Step-by-step explanation:
1 - 2t = 2(1 - t)
1 - 2t = 2 - 2t
there is no value for t.
Let f:R→S be a surjective homomorphism of rings with identity.
(a) If R is a PID, prove that every ideal in S is principal.
(b) Show by example that S need not be an integral domain.
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient
Let f:R⇒S be a surjective homomorphism of rings with identity.
We have to find if R is a PID, prove that every ideal in S is principal.
We know that,
Let I be the ideal of S
Since f is sufficient homomorphism.
So, f⁻¹(I) is an ideal of R.
Since R is PID so ∈ r ∈ R such that
f⁻¹(I) = <r>
I = <f(r)>
Therefore,
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
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Consider the function f (same as in the previous problem) defined on the interval [0, 4) as follows, F(x) = { 2/2 x. x € [0,2]. 2, x € [2, 4]Find the coefficients Cn of the eigenfunction expansion of function ff(x) = Σ[infinity], n=1 cnyn(x), where y... for n = 1,2,3,... are the unit eigenfunctions of the Regular Sturm-Liouville system - y^n = ꟾλy, y’(O) = 0, y(4) = 0Note: Label your eigenfunctions so the eigenfunction for the lowest eigenvalue corresponds ton = 1. Therefore, use 2n – 1 instead of 2n +1.C= ___
Coefficient Cn is determined by Cn = 1/2 ∫[0,2] (x+2)yn(x) dx
To find the coefficients Cn of the eigenfunction expansion of a function f(x), f(x) must be expanded with the eigenfunction yn(x). The expansion of f(x) with respect to the eigenfunction yn(x) is given by
f(x) = Σ[∞], n=1 cnyn(x)
To find the coefficient cn, we need to compute the dot product of f(x) and yn(x).
cn = (f,yn) = ∫[0,4]f(x)yn(x)dx
Since the eigenfunctions yn(x) are orthonormal, the scalar product is given by
cn = ∫[0,4]f(x)yn(x)dx = ∫[0,2]f(x)yn(x)dx + ∫[2,4]f(x)yn(x)dx
Since f(x) = 2/2 x for x in [0,2] and f(x) = 2 for x in [2,4], compute the coefficient cn as I can do it.
cn = ∫[0,2](2/2x)yn(x)dx + ∫[2,4](2)yn(x)dx
= ∫[0,2]xyn(x)dx + ∫[2,4]2yn(x)dx
= 1/2 ∫[0,2] (xyn(x) + 2yn(x)) dx
= 1/2 ∫[0,2] (x+2)yn(x) dx
Therefore, the coefficient Cn is given by
Cn = 1/2 ∫[0,2] (x+2)yn(x) dx
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15. A student has a stone. He wants to find its density. (a) He pours 110 cm^3 of water into a measuring cylinder. And then, he places the stone in the water. The water surface in the measuring cylinder moves up. The volume of water and stone is 150 cm^3. What is the volume of stone? (1 mark)
The volume of the stone if, The volume of the water is 110 cm³, and The volume of the water and the stone is 150 cm³, is 40 cm³.
What is volume?The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.
Given:
The volume of the water = 110 cm³,
The volume of the water and the stone = 150 cm³,
Calculate the volume of the stone as shown below,
The volume of stone = The volume of the water and the stone - The volume of the water
The volume of stone = 150 - 110
The volume of stone = 40
Thus, the volume of the stone is 40 cm³
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assume that we have a single-cycle implementation of a processor, which has a clock cycle of 14 ns. suppose that we split this single-cycle processor to a 5-stage pipelined processor where the times for each of t
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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I need help with this please help me
data were collected on the number of days per week that members visit a certain fitness center. the values varied from 0 to 7, and a distribution of relative frequencies for the values was created. let the random variable x represent the number of days per week that a member visits. the mean of x is 3.12. which of the following statements is the best interpretation of the mean? responses each member visits the fitness center 3 or 4 days per week. each member visits the fitness center 3 or 4 days per week. the average number of days that each member visits the fitness center is 3.12 days per week. the average number of days that each member visits the fitness center is 3.12 days per week. half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more. half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more. the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. for a random sample of members selected from the population, the average number of visits for the sample will be 3.12 days per week.
The statement that is the best interpretation of the mean is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
The data of the number of days members visited a certain fitness center varied from 0 to 7.
The mean of the random variable x = 3.12
The mean of the random variable is also known as the long-run average value of a random variable.
Hence, we conclude that the best interpretation of the mean in the given question is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
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The sum of an infinite geometric series with first term a and common ratio r < 1 is given by The sum of a given a/1-r infinite geometric series is 300, and the common
ratio is 0.1. What is the second term of this series?
The second term of the series will be 27.
What is a Geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.
Sum to infinity = a/1-r
where s = 300
r = 0.1
a = 300 (1 - 0.1)
a = 300 (0.9)
a = 270
The second term of the progression will be = ar
Second term = 270 x 0.1
Second term = 27
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12) Name three points collinear with point A.
Answer:
c, e, f
Step-by-step explanation:
Collibear means lying on or passing through the same straight line.
Sketch the space curve represented by the intersection of the surfaces. Surfaces Parameter x2 + y2 + z2 = 4,x+z=2 x=1+sin t Represent the curve by a vector-valued function r(t) using the given parameter. r(t) = (1+sin t)1+Y2cos(t)1+ (1-sin)k (positive y portion) r(t) =| (1 + sin t)i+(-V2cos t)j+ (1-sin)k 、(negative y portion)
As the point moves along the helix, it traces out a three-dimensional surface in space.The space curve would look like a helix in graph.
1. First, we need to find the vector-valued function r(t) using the given parameter.
2. We can use the parameter x+z=2 to solve for the y-coordinate in terms of t:
y = √(4 − (1+sin t)2 − (1 − sin t)2).
3. We can now substitute this expression into the vector-valued function to obtain:
r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k
4. The space curve represented by the intersection of the surfaces is a helix in a graph.
The space curve represented by the intersection of the surfaces is a helix. It is a three-dimensional curve that can be described by a vector-valued function r(t) with parameter t. The vector-valued function r(t) is given by:
r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k.
The helix can be visualized as a spiral that wraps around a cylinder and is generated by a point travelling around the circumference of the cylinder at a constant speed. This can be observed by noting that the x- and z-coordinates of the vector-valued function are constant and only the y-coordinate changes over time. As the point moves along the helix, it traces out a three-dimensional surface in space.
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A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per
hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per
week. His goal is to make at least $300 per week.
1. Create a system of equations or inequalities that models the situation. Define the variable you use
PLEASE I CANT FAIL MY FINAL
Answer:
idrk i would at least need how many hours he gardens and how many hours he mows the lawn, for just mowing the lawn he would need to do that for 20 hours completely, for gardening he would need to work 15 hours.
Step-by-step explanation: yaaa
To cater a holiday banquet, Food Service LLC agrees to buy one hundred pumpkin pies from Great Desserts Inc. To be enforceable, the agreement must be in writing if the pies cost at least
$500
In order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies from great desserts inc. to be enforceable, the agreement must be in writing if the pies cost at least $500.
What is an Agreement?
This refers to the legally binding contract that exists between two or more entities where the terms of the contract have been drawn up and the terms have been agreed upon by all parties involved, subject to certain conditions before it can be enforceable.
Hence, we can see that in order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies and because they are a limited liability company, there needs to be a minimum threshold and this can be done, if the cost of the pies is at least $500.
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Compare the function 3x + 2y = 8 to the function graphed below, then identify which statement is true.
The two functions have the same y-intercept.
The two functions have the same x-intercept.
The y-intercept of the graphed function is greater than the y-intercept of the function 3x + 2y = 8.
The x-intercept of 3x + 2y = 8 is greater than the x-intercept of the graphed function.
The two linear functions have the same y-intercept. Then the correct option is A.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The function 3x + 2y = 8 and the other function is graphed.
Convert the standard linear function into slope-intercept form. Then we have
3x + 2y = 8
2y = 8 - 3x
y = 4 - (3/2)x
The y-intercept of the linear function is 4 and the y-intercept of the graphed line is also 4.
The two capabilities have a similar y-catch. Then, at that point, the right choice is A.
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Cole has c oatmeal cookies. He lets 5 of his friends share them fairly. Write an expression that shows how many cookies each friend gets.
An expression that shows number of cookies each friend got is c/5.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, Cole has c oatmeal cookies. He lets 5 of his friends share them fairly.
Total number of cookies =c
Sharing among 5 friends
Number of cookies each friend got =Total number of cookies/5
= c/5
Therefore, an expression that shows number of cookies each friend got is c/5.
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Consider a set of cards that has four cards labeled 1, 3, 5, and 7. Suppose you pick two cards, without replacement, and obtain the mean of the two numbers that are drawn from the set. Which of the following tables shows the sampling distribution? a.) Sample (n = 2) x̄ S1 = {1, 1} 1 S2 = {1,This problem has been solved!You'll get a detailed solution from a subject matter expert that helps you learn core concepts.Consider a set of cards that has four cards labeled 1, 3, 5, and 7.Suppose you pick two cards, without replacement, and obtain the mean of the two numbers that are drawn from the set
Answer:
one 2
one 3
two 4's
one 5
one 6
Step-by-step explanation:
We can use the combination formula to derive how many sets of two can be obtained from this set of 4 numbers. We are using the combination formula instead of the permutation formula because, in this situation, order doesn't matter; the mean of 1 and 3 is the same as the mean of 3 and 1.
[tex]_nC_r = \dfrac{n!}{r!(n-r)!}[/tex] where [tex]n[/tex] is the number of things to choose from and [tex]r[/tex] is the number of things we are choosing. Hence the equation for this problem is:
[tex]_4C_2 = \dfrac{4!}{2!(4-2)!}[/tex]
[tex]_4C_2=\dfrac{24}{2(2)}[/tex]
[tex]_4C_2 = 6[/tex]
So, there are 6 ways to pick 2 cards from a total of 4. We can lay out these 6 possibilities from the given numbers on each card:
(1, 3) (3, 5) (5, 7)
(1, 5) (3, 7)
(1, 7)
Then, we can calculate the mean, or average, of each.
2 4 6
3 5
4
Finally, we can conclude that the distribution of the means for each possible set of number pairs is:
one 2
one 3
two 4's
one 5
one 6
Express in a single log term
The simplified form of the given logarithmic expression as required in the task content bis Choice B; 2log8.
What is the simplified form of the expression as a single log term?It follows from the task content that the simplified form of the logarithmic expression is to be determined as a single log term.
On this note, since the given expression is;
2log2 + 2log4
It follows from factorisation that we have;
2 ( log 2 + log 4 )
Therefore, the expression in the parentheses can be simplified as a single log term using the sum of logarithms law as follows;
= 2 ( log ( 2 × 4 ) )
= 2 log 8.
Ultimately, the answer choice which represents the simplified form of the expression as a single log term is; Choice B; 2 log 8.
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Samuel went to the grocery store and purchased cans of soup and frozen dinners.
Each can of soup has 300 mg of sodium and each frozen dinner has
450 mg
of
sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all
collectively contain 6000 mg of sodium. Write a system of equations that could be
used to determine the number of cans of soup purchased and the number of frozen
dinners purchased. Define the variables that you use to write the system.
A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is; 300a + 450b = 6000 and a + 5 = b.
The variables x and y respectively represents cans of soup and frozen dinners and a and b represents number of cans of soup and frozen dinners.
Let cans of soup be denoted by x
Let each frozen dinner be denoted by y
Now, we are told that each can of soup has 300 mg of sodium and each frozen dinner has 450 mg. Thus;
x = 300
y = 450
It is said that Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 mg of sodium.
Let the no. of cans of soup be 'a' and no. of frozen dinner be 'b'. Thus, we will have the equation as;
ax + by = 6000
a(300) + b(450) = 6000
300a + 450b = 6000 ------(1)
We are told that Samuel purchased 5 more frozen dinners than cans of soup. This can be represented by the equation;
a + 5 = b ------(2)
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=420(1.04)^x
4% is the percentage rate of increase or decrease in exponential function.
What exactly makes a function exponential?
A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.
The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
We have,
y = 420( 1.04)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is
y(x)= a(1-r)^x such that r is the growth percent.
1 + r = 1.04
r = 0.04 ⇒ 4%
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If a population of weights is normal with a mean of 75 pounds and a standard deviation of 5.9 pounds, the probability an individual from this population will have a weight greater than 72 pounds is 0.31. O True O False
It is false that the probability of an individual from this population will have a weight greater than 72 pounds is 0.31 instead it is 0.70
According to the question,
Weight of population follows normal distribution
Mean of population : u = 75 pounds
Population Standard deviation : σ = 5.9 pounds
We have to Check if the probability an individual from this population will have a weight greater than 72 pounds is 0.31
Probability that weight is greater than 72 = P( x > 72)
Subtracting by 75 both sides and then dividing by 5.9
=> P( x - 75 / 5.9 > 72 - 75 / 5.9)
Using Z-statistics,
=> P( z > -3/5.9)
=> P( z > -0.508)
=> 1 - P(z < -0.50)
Using Probability distribution table for z,
=> 1 - 0.305
=> 0.70
Which is not equal to 0.31
Hence, It is false that Probability that weight is greater than 72 is 0.31
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If a 5 1/4 inch line on a map represents a 9 mile road, how many miles would be represented by a 3 1/2 line
A (3 + 1/2) inches line represents a real distance of 5.985 miles.
How many miles would be repesented by a (3 + 1/2) inch line?First, we know that a (5 + 1/4) inch line on a map represents a 9 mile road, then the conversion from miles to inches is given by the quotient between these two, we will get:
9mi/(5 + 1/4) in = 9mi/(5.25) in = 1.71 mi/in
So, any distance in inches can be multiplied by the above number to get the corresponding measure in miles.
Then for (3 + 1/2) inches we will get:
(3 + 1/2) in*1.71 mi/in = 5.985 mi
So a line of (3 + 1/2) inches has represents a distance of 5.985 miles.
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Billy is saving for a new DVD that costs $64. He already has $16. What % of the total cost has he
already saved?
Billy has already saved 25% of the total cost.
What is percentage?
A percentage in mathematics is a number or ratio that may be stated as a fraction of 100.In determining a percentage of a number, we should first divide it by 100 before multiply the outcome by 100. As a result, the proportion refers to a part per 100. The word "percent" refers to a fraction of one hundred. The letter "%" stands for it.
Given that, the cost of the DVD is $64.
He saved $16 for the DVD.
The percent of saving
= Saving amount/ cost of DVD × 100%
= (16/64) × 100%
= 0.25 × 100%
= 25%.
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Annette's Floral Shop has a charge account with Southern Flowers, a wholesaler where she
buys her floral supplies. This month, Annette has purchased 16 dozen roses at $30.96 per
dozen, 40 dozen chrysanthemums at $17.80 per dozen, and 20 dozen tulips at $21.10 per
dozen. In her state, Annette must pay a 6% sales tax on all orders. At the end of the month,
what is the balance on Annette's charge account?
Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.
What is Percentage ?The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
= 16 * 30.96 + 40 * 17.80 + 20 *21.10
= $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 = $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.
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Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.
What is Percentage ?
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
Use the unitary approach.
by adjusting the fraction's denominator to 100.
It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
= 16 * 30.96 + 40 * 17.80 + 20 *21.10
= $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 = $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.
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How do you form the complex conjugate of a complex number a+bi?
Step-by-step explanation:
How do you form the complex conjugate of a complex nuciu
HELP PLEASE all I need is the answer of b and c. The whole of the table is correct
if ride cast birr 50 to pick up and 10 birr per km how much you go with birr1350
The distance the ride will go for birr 1350 is 130 kilometres.
How to find the distance the ride can go base on the amount?The ride cost birr 50 to pick up and 10 birr per km. The distance you can go with birr 1350 can be calculated as follows;
Let's use equation to represent the total amount spent on the distance covered.
Therefore,
let
x = total distance travelled in kilometresy = total amount in birrHence,
y = 50 + 10x
Therefore,
where
y = 1350
y = 50 + 10x
1350 = 50 + 10x
1350 - 50 = 10x
1300 = 10x
divide both sides by 10
x = 1300 / 10
x = 130 km
Therefore, the ride will go 130 km.
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Which of the following statements are always true? A) If f(t) is increasing, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt. B) If f(t) is concave up, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
The statement that is true about integrals is; A) If f(t) is increasing, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.
How to interpret Riemann sums?Left-Hand Sums and Right-Hand Riemann sums usually give us different approximations of the specific area under a curve.
Now, If one sum gives us an overestimated value and then the other gives us an underestimated value, then we can try to find out what exactly the actual area under the curve might possibly be. It should be noted that left-hand sum will be an under-estimate of the specific area of R. Thus, as f is increasing, a left-hand sum will definitely use the smallest value of f on each sub-interval. This therefore tells us that any left-hand sum will not cover all of R and also any right-hand sum will be an over-estimated value of the area of R.
Thus, Since f is increasing, a right-hand sum will utilize the largest value of f on each specific sub-interval. Thus, right-hand sum will definitely cover R and others.
From the above, option A is true because if the graph is increasing then the left-hand sum gives an overestimated value of the actual value.
Meanwhile, option B is false because if the graph is concave upwards, then the trapezoid approximation is an overestimated value, and as such the midpoint will be underestimated.
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Isosceles trapezoid ABCD is shown.
A
B
D
C
Which three statements are correct?
ZBAC ZCAD
ZACD ZACB
ZADC ZBCD
AD
AB
AC
BC
CD.
BD
ہے
From the given Isosceles trapezoid ABCD, the three correct statements are:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
What is Isosceles trapezoid?An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths.
Particularly in isosceles trapezoids, there are unique correlations. "Equal legs" is what the term "isosceles" denotes. Non-parallel sides on isosceles trapezoids have the same lengths. The "legs" are another name for these equal sides.
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. A triangle with two congruent sides is referred to as being isosceles, in other words.
Thus, three correct statements are -
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PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
Answer:
Since YA=AX, XB=BZ, ZC=CY, it follows that A, B and C are the midpoints of the sides TX, XZ, ZY. AB, BC, AC are parallel to the sides and equal to their half. In fact, AB = YC=ZC. Therefore BC=AY.)
Good luck;)
Step-by-step explanation:
find the most general antiderivative or indefinite integral. check your answers by differentiation cos2x-sec^2x
The general anti derivative or indefinite integral of the function
cos2x - sec²x is 1/2 sin2x + tan x + C .
The given function is of the form : cos2x - sec²x
Now we will use the indefinite integral on the above expression:
∫cos2x - sec²x
This can be broken into :
∫cos2x - ∫sec²x
Now we will integrate them separately:
∫cos2x, we will use u-substitution.
Let 2x = u
Differentiation both sides we get:
2 dx = du
or, dx = 1/2 du
Hence we will use this value:
∫cos2x
= ∫cos u · 1/2du
= 1/2 ∫ cos u du
=1/2 sin u + C , where C is a constant.
Again we will do the second part of the integral:
∫sec²x
= tan x + C
Hence the required integral will be:
1/2 sin2x + tan x + C .
Now we will use differentiation to check the integral
d/dx (1/2 sin2x + tan x + C )
= d/dx (1/2 sin2x) + d/dx (tan x) + d/dx (C)
= cos 2x + sec² x
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t=10-x identify to dependent and independent variable
Answer: t is the dependent variable and x the independent variable
Step-by-step explanation: t is the dependent variable it depends upon the values of x that we put in.
x is the independent variable as we can use whatever values we want for x it is not affected by t
Advanced Algebra - please help
Answer:
Below
Step-by-step explanation:
Only the middle three are tri -nomials ( three terms)
the third one reduces to (x+ 2)^2
Answer:
3
Step-by-step explanation:
(x+2)^2
