how do you find the answer to
5 to the power of -3 times 5 to the power of 3

In the expression (-6)⁴, the power and exponent is 4

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the power or exponents us the number of times the number is raised which is 4.

Learn more about exponents on:

brainly.com/question/13669161

#SPJ1

The number of different unique cleaning teams should be 1540.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, A class has 10 boys and 12 girls and 3 students are chosen at random.

So, the team of 3 can be chosen as 3 boys, 3 girls, 1 boy 2 girls, and 1 girl and 2 boys and the total teams will be the sum of different combinations which is,

= \(^{10}C_3 + ^{12}C_3 + ^{10}C_1\times^{12}C_2 + ^{12}C_1\times^{10}C_2\).

= (10×9×8)/6 + (12×11×10)/6 + 10×(12×11)/2 + 12×(10×9)/2.

= 120 + 220 + 660 + 540.

= 1540.

learn more about permutation and combination here :

https://brainly.com/question/28720645

#SPJ1

The two related linear equations for |x – 2| = 5 are x - 2 = 5 and x - 2 = -5

From the question, we have the equation to be

|x - 2| = 5

This equation is an absolute value function

The general rule of an absolute value function is that:

An equation represented as y = |x| can be expressed as y = x or y = -x

Using the above guideline as a guide, we have the following representation of |x – 2| = 5

x - 2 = 5 and x - 2 = -5

Hence, the equations are x - 2 = 5 and x - 2 = -5

Read more about absolute value at

https://brainly.com/question/24368848

#SPJ1

Answer:

D. im answering for the purpose of the first person getting brainliest

Step-by-step explanation:

Answer:

x+5

Step-by-step explanation:

Answer:

which expression represents the measure of segment RS? x + 5

Step-by-step explanation:

on engenuity

Answer: 6x^3  I hope this helps! :D

Step-by-step explanation: The GCF of 18^3 and 30x^5 is 6x^3.

Answer:

1/2

Step-by-step explanation:

Answer:

ac avavavavavavavavavavavvavavacavacacacacacav

Comparing the surface areas of the three containers, we find that the cylinder requires the least amount of material to make, with a surface area of approximately 39.99 cm².

To determine which container requires the least amount of material to make, we need to compare the surface areas of the three containers: the cylinder, the regular pentagon-based prism, and the square-based prism.

1. Cylinder:

The formula for the lateral surface area of a cylinder is given by:

A_cylinder = 2πrh,

where r is the radius of the base and h is the height of the cylinder.

Given that the volume of the cylinder is 20 cm³ and the height is 5 cm, we can calculate the radius:

V_cylinder = πr²h,

20 = πr²(5),

r² = 4/π,

r ≈ 1.27 cm.

Substituting the values into the lateral surface area formula, we get:

A_cylinder = 2π(1.27)(5) ≈ 39.99 cm².

2. Regular Pentagon-Based Prism:

To find the surface area of a regular pentagon-based prism, we need to know the apothem (a line segment from the center of the polygon to the midpoint of one of its sides) and the height of the prism.

Since the container holds 20 cm³ of water and has a height of 5 cm, each layer of water has a volume of 20/5 = 4 cm³. As the prism is regular, we can find the side length of the pentagon by calculating the square root of the prism's volume:

side length = √(4/tan(π/5)) ≈ 2.12 cm.

The apothem of a regular pentagon can be calculated using the formula:

apothem = side length / (2tan(π/5)) ≈ 1.85 cm.

The lateral surface area of the pentagon-based prism is given by:

A_pentagon = 5 × (1/2 × perimeter × apothem) = 5 × (5 × 2.12 × 1.85) ≈ 49.17 cm².

3. Square-Based Prism:

Since the container holds 20 cm³ of water and has a height of 5 cm, each layer of water has a volume of 20/5 = 4 cm³. Thus, the base area of the square is 4 cm².

The lateral surface area of a square-based prism is given by:

A_square = 4 × side × height,

where side is the length of one side of the base and height is the height of the prism.

Given that the base area is 4 cm² and the height is 5 cm, we can calculate the side length of the square base:

4 = side²,

side ≈ 2 cm.

Substituting the values into the lateral surface area formula, we get:

A_square = 4 × 2 × 5 = 40 cm².

Comparing the surface areas of the three containers, we find that the cylinder requires the least amount of material to make, with a surface area of approximately 39.99 cm².

to know more about cylinder visit:

brainly.com/question/30390407

#SPJ11

Answer: B

16/100 = 0.16

0.16 is 16/100 exactly.

1/16 = 0.000625

1/6 = 16.666...

1/3 = 33.33...

So, the answer is 16/100.

Hope this helps!

The fraction is equivalent to the decimal number 0.16 will be 16/100. Then the correct option is B.

The equivalent is the expression that is in different forms but is equal to the same value.

The decimal number is the sum of a whole number and part of the fraction number. The fraction number is greater than zero but less than one.

The decimal number is given below.

⇒ 0.16

The fraction is equivalent to the decimal number 0.16 will be

Multiply and divide the number by 100. Then the fraction number will be

⇒ 0.16 x 100 / 100

⇒ 16 / 100

The fraction is equivalent to the decimal number 0.16 will be 16/100. Then the correct option is B.

More about the equivalent link is given below.

https://brainly.com/question/889935

#SPJ2

Answer:

finite - it is equal to 15.625

HOPE THIS HELPS!!!

Answer:

Finite.

Step-by-step explanation:

125/8=15.625

Answer:

56

Step-by-step explanation:

7⁶ = ~117,649

(2/7)⁵ = ~0.0019

2² = 4

~117,649 x ~0.0019 = 224.

224 / 4 = 56

Answers:

Lisa is currently   9  years old  

Olivia is currently    19 years old  

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

Explanation:

L = Lisa's current age

2L+1 = Olivia's current age

This is because the 2L represents being twice as old as Lisa, then we add on an extra year.

Then we refer to the first sentence:

\(\text{The sum of 4 times Lisa's age and 7 times Olivia's age is 169}\)

to form this equation

4*(Lisa's age) + 7*(Olivia's age) = 169

4L + 7(2L+1) = 169

-------------------

Let's solve for L

4L + 7(2L+1) = 169

4L + 14L + 7 = 169

18L + 7 = 169

18L = 169-7

18L = 162

L = 9

Lisa is currently 9 years old.

That leads to,

2L+1 = 2*9+1 = 18+1 = 19

Olivia is currently 19 years old.

-----------------

Check:

4*(Lisa's age) + 7*(Olivia's age) = 169

4*9 + 7*19 = 169

36 + 133 = 169

169 = 169

The answers are confirmed.

9514 1404 393

Answer:

  BC = 6

Step-by-step explanation:

Tangents from the same point are congruent, so ...

  2x = x+3

  x = 3 . . . . . . . subtract x

  BC = x+3 = 3+3 = 6 . . . . . . substitute for x

The length of BC is 6.

Answer:The solution is in the attached file

Step-by-step explanation:

Answer:

\(y = -1x + 4\)

Step-by-step explanation:

Hello!

The equation of a line is written in slope-intercept form.

Slope - Intercept Form: \(y = mx + b\)

The slope of the line is the rate of change, or how much the y-values change as x-values change.

Slope is calculated by the Rise of the graph divided by the Run of the graph. Rise is how much the graph goes up or down between 2 points, while Run is how much the graph goes left or right between 2 points.

Points: (0,4) and (4,0)

Calculate:

The slope is -1.

The y-intercept is where the graph intersects the y-axis (x = 0).

The graph intersects it at (0,4), so the y-intercept is 4.

We can plug in the values for slope and y-intercept to find the equation.

Equation: \(y = -1x + 4\)

The system of equations has a unique solution when the determinant of the coefficient matrix is non-zero.

In this case, the coefficient matrix is:

|  0  1  2k |

|  1  2   6  |

|  k  0   2  |

The determinant of this matrix is given by:

D = 0(2(2) - 0(6)) - 1(1(2) - 6(k)) + 2k(1(0) - 2(2))

 = -12k + 12k

 = 0

When the determinant is zero, the system may have infinitely many solutions or no solution. Therefore, we need to investigate further to determine the values of k for which the system has a unique solution.

(b) To determine the values of k for which the system has no solution, we can check if the rank of the coefficient matrix is less than the rank of the augmented matrix. If the ranks are equal, the system has a unique solution. If the ranks differ, the system has no solution.

By performing row reduction on the augmented matrix, we find that the ranks of both the coefficient matrix and the augmented matrix are equal to 2. Therefore, for any value of k, the system has a unique solution.

In summary, for all values of the constant k, the given system of equations has a unique solution and does not have any solution.

Learn more about coefficient matrix here:

https://brainly.com/question/3086766

#SPJ11

The null hypothesis to test the faculty member's claim that the improvement is no more than 3% at the 5% significance level is that the true mean score improvement on the outcomes assessment test is equal to or less than 3%.

The null hypothesis is a statement that assumes there is no significant difference or relationship between two variables in a population, or that any observed difference or relationship is due to chance or sampling error. It is usually denoted by "H0" and is used in statistical hypothesis testing to determine whether there is evidence to support an alternative hypothesis.

In the given question,

The null hypothesis to test the faculty member's claim that the improvement is no more than 3% at the 5% significance level would be:

H0: The true mean score improvement on the outcomes assessment test is equal to or less than 3%.

This hypothesis assumes that there is no significant improvement in the mean score on the outcomes assessment test as a result of the review course. The alternative hypothesis would be:

Ha: The true mean score improvement on the outcomes assessment test is greater than 3%.

This hypothesis assumes that there is a significant improvement in the mean score on the outcomes assessment test as a result of the review course.

To test these hypotheses, we would use a one-tailed t-test with a significance level of 0.05 and calculate the t-value and p-value based on the sample data. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that there is evidence of a significant improvement in the mean score on the outcomes assessment test as a result of the review course. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is no evidence of a significant improvement in the mean score on the outcomes assessment test as a result of the review course.

To know more about null hypothesis, visit:

https://brainly.com/question/28920252

#SPJ1

(a) The marginal p.m.f.'s of X and Y are uniform distributions over 1, 2, and 3, (b) The probability of event A, X + Y being divisible by 4, is 0.694, (c) E(XY) = 7.194, (d) X and Y are independent, (e) The conditional p.m.f. P(X = Y = 1 | X = x) is 1/3 for all x, (f) The conditional E(XY = 1 | Y = 1) = 1, (g) Cov(X, Y) = 0, (h) The correlation of X and Y is 0, (i) X and Y are uncorrelated, (j) The value of a making Z and Y uncorrelated is -1/2.

(a) Marginal p.m.f.'s are found by summing the joint p.m.f. over the relevant values. In this case, the joint p.m.f. is constant, resulting in uniform distributions for X and Y.

(b) P(A) is computed by identifying (x, y) pairs where X + Y is divisible by 4. The probability of these pairs yields P(A) = 0.694.

(c) E(XY) is determined by summing the product of XY and their probabilities, resulting in 7.194.

(d) X and Y are independent because the joint p.m.f. can be factored into the product of the marginal p.m.f.'s.

(e) The conditional p.m.f. P(X = Y = 1 | X = x) is consistently 1/3 for all x.

(f) The conditional expectation E(XY = 1 | Y = 1) equals 1, obtained by summing the product of XY = 1 and probabilities, given Y = 1.

(g) Cov(X, Y) = 0, indicating no linear relationship.

(h) The correlation between X and Y is 0, implying no linear association.

(i) X and Y are uncorrelated, indicating no linear dependence.

(j) The value of a for Z = X + aY to be uncorrelated with Y is -1/2.

To learn more about independent click here: brainly.com/question/15375461

#SPJ11

Answer:

4/5 of a minute (48 seconds)

Step-by-step explanation:

Pierce swims 10 laps in 8 minutes. This means that the time it takes for him to swim each lap is 8 minutes divided by 10 laps (because that's the total time, and you split it amongst the ten laps). 8/10 simplified is 4/5 (divide numerator and denominator by 2). Hope that helps!

The amount that they insurance will cover is $9000.

Insurance is a risk management tool. When you purchase insurance, you are purchasing protection against unforeseen financial losses. If something bad happens to you, the insurance company will pay you or someone you choose.

The deductible in an insurance policy is the amount paid out of pocket by the policyholder before the insurance provider will pay any expenses. In general, the term deductible refers to one of several types of clauses used by insurance companies as a payment threshold for policy payments.

In this case, the amount paid by insurance will be:

= Total amount - Deductible

= $10000 - $1000

= $9000

Learn more about insurance on:

https://brainly.com/question/25855858

#SPJ1

Answer:

Step-by-step explanation:Health insurance doesn’t pay all of your healthcare expenses. Instead, you’re expected to foot the bill for part of the cost of your care through your health plan’s cost-sharing requirements like your deductible, copayments, and coinsurance.

This article will explain how coinsurance works, how it differs from deductibles and copays, and how you can know what to expect in terms of the bills you may receive from your medical providers.

Since deductibles and copayments are fixed amounts, it doesn’t take a lot of math to figure out how much to pay. A $30 copayment to fill a prescription or see a doctor will cost you $30 no matter how much the total bill for the prescription or office visit was.

Your health insurance picks up the rest of the tab (note that this generally only applies if you use an in-network provider and fulfill any prior authorization requirements that your insurance plan has).

A nurse talking to her patient in the clinic lobby

Hero Images / Getty Images

However, calculating your health insurance coinsurance payment is trickier. Since coinsurance is a percentage of the total cost for the service, you’ll owe a different amount of coinsurance for each service you receive.

If the healthcare service you received was cheap, your coinsurance won’t be much. However, if the healthcare service was expensive, your coinsurance could wind up being hundreds or even thousands of dollars (on the high end, your coinsurance will be limited by your health plan's maximum out-of-pocket).

You need to understand how to calculate your health insurance coinsurance payment so you’ll know how much you’ll owe for coinsurance and you can budget for it.

Find Your Coinsurance Rate

You’ll need to find your coinsurance rate for the type of care you’re getting. You should be able to locate this in the Summary of Benefits and Coverage you got when you enrolled in your health plan. Sometimes you can even find it on your health insurance card.

Coinsurance typically kicks in after you've met your deductible, so you'll want to understand how much your deductible is as well. You'll pay your medical bills in full (at the negotiated discounted rate that your insurer has with your medical provider) until you've met your deductible. Then you'll start to pay coinsurance.

On some health plans, coinsurance can be the same percentage no matter what type of service you get. For example, 30% coinsurance for hospitalization and 30% coinsurance for specialty drug prescriptions.

In other health plans, you might have a low coinsurance rate for some services and a higher rate for other types of services. For example, you could have 35% coinsurance for hospitalization, but only 20% coinsurance for surgery at an outpatient surgery center.

And it's very common for prescription drug coverage to be structured with copayments for drugs that are in lower-cost tiers, but coinsurance for higher tier or specialty drugs. So you may be accustomed to paying a flat dollar amount at the pharmacy, but then end up having to pay a percentage of the cost of a new prescription—which can get quite expensive, depending on the drug.

Find the Cost of Your Care

Once you know your coinsurance rate, you need to determine the total cost of the healthcare service you received. If you’re using an in-network provider, your health plan has already negotiated discounts from that provider.

Calculate your health insurance coinsurance payment based on the discounted rate, not the standard rate charged to people who don’t belong to your health plan.

Find this in-network discounted amount on your Explanation of Benefits (EOB) listed as “allowed amount" (the EOB will also show the amount the provider billed, which will generally be higher than the allowed amount).

If you haven’t gotten the healthcare service yet, you won’t have an EOB to check. You can try asking your medical provider or health insurer what the in-network rate for that particular service is.

But know that sometimes you simply won't be able to get an accurate estimate of the total cost of your treatment in advance, either because the information is considered proprietary (as part of the network negotiations between the insurer and the medical provider) or because the medical provider won't know in advance exactly what services need to be performed.

The Trump administration finalized a healthcare transparency rule that will be phased in starting in mid-2022 (and fully in force by 2024), requiring health plans to make pricing and network-approved costs available to consumers upon request.1

This rule is controversial, with insurers deriding it as unnecessary and costly (it is expected to result in lower MLR rebates, as well as higher premiums in the individual/family health insurance market), while HHS officials herald it as a big step forward for healthcare price transparency.2

Equation -1 = 0 doesn't have solution, no value of r that satisfies all coefficients. Equation r f(x, y) + y f(x, y) = 3 not satisfied for any value of r. Equation r f(x, y) + y f(x, y) = 3 doesn't hold no value of r that satisfies it.

In this problem, we are given a function f: R² → R defined as follows:

f(x, y) = 5x² if (x, y) = (0, 0)

f(x, y) = -x² + 7y² if (x, y) ≠ (0, 0)

We need to determine if the function f has a limit at (0, 0) and analyze its continuity.

(a) To determine if the function f has a limit at (0, 0), we need to compute the limit of f(x, y) as (x, y) approaches (0, 0) along different paths.

Along the x-axis: Letting y = 0, we have f(x, 0) = 5x². Taking the limit as x approaches 0, we get lim(x→0) f(x, 0) = lim(x→0) 5x² = 0.

Along the y-axis: Letting x = 0, we have f(0, y) = -x² + 7y² = 7y². Taking the limit as y approaches 0, we get lim(y→0) f(0, y) = lim(y→0) 7y² = 0.

Since the limit of f(x, y) approaches 0 along both the x-axis and the y-axis, we can conclude that the function f has a limit at (0, 0).

(b) To determine the set of points for which f is continuous, we need to consider the function's definition at (0, 0) and its definition for all other points.

At (0, 0), the function is defined as f(0, 0) = 5x².

For all other points (x, y) ≠ (0, 0), the function is defined as f(x, y) = -x² + 7y².

Therefore, the set of points for which f is continuous is R², except for the point (0, 0) where f has a removable discontinuity.

(c) To show that r f(x, y) + y f(x, y) = 3, we substitute the given definitions of f(x, y) into the equation:

r f(x, y) + y f(x, y) = r(5x²) + y(-x² + 7y²)

= 5rx² - xy² + 7y³

Now, we need to find the value of r such that the expression equals 3. Setting the expression equal to 3, we have:

5rx² - xy² + 7y³ = 3

To find r, we can equate the coefficients of like terms on both sides of the equation. Comparing the coefficients, we get:

5r = 0 (coefficient of x² term)

-1 = 0 (coefficient of xy² term)

7 = 0 (coefficient of y³ term)

To learn more about function click here:

brainly.com/question/30721594

#SPJ11

the function f(x) is invertible on the intervals:

B: -7 ≤ x ≤ -4

C : 1 ≤ x ≤ 3

A function f(x) can only be invertible if it is one-to-one in its domain, where one-to-one means that each output is related to only one input.

So, if for two different values x₁ and x₂ we have that:

f(x₁) = f(x₂) = y, then the function is not invertible.

So here what we need to do is identify in which interval is the function one-to-one.

If you look at the last option, we have the interval [1, 3]

We have that f(1) = 2, and then the function increases until f(3) = 4

In that interval the function is cleraly one-to-one, so, on that interval, we can find an inverse function to f(x).

Similarly, on the second option [-7, -4] we also can see that:

f(-7) =  2

And then the function increases until f(-4) = 4

Then the function is also invertible on that interval.

We conclude that the function f(x) is invertible on the intervals:

B: -7 ≤ x ≤ -4

C : 1 ≤ x ≤ 3

If you want to learn more about invertible functions:

https://brainly.com/question/14391067

#SPJ1

Answer:-3<x<-1 is incorrect, all else are correct.

Step-by-step explanation:

Answer:

a = 1, b = 5, c = 9

Step-by-step explanation:

3 1/2 ÷ 2 1/4

= 7/2 ÷ 9/4

= 7/2 × 4/9

= (7*4)/(2*9)

= 28/18

= 14/9

= 1 5/9

Therefore

3 1/2 ÷ 2 1/4 = a b/c

Where,

a = 1, b = 5, c = 9

Answer:

above is right

Step-by-step explanation:

ig hanganaahajssislaalalla

Answer:

16 + 9 = 25

Step-by-step explanation:

For each term in the sequence, we can see that the second number being added increases by 2 each time (3, 5, 7)

And that the first number of each term increases by the value of the second term

(1 increases by 3; 4 increases by 5)

we can follow out these two observations to find T4

the first term (9) will increase by the value of the second term (7)

{the sum of the previous term is the first number}

so the first number of T4 will be 16.

Because we left off on +7, we are now on +9

so, T4 is

16 + 9 {and then do the math accordingly}

16 + 9 = 25

So, T4 is

16 + 9 = 25

hope this helps!! have a lovely day!! :)

Answer: 4 feet

Step-by-step explanation:

\(Let\ width=x > 0\\Hence,\\(8+2x)(7+2x)=240\\(8)(7)+(2x)(7)+(8)(2x)+(2x)(2x)=240\\56+14x+16x+4x^2=240\\4x^2+30x+56=240\\4x^2+30x+56-240=240-240\\4x^2+30x-184=0\\\)

Divide both parts of the equation by 4 :

\(x^2+7.5x-46=0\\x^2+11.5x-(4)(x)-(4)(11.5)=0\\(x)(x+11.5)-(4)(x+11.5)=0\\(x+11.5)(x-4)=0\\x+11.5=0\\x=-11.5\ feet\notin, \ hence\ x > 0\\x-4=0\\x=4\ feet\in,\ hence\ x > 0\)

Since it is based on actual facts, the likelihood that the baseball player will get a hit in his subsequent at-bat is an empirical probability (the number of times the player got a hit out of the total number of times at bat).

A. Because it is based on observable data, the likelihood that the baseball player will get a hit in his subsequent at-bat is an empirical probability (the number of times the player got a hit out of the total number of times at bat).

b. Because it is based on equally plausible events in a limited sample space, the possibility that any one of the five students will be picked at random to serve as the spokesperson is a classical probability.

c. Because it is based on equally likely occurrences in a limited sample space, the chance of winning the $1 million prize in the Lotto Canada lottery is a classical probability.

d. The likelihood of an earthquake in northern California with a magnitude of 11.0 or higher during the next ten years is susceptible to interpretation because it is based on expert opinion rather on data collected from observation or equally plausible outcomes.

To learn more about empirical probability, refer to:

https://brainly.com/question/16972278

#SPJ1

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To know more about asymptotic complexity refer here:

https://brainly.com/question/30214690#

#SPJ11

Therefore, the derivative of f(x)=cos(x)sin(x) is given by f'(x)=cos²(x) - sin²(x). The correct answer is option b. 2cos²(x) - 1.

To arrive at this conclusion, we can use the product rule of differentiation. Applying the product rule, we have:
f'(x) = (cos(x))(d/dx(sin(x))) + (sin(x))(d/dx(cos(x))).

Differentiating sin(x) and cos(x) with respect to x, we get:
d/dx(sin(x)) = cos(x) and d/dx(cos(x)) = -sin(x).

Substituting these values into the equation, we have:
f'(x) = (cos(x))(cos(x)) + (sin(x))(-sin(x)).
     = cos²(x) - sin²(x).

Therefore, the correct answer is option b. 2cos²(x) - 1.

To know more about derivative visit:

https://brainly.com/question/29144258

#SPJ11