show that xcosec^2x = cotx - d/dx xcotx

Question The price of a sofa is Sx. A man buys the sofa on hire purchase according to the following terms:

a downpayment of 25 % and the remaining to be paid in monthly instalments over 30 months at a

simple interest rate of 12 % per annum. Given that his monthly instalment is $52, find the value of x.

Answer:

376.8 [tex]units^{2}[/tex]

Step-by-step explanation:

There are a lot of moving parts.  We need to find the area of the bottom of the circle the center and the top circle.

The top and the bottom will be the same.

The area of a circle:

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

a = 3.14([tex]5^{2}[/tex])

a = 3.14(25)

a =78.5  

The center:  Think of this as a label on soup can.  If you tear the label off it would be a rectangle.  To find the area we would multiply the height of the can by the circumference of the circle.  They tell us the height is 7 and we can calculate the circumference.

C = [tex]\pi[/tex]d The d is the diameter it is 2 of the radiuses.  

C = [tex]\pi[/tex]10

C = 3.14(10)

C = 31.4

Now we multiply 31.4 and 7 together to find the area of the center of the cylinder.

(31.4)(7) = 219.8

The total area:

top 78.5

center 219.8

bottom 78.5

Total 376.8

Answer:

-7x + 1

Associative Property can be used.

Step-by-step explanation:

Hello!

We can simply the expression by combining like terms.

Like terms are terms with the same variable and degree. They may have different coefficients.

The simplified form is 1 - 7x, or -7x + 1.

We can also represent this using the Associative property, by grouping like terms:

Answer:

Step-by-step explanation:

i'd say with the given info it will be the same

The form of deductive reasoning used in the given argument is; Law of Syllogism

The argument we are given is;

If a number ends in 0, then it is divisible by 10.

If a number is divisible by 10, then it is divisible by 5.

If a number ends in 0, then it is divisible by 5.

The law used for the deductive reasoning in the given argument is called Law of Syllogism. This is because this law of mathematical logic states that;

If the following two statements are true:

(1) If p , then q .

(2) If q , then r .

Then we can derive a third true statement:

(3) If p , then r .

Read more about Logic Laws at; https://brainly.com/question/13419663

#SPJ1

The sum of all five numbers in the list is 25.

According to the question,

The first number on my list of five numbers is 1, and the fifth is 5. The other figures are all one more than their two nearest neighbors' averages.

Let the list of numbers be 1,x,y,z,5.

As each of the other numbers is equal to one more than the average of its two neighbors.

x=(1+y)/2+1

2x=3+y   -(1)

Similarly,

y=(x+z)/2+1

2y=x+z+2   -(2)

z=(y+5)/2+1

2z=y+7    -(3)

Multiply equation (2) by 2 and then substitute equations (1) and (3),

4y=3+y+y+7+4

4y=2y+14

2y=14

y=14/2

y=7

From equation (1),

2x=3+7

2x=10

x=5

From equation (3),

2z=7+7

2z=14

z=14/2

z=7

The list is: 1,5,7,7,5

Sum of the numbers of list = 1+5+7+7+5 = 25

Learn more about sum here:

https://brainly.com/question/17695139

#SPJ1

The amount made per minute is $1.28 * 10^7

Fractions are written as a ratio of two numbers. For instance a/b is a fraction.

According to the question, a certain animated movie earned $1.1 * 10^9 every 9.1 * 10^1 minutes.

$1.1 * 10^9 = 9.1 * 10^1

In order to determine the amount earned per minute;

x = 1minute

Divide both expressions

1.1 * 10^9/x = 9.1 * 10^1

x = 1.1 * 10^9 /9.1 * 10^1

Divide the result

x = 1.1 * 10^9 /9.1 * 10^1

x = 0.12 *10^8
x = $1.28 * 10^7

Hence the amount made per minute is $1.28 * 10^7

Learn more on ratio here: https://brainly.com/question/2328454

#SPJ1

Answer:

-1 and 1

Step-by-step explanation:

Reflecting D over the y-axis maps it onto (1,2).

This is supposed to map onto F(0,3), so this is a shift 1 unit left and 1 unit up.

So, the blanks are -1 and 1, respectively.

Answer: (x + [-1], y + [1])

Step-by-step explanation:

      See attached. We can draw, or picture it in our heads, what the reflection would look like. Then we can pick one (or multiple to test) points and see the translation.

      We can also test with a set of points. B', (2, 4) becomes G in the transformation. G is at (1, 5)

      (1 - 2, 5 - 4) -> (-1, 1)

Based on the given parameters, the number of filet mignon the restaurant served is 14

From the question, the given parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

This means that the proportion of filet mignon is

filet mignon = 100%- Salmon filets

This gives

filet mignon = 100%- 80%

Evaluate the difference

filet mignon = 20%

The number of filet mignon is calculated as:

filet mignon = 20% * Dinner specials

Substitute the known values in the above equation

filet mignon = 20% * 70

Express 20% as decimal

filet mignon = 0.20 * 70

Evaluate the product

filet mignon = 14

Hence, the number of filet mignon the restaurant served is 14

So, the complete parameters are:

Dinner specials =  salmon filet and filet mignon.

Dinner specials = 70 dinner specials

Salmon filets =  80%

filet mignon = 14

Read more about proportions at:

https://brainly.com/question/1781657

#SPJ1

Answer:

Negative.

Step-by-step explanation:

b is above zero. So, it is positive.

c is below zero. So, it is negative.

A positive divided by negative number results in negative.

Answer:

B. negative

Step-by-step explanation:

-2 is negative. That's why.

The next year's expected cash flow if there is a 50/50 probability that it will be either $10 million or $60 million is $35 million.

Probability refers to possibilities. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. The probability formula states that the ratio of positive outcomes to all other outcomes determines how likely an event is to occur.

Sum of outcomes= 410+$60=$70 million

Number of outcomes=2

As the probability is 50/50, the next year’s expected cash flow will be

10+60/(2)

=70/2

=35 million dollars.

To learn more about probability, visit: https://brainly.com/question/9793303

#SPJ4

Based on the task content; If you multiply both sides of an inequality by a negative number, the inequality symbol should be reversed always. Option B

Based on the rule of inequality, whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign.

For instance,

-4x > 12

divide both sides by -4

x < 12/-4

x < -3

If you multiply both sides of an inequality by a negative number, the inequality symbol should be reversed always.

Learn more about inequality:

https://brainly.com/question/25275758

#SPJ1

The volume of the similar triangular prism is:  1,280 cm³.

Volume of a right triangular prism = 0.5 × b × h × altitude, where:

b is the base length of the triangular base

h is the height of the triangular base

Find the of the first triangular prism

Base length of the triangular base (b) = 4 cm

Height of the triangular base (h) = 4 cm

Altitude of the prism = 20 cm

Volume of the first triangular prism = 0.5 × 4 × 4 × 20 = 160 cm³.

Volume of the first prism/Volume of the second prism = (leg of first prism)³/(leg of second prism)³

160/Volume of the second prism = (4)³/(8)³

160/Volume of the second prism = 64/512

160/Volume of the second prism = 0.125

Volume of the second prism = 1,280 cm³.

Thus, applying the volume formula for a right triangular prism, the volume of the given similar prism is calculated as: 1,280 cm³.

Learn more about volume of triangular prism on:

https://brainly.com/question/21173224

#SPJ1

The value of tanθ = ±∞ or tanθ = ±√(7/5)

The question is a trigonometric equation

A trigonometric equation is an equation that has unknowns that contain trigonometric ratios.

Given the trigonometric equation 7cosec²θ - 9cot²θ = 7, we require tanθ.

So, 7cosec²θ - 9cot²θ = 7

using the trigonometric identity 1 + cot²θ = cosec²θ.

Substituting this into the equation, we have

7cosec²θ - 9cot²θ = 7

7(1 + cot²θ)² - 9cot²θ = 7

7(1 + 2cot²θ + cot⁴θ) - 9cot²θ = 7

7 + 14cot²θ + 7cot⁴θ - 9cot²θ = 7

14cot²θ + 7cot⁴θ - 9cot²θ = 7 - 7

14cot²θ + 7cot⁴θ - 9cot²θ = 0

7cot⁴θ + 14cot²θ - 9cot²θ = 0

7cot⁴θ + 5cot²θ = 0

Factorizing out cot²θ, we have

cot²θ(7cot²θ - 5) = 0

⇒ cot²θ = 0 or 7cot²θ - 5 = 0

⇒ cotθ = ±√0 or 7cot²θ = 5

⇒ cotθ = ±0 or cot²θ = 5/7

⇒ cotθ = ±0 or cotθ = ±√(5/7)

⇒ 1/tanθ = ±0 or 1/tanθ = ±√(5/7)

⇒ tanθ = ±1/0 or tanθ = ±√(7/5)

⇒ tanθ = ±∞ or tanθ = ±√(7/5)

So, the value of tanθ = ±∞ or tanθ = ±√(7/5)

Learn more about trigonometric equation here:

https://brainly.com/question/28025415

#SPJ1

The slope of the red line that is perpendicular to the green line is: -5/2.

When one line lies perpendicular to another line, the slope of one must be the negative reciprocal of the other line.

If given a number, i.e. a/b, the negative reciprocal of a/b would the opposite value of the reciprocal of a/b.

Reciprocal of a/b is b/a. Negative reciprocal of a/b would therefore be: -b/a.

Given that the slope of the green line is: 2/5. And it is perpendicular to the red line. The slope of the red line would be the negative reciprocal of 2/5.

Negative reciprocal of 2/5 is -5/2.

Therefore, the slope of the red line is: -5/2.

Learn more about slope of perpendicular lines on:

https://brainly.com/question/1362601

#SPJ1

The time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds

The function is given as:

y = -16x^2 + 48x

When the ball hits the ground, we have

y = 0

Substitute the known values in the above equation

-16x^2 + 48x = 0

Factor out -16x

-16x(x - 3) = 0

Divide through by -16x

x - 3 = 0

Add 3 to both sides

x = 3

Hence, the time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds

Read more about quadratic functions at:

https://brainly.com/question/8992769

#SPJ1

The survey method was flawed since the sample was not random.

A survey is an investigation that is carried out on a sample of a population. However, for the sample to be representative of the population,  care must be taken to pick the participants in the survey at random. The principal ought to have carefully crafted a method in which the sample can be selected in a randomized manner.

For instance, the principal could have decided to take the fifth student in every row in all the classes in the school. In that way, the sample would be adequately randomized hence the result of the survey would be adjudged as representative of the situation in the entire population and thus it will be reliable as a tool that can be used to make scientific inferences.

Thus, the survey method was flawed since the sample was not random.

Learn ore about random sampling:https://brainly.com/question/12719656

#SPJ1

Answer: C

Step-by-step explanation:

The survey method was flawed since the sample was not random.

Answer:

15

Step-by-step explanation:

from the first then it is 0+7=7

and from the last it is 0+8=8

then the number of cars available in the station is 8+7=15

The line of best-fit that represents the relationship between velocity and time is:

v = 2.19t + 6.7.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (t,v) are given as follows:

(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).

Hence, inserting these points into a calculator, the equation is given by:

v = 2.19t + 6.7.

More can be learned about a line of best-fit at https://brainly.com/question/22992800

#SPJ1

The lateral surface area of a right circular cone is 234.09 [tex]cm^2[/tex]

Given that volume = [tex]320cm^3[/tex]

Radius = 8cm

we know that

The volume of the right circular cone = [tex]V = \frac{\pi r^2h}{3}[/tex]

[tex]320 = \frac{22 \times 8^2h}{3 \times 7}[/tex]

after solving the equation we get

h =  4.77cm

now, the lateral surface area of the cone = [tex]A = \pi \times r \times \sqrt{h^2 + r^2}[/tex]

now putting the values in the above equation

[tex]A = \pi \times 8 \times \sqrt{4.77^2 + 8^2}[/tex]

A = 234.09 [tex]cm^2[/tex]

To learn more about lateral surface area with the given link

https://brainly.com/question/14001755

#SPJ4

The unit rate with the turtle crawling is 6/23 mile per hour.

According to the statement

we have given that the every 1/3 of an hour that the turtle is crawling, he can travel 2/23 of a mile. and

we have to find the unit rate with the turtle crawling

So, For this purpose,

we know that the

The unit rate of speed in miles per hour the number of miles in one hour.

So, to find the unit rate:

Divide distance in miles with the time which is in hours.

So,

unit rate of speed = distance / time

unit rate of speed = (2/23) / (1/3)

unit rate of speed = 6/23 mile per hour.

So, The unit rate with the turtle crawling is 6/23 mile per hour.

Learn more about unit rate here

https://brainly.com/question/4895463

#SPJ1

Answer:

1: Linear

2: Linear

Step-by-step explanation:

Scenario 1:

Equation: y=8x  (where x represents # of hours worked)

The graph would be linear.

Scenario2:

Equation: y=5x (where x is the # of boxes of donuts purchased)

The graph would be linear. ( I assumed that each box is $5 since 5/1=10/2 )

A similar situation could be: In an art shop, crayons are sold. It costs $7 for 1 box of crayons.

- The graph would be linear, and it would be constant as long as the price for each box of crayons is not changed. Equation is: y=7x

I'm not sure if this is exactly what the last question asked, pretty sure this would be an okay example.

Answer:

x=10.5

Step-by-step explanation:

if the two triangles were ratios it would be like

19.3:7.2 to x:3.9

so 75.27 = 7.2x

whcih is 10.45 which is approximately 10.5

The area of the barn quilt is 3 sq.ft.

The amount of sugar needed to make 1/2 of a batch of cookies is 1/5 of a cup.

Number of boys are practicing hitting the ball = 4

Number of bags of lemons used by Rachel on Tuesday = 1[tex]\frac{3}{4}[/tex]

1. A painted barn blanket needed to be 1 1/3 feet by 2 1/4 feet in size.

Area of the barn quilt = 1 1/3*2 1/4

                                  = 4/3*9/4

                                  = 3 sq. ft.

2. The recipe for Mrs. Smith's oatmeal cookies asks for 2/5 cups of sugar.

Sugar needed for making 1/2 of a batch of cookies = 1/2*2/5

                                                                                 = 1/5 of a cup

3. Six boys are practicing baseball throwing, catching, and hitting in the park. Two thirds of those six youngsters are practicing hitting.

Number of boys practicing hitting the ball = 6*2/3 = 4

4. At the park's lemonade kiosk, Rachel works. She used 1 and 2/5 bags of lemons on Monday. She used 1 and 1/4 times as many lemons on Tuesday as she did on Monday.

Number of bags of lemon used on Tuesday = 7/5*5/4

                                                                     = 7/4

                                                                     = 1 and 3/4 bags

Learn more about area here:

https://brainly.com/question/25292087

#SPJ1

Answer:  $34.32

Step-by-step explanation: We first calculate the price of the dress that was on sale. 30% of 35 is 35/10 x3. This is equal to 3.5x3 which is 7+3.5 = 10.5 We subtract this from 35 to get $24.5. So, the dress cost $24.5. Next 1/2 of 17 is 8.5. In total, the items cost $24.5+$8.5 = $33. Then, there is a 4% sales tax we have to add on to 33. 1% of 33 is 33/100 which is 0.33. This time 4 is 1.32. 33+1.32 is 34.32.

Answer:

  BD = √97 cm ≈ 9.849 cm

Step-by-step explanation:

Diagonal BD of rectangle ABCD is the hypotenuse of right triangle ABD. Opposite sides of the rectangle are the same length, so we have ...

  AB = 4 cm

  AD = 9 cm

The sides are related to the diagonals by the Pythagorean theorem.

The Pythagorean theorem tells you the relation between sides and hypotenuse of a right triangle:

  AB² +AD² = BD²

  4² +9² = BD² = 16 +81 . . . . . evaluating the squares

  BD = √97 . . . . . take the square root

The length of BD is √97 cm, about 9.849 cm.

Answer:

It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).

The work done (in foot-pounds) in stretching the spring from its natural length to 0.7 feet beyond its natural length is 1.23 foot-pound

From the question given above, the following data were obtained:

F = Ke

Divide both sides by e

K = F/ e

K = 3 / 0.6

K = 5 pound/foot

Thus, the spring constant of the spring is 5 pound/foot

Wd = ½Ke²

Wd = ½ × 5 × 0.7²

Wd = 2.5 × 0.49

Wd = 1.23 foot-pound

Therefore, the work done in stretching the spring 0.7 feet is 1.23 foot-pound

Learn more about spring constant:

https://brainly.com/question/9199238

#SPJ1

58 min/day  rate did she practice in minutes per day.

What is  time?

1 day = 2030 min ÷ (5 weeks × 7 days)

1 day = 2030 ÷ 35

1 day = 58 minutes

rate = 58 min/day

Therefore, 58 min/day  rate did she practice in minutes per day.

Learn more about time

brainly.com/question/19051312

#SPJ4

The smaller number, x from the inequality x + 2x + 6 < 50 is x < 14.67

x + 2x + 6 < 50

3x + 6 < 50

3x < 50 - 6

3x < 44

x < 44/3

x < 14.6666666666666

Approximately,

x < 14.67

Therefore, the smaller number, x is approximately x < 14.67

Learn more about inequality:

https://brainly.com/question/25275758

#SPJ1