Which of the following is rational
A. 3*pi
B. 2/3+9.26
C. sqrt of 45 + sqrt of 36
D.14.3... + 5.78765239...
How would I find a given triangle where: A=0.1, B=1 and c=9? Thanks in advance.
C=
a=
b=
Estimate instantaneous rate of change of the point indicated p(x) = 3x^2-5, x = 2
Hi, How do you find the first and second derivatives of the function.
y=(x^2-7/63x) (x^4+1/x^3)
I think for the first derivative dy/dx it's 2/63x-3/63x^-3+4/9x^-5 but I'm not sure, and I have no clue for the second derivative d^2y/dx^2.
The first hand derivative of the function is [tex]6x^5 - \frac{35}{63}x^4 - \frac{1}{x^2} - \frac{4}{63x^3}[/tex] and the second derivative is [tex]30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]. To find the first derivative, apply the product rule to the given function. Then, differentiate the first derivative to obtain the second derivative. Simplify each step carefully.
To find the first derivative of the given function [tex]y = \left( x^2 - \frac{7}{63}x \right) \left( x^4 + \frac{1}{x^3} \right)[/tex], we'll use the product rule, which states that if [tex]y = u(x) \cdot v(x)[/tex], then [tex]y' = u' \cdot v + u \cdot v'[/tex].
First, define u(x) and v(x) as following:
[tex]u(x) = x^2 - \frac{7}{63}x = x^2 - \frac{1}{9}x[/tex][tex]v(x) = x^4 + \frac{1}{x^3}[/tex]Compute u'(x):
[tex]u'(x) = 2x - \frac{1}{9}[/tex]Compute v'(x):
[tex]v'(x) = 4x^3 + (-3)x^{-4} = 4x^3 - \frac{3}{x^4}[/tex]Apply the product rule: [tex]y' = u' \cdot v + u \cdot v'[/tex]
Thus,
[tex]y' = \left(2x - \frac{1}{9}\right)\left( x^4 + \frac{1}{x^3} \right) + \left( x^2 - \frac{1}{9}x \right) \left( 4x^3 - \frac{3}{x^4} \right)[/tex]Simplify this expression step-by-step to find the first derivative.
[tex]y' = \left(2x - \frac{1}{9}\right)\left( x^4 + \frac{1}{x^3} \right) + \left( x^2 - \frac{1}{9}x \right) \left( 4x^3 - \frac{3}{x^4} \right)[/tex][tex]y'[/tex] [tex]&= \left(2x \cdot x^4 + 2x \cdot \frac{1}{x^3} - \frac{1}{9} \cdot x^4 - \frac{1}{9} \cdot \frac{1}{x^3} \right)[/tex][tex]&\quad + \ \left( x^2 \cdot 4x^3 - x^2 \cdot \frac{3}{x^4} - \frac{1}{9}x \cdot 4x^3 + \frac{1}{9}x \cdot \frac{3}{x^4} \right)[/tex][tex]y'[/tex] [tex]&= 2x^5 + \frac{2}{x^2} - \frac{1}{9}x^4 - \frac{1}{9x^3} \\[/tex] [tex]&\quad + \ 4x^5 - \frac{3}{x^2} - \frac{4}{9}x^4 + \frac{1}{3x^3}[/tex][tex]y'[/tex] [tex]&= 6x^5 - \frac{1}{x^2} - \frac{5}{9}x^4 + \frac{2}{9x^3}[/tex][tex]y'[/tex] [tex]&= 6x^5 - \frac{5}{9}x^4 - \frac{1}{x^2} + \frac{2}{9x^3}[/tex]To find the second derivative, differentiate the first derivative, carefully differentiating each term:
[tex]y'' &= \frac{d}{dx}\left( 6x^5 \right) - \frac{d}{dx}\left( \frac{5}{9}x^4 \right) - \frac{d}{dx}\left( \frac{1}{x^2} \right) + \frac{d}{dx}\left( \frac{2}{9x^3} \right) \\[/tex][tex]y''[/tex] [tex]&= 30x^4 - \frac{5}{9} \cdot 4x^3 - \left( -2x^{-3} \right) + \left( -\frac{2}{9} \cdot 3x^{-4} \right) \\[/tex][tex]y''[/tex] [tex]&= 30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]So, for the function [tex]y = \left( x^2 - \frac{7}{63}x \right) \left( x^4 + \frac{1}{x^3} \right)[/tex], we have:
First derivative [tex](y')[/tex] [tex]&= 6x^5 - \frac{5}{9}x^4 - \frac{1}{x^2} + \frac{2}{9x^3}[/tex]Second derivative [tex](y'')[/tex] [tex]&= 30x^4 - \frac{20}{9}x^3 + \frac{2}{x^3} - \frac{2}{3x^4} \\[/tex]lisha is making headbands using ribbon. she would like to make 12 head bands. Each one requires 15.5 inches of ribbon. She estimates that she will need to buy 160 inches of ribbon is her estimate reasonable? Explain your reasoning and lol I'm not in college i just did that
John throws a rock straight down with speed 12 m/s from the top of a tower. the rock hits the ground after 2.37 s. what is the height of the tower? (air resistance is negligible)
120 × a = 2889 what is the product
a line that intersects the points (-23,-17) and (-13,-7), find the slope, now fill in the missing inputs to the slope-intercept formula -17=1(?)+b or (?)=(-13)+b
What is the margin of error for a sample statistic for a population with a standard deviation of 11.3?
The margin of error for a sample statistic requires the population standard deviation, the desired confidence level, and the sample size. It is found by multiplying the z-score for the confidence level with the standard error, which is the population standard deviation divided by the square root of the sample size. For a 95% confidence interval, the error bound is factored into the sample mean to estimate the population mean.
The margin of error for a sample statistic depends on the level of confidence desired and the sample size. Using the population standard deviation, we can calculate the margin of error by finding the z-score associated with the desired confidence level and multiplying it by the standard error. The standard error is calculated as the population standard deviation (11.3) divided by the square root of the sample size (n).
Based on the example given referencing an error bound for the mean (3.2), a 95% confidence interval could be constructed by adding and subtracting the error bound from the sample mean (15). Therefore, the 95% confidence interval estimate for the population mean would be (11.8, 18.2).
When a sample standard deviation is provided instead of a population standard deviation, and if the sample size is small, the Student's t-distribution should be used instead of the normal distribution.
For a 95% confidence interval, we generally use 1.96 as the z-score for a normal distribution, but this value could change depending on specific confidence levels or other distributions like the t-distribution.
A point is located in a polar coordinate system by the coordinates r = 2.8 m and θ = 18°. find the x- and y-coordinates of this point, assuming that the two coordinate systems have the same origin.
You would like to join a fitness center. Fit-N-Trim charges $80 per month. Fit-For-Life charges a one tim e membership fee of $75 and $55 per month. The lines shown in the graph represent the cost y to attend each fitness center for x months. Are the lines parallel?
Jeff invests an amount at 4% interest compounded annually. After 3 years, he has $1687.30. What was the original amount Jeff invested?
$1500
$1200
$1450
$750
Two numbers total 53 and have a difference of 25. Find the two numbers.
A rectangular swimming pool has a volume capacity of 2160 cubic feet. Water is being added to the pool at a rate of about 20 cubic feet per minute. Determine about how long it will take to fill the pool completely if there were already about 1200 gallons of water in the pool.
Answer:
Step-by-step explanation:
y=mx+b
2160=20x+60.417)
2160= 20x+160.417
2160-160.417=20x+160.417-160.417
1999.583=20x
1999.583/20=20x/20
x= 99.98 min
Total time taken to fill the pool is 100 minutes
Given:
Amount of water already in pool = 1200 gallon
Total capacity of pool = 2160 cubic feet
Rate of water supply = 20 cubic feet per minute
Find:
Total time taken to fill the pool
Computation:
1 cubic feet = 7.5 gallon water
Amount of water already in pool = 1200 / 7.5
Amount of water already in pool = 160 cubic feet
Remain volume = 2160 - 160
Remain volume = 2000 cubic feet
Total time taken to fill the pool = 2000 / 20
Total time taken to fill the pool = 100 minutes
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At Crescent High School, 120 students plan on going to an in-state college and 70 students plan on going to an out-of-state college. What is the ratio of students planning on going to an in-state college to students planning on going to an out-of-state college?
One side of a rectangle is 3 inches shorter than the other side, and the perimeter is 54 inches. Which of the following equations could be used to determine the dimensions of the rectangle
A college freshmen must take a science course, a humanities course and a mathematics course. If she may select any of 6 science courses, any of 4 humanities and any of 4 mathematics courses, how many ways can she arrange her program? Make a tree diagram and list the possibilities.
You swim 121 out of 1,000 meters. How can you write this as a decimal
The number in decimal form will be 0.121 meters.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that you swim 121 out of 1,000 meters. The decimal for the number will be written by dividing the number by 1000.
Decinmal form = 121 / 1000
Decimal form = 0.121 meters
Therefore, the decimal form of the number will be 0.121 meters.
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Ordering Least to greatest 2 9/11, 4/5, 2.91, 0.9
A 20-foot cable hangs from the top of a building that is 50 feet high. if the cable weighs 2 pounds per foot, how much work is done in lifting up the entire cable to the top of the building?
To find the work done in lifting the entire cable to the top of the building, multiply the weight of the cable by the height of the building.
Explanation:To calculate the work done in lifting the entire cable to the top of the building, we need to find the weight of the cable. The weight of the cable can be found by multiplying the length of the cable (20 feet) by its weight per foot (2 pounds per foot). Therefore, the weight of the cable is 20 feet × 2 pounds per foot = 40 pounds.
The work done in lifting the cable to the top of the building is equal to the product of the weight of the cable and the height of the building. So, the work done is 40 pounds × 50 feet = 2000 foot-pounds.
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In an x-y plot of an experiment what is usually plotted on the x axis?
a. the independent variable, which is the parameter that was manipulated.
b. th
HELP! solve for p p+10/p-7=8/9
Solve for x.
−5x−4(x−6)=−3
-5x -(4x-6) = -3
-5x -4x + 24 = -3
-9x = -27
x= 3
marissa sprinted for 48 yards. how many feet did she sprint.
How would you define the traformation "dilation"? what happens to a shape when it is dilated? What changes? what stays the same?
Last year, there were 12,000 students at a local college. There were 2000 more female students than male students. How many male and female students attended the college?
what is the digit in the tenths place 15.16 ?
Lakeya makes cupcakes to sell at her friend's lemonade stand. She sold 24 cupcakes and sold them for $3 each. Write a number sentence using the variable m to represent the total amount of money she made.
Multiple choice strategy: some students have suggested that if you have to guess on a multiple-choice question, you should always choose
c. carl, the student, wants to investigate this theory. he is able to get a sample of past tests and quizzes from various teachers. in this sample there are 110 multiple-choice questions with four options (a, b, c, d). the distribution of correct answers from this sample is given in the frequency table below. correct answer frequency a 22 b 26 c 38 d 24
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5, and m∠JKL = x − 1. Find the measure of each angle.
∠DFG and ∠JKL are complementary angles
Measure of each angle
[tex]m<DFG=48\\m<JKL= 42[/tex]
Given :
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,
and m∠JKL = x − 1
When two angles are complementary then the sum of angles is 90 degrees
∠DFG and ∠JKL are complementary angles.
So, [tex]m<DFG+m<JKL =90[/tex]
Now replace the expressions and solve for x
[tex]x+5+x-1=90\\2x+4=90\\2x=90-4\\2x=86\\x=43[/tex]
Now replace x with 43 and find out each angle
[tex]m<DFG= x+5\\m<DFG= 43+5=48\\\\m<DFG=48\\m<JKL=x-1=43-1=42[/tex]
[tex]m<DFG=48\\m<JKL= 42[/tex]
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