Write a recursive definition for the set of odd positive integers.

Answers

Answer 1

a[1] = 1
a[n+1] = a[n] +2

Answer 2

Final answer:

A recursive definition for the set of odd positive integers starts with a base case of 1 and uses a recursive step where each subsequent odd integer is obtained by adding 2 to the current odd integer.

Explanation:

To write a recursive definition for the set of odd positive integers, you can define a base case and a recursive step. The base case is the smallest odd positive integer, which is 1. The recursive step will then generate the next odd integer by adding 2 to the current odd integer. Here's how you can express it:

Base case: Let O1 = 1, which establishes that 1 is the first odd positive integer.

Recursive step: For every odd positive integer On, there exists an On+1 = On + 2. This means that if you have an odd positive integer, the next one in the set can be found by adding 2 to the current one.

This definition ensures that every number generated by the recursive step will be odd since adding 2 to an odd number always results in another odd number, and starting from 1, guarantees that all numbers will be positive.

Related Questions

A map of a public park shows a circular pond. there is a bridge along a diameter of the pond that is 0.85 mi long. you walk across the bridge, while your friend walks halfway around the pond to meet you at the other side of the bridge. how much farther does your friend walk? round your answer to the nearest hundredth. use 3.14 for π.

Answers

To answer this question you will compare the distance you walked (0.85 miles) to the distance your friend walked ( half the circumference of the circle ; C = pi x d/2

Your friend walked 3.14 x 0.85/2 = 1.33 miles approximately

To find the difference in the distances, subtract 1.33 and 0.85.

1.33 - 0.85 = 0.48 miles

Your friend walked 0.48 miles further.

Answer:

Your friend walks about 0.48 miles farther than you.

Step-by-step explanation:

Find the circumference of the park.

C = πd Use the circumference formula.

C ≈ 3.14(0.85) Substitute for the diameter and π.

C ≈ 2.669 Multiply.

The circumference of the park is about 2.669 centimeters.

Find how far your friend walks when he or she walks halfway around the pond to meet you on the other side of the bridge. Divide the circumference by two.

0.785 ÷ 2 = 1.33

Your friend walks 1.33 miles.

Find how much farther your friend walks. Subtract the miles you walk from the miles your friend walks. Round your answer to the nearest hundredth.

1.33 − 0.85 ≈ 0.48

Which of the following equations can be used to solve for the radius (r)

Answers

i think it might be the third answer but im not sure

Answer:

The last option is the correct answer: [tex]r=\sqrt{\frac{A}{\pi}}[/tex]

Step-by-step explanation:

The area of a circle is given by :

[tex]A=\pi r^{2}[/tex] ; where r is the radius.

Now, lets find the radius.

[tex]\frac{A}{\pi } =r^{2}[/tex]

[tex]\sqrt{\frac{A}{\pi}} =r[/tex]

or [tex]r=\sqrt{\frac{A}{\pi}}[/tex]

Therefore, the last option is the correct answer.

Hakim invests $700 in a bank that pays 5% simple interest annually. After one year he uses the money in his account to buy a computer. The original cost of the computer is $750.00. The computer is on sale for a 20% discount off of the original cost. The sales tax is 4% of the sale price. After purchasing the computer, how much does Hakim have left in his bank account? Show your work.

Answers

To answer this question you will need to calculate the amount of interest he earns in a year, apply the discount on the sale price, and calculate the sales tax on the discounted price. Then you will take the amount in his bank account minus the sale price with tax.

Each of the steps is shown in the attached work.

He will have $111 left is his account.

Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1 f(n) = 35n Which one of these formulas show the sequence written rercursively and which shows it written explicity? Justify your explanantions. Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Use the explicit formula to demonstrate the most direct method to find f(40). Explain why you chose that method and what your answer means. Show your calculations. Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.

Answers

1. We use the recursive formula to make the table of values:
f(1) = 35
f(2) = f(1) + f(2-1) = f(1) + f(1) = 35 + 35 = 70
f(3) = f(1) + f(3-1) = f(1) + f(2) = 35 + 70 = 105
f(4) = f(1) + f(4-1) = f(1) + f(3) = 35 + 105 = 140
f(5) = f(1) + f(5-1) = f(1) + f(4) = 35 + 140 = 175

2. We observe that the pattern is that for each increase of n by 1, the value of f(n) increases by 35. The explicit equation would be that f(n) = 35n. This fits with the description that Bill saves up $35 each week, thus meaning that he adds $35 to the previous week's value.

3. Therefore, the value of f(40) = 35*40 = 1400. This is easier than having to calculate each value from f(1) up to f(39) individually. The answer of 1400 means that Bill will have saved up $1400 after 40 weeks.

4. For the sequence of 5, 6, 8, 11, 15, 20, 26, 33, 41...
The first-order differences between each pair of terms is: 1, 2, 3, 4, 5, 6, 7, 8...since these differences form a linear equation, this sequence can be expressed as a quadratic equation. Since quadratics are functions (they do not have repeating values of the x-coordinate), therefore, this sequence can also be considered a function.

The value of f(40) is 1400 .The sequence can be considered a function because each position has a unique value.

Let's analyze the given formulas for Bill's savings:

The recursive formula is: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1

The explicit formula is: f(n) = 35n

A recursive formula defines each term based on the previous terms, which we see in f(n) = f(1) + f(n-1). An explicit formula provides a direct calculation, shown in f(n) = 35n.

Recursive Formula Table for 1 ≤ n ≤ 5n = 1: f(1) = 35n = 2: f(2) = 35 + f(1) = 35 + 35 = 70n = 3: f(3) = 35 + f(2) = 35 + 70 = 105n = 4: f(4) = 35 + f(3) = 35 + 105 = 140n = 5: f(5) = 35 + f(4) = 35 + 140 = 175Using the Explicit Formula to Find f(40)

The explicit formula f(n) = 35n allows us to directly calculate:

f(40) = 35 * 40 = 1400

This method is chosen because it provides a straightforward calculation without needing to compute all the preceding values.

Analyzing the Sequence 5, 6, 8, 11, 15, 20, 26, 33, 41, ...

This sequence can be considered a function because each input (position in the sequence) has a unique output (value in the sequence).

If you take Coleman's test grade and divide by 2 and add 27, you get 67. Write and solve an equation to find Coleman's test grade.

Answers

Final answer:

To find Coleman's test grade, set up the equation x/2 + 27 = 67, solve for x by first subtracting 27 and then multiplying by 2 to get x = 80.

Explanation:

The student is asking to find Coleman's test grade given that if you take Coleman's test grade, divide by 2, and add 27, the result is 67. To solve for Coleman's test grade, we can set up an equation where Coleman's test grade is represented by x. The equation based on the provided information would be x/2 + 27 = 67. We can solve for x by first subtracting 27 from both sides of the equation to get x/2 = 40, and then multiplying both sides by 2 to find x. Therefore, x = 80, which means Coleman's test grade is 80.

Final answer:

To find Coleman's test grade, we can set up an equation: (x/2) + 27 = 67. By solving this equation, we find that Coleman's test grade is 80.

Explanation:

To find Coleman's test grade, we can set up an equation using the information given. Let's represent Coleman's test grade as 'x'. We have the equation: (x/2) + 27 = 67.

To solve this equation, we need to isolate 'x'. We can start by subtracting 27 from both sides of the equation: (x/2) = 40.

Next, we need to get rid of the fraction by multiplying both sides of the equation by 2: x = 80.

So Coleman's test grade is 80.

Find all the zeroes of the equation. -3x4+27x2+1200=0 I need to learn how to do it! Just not the answer please

Answers

The first thing you should do for this case is to rewrite the expression.
To do this, divide both sides of the equation between -3.
We have then:
(-1/3) * (- 3x ^ 4 + 27x ^ 2 + 1200) = (- 1/3) * (0)
x ^ 4-9x ^ 2-400 = 0
Then, we rewrite the polynomial:
(x-5) * (x + 5) * (x ^ 2 + 16) = 0
From here, we obtain the four roots:
Root 1:
x-5 = 0
x = 5
Root 2:
x + 5 = 0
x = -5
Root 3 and root 4:
x ^ 2 + 16 = 0
x3 = -4i
x4 = 4i

Answer:
all the zeroes of the equation are:
x1 = 5
x2 = -5
x3 = -4i
x4 = 4i

The answer are the following:
x1 = 5
x2 = -5
x3 = -4i
x4 = 4i

Step 1:
We have the equation
(-1/3) * (- 3x ^ 4 + 27x ^ 2 + 1200) = (- 1/3) * (0)
x ^ 4-9x ^ 2-400 = 0

Step 2: Write it in polynomial equation
(x-5) * (x + 5) * (x ^ 2 + 16) = 0
(x-5) * (x + 5) * (x+4)(x-4) = 0

From the factored form, we can get the roots which are
5, -5, 4, -4

Julia surveyed her friends to find the number of hours they spend on homework during the week. The data from her survey is displayed in the first table. She then took a random sample of five responses from the population as shown in the second table. Compare the mean of the population with the mean of the given sample.

Population Data
4
5
3
1
3
2
2
3
5
7
3
6
3
0
1
5
0
4
3
6

Sample Data
5
4
6
2
1

What is the difference between the mean of the sample and the mean of the population?
0.2
0.3
0.4
0.5

Answers

Solution:

we are given with two kind of data set , one is Population data and the other is sample data.

we have been asked to Compare the mean of the population with the mean of the given sample.

Given Population Data
is

[tex] 4
, 5
, 3
,1
,3
,2,2
,3
,5
,7
,3
,6
,3
,0
,1
,5
,0
,4
,3
,6 [/tex]

Its mean can be calculated as below

[tex] Mean=\frac{4+5+3+1+3+2+2+3+5+7+3+6+3+0+1+5+0+4+3+6}{20} \\\\\Mean=\frac{66}{20}=3.3\\ [/tex]

Now the Sample data is

5,4,6,2,1

[tex] Mean=\frac{5+4+6+2+1}{5}\\\\Mean=\frac{18}{5}= 3.6\\ [/tex]

Hence the value of difference of the Mean is [tex] =3.6-3.3=0.3 [/tex]

Answer:

The answer is B. 0.3

Step-by-step explanation:

If you need any help, ask me! :)

I understand that the remainder is 0, I kinda guessed and it told me.
But we're using long division or synthetic division.
Can you explain to me what the quotient is?
Thanks!

Answers

You need to add the x^4, x^3, x^2, and x term in there so you can have place holders to do the rest of the problem

You will have something like:
[tex] \frac{x^{5} + 0x^{4}+ 0x^3+0x^2+0x-32}{x - 2} [/tex]

Then you start the long division process

When you get done you will have [tex]x^4 + 2x^3 + 4x^2 + 8x + 16[/tex]
with a remainder of 0

There were some pencils in a pencil box. Zoe added 7 more pencils to the pencil box. Now there are 24 pencils in the box. How many pencils were in the box to start with?

Answers

This problem can be solved using subtraction. We want to know how many pencils were in the box before the 7 pencils were added, so we must subtract 7 from 24.

24 - 7 = 17.

There were 17 pencils in the box to start with.

So if Zoe added 7 more pencils then all you have to do is just do the opposite

being the equation stated
X+7=24
X being the number of pencils before added

To find the answer just do the opposite
24-7=X
and X=17

What is the equation of the line?

A) x + 3y = 9

B) 3x - y = 9

C) x - y = 9

D) 3x + y = 9

Answers

Hi there!

The answer is D.

Since the y intercept of the equation is 9 and the slope is negative 3, after multiplying the entire equation by -1, we will get D.

Hope this helps!

A dress that retails for 160 dollars was on sale 96 dollars by what percent was the dress discounted?

Answers

it was 40% off, and the total savings were 64 dollars

Help plz and explain. ..........

Answers

I worked backwards to solve this question, my explanation and working out is
in the picture. If you need any clarification, just ask in the comments.

Each morning papa notes the birds feeding on his bird feeder. so far tis month he has seen 59 blue jays, 68 black crows, 12 red robins and 1 cardinal. if 300 birds list papa's birdfeeder, how many blue jays can we expect to see?

Answers

Answer: Papa could expect to see about 126 blue jays.

First, we need to determine the percent of blue jays that he typically sees.

59 + 68 + 12 + 1 = 140 He saw a total of 140 birds.

59 of them were blue jays. So 59 / 140 = 42% of the birds were blue jays.

Multiply 300 by 42% and we have an expected number of 126 blue jays.

15. A restaurant has one type of milk that has 2% fat and another that has 7% fat. how many quarts of each type does the restaurant need to make 40 quarts of a milk mixture that is 5% fat?

a. 24 quarts of the 2% milk and 16 quarts of the 7% milk
b. 16 quarts of the 2% milk and 24 quarts of the 7% milk
c. 16 quarts of the 2% milk and 16 quarts of the 7 milk
d. 24 quarts of the 2% milk and 24 quarts of the 7% milk,

Answers

B. 16 quarts of the 2% milk and 24 quarts of the 7% milk First, let's create an equation to solve. x = quarts of 2% milk (40-x) = quarts of 7% milk So we have the equation x*2 + (40-x)*7 = 40*5 Now to solve for x x*2 + (40-x)*7 = 40*5 x*2 + 7*40 - 7*x = 40*5 x*2 - 7*x = 40*5 - 7*40 -5*x = - 2*40 x = 2*8 x = 16 So we need 16 quarts of 2% milk and 40-16 = 24 quarts of 7%, which matches option "B".

Select the locations on the number line to plot the points 4 1/ 3 and −1 1/3 .

Answers

we have that
4 1/ 3
−1 1/3
the answer in the attached figure

Answer:

The locations of given number are shown on the below number line.

Step-by-step explanation:

The given numbers are

[tex]4\dfrac{1}{3} and -1\dfrac{1}{3}[/tex]

We need to plot these points on the given number line.

In the given number write the integers -4,-3,-2,-1,0,1,2,3,4 on points indicated and two sub point between two consecutive points divides the line in three equal parts.

[tex]4\dfrac{1}{3}=4+\dfrac{1}{3}[/tex]

It means [tex]4\dfrac{1}{3}[/tex] lies next to 4 on right side.

[tex]-1\dfrac{1}{3}=-(1+\dfrac{1}{3})=-1-\dfrac{1}{3}[/tex]

It means [tex]-1\dfrac{1}{3}[/tex] lies next to -1 on left side.

Therefore, the locations of given number are shown on the below number line.

@ajaylounsber Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month?,

Answers

Jennifer has been saving $12 more each month. If she started saving $11 each month, the next month she would have to save $23. The third month she would save $35 and so on and so forth if she ended up saving 19779 by the end of the 57 months. When you multiply 11 by 57 months, you find that number and subtract it by the total which is 19779. This would bring you at 19152. Divide that by 1596 which we got using the derivation formula (s = n/2) and you would get $12 more saved up each month.

Multiply.

638 × 49

_____

Answers

31,262

Is that what you're looking for?

A shipping tube is shaped like a triangular prism. The bases are equilateral triangles with edges of 6 inches and a height of 5.2 inches. The tube is 14 inches long. Find the lateral surface area of the shipping tube.

Answers

Final answer:

The lateral surface area of the equilateral triangular prism shaped shipping tube is 252 square inches.

Explanation:

The question pertains to the calculation of the lateral surface area of a triangular prism shaped shipping tube, more specifically an

equilateral triangular prism

. The lateral area of a triangular prism can be calculated using the formula: Perimeter of the base x length of the prism. Here, the base of the prism is an equilateral triangle, so the perimeter of the base will be 3 x the length of one edge, which in this case is 3 x 6 inches = 18 inches. The length of the prism is given to be 14 inches. Hence, by substituting these values into the formula, the lateral surface area = 18 inches x 14 inches =

252 square inches.

Learn more about Lateral Surface Area here:

https://brainly.com/question/29007884

#SPJ12

Simplify 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n

Answers

The actual answer is 5.5n-0.5p-4

Final answer:

The simplified expression of 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n is -2 + 5.5n - 0.5p after combining like terms.

Explanation:

To simplify the algebraic expression 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n, we need to combine like terms. The constants 1 and -3 can be combined, and the terms with 'n' and 'p' can each be combined respectively. Let's do this step by step:

Combine the constants: 1 - 3 = -2.Combine the 'n' terms: 4.25n + 5/4n = (17/4)n + (5/4)n = (22/4)n = 5.5n.Combine the 'p' terms: (3/2)p + (-2p) = (1.5 - 2)p = -0.5p.

The simplified expression is -2 + 5.5n - 0.5p.

If i give my sister 17 dollars, then we will have the same amount of money. if instead she gives me 23 dollars, then i'll have three times as much money as she will have. how much money does she currently have (in dollars)

Answers

The Sister= $63
You= $97

The total number of dollars my sisters have is $60.

Given that, if I give my sister 17 dollars, then we will have the same amount of money.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of dollars I have be x and number of dollars my sisters have be y.

Now, if I give my sister 17 dollars, then we will have the same amount of money

y-17 = x

x - y = -17 ---------(1)

If she gives me 23 dollars, then I'll have three times as much money as she will have.

3(x-23) = y

3x-69 = y

3x-y = 69 ---------(2)

Subtract equation (1) from (2)

3x-y-(x-y) = 69 - (-17)

⇒ 2x = 86

⇒ x = $43

Put x = 43 in equation (1), we get

43 - y = -17

43+17 = y

y = $60

Therefore, the total number of dollars my sisters have is $60.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ5

Read the word problem. George has 2 times the amount of points that is 4 less than his sister’s. His sister has 16 points. How many points does George have? What operations are needed to solve this word problem, and in what order should they be used?
addition and subtraction, in that order
addition and multiplication, in that order
subtraction and division, in that order
subtraction and multiplication, in that order

Answers

For this case, the first thing we are going to do is define the following variables:
x: Sister points.
y: George's points.
We write the following mathematical equation:
y = 2 * (x-4)
His sister has 16 points:
y = 2 * (16-4)
y = 2 * (12)
y = 24

Answer:

How many points does George have?

George has 24 points.

What operations are needed to solve this word, and in what order should they be used?

subtraction and multiplication, in that order

D- subtraction and multiplication, in that order.

Step-by-step explanation:

EDG 2022

At the end of a factory assembly line, completed widgets are deposited into a box until it is filled. if after 10 minutes the box contains 25 widgets and it takes 2 hours total to fill up a box, how many widgets must each box hold?

Answers

in this question we are asked to calculate how many widgets a box can hold.
2 hours - 60 minutes / hour * 2 = 120 minutes
after 10 minutes - box contains 25 widgets
this means that it takes 10 minutes to fill - 25 widgets
in 1 minute - 25/10 widgets/minute
therefore within 120 minutes - 25/10 widgets/minute * 120 minutes
the number of widgets a box can hold - 300 widgets

Final answer:

Each box must hold a total of 300 widgets.

Explanation:

To determine how many widgets must each box hold, we need to calculate the rate of production and then use it to find the total number of widgets produced in 2 hours (the total time it takes to fill the box).

First, we'll find out how many widgets are produced per minute. Since 25 widgets are deposited in 10 minutes, we divide the number of widgets by the time (in minutes) to get the rate:

Rate of production = 25 widgets / 10 minutes = 2.5 widgets per minute.

Now, we need to find out how many minutes are in 2 hours:

2 hours = 2 hours * 60 minutes/hour = 120 minutes.

Finally, we multiply the rate of production by the total production time (in minutes) to find out the total number of widgets per box:

Total widgets per box = 2.5 widgets/minute * 120 minutes = 300 widgets.

From an airplane at an altitude of 1200m the angle of depression to a rock on the ground measures 28. Find the distance from the plane to the rock

Answers

Given that the plane is at altitude of 1200m and the angle of depression is 28°, to calculate the distance between the the plane and the rock we assume that we a have right triangle whereby the distance of the plane form the ground is the height, the distance from plane to the rock is the hypotenuse and the remaining distance is the base:
thus

sin θ=opposite/hypotenuse
θ=28°
opposite=1200m
hypotenuse=h
thus
sin 28=1200/h
h=1200/sin 28
h=2556.065 m

Final answer:

The distance from the plane to the rock can be calculated using trigonometry. Here, the tangent of the given angle is used, with the formula: Distance = 1200m / tan(28°).

Explanation:

The subject matter in the question relates to trigonometry. We can use the tangent of the given angle to find the distance to the rock. We are given an altitude of 1200m (which is equivalent to the opposite side in a right angle triangle) and an angle of depression of 28°. We know from trigonometry that the tangent of an angle is equal to the opposite side divided by the adjacent side (tan(θ) = opposite / adjacent).

Since we want to know the distance from the plane to the rock, we're trying to find the length of the hypotenuse. This forms a right-angled triangle with the height of the plane as the opposite side, and the line of sight to the rock as the hypotenuse.

We can use the following formula which is derived from the principles of trigonometry:

Distance to the rock (hypotenuse) = Opposite side / tan(θ)

Plugging the given values into this formula gives:

Distance to the rock = 1200m / tan(28°) This calculation will give the answer.

Learn more about Trigonometry here:

https://brainly.com/question/11016599

#SPJ11

Which of the following is the image of C after a rotation of 180° about the origin?

(-5, 2)
(-5, -2)
(-2, 5)

Answers

after a 180 rotation C would be at (-5,2)

Answer:

Option A.(-5, 2).

Step-by-step explanation:

Picture attached in the question we know the coordinates of the point C are (5, -2). Now we rotate C with a rotation of 180° about the origin.

As we can see a line connecting C and a new point C'. This line shows the rotation of the poit by 180°.

Therefore the new coordinates of C will be C'(-5, 2).

Option A is the correct option.

The perimeter of the rectangle is 64 cm. Find the value of x.

A. 7

B. [tex] \frac{64}{33} [/tex]

C. 32

D. 50

Answers

2(11 + 3x) = 64
11 + 3x =64/2
11 + 3x = 32
3x = 32 - 11
3x = 21
x = 21/3
x = 7

A.

The value of x is 7 and the right option is A. 7.

What is perimeter?

Perimeter is the total distance around an object.

To find the value of x, we use the formula of the perimeter of a rectangle.

Formula:

P = 2(L+W)............... Equation 1

Where:

P = Perimeter of the rectangleL = Length of the rectangleW = Width of the rectangle

From the question,

Given:

L = 3xW = 11 cmP = 64 cm

Substitute these values into equation 1 and solve for x

64 = 2(11+3x)64 = 22+6x6x = 64-226x = 42x = 42/6x = 7

Hence, the value of x is 7 and the right option is A. 7.

Learn more about perimeter here: https://brainly.com/question/19819849

#SPJ2

Find the product of (x + 7)2. (1 point)

x2 − 14x + 49

x2 + 14x + 49

x2 − 49

x2 + 49

Answers

General form for squaring a binomial is [tex] (a+b)^{2} = a^{2} + 2ab + b^{2} [/tex]
In this binomial, the a is x and b is 7 so plug in and chug:
[tex] x^{2} +2(x)(7) + 7^{2} [/tex]
[tex] x^{2} + 14x + 49[/tex] - Final answer

ANSWER

[tex] {(x + 7)}^{2} = {x}^{2} + 14x + 49[/tex]

EXPLANATION

The given expression is

[tex] {(x + 7)}^{2} [/tex]

We can rewrite this as,

[tex] = (x + 7)(x + 7)[/tex]

Recall that,

[tex](a + b)(c + d) = ac + ad + bc + bd[/tex]

This is called the distributive property.

We apply the distributive property to get,

[tex] {(x + 7)}^{2} = {x}^{2} + 7x + 7x + {7}^{2} [/tex]

This simplifies to

[tex] {(x + 7)}^{2} = {x}^{2} + 14x + 49[/tex]
The correct answer is B.

How do you prove cotx/(cscx-sinx)=secx

Answers

[tex]\dfrac{\cot x}{\csc x-\sin x}=\dfrac{\frac{\cos x}{\sin x}}{\frac{1}{\sin x}-\sin x}= \dfrac{\frac{\cos x}{\sin x}}{\frac{1}{\sin x}-\frac{\sin^2x}{\sin x}}= \dfrac{\frac{\cos x}{\sin x}}{\frac{1-\sin^2x}{\sin x}}=\\\\\\= \dfrac{\frac{\cos x}{\sin x}}{\frac{\cos^2x}{\sin x}}=\dfrac{\cos x\cdot\sin x}{\sin x\cdot\cos^2x}=\dfrac{1}{\cos x}=\boxed{\sec x}[/tex]

what is the slope? 0 or undefined

Answers

Slope is zero.
It is undefined when the line is vertical.

True of False: If the measure of theta is A radians and B degrees, then A = 180B/pi. Please explain!

Answers

False.

A = B*π/180 . . . . the form in the statement uses the inverse of the proper conversion factor.

How to find the derivative of a fraction without using the quotient rule?

Answers

Hello,

(u/v)'=(u*v^(-1))'=u'*v^(-1)+u*(-1)*v^(-2)*v'=u'/v-u*v'/v²=(u'v-uv')/v²

Final answer:

To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule.

Explanation:

To find the derivative of a fraction without using the quotient rule, you can use the chain rule and the product rule. Here's an example:

Let's differentiate the function f(x) = (3x + 2) / (2x + 1).

First, identify the numerator and the denominator. In this case, the numerator is 3x + 2 and the denominator is 2x + 1.Apply the product rule by differentiating the numerator and the denominator separately. The derivative of the numerator is 3, and the derivative of the denominator is 2.Next, apply the chain rule by multiplying the derivative of the numerator by the denominator, and subtracting the derivative of the denominator multiplied by the numerator. In this case, the derivative of f(x) is (3 * (2x + 1) - (2 * (3x + 2))) / ((2x + 1)^2).

Simplifying further, the derivative of f(x) is (6x + 3 - 6x - 4) / ((2x + 1)^2) = -1 / ((2x + 1)^2).

Other Questions

Pathogenic organisms do not include _____.bacteriavirusesrickettsiaeticks Fan + Medal. Check my work? 1) in the late 1970's, liberals supported? A. deregulation of industry B. tax cuts and reduced social spending C. laws protecting the rights of minorities and women*2) which of the following explains one reason that conservatives gained power in the 1970's?A. liberals became more involved with religious groupsB. many white southern's opposed the civil rights laws of the 1960's *C. the counterculture movement drove many middle americans into the democratic party, "A man must be big enough to admit his mistakes, smart enough to profit from them, and strong enough to correct them." What does this quote mean and why does it matter? What is the ozone layer? Where is it?what purpose does it have ? Fill in the blanks to show how the election of 1800 was finally decided Rewrite the following equation in slope-intercept form. 19x 20y = -13 Write your answer using integers, proper fractions, and improper fractions in simplest form. Please Help!!! The only coins Alexis has are dimes and quarters. Her coins have a total value of $5.80. She has a total of 40 coins. Which of the following systems of equations can be used to find the number of dimes,d, and the number of quarters, q, Alexis has. Explain your choice.A.) d + q = 5.80 40d + 40 q= 5.80B.) d + q = 40 0.25d + 0.10q = 5.80C.) d + q = 5.80 0.10d + 0.25q = 40D.) d + q = 40 0.10d = 0.25q = 5.80 what events from "the black cat" seem to prove the wife's superstition about cats to be correct? a. the narrator relates the tale of his life to the reader from his jail cell as he waits to be executed. b. the first black cat bites the narrator's hand after the narrator grabs him in anger. c. the narrator begins drinking heavily and physically abuses both his wife and his pet cat. d. a second black cat, very similar to the narrator's first cat, appears out of Lara was really nervous before her speech, but she just kept concentrating on how important she believed her message to be. her belief in her message finally helped her dispel her nervousness before the presentation. which tip about developing confidence in public speaking does this example reflect? Find each missing length to the nearest tenth A thermometer is removed from a room where the temperature is 70 f and is taken outside, where the air temperature is 30 f. after one-half minute the thermometer reads 50 f. what is the reading of the thermometer at t = 1 min? (round your answer to two decimal places.) Which type of disorder causes further breakdown of body tissue?A. Degenerative B.ChronicC.CongenitalD.Noncommunicable in "Eavesdropping", how did author Eudora Welty forshadow her eventual epiphany and writing style in the beginning of the book? Reflection across the y -axis What happen when Gideons army blew their trumpet and waves their torches? The Bible story Maria would like to leave a tip (t) of at least 15% of her dinner bill (b). Which inequality best could be used to find the amount of the tip Maria would like to leave? This figure is made up of a triangle and a semicircle. What is the area of this figure? Use 3.14 for pi. Round only your final answer to the nearest tenth. Enter your answer, as a decimal, in the box. unitshttps://static.k12.com/nextgen_media/assets/8124428-GA_GMT_IT_03_DP100_885_008.png PLEASE HELPWILL GIVE BRAINLIESTSome local Culinary Art students are planning a trip to France for a special workshop on "Pastry Making & Baking." Because of your knowledge of the French language, you have been asked to write to these Culinary Art students about the many great benefits that learning another language can have for them in their future career.Write a short essay in English to these students to let them know the advantages of knowing French in a career in Culinary Art. You can also tell them about what to expect from taking a French class and share experiences that have made you want to study French. Who is regarded as the first important artist of the italian renaissance? an angle whose measure is 50 degrees is in standard position. in which quadrant does the terminal side of the angle fall?