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3 years ago

Solve for x : 3/2 + 1/2x =2x

Mathematics

1 answer:

True [87]3 years ago

5 0

Answer: answer is x=1

Step-by-step explanation :Let's solve your equation step-by-step.

=2x

Step 1: Simplify both sides of the equation.

=2x

(

)=2x(Combine Like Terms)

2=2x

Step 2: Flip the equation.

2x=2

Step 3: Divide both sides by 2.

x=1

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Integrate 1/((x^5)*sqrt(9*x^2-1)) ...?

Korolek [52]

Let 9x^2-1 = y^2
=> 18xdx = 2ydy 
=> ydy = 9xdx 

lower limit = sqrt(9*2/9 - 1) = sqrt(1) = 1 
upper limit = sqrt(9*4/9 - 1) = sqrt(3) 

Int. [sqrt(2)/3,2/3] 1/(x^5(sqrt(9x^2-1)) dx 

= Int. [sqrt(2)/3,2/3] xdx/(x^6(sqrt(9x^2-1)) 
= 81* Int. [1,sqrt(3)] ydy/((y^2+1)^3y) 
=81* Int. [1,sqrt(3)] dy/(y^2+1)^3 

y=tanz 
dy = sec^2z dz 

=81*Int [pi/4,pi/3] cos^4(z) dz 
=81/4*int [pi/4,pi/3] (1+cos(2z))^2 dz 
=81/4* Int. [pi/4,pi/3] (1+2cos(2z)+cos^2(2z)) dz 

=81/4*(pi/3-pi/4) + 81/4*(sin(2pi/3)-sin(pi/2)) + 81/8 * (pi/3-pi/4) 
+ 81/32 *(sin(-pi/3)-sin(pi)) 
=81(pi/48+pi/96+1/4*(sqrt(3)/2 - 1) - 1/32 * sqrt(3)/2) 
=81/32*(pi+3sqrt(3)-8)

5 0

3 years ago

What is the surface area of this design?

Delvig [45]

Answer:

256

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

Greatest common factor of three univariate monomials. Find the greatest common factor of these three expressions.

Mice21 [21]

Answer:

$9w^{2}$

Step-by-step explanation:

An easy way to find the GCF of different numbers is to list out all of their factors. In this case, the coefficients share multiple factors, but the largest is 9.

Additionally, when dividing variables with different powers you subtract the exponents. So, if you were to divide $\frac{w^3}{w^2}$ the final answer would be $w$ because 3-2 is 1. So, to find the GCF of like variables find the biggest number that can be subtracted from all of them. In this case, that is 2; therefore, the GCF of the variables is $w^2$ . Put the 2 parts together for the final answer $9w^{2}$ .

7 0

3 years ago

Harrizon [31]

Answer:

none of the above

Step-by-step explanation:

the decimal equal to 32 is 32

7 0

3 years ago

Select the most accurate statement regarding the normal distribution. Group of answer choices It is always the appropriate distr

PSYCHO15rus [73]

Answer:

There is a 95% chance that values will be within ±2 standard deviations of the mean.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this question:

According to the empirical rule, 95% of the measures are within 2 standard deviations of the mean. So the correct statement is:

There is a 95% chance that values will be within ±2 standard deviations of the mean.

4 0

3 years ago