Prove that limx→2. 1/1-x= -1 using the definition of limit .​

On solving the provided question we can say that - the value of the trignometric function will be -cos(t)+2cosec(t)

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

here,

(sint(t) + cos(t))[tex]^{2}[/tex] =(sint +cost)(sint - cost)

=|  -cos(t)+2cosec(t) |

= -cos(t)+2cosec(t)

To know more about trigonometry visit:

https://brainly.com/question/29002217

#SPJ1

Answer: He was 32 years old 8 years ago, than a) x-40 b) x-24 c) 40-x d) 24-x e) 24+x

Step-by-step explanation:

Mario was '40 - x' years old when he was 'x' years old.

If he was 32 years old, 8 years ago, then he is 40 now as (32+8) equals 40.

If he is 40 years old now, then he was '40 - x',  x years ago.

Hence, '40 - x' is the answer to this sum.

To learn more about age-related algebraic sums, refer to

https://brainly.com/question/22875998

After completing the square, the solution of equation are,

⇒ x = (2 + √2i)

And, x = 2 - √2i

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ x² - 4x + 6 = 0

Completing the square as;

⇒ x² - 4x + 6 = 0

⇒ x² - 4x + 4 + 2 = 0

⇒ (x - 2)² + 2 = 0

⇒ (x - 2)² - (√2i)² = 0

⇒ (x - 2 - √2i) (x - 2 + √2i) = 0

This gives two complex solution as;

⇒ x = (2 + √2i)

And, x = 2 - √2i

Learn more about the quadratic equation visit:

https://brainly.com/question/28038123

#SPJ1

Step-by-step explanation:

please refer to the sketch

The system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, is an equation, x² = 2x+3, we need to find a system of equations that can be graphed to give the solution of the equation given,

So, the equation is x² = 2x+3

We can write this as,

x²-2x-3 = 0

Now, factorize to find the solution of the equation,

x²-3x+x-3 = 0

x(x-3)+1(x-3) = 0

(x+1)(x-3) = 0

x = -1 and x = 3

So, the solution of the equation is -1 and 3

However, if we consider the equation to be two different systems combined, that is the equation of the straight line and the equation of the basic quadratic function,

y = x² and y = 2x+3

Then the solution to is the intersection of the graph of the straight line and the graph of the quadratic curve.

That is the x-coordinates of the points of intersection are the solutions.

Since, the graphs are intersecting at (3, 9) and (-1, 1) [see the graph]

Therefore, the system of equation is y = x² and y = 2x+3

Hence, the system of the equations to be used to graph the solution of the equation given is y = x² and y = 2x+3

Learn more about system of equations click;

https://brainly.com/question/12895249

#SPJ5

If cosec (tetha) = 17/15 then cos (tetha) = 8/17

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

cosec , sine, cotangent, cosine , secant and tangent are trigonometry function.

cosec( tetha) = 1/sin(tetha)

tangent (tetha) = 1/ cot ( tetha)

sec (tetha) = 1/ cos(tetha)

cosec (tetha) = 17/15

therefore 1/sin ( tetha) = 17/15

sin( tetha ) = 15/17 = opp/ hyp

therefore using Pythagoras theorem adj² = 17²-15²

adj² = 289-225

adj² = 64

adj = √64 = 8

cos ( tetha) = adj/hyp

therefore cos ( tetha) = 8/17

learn more about trigonometry ratio from

https://brainly.com/question/24133971

#SPJ1

Answer:

9:15

Step-by-step explanation:

Time needed to deliver 100 letters: 100 : 40 = 2,5 hours = 2:30min
Your break: 6:45 + 2:30 = 9:15

Answer:

3 × 7 = 21

21 - 6 = 15

15 is the answer

Answer: To solve this problem, we can use the information provided to set up and solve an equation. Let x be the number of countries that participated in the 1896 Olympic games.

According to the problem, we know that the number of countries in the 2004 Olympic games was more than 14 times the number of countries in the 1896 games. So we can write the following equation:

x * 14 < 202

To solve for x, we can divide both sides of the inequality by 14:

x < 202/14

x < 14.43

x is the number of countries, it must be an integer.

so x = 14

Therefore, 14 countries participated in the 1896 Olympic games.

Step-by-step explanation:

Answer:

Here is an example. Check out the uploaded image.

Step-by-step explanation:

Draw Points   XY  using a Straight Line

Draw a bisector in the middle of the line

Repeat Procedure for lines XZ  and YZ

Where the two lines meet is the Center

Extend the compass from the center to any point and complete the circle.

Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

The term "volume" refers to how much general space an object occupies. Unlike mass, volume changes depending on the surroundings. The mass of a substance in a given volume is referred to as its "density." It describes the relationship between mass and volume.

Here,

A cylinder has a volume of V = r2h.

As a result, V = r2[(1/3)]h is obtained by multiplying h by 1/3.

The (1/3) can be moved to the front to obtain V = [(1/3)]r2h because you are free to multiplied in any ratio you choose.

Thus, you would receive one-third of the initial mass.

What would occur if you increased the radius by 1/3 in contrast to this?

Next, you would have

=> V = π[(1/3)r]2h

=> V = π(1/9)r2h

=> V = (1/9)πr2h

You would then possess 1/9 of the volume.

Therefore , the solution of the given problem of volume comes out to be

you would then possess 1/9 of the volume.

To know more about volume , visit

brainly.com/question/1578538

#SPJ1

Answer: The statement you've provided describes the economic concept of elasticity. Elasticity is a measure of how responsive the quantity demanded or supplied of a good or service is to a change in its price. It measures the responsiveness of the consumers' and producers' behaviors to changes in price, in other words, how sensitive the consumers or producers are to changes in the good or service prices.

There are different types of elasticity, such as price elasticity of demand and price elasticity of supply. Price elasticity of demand measures how much the quantity demanded of a good changes in response to a change in its price. If a good has a high price elasticity of demand, then a small change in its price will result in a large change in the quantity demanded of the good. On the other hand, price elasticity of supply measures how much the quantity supplied of a good changes in response to a change in its price. A good with a high price elasticity of supply will see a large increase in the quantity supplied in response to a small price increase.

Elasticity is a very important concept in economics because it helps to understand how consumers and producers will react to changes in prices and how it would affect the overall economy.

Step-by-step explanation:

Answer:

g(f(x)) = 4x² - 12x + 10

Step-by-step explanation:

to find g(f(x)) substitute x = f(x) ino g(x)

g(f(x))

= g(2x - 3)

= (2x - 3)² + 1 ← expand parenthesis using FOIL

= 4x² - 6x - 6x + 9 + 1

= 4x² - 12x + 10

Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20

A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.

Here,

Solve for y.

Replace y by f-1(x).

y=x-20

x=y-20

Solve for y,x = y-20

x+20

To learn more about inverse function visit:

brainly.com/question/2541698

#SPJ1

Answer:

ƒ^(-1)(x) = x + 20

Step-by-step explanation:

To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.

Let's start by replacing ƒ(x) with y:

y = x - 20

Next, swap x and y:

x = y - 20

Now, solve for y by isolating it:

x + 20 = y

Therefore, the inverse of the function ƒ(x) = x - 20 is given by:

ƒ^(-1)(x) = x + 20

The length of time to build the fence is 8 hours

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

Length of the fence = 1 1/3 miles

Rate of building = 1/6 miles per hour

The length of time to build the fence is then calculated as

Length of time = Length of the fence/Rate of building

Substitute the known values in the above equation, so, we have the following representation

Length of time = (1 1/3 miles)/(1/6 miles per hour)

Evaluate the quotient

This gives

Length of time = 8 hours

Hence, the time taken is 8 hours

Read more about rate at

https://brainly.com/question/24178013

#SPJ1

Answer: 121%

Step-by-step explanation:

move the decimal place two to the right

The unbiased estimator of 1/p does not exist.

An estimate that deviates from the genuine population value is said to be biased. If the kind and extent of the bias are known, a biased sample may still be informative. When a sample's value matches the actual value of a population parameter, that is an unbiased estimator.

Given:

If the random variable X has the binomial.

1/p = 1 /{1-(1-p)} = 1 + (1-p) + (1-p)²/2! + ....

And let an unbiased estimator of 1/p exist.

[tex]\sum^n_k_=_0T(k)(^n_k)p^k(1-p)^k[/tex] = 1 + (1-p) + (1-p)²/2! + ....

The above series is finite on the LHS and infinite power series on the RHS.

That is contradiction.

The basic idea is that an unbiased estimator of 1/p would have to have the property that its expected value as a function of p would have to tend to infinity as p tends to 0.

But since Ep[U(x)] is bounded above by some function of n that is independent of p, no such estimator can exist.

Therefore, the unbiased estimator 1/p can not exist.

To learn more about the unbiased estimator;

https://brainly.com/question/14368422

#SPJ1

The number of seconds it takes ball to before hit the ground is 6 seconds.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, a ball is thrown from the top row of seats in a stadium the function h(t)=-16t²+80t+96 gives the height, in feet, of the ball t seconds after it is thrown.

When ball hits the ground h=0

So, -16t²+80t+96=0

-16(t²-5t-6)=0

t²-5t-6=0

By using splitting middle term method, we get

t²-6t+1t-6=0

t(t-6)+1(t-6)=0

t-6=0 or t+1=0

t=6 or t=-1

Time can not be negative integer.

Therefore, the number of seconds it takes ball to before hit the ground is 6 seconds.

To learn more about the solution of quadratic equation visit:

https://brainly.com/question/18305483.

#SPJ1

Answer:

Step-by-step explanation:

11 -(-2) x 4

11 + 2 x 4

11 +8

= 19

The measure for θ is 25.747121°.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Hypotenuse = 14.5 meters

Opposite side = 6.3 meters

Now, using Trigonometry

sin θ = Opposite side / Hypotenuse

by putting the given values we get

sin θ = 6.3 / 14.5

sin θ = 63/145

sin θ = 0.4344

θ =25.747121°

Hence, the angle is 25.747121°.

Learn more about Trigonometry here:

https://brainly.com/question/29002217

#SPJ1

The percent markup of the supplied statement is equal to 50% after the problem is solved.

There isn't a predetermined "optimal" markup percentage, however most companies set their markup at 50%. A 50% markup, also referred to as "keystone," denotes a price that is 50% greater than the cost of the commodity or service.

The gross profit of a unit is determined by subtracting its cost to produce or acquire for resale from its sales price to determine the markup percentage. The markup percentage is computed as (12 - 8) / 8 and equals 50% if an item is priced at $12 but costs the manufacturer $8 to produce.

Cost price of game=$25

Selling price of game=$37.50

Profit =  selling price - cost price

Profit =  37.50 - 25

Profit / markup percentage = (profit /cost price ) * 100

= (12.50/25) * 100

= 50%

The percent markup of the supplied statement is equal to 50% after the problem is solved.

To know more about percent markup visit:

https://brainly.com/question/8834585

#SPJ1

Answer:

(y+72)

I'm not sure because your answer is not very clear

Dilation is a type of transformation that enlarges or shrinks shapes (called archetypes) to create new shapes (called images). Archetype area is 5050 [tex]unit^2[/tex] * 3 = 15,150 [tex]unit^2[/tex]

Add the square of the scaling factor s to the area of ​​the figure before stretching Ap. In other words, the equation Ad = s2Ap gives the area of ​​the figure after dilation Ad. a d = s2a p .

To find the archetype area, we need to undo the applied stretch. Since the stretch factor was 1/3, we can undo it by multiplying the image area by the inverse of the scale factor (1/1/3 = 3). So the area of ​​the archetype is 5050 [tex]unit^2[/tex] * 3 = 15,150.[tex]unit^2[/tex]

To Learn more about scale factor visit:

https://brainly.com/question/30215119

#SPJ1

Answer:

The manager is not correct in her calculation.

Step-by-step explanation:

There are 244 males and n females who entered the mall as the manager at the shopping mall counts.

If 25% of all males are children, then the number of male children are .

Again, the 25% of all female are children, then the number of female chilfren are .

Therefore, the total number of children will be (60 + 0.25n).

But the manager gives the number of children to be 0.25n + 61 who entered the mall.

So, the manager is not correct in that calculation. (Answer)

Step-by-step explanation:

37.5% of the cars have a fuel efficiency of at least 35 miles per gallon.

To find the percentage of cars that have a fuel efficiency of at least 35 miles per gallon,

We first need to determine how many of the eight cars meet that threshold.

To do this, we can compare each car's fuel efficiency to 35 miles per gallon, and count the number that is greater than or equal to 35.

Identify the cars that have a fuel efficiency of at least 35 mpg: 42, 42, 54,

count the number of cars which is 3

divide it by 8 which is the total number of cars

Multiply the result by 100 to get the percentage, so:

3/8 * 100 = 37.5%

Read more about percentages here:

https://brainly.com/question/24877689

#SPJ1

Answer:yesb

Step-by-step explanation:

because u

Therefore , the solution to the given problem of expression comes out to be  149-k =x be used it as its expression.

A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Here,

Given :  Lena has $149

she spends k amount of money

The money left be x

=> 149-k =x

Therefore , the solution to the given problem of expression comes out to be  149-k =x be used it as its expression.

To know more about expression , visit

https://brainly.com/question/14083225

#SPJ1