Determine the first derivative of the following functions:
(a) y(x)=e^cosx
(b) y(x)=3x−2/x+1

Answers

Answer 1

(a) The first derivative of the function y(x) = e^cosx is y'(x) = -sinx * e^cosx. (b) The first derivative of the function y(x) = (3x - 2)/(x + 1) can be found using the quotient rule and simplifying the expression.

(a) To find the first derivative of y(x) = e^cosx, we can apply the chain rule. The derivative of e^cosx with respect to x is e^cosx multiplied by the derivative of cosx with respect to x, which is -sinx. Therefore, the first derivative of y(x) = e^cosx is y'(x) = -sinx * e^cosx.

(b) To find the first derivative of y(x) = (3x - 2)/(x + 1), we can use the quotient rule. The quotient rule states that for a function of the form f(x)/g(x), the first derivative is given by [g(x) * f'(x) - f(x) * g'(x)] / [g(x)]^2. Applying this rule to the given function, we can find the first derivative. After simplification, the expression can be further simplified if desired.

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Related Questions

Surface Area of Cylinders
9 mm
20 mm
Find the surface area.
mm
(Use 3.14 for )
what is the answer

Answers

Answer: 1639.08

Step-by-step explanation: To find the surface area of a cylinder, multiply 2(3.14)times the radius squared. Your answer is 508.68. Then multiply 2(3.14)times the radius and the height. You'll get 1130.08. add the answers you got from both equations together. That's the surface area of your cylinder. If you have any more questions, please let me know.

najib cuts out a rectangle that has a perimeter of 50 inches and a length of 17 inches. he cuts out another rectangle that is the same length and twice as wide.

Answers

Answer:

66 inches

Step-by-step explanation:

perimeter = 2(l+b)

here, perimeter is 50 and length is 17

let the width be x,

=> 50 = 2(17+x)

=> 50 = (2*17)+(2*x)

=> 50 = 34 + 2x

=> 50 - 34 = 2x [transposing method]

=> 16 = 2x

=> 16/2 = x

=> 8 = x

8 inches = width of the first triangle

we know, the other rectangle's length is 17

and it is said that the width is twice the width of the first triangle

so the length = 17, width = 2*8 = 16

for the perimeter

p = 2(l+b),

=> p = 2(17+16)

=> p = (2*17)+(2*16)

=> p = 34+32

=> p = 66

so the perimeter of the other rectangle is 66

If you accumulate 6 or more points within 3 years you are subject to a surcharge of $150. How much is the surcharge for each additional point after 6

Answers

The surcharge for each additional point after 6 is $25 per point.

This means that if you accumulate 7 points within 3 years, you will be subject to a surcharge of $175 ($150 for the first 6 points and $25 for the additional point).

If you accumulate 8 points within 3 years, the surcharge will be $200 ($150 for the first 6 points and $50 for the additional two points), and so on.

This information is based on the New Jersey Motor Vehicle Commission's (NJMVC) point system. The NJMVC assigns points for various traffic violations, such as speeding, reckless driving, and failure to yield.

If you accumulate too many points within a certain period of time, your driving privileges may be suspended or revoked.

It's important to note that the NJMVC point system is just one example of how states in the US handle driver's license points and surcharges. Each state has its own system, so it's important to check with your local Department of Motor Vehicles (DMV) or equivalent agency to understand how points and surcharges work in your area.

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what is the standard deviation of {0, 3, 1, 1, 0, 5, 1, 0, 3, 0},

Answers

Answer:

1.7

Step-by-step explanation:

At a department store kendra has a debt greater than $25.00 which could be kendras balance? A-$32.00 B-$22.00 C -$19.00 D-$11.00

Answers

Answer: A

Step-by-step explanation: 22.00, 19.00 and 11.00 are all less than 25. $32.00 is the only logical explanation.

Answer:

A. -$32.00

Step-by-step explanation:

This is because it is a greater debt than 25 and all the other choices are greater than $25.

Simplify.
5i square root -54

Answers

Answer:

Step-by-step explanation:

Answer: aye can I get brainlest?

also hope this helps

Step-by-step explanation:

Determine whether the given matrices are inverses of each other by computing their product. 0.3 0.20.3 A 5 3 0B--0.5 0 0.5 1.2 0.2-0.2 1 3 1 Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimals for each matrix element.) A. The given matrices are not inverses of each other because their product is the matrix B. The given matrices are inverses of each other because their product is the matrix

Answers

The correct choice is: A. The given matrices are not inverses of each other because their product is the matrix 0.13 0.4 1.1 1.5 1.9 3.5

To determine whether the given matrices are inverses of each other, we need to compute their product. We can do this by multiplying matrix A by matrix B:
A x B =
(0.3)(-0.5) + (0.2)(1.2) + (0.3)(-0.2) (0.3)(0) + (0.2)(0.5) + (0.3)(1)
(5)(-0.5) + (3)(1.2) + (0)(0.2) (5)(0) + (3)(0.5) + (0)(1)
(-0.2)(-0.5) + (1)(1.2) + (3)(0.2) (-0.2)(0) + (1)(0.5) + (3)(1)
Simplifying this expression, we get:
A x B =
-0.05 + 0.24 - 0.06 0 + 0.1 + 0.3
-2.5 + 3.6 + 0 0 + 1.5 + 0
0.1 + 1.2 + 0.6 0 + 0.5 + 3
A x B =
0.13 0.4
1.1 1.5
1.9 3.5
Now, we need to determine whether this product is the identity matrix or not. The identity matrix is a matrix with 1's on the diagonal and 0's elsewhere. In this case, the identity matrix would be:
1 0 0
0 1 0
0 0 1
We can see that the product of matrices A and B is not equal to the identity matrix. Therefore, the given matrices are not inverses of each other.
The correct choice is: A. The given matrices are not inverses of each other because their product is the matrix 0.13 0.4 1.1 1.5 1.9 3.5

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when variables compete to explain the same effects, what are they sometimes called?

Answers

When variables compete to explain the same effects, they are sometimes called "colliders".

Variables are units of measure that may take on various values and affect the outcome of the analysis. As a result, the effect size of one variable might alter the effect size of another, which can cause problems in correctly evaluating the influence of one variable on the outcome variable.

In science, an effect refers to the impact of one event, process, or object on another, and it can be positive or negative.

Effects can be evaluated to determine their degree and impact, as well as the causes that underlie them.

In some instances, one variable (V1) might influence another variable (V2), which in turn affects a third variable (V3). When the two variables are related but are not directly connected, this situation is known as a collider.

In summary, when variables compete to explain the same effects, they are referred to as "colliders."

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Choose the equation that represents the graph.

graph of a line passing through points negative 3 comma 0 and 0 comma 3

y = x − 3
y = −x + 3
y = −x − 3
y = x + 3

Answers

Answer:

Answer: Option D

Step-by-step explanation:

Hey there!

From the above question;

The line passes through (-3,0) and (0,3).

Use double point formula;

$( y - y1) = \frac{(y2 - y1)}{(x2 - x1)} (x - x1)$

Keep all values;

$(y - 0) = \frac{(3 - 0)}{(0 - ( - 3))} (x + 3)$

Simplify it;

$y = \frac{3}{3} (x + 3)$

Therefore, y = x+3.

Hope it helps!

Answer:

Step-by-step explanation:

pls answer my question

Answers

Hello!

In this question, you are finding the square root of 100-84.

The first thing you should do is do whatever is inside the square root sign. So, do 100-84:

100-84= 16

Now, you can take the square root of that number. Taking the square root means which number, when multiplied by itself, equal the number under the square root sign? In this case, the answer is 4!

This is because 4 multiplied by itself ( 4 times 4) is 16!

Answer: 4

I hope this helped! Comment if you have questions!

Answer:

have a great day

god is great

Your family of 5 went to the Chinese buffet. The cost for each person was $8.95. The sales tax was
11%. How much sales tax did you pay?

Answers

Answer:

9.93

Step-by-step explanation:

Just add your tax to your price.

sam and jose mowed 2/3 of the yard. jose mowed 3/4of that amount. whta part of the yard did jose mow?

Answers

Answer:

Step-by-step explanation:

Mike can sell 20 glasses of lemonade for 10¢ each. If heraises the price to 20¢, he estimates that he'll only be able tosell 15 glasses. How much more money can he earn if hecharges 20¢ per glass instead of 10¢?

Answers

Okay, here we have this:

First let's calculate how much is he earning selling 20 glasses each glass for 10¢:

Actual Earnings=20*10¢=200¢

Now, let's calculate how much will he earn if raises the price to 20¢ and sell the 15 glasses that he is estimating:

Future Earning=15*20¢=300¢

Let's calculate the diference now:

Diference=300¢-200¢=100¢

According with this he will earn 100¢ more if he charges 20¢ per glass instead of 10¢.

Write an equation of the line in slope-intercept form.

y=

Answers

Answer:

y = x - 2

Step-by-step explanation:

points: (3, 1) and (0, -2)

slope = m = (-2 - 1)/(0 - 3) = 1

y-intercept = b = -2

y = x - 2

Simplify: 3(2x+7)-2(x+5)

Answers

Answer:

4x-11

Step-by-step explanation:

1. Distribute

6x+21-2x-10

2. Subtract the same numbers

3. You have your answer.

Answer:4x+11

Step-by-step explanation:

Two integers have a difference of 18 and a sum of 2. What is the product of the two integers?

Answers

Answer:

the product of the two integers is -80

Two integers have a difference of 18 and a sum of 2. What is the product of the two integers?

Answer:

-80

Explanation:

it was on a mathcounts competition

Find the LCM of the pair of polynomials.4x² - 9 and 4x² + 12x +9

Find the LCM of the pair of polynomials.4x - 9 and 4x + 12x +9

Answers

We need to find the Least Common Multiple between 4x² - 9 and 4x² + 12x +9.

First, we need to factorize each expression:

4x² - 9 can be factorized using the difference of squares given by:

$a^2-b^2=(a+b)(a-b)$

Then:

$4x²-9=(2x+3)(2x-3)$

Now, for 4x² + 12x +9

Can be factorized using:

$(a+b)^2=a^2+2ab+b^2$

Then:

$4x²+12x+9=(2x+3)^2$

Now, we need to find the LCM between (2x+3)(2x-3) and (2x+3)².

Then, the LCM is (2x+3)²(2x-3).

The correct answer is the third option.

Answer ASAP please!!

Answers

The area of the triangle ABC, obtained using the formula for a triangle where two sides and the included angles are known is the option C

C. 81.1 cm²

What is the formula for the area of a triangle?

The formula for the area of a triangle, where the lengths of two sides and the included angle are known, can be presented as follows;

Area, A = (1/2) × a × b × sin(C)

Where a and b are the lengths of the two sides and the included angle C is the measure of the included angle between the two sides, therefore;

The diagram indicates that we get;

Where;

a = 11 cm and b = 18 cm and the measure of the included angle C = 55°, we get;

A = (1/2) × 11 × 18 × sin(55°) ≈ 81.1

The area of the triangle is about 81.1 cm²

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(३) एक शब्द में उत्तर लिखो:
१. कवि की जिह्वा पर इसके गीत हों -
२. मातृभूमि के चरण धोने वाला
३. मातृभूमि के सपूत -
४. प्रतिदिन सुनने/सुनाने योग्य नाम -
५. मातृभूमि के चरणों में इसे नवाना है

Answers

करना चाहिए। वे तुम्हें नष्ट कर देंगे।

आप कोई मौका नहीं खड़े हैं। तुम

उसके हाथ पर मर जाओगे। पछताना

Find the area of the shape shown below.

Answers

Split the shape into a square and a triangle:
Square: 2x2 = 4
Triangle: 2x2/2= 2
Add the square and triangle;
4+2= 6 units^2
6units^2

The 10 decimal digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are arranged in a uniformly random per- mutation. We denote by a the integer formed in base 10 by the first five positions in this permutation and by b the integer formed in base 10 by the last five positions in this permuta- tion (either a or b may begin with 0 which in such a case is ignored). For example, if the random permutation is 8621705394 then a = 862, b = 175, and c = 394. Consider the probability space whose outcomes are these random permutations and a random variable X defined on this probability space such X = 1 when the product xyz is even and X = 0 when that product is odd. Required:

Calculate E[X].

Answers

Random permutations and a random variable X are defined on this probability space such as X = 1 when the product XYZ is even and X = 0 when that product is odd. $E[X] = \[\frac{53}{63}\]$

To determine the expected value of the random variable X given the permutation of 10 decimal digits, we will find the probability of the random variable X being odd or even. If the product XYZ is odd, then X is odd, otherwise, X is even.

Consider A be the event that x is odd, B be the event that y is odd and C be the event that z is odd. The probability of A occurring is:

$P(A) = \[\frac{5}{9}\]$

since there are 5 odd digits out of the 9 remaining after any digit is chosen as the first digit in x.

, $P(B) = \[\frac{4}{7}\]$

since there are 4 odd digits out of the 7 remaining after any digit is chosen as the first digit in y.

Also, $P(C) = \[\frac{3}{6}\]$

Since there are 3 odd digits out of the 6 remaining after any digit is chosen as the first digit in z.

Therefore, P(A ∩ B ∩ C) is the probability of the product being odd which is given as:

P(A ∩ B ∩ C) = P(A) × P(B) × P(C)

$= \[\frac{5}{9}\] \times \[\frac{4}{7}\] \times \[\frac{3}{6}\]$

= 10/63

Thus, the probability of the product being even

P(A ∩ B ∩ C)¯ = 1 − P(A ∩ B ∩ C) = 1 − 10/63= 53/63

Therefore, the expected value of X is given as:

$E[X] = (0 \times \[\frac{10}{63}\]) + (1 \times\[\frac{53}{63}\])$

= 53/63

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PLEASE HELP ME SOLVE THIS
2x-11>3

Answers

Answer:

The answer is x>7

Step-by-step explanation:

Answer:

x > 7

Step-by-step explanation:

Isolate x:

2x - 11 > 3

2x > 14

Divide each side by 2:

x > 7

So, the answer is x > 7

Consider the expressions shown below.
A. -8x^2 - 3x + 4
B. 8x^2 - 3x + 8
C. 8x^2 + 3x - 4

Complete each of the following statements with the letter that represents the expression.
(3x^2 - 7x + 14) + (5x^2 + 4x - 6) is equivalent to expression
(2x^2 - 5x - 3) + (-10x^2 + 2x + 7) is equivalent to expression
(12x^2 - 2x - 13) + (-4x^2 + 5x +9) is equivalent to expression

Answers

===> Exercise 1

(3x² - 7x + 14) + (5x² + 4x - 6)

Match 3x² and 5x² to get 8x².

8x² - 7x + 14 + 4x - 6

Combine −7x and 4x to get −3x.

8x² −3x + 14 − 6

Subtract 6 from 14 to get 8.

8x² - 3x + 8

Therefore, the expression (3x² - 7x + 14) + (5x² + 4x - 6), is equivalent to the expression "B".

===> Exercise 2

(2x² - 5x -3) + (-10x² + 2x + 7)

Combine 2x² and -10x² to get −8x².

−8x² −5x − 3 + 2x + 7

Combine −5x and 2x to get −3x.

-8x² − 3x − 3 + 7

Add −3 and 7 to get 4.

-8x² - 3x + 4

Therefore, the expression (2x² - 5x -3) + (-10x² + 2x + 7), is equivalent to the expression "A".

===> Exercise 3

(12x² - 2x - 13) + (-4x² + 5x +9)

Combine 12x² and -4x² to get 8x².

8x² − 2x −13 + 5x + 9

Combine −2x and 5x to get 3x.

8x² + 3x − 13 + 9

Add −13 and 9 to get −4.

8x² + 3x - 4

Therefore, the expression (12x² - 2x - 13) + (-4x² + 5x +9), is equivalent to the expression "C".

Two sample Z-test for Proportions: Formula & Examples

Answers

A two-sample z-test uses the following null and alternative hypotheses:

H0: μ1 = μ2 (the two population means are equal)

HA: μ1 not equal to μ2 (the two population means are not equal)

A two-sample z-test is used to test whether two population means are equal.

This test assumes that the standard deviation of each population is known

Two Sample Z-Test: Formula

A two-sample z-test uses the following null and alternative hypotheses:

H0: μ1 = μ2 (the two population means are equal)

HA: μ1 not equal to μ2 (the two population means are not equal)

$z=(x'_1-x_2')/\sqrt{s_1^2/n_1^2+s_2^2/n_2^2$

Example,

Suppose the IQ levels among individuals in two different cities are known to be normally distributed each with population standard deviations of 15.

A scientist wants to know if the mean IQ level between individuals in city A and city B are different, so she selects a simple random sample of 20 individuals from each city and records their IQ levels.

To test this, she will perform a two-sample z-test at significance level α = 0.05 using the following steps:

Suppose she collects two simple random samples with the following information:

x1 (sample 1 mean IQ) = 100.65

n1 (sample 1 size) = 20

x2 (sample 2 mean IQ) = 108.8

n2 (sample 2 size) = 20

Z=-1.718

According to the Z Score to P Value Calculator, the two-tailed p-value associated with z = -1.718 is 0.0858.

Since the p-value (0.0858) is not less than the significance level (.05), the scientist will fail to reject the null hypothesis.

There is not sufficient evidence to say that the mean IQ level is different between the two populations.

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A recipe requires 1/3 cup of milk for each 1/4 cup of water. How many cups of water are needed for each cup of milk?

Answers

Answer:

Step-by-step explanation:

A comparison between the cups of milk and cups of water can be written as a ratio: Note that:

1/3 >1/4

1/3 : 1/4 ← x 12 to get rid of fractions 12/1 x 1/3 : 12/1 x 1/4=4:3 4 cups of milk are used with 3 cups of water ←÷ 41 cup of milk is used with 3/4 cup of water

30 points!!!!
Solve the following linear equation for x
-4(2x - 9) + 6(-x + 1) = -8x - 5(3x - 3)

A) X = 4
B) X = 3
C) X = -3
D) X = 0

Answers

X = -3

this is because the internet said so

A x = 4 is the correct answer

what is the simplified form of the expression 0.2 (3x-3y)?

Answers

Answer:

0.6x - 0.6y.

Step-by-step explanation:

0.2 (3x - 3y)

= 0.2*3x - 0.2*3y

= 0.6x - 0.6y.

a caterer makes 3 extra sandwiches for every 12 sandwiches a customer orders. The caterer makes a total of 120 sandwiches for a customer. How many sandwiches did the customer order? (Not including the extra sandwiches)

Answers

Answer:

Step-by-step explanation: 12+3=15 15x8= 120 then take out the 3 from the 15 and do 12x8 and it's 96.

Beatriz Cruz purchased a home for $98,500. She made a $28,500
down payment and mortgaged the rest. Her annual expenses
for mortgage interest, taxes, repairs, insurance, and depreciation
totaled $6,890. She rented the house for $750 a month.
a. What is the annual net income?
b. What is the annual yield?
e. What monthly rent would she have to charge to get
a yield of 90%?

Answers

Answer:

a. To find the annual net income, subtract the annual expenses from the annual rental income.

The annual rental income = $750 * 12 months = $9,000

So, the annual net income = $9,000 - $6,890 = $2,110

b. To find the annual yield, divide the annual net income by the investment cost (the down payment) and multiply by 100 to get the answer as a percentage.

The annual yield = ($2,110 / $28,500) * 100 = 7.41%

c. To find the monthly rent required to get a yield of 90%, divide the investment cost by the desired yield and divide by 12 to get the monthly rent.

The investment cost = $28,500

The desired yield = 0.90

So, the monthly rent = ($28,500 / 0.90) / 12 = $2,306.25

Step-by-step explanation:

y=? what does this even meannnnn

Answers

The calculated measure of angle y is 60 degrees

How to calculate the value of y

from the question, we have the following parameters that can be used in our computation:

The figure

From the figure, we can see that

The shape can be divided into two triangles such that

Each triangle is an equilateral triangle

The measure of an angle in an equilateral triangle is 60 degrees

using the above as a guide, we have the following:

y = 60

Hence, the value of y is 60 degrees

Determine the first derivative of the following functions: (a) y(x)=e^cosx (b) y(x)=3x−2/x+1

Answers

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Determine the first derivative of the following functions:
(a) y(x)=e^cosx
(b) y(x)=3x−2/x+1