The approximate speed-up ratio between pipelined and non-pipelined system to execute 100 instructions is 4.03
The term ratio in math defines as an ordered pair of numbers a and b, written a / b where b does not equal 0.
Here we have given that
And we need to determine the approximate speed-up ratio between pipelined and non-pipelined system to execute 100 instructions.
While we looking into the given question we have identified the following values,
=> Number of pipeline segments = stages in pipeline,
=> n = 5
Here we know that,
=> Clock cycle time per operation = clock cycle per stage = 14 ns
And the number of instructions = 100
Here the formula to calculate the startup is written as,
=> T[without pipeline] = no. of instructions × stages in pipeline × clock cycle per stage
=> 100 × 5 × 14
=> T[with pipeline] = (time for pipelined execution without stalls) + (overhead due to stalls)
=> (5 + 99) × 20 + 20 × 20 = 124 × 20
Therefore, the startup is
=> [500 x 14] / [124 x 14]
=> 4.03
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study smarter a scatterplot of versus shows a positive, nonlinear association. two different transformations are attempted to try to linearize the association: using the logarithm of the -values and using the square root of the -values. two least-squares regression lines are calculated, one that uses to predict and the other that uses to predict which of the following would be the best reason to prefer the least-squares regression line that uses to predict
The best reason to prefer the least-squares regression line that uses to predict is the Standard Deviation of the residuals is smaller.
Least Squares Regression:
Least squares is a mathematical technique that allows analysts to determine the best way to fit a curve to a graph of data points. It is commonly used to make scatterplots easier to interpret and is associated with regression analysis. Least squares is now available as part of most statistical software programs.
There are two least-squares regression lines, one to predict log(y) using x and the other to use for prediction.
a. A small value of means that the variance is explained poorly compared to the model that predicts instead, and thus the model is a poorer model. Therefore, there is no compelling reason to choose a model that predicts logic in.
b. If the standard deviation of the residuals is not too high, there will be less variability between the actual and predicted values, and thus the model will be more accurate. Therefore, there are compelling reasons to favor a model that predicts.
C. The magnitude of the slope has no effect on whether a model is good or bad, so it's not the best reason to favor a model that expects log y and x.
d. The presence of more random variation in the number of residuals does not necessarily indicate a superior model. The reason for this is that the variation between the expected and actual values is large, which can lead to large variability. This means that there is no compelling reason to prefer a model that uses to predict log y. It is normal that the distribution of residuals of residuals does not affect model quality. As a result, this is not the best reason.
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A biologist is studying a plant blight. At the start of their research, the blight covers a circular area with a radius of 5 kilometers. When they re-examine the blight two years later, the area has grown to a circular area with a radius of5.2kilometers. How rapidly did the radius change over the interval? _____Year/km
Step-by-step explanation:
Area of circle 1= pie r²
=3.14 x 5²
=3.14x 25
= 78.5km²
Area of circle 2=3.14 x 5.2²
= 3.14 x 27.04
= 84.9km²
change in area= 84.9-78.5
=6.4
radius²= 6.4/ 3.14
r²=2.03
r =√2.03
r=1.42
Debs and Jamie share sweetss in the ratio 3:7. Debs has 20 less sweets than Jamie. How many sweets are there in total? Show all workings please
Using ratios we know that the total number of sweet Debs and Jamie has is 50.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
Two quantities are compared to form a ratio.
An equality of two ratios is a proportion.
How to format a ratio Analyze the ratio to see whether it is part to part or part to whole.
Calculate the whole and the pieces as necessary.
So, we have a ratio of 3:7.
Debs has 20 fewer sweets than Jamie.
Let, Jamie have x sweets and Debs has x - 20.
Now, we get the equation:
3/x - 20 = 7/x
Now, solve as follows:
3/x - 20 = 7/x
3x = 7(x - 20)
3x - 7x - 140
7x - 3x = 140
4x = 140
x = 140/4
x = 35
x - 20 = 35 - 20 = 15
Total: 35 + 15 = 50
Therefore, using ratios we know that the total number of sweet Debs and Jamie has is 50.
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Write an equation of the line that passes through (-1,3) and is parallel to the line y=-3x+2
Slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptParallel lines always have the same slopes and different y-intercepts.
Solving the QuestionWe're given:
Parallel to [tex]y=-3x+2[/tex]Passes through (-1,3)Because parallel lines have the same slopes, this line therefore has a slope of -3.
[tex]y=-3x+b[/tex]
Now, plug in the given point to solve for b:
[tex]3=-3(-1)+b\\3=3+b\\b=0[/tex]
Therefore:
[tex]y=-3x[/tex]
Answer[tex]y=-3x[/tex]
Decide if the given value of x is a critical number for f, and if so, decide whether the point for x on f is a relative minimum, relative maximum, or neither.
f(x) = ( x + 5)^4; x = - 5
A. Critical number; maximum at (-5 , 0)
B. Critical number; minimum at (-5 , 0)
C. Not a critical number.
D. Critical number but not an extreme point.
The value of the function after evaluation is , f(x)=0 . Hence it is neither a minima nor a maxima.
f(x) =(x + 5)^4; x = - 5
=(-5+5)^4
=(0)^4
=0
The critical value is crucial for accurately portraying a range of properties in statistics. The critical value can be helpful for proving or disproving ideas when they are tested, in addition to validity and accuracy.
If you're taking a statistics course or are just interested in how these concepts work, it is essential to comprehend critical value and how to compute it before analyzing other statistical functions, such as margin of error and significance.
When calculating the margin of error for a set of data, statisticians utilize a measurement known as the critical value.
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Find the distance between the points.
(3,4) and (3,1)
. To find the distance between two points, use the distance formula.
It will be the square root of (x2-x1)squared + (y2-y1)squared.
Use (3,-4) as x1, y1. Use (5,1) as x2, y2.
We get the square root of (5-3)squared + (1- -4)squared.
That gives us the square root of 2 squared + 5 squared.
Now we have the square root of 4 + 25, = the square root of 29.
That is the distance between the two points.
Cylinders A and B are similar solids. The base of cylinder A has a circumference of 47 units. The base of cylinder B
has an area of 97 units.
The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
+/a N/mm/~ alt
The factor that produces the corresponding dimensions of cylinder B is: 3/2.
What are Similar Solids?Similar solids have the same shape but different sizes, and which means the ratio of their corresponding linear measurements are the same.
How to Find the Scale Factor of Similar Solids?To find the scale factor of similar solids, you can use the formula:
scale factor = (size of the similar solid) / (size of the original solid)
For example, if you have two similar solids, one with a volume of 64 cubic units and the other with a volume of 16 cubic units, the scale factor would be:
scale factor = (16 cubic units) / (64 cubic units) = 1/4
This means that the smaller solid is 1/4 the size of the larger solid.
Given the following:
Circumference of the base of cylinder A = 4π units [the radius = 2 units]
Area of the base of cylinder B = 9π units² [the radius = 3 units]
Scale factor = radius of the base of cylinder B / radius of the base of cylinder A
Scale factor = 3/2
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Complete Question:
Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units. The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
Analysis of daily output of a factory shows that, on average, the number of units per hour y produced after t hours of production is
y = 102t + 0.5t2 − t3, 0 ≤ t ≤ 10.
(a) Find the critical values of this function. (Assume −[infinity] < t < [infinity]. Enter your answers as a comma-separated list.)
t =
(b) Which critical values make sense in this particular problem? (Enter your answers as a comma-separated list.)
(c) For which values of t, for 0 ≤ t ≤ 10, is y increasing? (Enter your answer using interval notation.)
The critical values for the function are t = 6 , -5.667 where t = 6 makes sense . At t = 6 , y is increasing
According to the question,
After t hours of production, a plant produces an average of y units per hour, according to analysis of its daily output is
y = 102t + 0.5t² - t³ , 0 ≤ t ≤ 10
(a) To calculate critical values for the given function
We have to differentiate it w.r.t time and then have to put y'=0
=> y = 102t + 0.5t² - t³
Derivating w.r.t time
=> y' = 102 + t - 3t²
Equating to zero,
=> 102 + t - 3t² = 0
Solving quadratic equation,
=> t = 6 , -5.667 are critical values
(b) t = 6 makes sense in particular problem because time cannot be negative.
(c) To check increasing value
Derivate y' w.r.t time again
=> y" = 1 - 6t
Putting critical value,
At t = 6
y" < 0 , Therefore at t = 6 function is increasing
Hence , For t = 6 y is increasing
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Out of 400 plants sold daily at a nursery, 90% of them have flowers. How many of the
plants have flowers?
A. 40
B. 90
C. 310
D. 360
10 points.
Answer: D; 360
Step-by-step explanation: To find percentages, I like to set up proportional relationships to find the amount. It would look like this:
[tex]\frac{90}{100}[/tex] = [tex]\frac{?}{400}[/tex]
90= part %
100= whole %
?= amount of the %
400= all of the item(s)
So, we would cross multiply the 90 and the 400, then divide it by 100. That would be 36,000. So, that divided by 100 leaves us with 360. I hope this helped!
1. According to the text, the three IT trends that are having the greatest impact on the IT environment are: A. Privacy management, virus suppression, and enterprise portals B. Grid computing, on-demand computing, and real-time computing C. Digital forensics, the distributed workforce, and grid computing D. Knowledge management, privacy management, and intranets E. Privacy management, enterprise warehouses, and knowledge management
Computing on demand, on the cloud, and in real time IT Enviroment is most impacted by Are is known as gird computing.
What is Data Analysis?
Data analysis is the methodical application of logical and/or statistical approaches to describe and demonstrate, summarise and assess, and assess data.
Concept:
Step 1: A network of connected computers that act as a single supercomputer to complete complex tasks like modelling or data analysis is known as gird computing.
Step 2 : On-demand computing is a delivery method in which users are provided with computing resources as needed.
Step 3 : Real-time computing refers to a computer system that responds to an event by completing a task in a predetermined amount of time. a system for air traffic management as an example.
Grid computing, on-demand computing, and real-time computing
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(7x6)÷2[{45÷3(7×2-15+6)}+4)
Answer:
21/79
Step-by-step explanation:
(7x6)÷2[{45÷3(7×2-15+6)}+4)
(7*6)/2[{15(7*2-15+6)}+4)
(42)/2[{15(14-15+6)}+4)
(42)/2[{15(5))}+4)
(42)/2[{75}+4)
(42)/2[75 + 4]
(42)/2 * 79
42/2 * 79
21/79
Prove that if a ≡ b mod m and c ≡ d mod m, then ac ≡ bd mod m. [duplicate]
The four integers say a,b,c and d. If a and b are congruent to moulo m and c ,d are congruent to modulo m then ac and bd are must be congruent to modulo m .
What is congruent modulo ?Two integers a and b are "congruent modulo n" if their difference is a multiple of n or in other words we say n/(b-a) . For example, 17 and 5 are congruent modulo 3 because 17 - 5 = 12 = 4×3
We have, a ≡ b mod m => m/(a - b)
and c ≡ d mod m => m/(c-d)
Now, a + c - b - d = (a-b) + (c-d)
because, m/( a - b) and m/(c-d)
=> m/( a-b+ c-d )
=> m/(a+c)-(b+d)
=> a+c ≡ b+d mod m
We have to prove that ac ≡ bd mod m.
ac - bd = c(a-b) + b(c- d)
Now, as we see, m/(a-b) => m/c(a-b)
and m/(c-d) => m/b(c-d)
=> m/(c(a-b) + b(c-d))
=> m/(ac - bc + bc - bd)
=> m/(ac - bd)
=> ac ≡ bd mod m
Hence proved.
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The polynomial of degree 5,
P(x) has leading coefficient 1, has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=−5 Find a possible formula for P(x).
The possible formula for P(x) is x⁵-x⁴-21x³+45x²
What is a polynomial?
Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). Based on the number of terms present in the expression, it is categorised as monomial, binomial, and trinomial.
P(x) has roots of multiplicity 2 at x=3 and x=0.
The equation stands, P(x) = x²(x-3)²
P(x) has a root of multiplicity 1 at x=-5
The equation stands, P(x) = x²(x-3)²(x+5)
Simplifying the equation,
P(x) = x²(x²+9-6x)(x+5)
⇒ P(x) = (x⁴+9x²-6x³)(x+5)
⇒ P(x) = x⁵+5x⁴-6x⁴-30x³+9x³+45x²
⇒ P(x) = x⁵-x⁴-21x³+45x²
The possible formula for P(x) is x⁵-x⁴-21x³+45x²
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Given h(x) = −3x + 15, calculate h(−3).
The value of the function instance h (-3) as required to be determined given the function declaration; h(x) = −3x + 15 is; 24.
What is the value of the function instance h (-3) as given?It follows from the task content that the value of the function instance h (-3) is to be determined given the function h (x) = -3x + 15.
Since the given function is; h (x) = -3x + 15.
The value of the function instance; h (-3) can be determined by evaluating as follows;
h (-3) = -3 (-3) + 15
h (-3) = 9 + 15
h (-3) = 24.
On this note, the value of the function instance h (-3) as required is; 24.
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7. Heather used a basic fact to complete
the equation below. What is the
missing number? Explain how you
can use a basic fact to find the
missing number.
4,200 + = 700
The missing value of x = 6
What is value ?
Value in mathematics can refer to a number of closely related ideas. A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42.
Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value.
Values are the benchmarks or ideals by which we judge the acts, traits, possessions, or circumstances of others. Values that are embraced by many include those of beauty, honesty, justice, peace, and charity.
4200 / x = 700
If the fraction is defined, the denominator cannot equal 0:
x ≠ 0
Append the inequality as the domain:
x ≠ 0
Multiply both sides of the equation by the common denominator:
400x / x = 700 x
Reduce the fractions:
4200 = 700 x
Swap the sides:
700 x = 4200
Divide both sides of the equation by the coefficient of variable:
x = 4200 / 700
Cross out the common factor:
x = 6
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Calcular el valor de x+y+z
x+y+z= 6
2x = y + z = 3
4x - y z = 4
The calculation of el valor de "x, y, and z" is "2, 3, 1"
How to calculate el valor de?Equation [1] must be solved for the variable z.
[1] z = -x - y + 6
/ Replace this in equation [2]'s variable z.
[2] 2x - y + 3•(-x -y +6) = 3
[2] -x - 4y = -13
Add this to the equation [3]'s variable z.
[3] 4x + 5y - 10•(-x -y +6) = 13
[3] 13x + 14y = 72 Equation [2] must be solved for x.
[2] x = -4y + 13
/ Replace the value of x in equation [3] with this.
[3] 14•(-4y+14) + 15y = 73 [3] - 41y = -122
Equation [3] must be solved for the variable y.
[3] 41y = 122
[3] y = 3 We already know the following:
y = 3, z = -x-y+6, and x = -4y+14 To find x, use the value of y.
x = -4+3 = 1 To find z, use the x and y values.
z = -(2)-(3)+6 = 1
Answer: "x, y, and z" = "2, 3, 1"
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I need. Help with this question
Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
What is differentiation?
In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.
Main body:
by using product rule;
Let = u = x² + 4x + 6
⇒ du/dx = 2x + 4 .
Now y = u⁵
⇒ dy/dx = 5u⁴ .
dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)
= 5 * (x² + 4x + 6)⁴ * (2x + 4)
= 5(2x + 4) * (x² + 4x + 6)⁴
hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
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a room three times as long as it is broad and height is 4.6m. st of carpeting its floor at Rs. 240 per sq.m. be Rs. nd the cost of painting the 4 walls at Rs. 24 per sq.m.
The total cost of painting and carpeting the 4 walls and the floor is C = ₹(720x² + 1324.8x).
What is the area and perimeter of a rectangle? What is a mathematical function, equation and expression? rectangle perimeter : 2{L + B} (L - length, B - breadth)rectangle area : {L x B} (L - length, B - breadth)function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a room three times as long as it is broad and its height is 4.6 m. The cost of carpeting its floor at Rs. 240 per square meter be the cost of painting the 4 walls at Rs. 24 per sq. m.
Assume that the breadth to be equivalent to [x] meters. Then its length will be [3x] meters.
Area of floor = {3x} x {x} = 3x² sq. m.
The cost of carpeting the floor = Rs. 240 per sq. m.
For 1 sq. m., the cost is 240 sq. m.
For {3x² sq. m}, the cost will be -
C{f} = 240 x 3x² = 720x²
C{f} = 720x²
The total area of the 4 walls = 4 × (3x) × 4.6 = 55.2x sq. m.
The cost of carpeting the walls = Rs. 24 per sq. m.
For {55.2x sq. m}, the cost will be -
C{w} = 24 x 55.2x = 1324.8x
C{w} = 1324.8x
The total cost of painting and carpeting -
C = C{w} + C{f} = 720x² + 1324.8x
C = ₹(720x² + 1324.8x)
Therefore, the total cost of painting and carpeting the 4 walls and the floor is C = ₹(720x² + 1324.8x).
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Find out the missing frequency in the following incomplete distribution
CI F
0-10 3
10-20 ?
20-30 20
30-40 12
40-50 ?
The Value of median and mode are 27 and 26 respectively.
8 and 7 are missing frequency in the incomplete distribution.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Class Interval frequency Cumulative frequency
0 - 10 3 3
10 - 20 a 3+a
20 - 30 20 23+a
30 - 40 12 35+a
40 - 50 b 35+a+b
Mode = 26 hence lies in 20 - 30
f of modal class = 20
Mode = 20 + 10( 20 - a) / (20 - a + 20 - 12)
26 = 20 + 10 (20 - a) / (28 - a)
60(28 - a) = 10 ( 20 - a)
168 -6a = 200 - 10a
4a = 32
a = 8
Class Interval frequency Cumulative frequency
0 - 10 3 3
10 - 20 8 11
20 - 30 20 31
30 - 40 12 43
40 - 50 b 43+b
Median = 27
27 = 20 + 10 ( (43 + b)/2 - 11)/ 20
7 = ( (21 + b)/ 4
28 = (21 + b)
b = 7
Hence, the missing frequencies are 8 and 7.
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answer question below
The equations that represent a linear function are :
y = 2x - 94x + y = 7y = 1 / 2 xHow to know a linear function?A linear function is a function that represents a straight line on the coordinate plane. The degree of a linear equation must be 0 or 1 for each of its variables.
A linear function has the following form. y = mx + b.
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
Therefore, linear function can be represented in slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, the linear function of the equations are as follows;
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A video store manager observed that the number of DVDs sold seem to vary inversely as the price per DVD. If the store sells 710 DVDs per week when the price per DVD is $18.90, how many does he expect to sell if he lowers the price to $11.40.
If the price is reduced to $11.40 the number of DVDs sold will be 1177.
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 a video store manager observed that the number of DVDs sold seems to vary inversely to the price per DVD. If the store sells 710 DVDs per week when the price per DVD is $18.90.
The number of DVDs sold for $11.40 will be calculated by forming the inverse equation for the number of DVDs.
N = K / P
Here, N is the number and P is the price and K is the inverse constant.
The value of K will be,
K = N x P
K = 18.90 x 710
K = 13419
The number of DVDs for $11.40 will be,
N = K / P
N = 13419 / 11.40
N = 1177
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Unique buys 918 Spyder Porsche worth $845,000 every year that he owns the car
the car depreciates in value at a rate of 32% per year.
Write a function that models the value of the Porsche after t years.
*
The function for the value of the Porsche after t years is [tex]y = 845000(1-\frac{32}{100} )^t[/tex].
What is function?Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
Given that,
The initial price of the 918 Spyder Prosche car = $845,000
Since, the price of car depreciated at the rate of 32% per year.
The function for the value of Porsche car, after t years, can be given as,
The price of car after t year is y,
[tex]y = 845000(1-\frac{32}{100} )^t[/tex]
The required function, the models, the value of the Porsche after t years is [tex]y = 845000(1-\frac{32}{100} )^t[/tex].
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what is a constant in math
A constant term in mathematics is a term in an algebraic equation whose meaning is constant or cannot change because it has no modifiable variables. For example, in the quadratic polynomial x² + 2x + 3 = 0, the term 3 is a constant.
Witch rate is equivalent to 15 milesper hours
Answer: 60 miles per 4 gallons. If that's the question.
Step-by-step explanation:
give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles. the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are______.
a.adjascent angles
b.linear pair
c.congruent
d.intersecting
The correct statement is: the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are congruent.
The correct answer is an option (c)
In this question we have been given a statement 'the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are______'
We need to select a correct choice to complete the given statement.
Also, we need to give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles.
We know that by Alternate Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent.
Consider the following figure.
A pair of alternate interior angles: ∠4 and ∠6
a pair of corresponding angles: ∠2 and ∠6
and a pair of alternate exterior angles: ∠2 and ∠8
Therefore, the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are congruent.
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This problem reads as follows:Use cylindrical coordinates to evaluate E = This problem reads as follows: Use cylindricax2 dV, where E is the solid that lieswithin the cylinder x2 + y2 = 9, above theplane z = 0, and below the conez2 = 36x2 + 36y2Similar to 16.8 #11 in James Stewart Calculus 5thedition.
As per the cylindrical coordinate, the value of E is (0, 2π/5)
In math, coordinates refers the set of values that show an exact position.
Here we have given that x² + y² = 9, above the plane z = 0, and below the cone z² = 36x² + 36y²
And we need to find the value of E.
While we looking into the given question, we have identified that in cylindrical coordinates the region E is described by
=> 0 ≤ r ≤ 1, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 2r.
Here the given equation will go through the double integral, then we get,
=> ∫∫∫ₓ x² dV
And it can be rewritten based on the differentiation,
=> ∫₂⁰ ∫¹₀ ∫²₀ (r cos θ)² r dz dr dθ
=> ∫₂⁰ cos² θ dθ
=> ∫¹₀ 2r⁴ dr = 2π/5
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consider having two jars with numbers 1,23. find the probability of drawing two numbers from both the jars whose product is even
The probability of drawing two numbers from both jars whose product is even = 5/9.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
Total number of outcomes =9
Favorable cases = (1,2), (2,1), (3,2), (2,3), (2,2)
The probability of drawing two numbers from both the jars whose product is even = 5/9
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which of the above diagrams correctly portray a perfectly competitive firm's demand ( d) curve? a. a b. d c. b d. c
Correct option will be (C) In the short run, firms may incur economic losses or earn economic profits, but in the long run they earn normal profits.
The short run is a concept that states that, within a certain period in the future, at least one input is fixed while others are variable. In economics, it expresses the idea that an economy behaves differently depending on the length of time it has to react to certain stimuli. The short run does not refer to a specific duration of time but rather is unique to the firm, industry or economic variable being studied.
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Problem 3: Integration via the Substitution Method ( 16 points) Evaluate each of the following. Explain and show your work. You do not need to simplify your final answer. a)
(8
points
)∫ 0
3
ㅌㅣ
(2e 5t
+3) 2
3e 5t
dt
VALUE: b) (8 points)
∫( sin 2
(t 2
)+1
tcos(t 2
)
)dt
The value of the given integral [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] is 2/75.
The given integral is [tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex].
We have to evaluate the given integral.
The given integral is definite integral. To evaluate the given integral we firstly solve the integral then we put the value in the solved integral to find the value.
We solving the integral [tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]
Let u = 2e^{5t}+3
Now differentiating
du/dt = 10e^{5t}
e^{5t}dt = du/10
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int\frac{1}{u^2}dt[/tex]
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=\frac{3}{10}\int{u^{-2}}dt[/tex]
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-2+1}/(-2+1)]+C
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 3/10 [u^{-1}/(-1)]+C
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/u)+C
[tex]\int\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10(1/2e^{5t}+3)+C
Now;
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5t}+3}\right]^{\text{In}3/5}_{0}[/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{5({\text{In}3/5})}+3}-\frac{1}{2e^{5(0)}+3}\right][/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2e^{({\text{In}3})}+3}-\frac{1}{2e^{0}+3}\right][/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{2\cdot3+3}-\frac{1}{2+3}\right][/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt=-\frac{3}{10}\left[\frac{1}{6+3}-\frac{1}{2+3}\right][/tex]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[1/9 - 1/5]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[5-9/45]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = -3/10[-4/45]
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex] = 2/75
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The right question is:
Problem 3: Integration via the Substitution Method ( 16 points) Evaluate each of the following. Explain and show your work. You do not need to simplify your final answer.
[tex]\int^{\text{In}3/5}_{0}\frac{3e^{5t}}{(2e^{5t}+3)^2}dt[/tex]
simplify (5/3-7/4)+√1/16+√1/9
Answer:
1/2
Step-by-step explanation:
(5/3-7/4)+√1/16+√1/9
= {(5x4-7x3)/12} + 1/4 + 1/3
= -1/12 + (3+4)/12
= (-1+7)/12
= 6/12
= 1/2
