results in 2 ( (64) + (24) + (26) )Multiply the dimensions the area of length• width is 24 (six times four is twenty-four), the area of height•width is 8 (two times four is eight), and the area of height•width is 12 (two times six is twelve). At the end of this step it becomes 2 ((24) + (8) + (12))Add all the numbers inside the parentheses then it becomes 2 (44) Multiply the number in parentheses by 2 the final answer is 88 in²

Shreya is training for a marathon. The graph shows the miles she ran each day of her training. Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. How far did Shreya run on day 5 of her training? Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.

Answers

She ran the distance on the day of 5 is 2miles.

Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.

⇒ (8-6-3-7)/5

⇒ (-8)/5

⇒ 1.8

⇒ 2 miles

The fraction whose numerator is 8 minus 6 minus 3 minus 7, whose denominator is 5 which is equal to the fraction of 2 miles.

Hence, Shreya ran on the day of 5 in her training is 2 miles.

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To find the quotient 104/8 104 as an expression with partial products

Answers

The value of the quotient 104/8 is 13

How to rewrite the expression as a partial product?

The quotient expression is given as

104/8

Express 104 as 80 + 24

So, we have

104/8 = (80 + 24)/8

Split the fraction in the above expression

So, we have

104/8 = 80/8 + 24/8

Evaluate the quotients

So, we have

104/8 = 10 + 3

Evaluate the sum

So, we have

104/8 = 13

Hence, the value of the quotient 104/8 is 13

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Answer this!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Based on the distance between the park bench and the basketball court, the distance between the park bench and the pond is 57¹/₈ feet

What is the distance between the park bench and pond?

The distance between the park bench and the basketball is the sum of the distance between the park bench and the pond and the pond and the basketball court.

The distance between the park bench and the pond is therefore:

= Distance between park bench and basketball court - Distance between pond and basketball court

Solving gives:

= 75³/₄ - 18⁵/₈

= 75.75 - 18.625

= 57.125

= 57¹/₈ feet

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Answer:h

el]lo you commented on a post that helped me alot

Step-by-step explanation:

PLS HELP!! Write an equation in point-slope form for a line that passes through the given set of points. (-1,-2)(-3,1)

Answers

m=-3/2 hope this helps

if a ball is thrown into the air with a velocity of 20 ft/second it's height in feet and seconds is given by f(t) = 20t - 10t^2. find average velocity for the time period t0 = 1 to t=2

Answers

The average velocity is  -10 ft/s.

What is Average velocity?

Average velocity is just the average speed with a direction. If a trip starts and ends at the same point, the total displacement is zero, so the average velocity is zero.

For example, someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph).

Given:

f(t) = 20t - 10t²

Now, from t=1 to t=2

f(1)= 20*1 - 10 * 1*1

f(1)= 10

and, f(2)=20*2-10*2*2

f(2)= 40-40

f(2)=0

Now,

Average velocity:

v = ( 0-10 ) / ( 2- 1 )

  = -10 ft/s

hence, the average velocity is  -10 ft/s.

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trista has 3 3/4 yards of ribbon to use for making decorative pillows. if the first pillow used 2 1/6yards of ribbon then how much risson is remaining

Answers

Answer:

1 1/2 yards

Step-by-step explanation:

Give Brainliest if I helped!

Evaluate. Write your answer as a fraction in simplest form. 3/8 - 1/6 + 5/12​

Answers

Answer:

5/8

Step-by-step explanation:

Get LCD of 24  and do the math

9/24 - 4/24 - 10/24

15/24

Divide top and bottom by 3

5/8

Answer is 5/8 that is what I got

Find the mean of the data set shown in the table below.
Data Set E
1.69
0.85
0.23
1.6
0.08

Answers

Mean =total value/number of values
= (1.69+0.85+0.23+1.6+0.08)/5
=4.45/5
=0.89
4.45 I believe!!!!!!!!!!!

I have no clue, someone help me out

Answers

The answer would be 6 units I believe.
Counting the squares that form the rectangles gives you 6. Two triangles are halves of a a square, so two triangles give you one unit.

532,8 g = kg? [1]
O 5,328 kg
O 5 328 kg
O 0,532 8 kg
O 53,28 kg
O None of the given answers

Answers

The answer is 0,532 8 kg

Explanation:

Convert from g to kg by dividing by 1000.

532,8/1000 = 0,532 8kg

I hope this helps!!

The aquarium has 10 more red fish than blue fish. 60% of the fish are red. How many blue fish are in the aquarium?

Answers

Blue fish= 20
Red fish=30
EXPLANATION:
60%=red (10more than blue)
40%=blue(10 less)
60-40=20 (20%=10)
10%=5 meaning 100%=50
40% of 50= 20
VERY SORRY IF IM WRONG OR IF IM TOO LATE AND U ALREADY DID IT

please help
maths geometry

Answers

Step-by-step explanation:

ABCD is a rectangle.

so, it has 2 pairs of equal and parallel sides.

all 4 angles are 90°.

both diagonals are equally long and intersect each other at their midpoint. so, all 4 half-diagonal segments are equally long.

(1)

2x + 4y = 4x - y = 36/2 = 18 cm

we can split this into 2 equations

2x + 4y = 4x - y

5y = 2x

x = 5y/2

and e.g.

4x - y = 18

now we use the first equation in the second

4(5y/2) - y = 18

20y/2 - y = 18

10y - y = 18

9y = 18

y = 2

x = 5y/2 = 5×2/2 = 5

(2)

I cannot draw here, but the shortest distance between a point and a line is always a height (a line segment from the point meeting it intersecting the line at a right angle, 90°).

(3)

e.g.

AE, AD/2 and the drawn height from E to AD create a right-angled triangle.

we know AD/2 = 15 cm

from (1) we know AE = 4x - y = 4×5 - 2 = 20 - 2 = 18 cm.

the height E to AD we get via Pythagoras

AE² = (AD/2)² + height²

height² = AE² - (AD/2)² = 18² - 15² = 324 - 225 = 99

height = sqrt(99) = sqrt(9×11) = 3×sqrt(11)

remember trigonometry ?

this height = sin(theta) × AE

sin(theta) = height / AE = 3×sqrt(11) / 18 = sqrt(11)/6 =

= 0.552770798...

theta = 33.55730976...° ≈ 34°

(4)

the diagonals of a square bisect the angles of the square, so that theta would become 90/2 = 45°.

An isolated agricultural country has two distinct regions: a lowland plain and an upland of rugged hills. On one unit of land on the PLAIN, a farmer can raise 10 bushels of grain or graze 10 sheep. On one unit of land in the HILLS, a farmer can raise 2 bushels of grain or graze 4 sheep.
Determine which region has the absolute advantage for sheep production. Explain your answer.

Answers

Hills region has the advantage for sheep production because when a farmer raised 2 bushels of grain, then gaze 4 sheep.

The most popular animal fiber is sheep's wool, which is often gathered by shearing. In Commonwealth nations, ovine meat is referred to as lamb when it comes from younger animals and mutton when it comes from older ones; in the United States, meat from both older and younger animals is often referred to as a lamb.

Today, sheep are still farmed for their meat and wool, as well as on occasion for their pelts, as dairy animals, or as scientific model organisms. Most of the world's populated areas engage in sheep farming, which has been a foundational activity for several civilizations.

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Bailey Co earns $13249 of revenue on account and in $6167 cash revenue transactions in Year 1. Cash collections of receivables amount to $5849 in Year 1 with the remainder being collected in Year 2. Based on this information alone the company’s financial statements would show

Answers

Based on this information alone the company’s financial statements would show Cash inflows for Year 1 $13,567

What is cash inflow from sales?

The cash inflow from sales indicates the amount of cash received from customers in the current based on sales made to customers, which is the sales revenue, cash and credit added together minus the balance of credit sales left uncollected from customers at the end of the year.

Cash inflows for Year 1=credit sales+cash sales+receivables

credit sales=$13249

cash sales=$6167

receivables= $5849

Cash inflows for Year 1=$13249+$6167-$5849

Cash inflows for Year 1=$13,567

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Full question:

Bailey Co earns$13249  of revenue on account and in $6167 cash revenue transactions in Year 1. Cash collections of receivables amount to $5849 in Year 1 with the remainder being collected in Year 2. Based on this information alone the company’s financial statements would show Cash inflows for Year 1 $_

Alejandro's goal was to ride 36 kilometers. His app says he rode 75% of his goal. How far did he ride?

Answers

Answer:

27 kilometers

Step-by-step explanation

i big brain and u not

u can use a calculator lol

represent the expression please help

Answers

Answer:

  10,350.98

Step-by-step explanation:

The decimal number is the sum of the terms of the expression.

Sum

  (1×10,000) +(3×100) +(5×10) +(9×1/10) +(8×1/100)

  = 10,000 +300 +50 +0.9 +0.08

  = 10,350.98

__

Additional comment

If you can't do this in your head, you can input the expression to your calculator, and it will give this same result.

The data represents the time in minutes spent reading a political blog in a day construct a frequency distribution focuses in the table include the midpoint related frequencies and cumulative frequencies which class has the greatest frequency in which class has the least frequency

Answers

The required midpoint of the given data is 16,  and, class interval 10 - 15 has the higher frequency, and class interval 5 - 10 has a null frequency.

Here,
Arranging the time in minutes spent on reading a political blog in a day,
3 3 11 12 13 13 15 16 19 19 20 22 25 26 26
The required mid-point is 16.

Since the values vary from 3 to 26 and we have to make 5 classes,
So the number of
          classes     midpoint            frequency            cumulative
         0 - 5              2.5                          2                       2
         5 - 10             7.5                          0                       2
         10 - 15           12.5                         5                       7
         15  - 20         17.4                         4                       11
        20  - 25         22.5                        3                       14
        25  - 30         27.5                        2                       16


Thus, the required midpoint of the given data are shown, and, class interval 10 - 15 has the higher frequency, and class interval 5 - 10 has a null frequency.

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Round 24,990 to the nearest ten thousand

Answers

Answer:

30,000

Step-by-step explanation:

If not, try 25,000

Answer:

25,000

Step-by-step explanation:

brainlest please

Use algebraic methods to prove that the given function has an x-intercept that is equal to its y-intercept. In your final
answer, include all of your calculations.
y= x/x^2-1

Answers

Step-by-step explanation:

the y-intercept is the y value when x = 0.

the x-intercept is the x value when y = 0.

for x = 0

y = 0 / (0² - 1) = 0/-1 = 0

this automatically answers also our question about the x value when y = 0. we found this out already with the y-intercept.

the interception point with both coordinate axis is (0, 0).

A casual fast food restaurant offers 4 different toppings that each can be served over one of 3 bases: a piece of fry bread, a salad, or on rice. Further, customers can choose one of 3 different sauces to be served with their order.



How many distinct filling-base-sauce combinations does a customer at this restaurant have to choose from?

Answers

Answer: 36 combinations

Step-by-step explanation:

Since you have 4 toppings, 3 bases and 3 sauces, you can just multiply them to get the different combos.

4 * 3 * 3

= 36

An accounting machine operator wanted to divide a 65 minute job between two identical machines so that one machine would take one and a half times as long as the other. How much time was taken by the machine doing the longer job?

Answers

The slow machine did the job is 39 minutes as calculated with the help of a linear equation in one variable.

A linear equation in one variable is given by the combination of the variable with constants and coefficients such that a unique relationship is established between the terms.

Let us consider the faster machine takes x minutes the finish the job.

Hence the slower machine will take one and a half times .

∴ slower machine takes 1.5 x minutes.

Total time taken by the two machines = x + 1.5x = 2.5 x

But together the two machines will take 65 minutes to complete the job .

So now we form a linear equation with the variable x to solve for the value of x

∴ 2.5 x = 65

or, x = 65 ÷ 2.5

or, x = 26 minutes

Therefore the faster machine takes 26 minutes.

Hence the slower machine will take 1.5 x = 1.5 × 26 = 39 minutes.

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6. Bill can afford a monthly payment of $475. He wants to take out a $20,000 loan at 4.25%
interest rate. What should the length of the loan be? Round your answer to the nearest year.

Answers

Answer:   4 years

====================================================

Work Shown:

L = 20,000 = loan amountP = 475 = monthly paymenti = 0.0425/12 = 0.0035417 approximately is the decimal form of the monthly interest raten = unknown number of months

Let A = P/i = 475/0.0035417 = 134116.384787 approximately

Then,

[tex]n = \frac{\text{Ln}(A) - \text{Ln}(A-L)}{\text{Ln}(1+i)}\\\\n \approx \frac{\text{Ln}(134116.384787) - \text{Ln}(134116.384787-20000)}{\text{Ln}(1+0.00354)}\\\\n \approx \frac{11.80646 - 11.64497}{0.00353}\\\\n \approx \frac{0.16149}{0.00353}\\\\n \approx 45.74788\\\\n \approx 46[/tex]

It will take about 46 months to pay off the loan.

Divide by 12 to convert from months to years.

46 months = 46/12 = 3.83333 years approximately

That rounds to 4 years

Which number set is the most reasonable to describe a baby’s weight at birth?


Whole numbers


Rational numbers


Irrational numbers


Integers

Answers

Rational numbers… most babies don’t weigh exactly a whole number, so you might need to use decimals or fractions. (i.e. 3.2 kg/7 lbs 1 oz)

You order two coffees and a cookie. The cookie costs $2.40. You pay 5% sales tax
and leave a $1.75 tip. You pay a total of $11.20. How much does one coffee cost?

Answers

Answer:

~ $3.29

Step-by-step explanation:

$11.20 - $1.75 = $9.45

$9.45 - $0.48 5% = $8.97

$8.97 - $2.40 = $6.57

$6.57 ÷ 2 = $3.285 rounded to $3.29

Which set of numbers includes both rational and irrational numbers? Please HELPP IVE BEEN TRYING FOR 2 HRS ​

Answers

Answer: Option 2 should be the answer.

Step-by-step explanation: Real numbers are divided into two groups called rational and irrational numbers. Irrational numbers cannot be expressed as fractions.

Hopefully, this question will help you.

Have a great day!

PLEASE HELP ME WITH THIS I HAVE A TEST TMR

Answers

Answer:

Go to Khan Academy and Search "Finding Slope from graph"

Step-by-step explanation:

That video will help better instead of typing it!

Problem 2: A storm causes a 14m hydro pole to lean over. The pole leans at an angle of 72° to
the ground. How high is the top of the pole from the ground?

Answers

The top of the pole from the ground is 13.314798.

Given condition, formulate :

= 14 * sin (72°)

= 4 sin 72°

= 14 * 0.951057

= 13.314798

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant, cosine , cotangent , secant , sine , and tangent .

The trigonometric function can be described as being even or odd.

Odd trigonometric functions: A trigonometric function is said to be an odd function if f(-x) = -f(x) and symmetric with respect to the origin.

Even trigonometric functions: A trigonometric function is said to be an even function, if f(-x) = f(x) and symmetric to the y-axis.

Hence, the top of the pole from the ground is 13.314798.

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Members of a softball team raised $1353 to go to a tournament. They rented a bus for $943.50 and budgeted $31.50 per player for meals. Write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
equation:
x=

Answers

Answer:

13 players

Step-by-step explanation:

1353 - 943.50 = 409.50

$31.50 per player for meals

31.50*x = 409.50

x = 13

13 players

To test the ability of mechanics to identify simple engine problems, a car with a single such problem was taken in turn to 72 different car repair facilities. Only 42 of the 72 mechanics who worked on the car correctly identified the problem. Does this strongly indicate that the true proportion of mechanics who could identify this problem is less than 0.75?


a) Perform the appropriate test of hypothesis using = 0.01. Clearly show the eight (8) steps

Answers

Using the z-distribution, it is found that since the p-value is less than 0.01, there is strong indication that the true proportion of mechanics who could identify this problem is less than 0.75.

What are the hypotheses tested?

At the null hypotheses, it is tested if there is not enough evidence that the proportion is less than 0.75, that is:

[tex]H_0: p \geq 0.75[/tex]

At the alternative hypotheses, it is tested if there is enough evidence that the proportion is less than 0.75, that is:

[tex]H_1: p < 0.75[/tex]

What is the test statistic?

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.

For this problem, the parameters are given as follows:

[tex]n = 72, \overline{p} = \frac{42}{72} = 0.5833, p = 0.75[/tex]

Hence the test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.5833 - 0.75}{\sqrt{\frac{0.75(0.25)}{72}}}[/tex]

z = -3.27.

What is the p-value of the test?

Considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -3.27, the p-value is < 0.01.

Since the p-value is less than 0.01, there is strong indication that the true proportion of mechanics who could identify this problem is less than 0.75.

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