a solid object is made with the combination of a cylinder and cone having the same radii. The height of cylinder is 21cm and the slant height of the cone is 10cm .If the total cost of painting the Total surface of the solid object at the rate of RS 140 per 100 sq cm is RS 1531.20. find the height of the cone.​

A Solid Object Is Made With The Combination Of A Cylinder And Cone Having The Same Radii. The Height

Answers

Answer 1

Step-by-step explanation:

The lateral surface area of a cone is A = π r L, where L = √(r² + h²) is the slant height.

The lateral surface area of a cylinder is A = 2 π r H.

The area of the cylinder's base is A = π r².

The total area is therefore:

A = π r L + 2 π r H + π r²

A = π r² + (π L + 2 π H) r

The total cost of painting the surface is Rs. 1531.20 at a rate of Rs. 140 per 100 cm². Therefore the total surface area is:

A = Rs. 1531.20 / (Rs. 140 / 100 cm²)

A = 1093.71 cm²

Plug in and solve for r:

1093.71 = π r² + (10π + 42π) r

348.14 = r² + 52r

r² + 52r − 348.14 = 0

r = [ -52 ± √(52² − 4(1)(-348.14)) ] / 2

r = [ -52 ± √(52² − 4(1)(-348.14)) ] / 2

r = (-52 ± 64) / 2

r = -58 or 6

Since r > 0, r = 6.

Solve for h:

L² = r² + h²

10² = 6² + h²

h = 8 cm


Related Questions

Which of the following choices is not an example of a unit rate?
earnings per hour dollars per pound calories per serving $25.50 for 5 gallons

Answers

Examples of unit rates are Dollars per pound calories and earnings per hour. The rest is not the unit rate.

What is the unit rate?

An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. 70 yards in 10 seconds and 7 yards in 1 second are both ratios, although only the latter is a unit rate.

Earnings per hour are a unit rate since it is calculated for an hour.

Dollars per pound calories is a unit rate.

Serving $25.50 for 5 gallons is not a unit rate, the cost is for 5 gallons. If the cost is for 1 gallon then it will unit rate.

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{ ( 2 , 3 ) , ( − 2 , 5 ) , ( 4 , 4 ) , ( − 4 , 5 ) , ( x , y ) }

Answers

Answer:

Its gotta be (6, 5)

Step-by-step explanation:

If we look at the sequence, the x coordinates are 2, -2, 4, -4. In the first & third x coordinates, there is an increment of 2 i. e. first 2 and then 2+2=4 so the fifth x coordinate should be 4+2=6.

The y coordinates are 3, 5, 4, 5. In the first and third y coordinates, there is an increment of 1 i. e. first 3 and then 3+1=4 so the fifth y coordinate should be 4+1=5.

The sequence goes like this

(2, 3), (-2, 5), (4, 4), (-4, 5), (6, 5), (-6, 5), (8, 6), (-8, 5), and so on

Joseph bought a brand new car 6 years ago for $22,250. The table below shows v(n), the value of the car t years since it was purchased
What is the correlation coefficient between 1 and v(n), and what does the coefficient indicate?
The correlation coefficient is -0.955 and indicates a very weak linear association
The correlation coefficient is -0.913 and indicates a very weak linear association
The correlation coefficient is -0.913 and indicates a strong negative linear association
The correlation coefficient is -0.955 and indicates a strong negative linear association
F.
G
H.
J
t
0
1
2
3
4
5
6
v(t) $22,250 $16.200 $11.700 $8,100 $6,300 $4.950 $3.825
5

Answers

Answer:

Step-by-step explanation:

The correlation coefficient between 1 and v(n) is -0.913, and this coefficient indicates a strong negative linear association. The correlation coefficient is a measure of the strength and direction of the relationship between two variables. In this case, the correlation coefficient is -0.913, which indicates a strong negative relationship between 1 and v(n). This means that as the value of 1 increases, the value of v(n) decreases, and vice versa. This relationship is linear, which means that it can be described by a straight line. Overall, the correlation coefficient indicates a strong negative linear association between 1 and v(n).

Help!!!! Please Help Me!!! I need the answer right now!!! Thanks!!!

The subject is Science and Not Mathematics.
I couldn't find the Science option.

Answers

The numbers of the atoms of each element are;

Carbon dioxide;

6 atoms of carbon, 12 atoms of oxygen

Water ;

12 atoms of hydrogen, 6 atoms of oxygen

Glucose;

6 atoms of carbon, 12 atoms of hydrogen, 6 atoms of oxygen

Oxygen molecule

12 atoms of oxygen

What is a reaction?

In a chemical reaction, there is the combination of the atoms of the reactants and a consequent recombination as the products are formed. In accordance with the law of the conservation of mass, we know that the number of atoms before reaction must be equal to the number of atoms after reaction.

Now we have to look at the atoms and count up the number of atoms of each element in each of the compounds and this is how we are able to obtain the number of each atom as shown above.

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Percents, decimals, and fractions

Answers

Answer:

1.) 0.25

2.) 0.50

3.) 0.125

4.) 2.25

Step-by-step explanation:

When turning percentages into decimals, you move the decimal point two places to the left.

EX:

25%

25.0 (move the decimal point two places to the left)

2.5

.25

0.25 (add any zeros if necessary)

Hope this helps!!

Tip:

It doesn't matter where the decimal point is in a percentage, as long as you move the point two places to the left, you are still turning it into a decimal.

Carlos graphed the system of equations that can be used to solve x cubed minus 2 x squared 5 x minus 6 = negative 4 x squared 14 x 12. On a coordinate plane, 2 functions are shown. The functions intersect at (negative 3, negative 66), (negative 2, negative 32), and (3, 18) What are the roots of the polynomial equation? –3, –2, 3 –3, 2 18, 32 18, 32, 66

Answers

Equations solve -3 -18

Answer: A

Step-by-step explanation: the other guy is wrong

9. The length of an arc of a circle is 12 cm. The corresponding sector area is 108 cm².
Find:
a) the radius of the circle
b) the angle subtended at the centre of the circle by the arc.

Answers

At the circle's center, the arc's radius and angle are 9 cm and 4/3 radians, respectively.

What is the arc of a circle?

Any section of a circle's circumference is considered an arc. Remember that the circumference of a circle is its perimeter or distance.

Given the length of the arc is 12cm and the area of the arc is 108 cm Square.

Since the length of the arc = θ × r

Area of the arc (A) =  (θ/360°) × πr2

Substituting values in the formulas

12  = θ × r

108 = θ × r²

comparing both equations

r = 9 cm

θ = 4/3 radian

Therefore, the radius and the angle subtended at the center of the circle by the arc are 9 cm and 4/3 radian respectively.

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Suppose that the function y = f(x) is decreasing on the interval (2,4). What can be said about the graph of y = - f(x)?

Answers

Answer:

Good question

yes so the answer will be on your screen in

3

2

1

here it is

Step-by-step explanation:

did u get it

Roxanne drew an indigo line that was 11 4/5 inches long. Then she drew a white line that was 6 3/5 inches long. How much longer was the indigo line than the white line?

Answers

The indigo line is longer than the white line by 5.2 inches.

What is a line?

A line is a one-dimensional figure that has length but no width.

The length of the indigo line can be represented as I and the length of the white line as W.

The length of the indigo line is 11 4/5, i.e., I = 11 4/5 = 11.8

The given length of the white line is 6 3/5, i.e. W = 6 3/5=  6.6

The difference in length between the indigo and white lines is given by

I-W =  11.8 - 6.6 = 5.2

Hence, the indigo line is 5.2 inches longer than the white line.

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Makayla has 25% as many bags of popcorn as her sister. How many bags of popcorn does her sister have if Makayla has 12 bags?

Answers

Answer:

Makayla's sister has 48 bags of popcorn

Step-by-step explanation:

25/100 = 4

12x4 = 48

12*4

= 48 is the answer

The Tri-State Pick 3 lottery game offers a choice of several bets. You choose
a three-digit number. The lottery commission announces the winning three-digit number,
chosen at random, at the end of each day. The "box" pays $83.33 if the number you choose
has the same digits as the winning number, in any order. Find the expected payoff for a
$1 bet on the box. (Assume that you chose a number having three different digits.)

Answers

Answer: The Tri-State Pick 3 lottery game offers a choice of several bets, including a "box" bet where you choose a three-digit number and win if the number you choose has the same digits as the winning number, in any order. The expected payoff for a $1 bet on the box is $83.33.

To find this expected value, we need to consider all the possible ways that the winning number could be chosen and calculate the probability of each outcome. Since the winning number is chosen at random, each of the 10 possible digits (0 through 9) is equally likely to be chosen for each of the three positions in the winning number.

Since the box bet pays off if the digits of your chosen number match the digits of the winning number, regardless of their order, the number of winning combinations is equal to the number of ways to arrange the three digits of the winning number. This is equal to 3! (3 factorial), which is equal to 6.

Since there are a total of 10 possible digits for each position and the winning number has three positions, there are a total of 10 x 10 x 10 = 1000 possible winning numbers. Of these, 6 will pay off for a box bet, so the probability of winning a box bet is 6/1000 = 0.006.

Since the expected value of a bet is equal to the probability of winning multiplied by the payoff, the expected value of a $1 bet on the box is 0.006 x $83.33 = $0.05. Therefore, the expected payoff for a $1 bet on the box is $0.05.

Walmart is open Monday through Saturday from 8.00 AM to midnight and Sunday from 10.00 AM to 8:00 PM. How many hours is it open in one week? Show all work!

Please explain ​

Answers

The total number of hours that it opens in one week will be 104 hours.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Walmart is open Monday through Saturday from 8:00 AM to 12:00 AM and Sunday from 10:00 AM to 8:00 PM.

From 8:00 AM to 8:00 PM, there are 12 hours and from 8:00 AM to 12:00 AM there are 4 hours. Then the total hours from Monday to Saturday will be calculated as,

⇒ 6 x (12 + 4)

⇒ 6 x 16

⇒ 96 hours

From 10:00 AM to 8:00 PM, there are only 10 hours. Then the total number of hours that it opens in one week will be given as,

⇒ 96 + 8

⇒ 104 hours

The total number of hours that it opens in one week will be 104 hours.

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a 52-foot ladder is leaning against a vertical wall. if the bottom of the ladder is being pulled away from the wall at the rate of 8 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall?

Answers

The rate of change of the area of the triangle, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall is 26 square feet per second.

Let's call the distance between the bottom of the ladder and the wall x. We can express the area of the triangle in terms of x as follows:

Area = (1/2) * 52 * x

The area of the triangle is changing at a rate of 8 square feet per second as x changes at a rate of 8 feet per second. We can find the rate of change of the area with respect to x by taking the derivative of the area expression with respect to x:

d(Area)/dx = (1/2) * 52 = 26

Therefore, the rate of change of the area of the triangle, in square feet per second, at the instant the bottom of the ladder is 48 feet from the wall is 26 square feet per second.

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s i have 24 vanilla wafer cookies to put in a bag how many bags can i fill if i put the same number in each

Answers

She can put it into 2, 4, and 8 bags such that wafer cookies will same number in each bag.

What is a number system?

A way to express or represent numbers is through the number system.

The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.

We often employ decimal numbers because they are so widely used.

The base of the decimal number system, which uses ten digits from 0 to 9, is 10.

A system of writing numbers is known as a number system. It is a mathematical notation that uses digits or other symbols to consistently express the numbers in a given set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

Given,

Number of wafer cookies = 64

To put into 2 bags = 64/2 = 32 in each bag.

To put into 4 bags = 64/4 = 16 in each bag.

To put into 8bags = 64/8 = 8 in each bag.

The complete question is : Lindy has 64 vanilla wafer cookies to put in bags. How many bags can she fill if she puts the same number in each bag and uses them all? Find all the possibilities. Explain your reasoning.

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Lisa has x $5 bills and y $10 bills in her purse. The total value of the bills is more than $100. Which Inequality models this situation?

Answers

Answer:

D)  5x + 10y > 100

Step-by-step explanation:

We know that the sum of x $5 bills and y $10 bills in more than $100:

  5x + 10y > 100

c)  5x + 10y > 100

The sentence did not say equal or greater than (≥).

Which stataments are true regarding undifinable terms in geometry?

Answers

Answer:

A point has no length or widthA line consists of an infinite number of pointsA plane consists of an infinite set of lines

Step-by-step explanation:

The statements that are true regarding undefined terms are;

A point has no length or widthA line consists of an infinite number of pointsA plane consists of an infinite set of lines

The reason these statements above are true are as follows:

Examples of undefined terms includes a point, a plane, a line and a set

A point is for representing a position in space. It has no dimensions

Therefore, the statement, A point has no length or width is true

A plane is defined as an interconnected set of points that lay on the same flat surface, and extends infinitely along the surface in all directions

A line is defined as an infinite set of points that are arranged in straight path and extends without end in opposite directions

Therefore, the statement, a line consists of an infinite number of points is true

Therefore, a plane can be considered as being made up of an infinite set of lines that are located on a flat surface

Therefore, the statement, a plane consists of an infinite set of lines is true

Alexis is `56` inches tall.



What is her height in centimeters?

Answers

the answer is 142.24 cm

Answer:

142.24 centimeters tall

Step-by-step explanation:

Can you mark me brainliest

What is the value of x in the solution to this system of equations?
5x - 5y = 120
y = -7x + 8
Enter your answer in the box.
X = what is x?!?!

Answers

Answer:

{x = 4

{y = -20

Step-by-step explanation:

{5x - 5y = 120

{y = -7x + 8

5x - 5(-7x +8) = 120

5x + 35x - 40 = 120

40x - 40 = 120

40x = 120 + 40

40x = 160

x = 160/40

(cross out common factor)

x = 4

-----------

x = 4 (next is y)

y = -7 x 4 + 8 (calculate)

y = 20

y = -20

solution of system;

{x = 4

{y = 20

*NEED HELP ASAP* See screenshot below.

Answers

The equation that gives the tree's height at any time in slope-intercept form is y = (9/2)x + 5. Select 2nd option

How to write equation in slope-intercept form the tree's height at any time?

The slope-intercept form equation of a line can be given as y = mx + c

where m is the slope and c is the y-intercept

Let y and x represent the height and time respectively

slope (m) =  y2-y1 / x2-x1

where x1 = 2, y1 = 14 and x2 = 4, y2 = 23 (from table)

m = 23-14 / 4-2 = 9/2

y = mx + c

14 = (9/2 )×2 + c

14 = 9 + c

c = 14-9 = 5

put m = 9/2 and c = 5 into y = mx + c. Thus, the equation will be:

y = (9/2)x + 5

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What percent is equal to the part-to-whole ratio 9:80?

Answers

9/80 = x/100
X=11.25
9:80 =11.25%

Choose the expression that is equivalent to a fraction with five raised to the negative third power in the numerator and the quantity three raised to the negative second power times five squared end quantity in the denominator and the entire fraction is cubed.

three raised to the sixth power divided by five raised to the fifteenth power

three squared divided by five raised to the fifth power

negative three raised to the sixth power divided by five raised to the fifteenth power

negative three squared divided by five raised to the fifth power

Answers

The equivalent expression is three raised to the sixth power divided by five raised to the fifteenth power. Option A

What is an equivalent expression?

An equivalent expression is simply described as an expression having the same solution as the original expression but have a different arrangement of its variables and numbers.

Equivalent expressions are also known as expressions that works the same even  they look different.

From the information given, we have that;

[tex][\frac{5^-3}{3^-2 * 5^2} ]^3[/tex]

Now, find the exponential values, we have

[tex][\frac{5^-^3^-^2^)^}{3^-^2}]^3[/tex]

Subtract the exponents, we have;

[tex][\frac{5^-^5}{3^-^2} ]^3[/tex]

Multiply the exponents by the cube, we get;

[tex]\frac{5^-^5^*^3}{3^-^2^*^3}[/tex]

Now, multiply the values

5^-15/3^-6

Hence, the value is 5^-15/3^-6

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Practice identifying solutions to linear equations.
This equation has one solution.

5(x – 1) + 3x = 7(x + 1)

What is the solution?

Answers

Answer: x=12

Step-by-step explanation: PEMDAS

first solve the parentheses. that would make the equation 5x-5+3x=7x+7. Since there are no exponents, we don't need to do the e. no multiplication or division. so now we add and subtract to get x. first ill subtract 3x from both sides. 5x-5=4x+7. now subtract 5x from both sides. -5=-x+7. after that, subtract 7 from both sides. -12=-x. then divide by -1 so we can get only x and not a negative x. 12=x. so, the answer is x=12.  

Select the correct answer. If ( x + 4 ) is a factor of polynomial p, which statement must be true? A. p ⁡ ( - 4 ) > 0 B. p ⁡ ( 4 ) = 0 C. p ⁡ ( - 4 ) = 0 D.

Answers

Only if (C) p(-4) = 0 will x + 4 be the polynomial p's factor.

What are the factors?

A factor is a number that completely divides another number.

To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

There is therefore no residual after division.

The numbers you multiply together to obtain another number are called factors.

A factor is therefore another number's divisor.

So, this is only true if, and only if, x + 4 is a factor of the polynomial p.

x + 4 = 0

x = -4

Comply with the polynomial equation that is:

p(-4) = 0

Therefore, only if (C) p(-4) = 0 will x + 4 be the polynomial p's factor.

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Complete question:
If (x + 4) is a factor of polynomial p, which statement must be true?

A.p(4) = 0

B. p(-4) > 0

C. p(-4) = 0

D. p(4) < 0

Please factorize [tex]\ln ^2\left(4-x\right)+\ln \left(4-x\right)\ln \left(x+\frac{1}{2}\right)-2\ln ^2\left(x+\frac{1}{2}\right)=0[/tex]

Answers

Answer:

[ln (4 - x) - ln (x + 1/2)] × [ln (4 - x) + 2 ln (x + 1/2)]  = 0

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

Given equation:

ln² (4 - x) + ln (4 - x) ln (x + 1/2) - 2 ln² (x + 1/2) = 0

Substitute:

ln (4 - x) = p, ln (x + 1/2) = q

Then we have:

p² + pq - 2q² = p² - q² + pq - q² = (p + q)(p - q) + q(p - q) = (p - q)(p + q + q) = 0(p - q)(p + 2q) = 0

Substitute back:

ln² (4 - x) + ln (4 - x) ln (x + 1/2) - 2 ln² (x + 1/2) = 0 [ln (4 - x) - ln (x + 1/2)] × [ln (4 - x) + 2 ln (x + 1/2)]  = 0

A garden snail travels at a rate of 2.2 feet per minute.
At this rate, how long will it take for the snail to travel 55 feet?
At this rate, it will take the snail [___ minutes to travel 55 feet.

WHAT IS THE ANSWER.

Answers

If the snails moves at a constant rate, it will take 25 minutes to travel 55 feet.

How long will it take for the snail to travel 55 feet?

We know that the snail travels at a rate of 2.2 feet per minute, so after x minutes, the distance traveled by the snail is:

D = 2.2ft*x

To see how many minutes it takes the snail to travel 55 feet, we need to solve the equation:

55 ft = 2.2ft*x

If we divide both sides by 2.2ft, we will get:

55ft/2.2ft = x

25 = x

So the snail takes 25 minutes to travel the 55 feet.

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PLEASE ANSWER FAST

Find the missing values in the table below so that it represents a linear function.




Answers

The value of y₂, y₃ and y₄ in the linear function are -21, -26 and -31 respectively.

How to  represent linear function?

Linear function can be represented in slope intercept form as follows:

y = mx + b

where

m = slopeb = y-intercept

Therefore, to find the missing values in the table we have to use the equation of the linear function.

y = mx + b

let's find m.

using (4, -16) and (8, -36)

m = slope = -36 + 16 / 8 - 4

m = -20 / 4

m = -5

Hence, let's find y-intercept using (4, -16).

y = -5x + b

-16 = -5(4) + b

-16 + 20 = b

b = 4

Therefore, the equation is y = -5x + 4.

Let's find y₂, y₃ and y₄

y₂ = -5(5) + 4 = -25 + 4 = - 21

y₃ =  -5(6) + 4 = -30 + 4 = -26

y₄ =  -5(7) + 4 = -35 + 4 = - 31

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y is directly proportional to the cube of x. If y = 20 when x is 3 find y when x is 5

Answers

The solution is y = 2500/27

The value of y is 2500/27 when x = 5

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

Given data ,

Let the proportionality constant be represented as = k

Now , the value of k is calculated by

y is directly proportional to the cube of x

Substituting the values in the equation , we get

y ∝ x³

On simplifying the equation , we get

y = kx³   where k is the proportionality constant

Now ,

when x = 3 , y = 20

Substituting the values in the equation , we get

20 = k ( 3 )³

20 = k x 27

Divide both sides by 27 , we get

k = 20/27

So , the proportionality constant k = 20/27

Now , when x = 5 ,

y = 20/27 ( 5 )³

y = ( 20 x 5 x 5 x 5 ) / 27

y = 2500/27

Therefore , the value of y is 2500/27

Hence ,

The value of y is 2500/27 and the proportionality constant is 20/27

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1. In linear equation with two variables "ax + by = c", a and b cannot be equal to
(a) One
(b) Zero
(c) Integer
(d) Rational number

Answers

In linear equation with two variables "ax + by = c", a and b cannot be equal to Zero. which is the correct answer would be an option (A).

In a linear equation with two variables "ax + by = c", a and b can be any real numbers, including zero and integers. They can also be irrational numbers or rational numbers.

There is no restriction on the values of a and b in this equation.

As per the question, the following are all valid linear equations :

x + 0y = 2 ⇒ x = 2

0x + y = 1 ⇒ y = 1

Here above linear equations having only one variable so a and b cannot be equal to zero.

Thus, in a two-variable linear equation, a and b cannot be equal to zero.

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if lin and diego want to run a race where they will both finish when the timer hits 30 seconds exactly but diego runs 5.5 meters per 1 second and lin runs 4 meters per 1 second how long of a head start should lin get?

Answers

Lin needs a 45-meter head start as  Lin will travel 120 meters in 30 seconds, and Diego will travel 165 meters in 30 seconds.

Time = 30 sec

Lin's speed = 4m/s

Diego's speed = 5.5m/s

Distance travelled by ,

Lin = speed * time = 4 * 30

= 120 m

Diego = 5.5 * 30

= 165

Therefore, Diego will travel 45 m more than Lin in 1 sec.

Therefore, the head start should be of 45m.

The most crucial scientific notion is measurement is speed . Base or physical fundamental units are used to quantify a wide range of quantifiable quantities. One such measurable metric is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

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Prove that tanx sinx + cosx = secx

Answers

The proof that tan(x) sin(x) + cos(x) = sec(x) is represented by the trigonometric equation sec(x) = sec(x)

How to prove the trigonometric equation

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

tan(x) sin(x) + cos(x) = sec(x)

Express tan(x) as sin(x)/cos(x)

So, we have the following representation

sin(x)/cos(x) * sin(x) + cos(x) = sec(x)

Evaluate the products

So, we have the following representation

sin²(x)/cos(x)  + cos(x) = sec(x)

Take the LCM

[sin²(x) + cos²(x)]/cos(x) = sec(x)

Express sin²(x) + cos²(x) as 1

So, we have

1/cos(x) = sec(x)

Evaluate

sec(x) = sec(x)

Hence, the equation has been proved

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