lim x rightarrow 0 1 - cos ( x2 ) / 1 - cosx The limit has to be evaluated without using l'Hospital'sRule.

Answers

Answer 1

Answer:

Answer with Step-by-step explanation:

Given

$f(x)=(1-cos(2x))/(1-cos(x))\n\n\lim_(x \rightarrow 0)f(x)=\lim_(x\rightarrow 0)(\frac{1-(cos^2{x}-sin^2{x})}{1-cos(x)})\n\n(\because cos(2x)=cos^2x-sin^2x)\n\n\lim_(x \rightarrow 0)f(x)=\lim_(x\rightarrow 0)((1-cos^2x)/(1-cos(x))+(sin^2x)/(1-cosx))\n\n=\lim_(x\rightarrow 0)(((1-cosx)(1+cosx))/(1-cosx)+(sin^2x)/(1-cosx))\n\n=\lim_(x\rightarrow 0)((1+cosx)+(sin^2x)/(1-cosx))\n\n\therefore \lim_(x \rightarrow 0)f(x)=1$

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Drag each equation to show if it could be a correct first step to solving the equation 2(x+7) =36

Alice solved the following equation:-18 - 3x = 12
-3x = 6
x =-2

Which of the following statements is true?

Answers

Answer:

the first line

Step-by-step explanation:

because the second line should be -3x=30

Three instrument panel designs are being considered. We are interested in pilot response times as a function of these panel designs. Randomly selected pilots are randomly given simulated emergency situations and response times are measured. We are concerned that pilot experience may also influence our results. Analyze the data both including and not including the covariate of experience. Does including the covariate matter in this case? Is there another covariate we should have included?

Answers

Answer:

see the analysis below

Step-by-step explanation:

Which type of angle is formed by sides of a square?

Answers

I believe it would be a right angle. Each corner of a square is a right angle.

Find the value of the variable.
66

32

29

43

Answers

Answer:

The correct answer is x = 32.

Step-by-step explanation:

To solve this problem, we must remember the concept of supplementary angles. Two angles that are supplementary together make an angle of 180 degrees (a straight line).

In this case, we can see that inside the triangle, we will have an angle of 80 degrees. We know this because the angle at the top of the triangle is supplementary with the angle measuring 100 degrees, so its measure should be 180-100 = 80 degrees.

On the lower right hand of the triangle, a similar rationale can be applied. The angle inside of the triangle must measure 68 degrees, since it is supplementary to an angle measuring 112 degrees, and 180-112=68.

Finally, to solve this problem, we must remember that the sum of the three interior angles of a triangle should be 180 degrees. This lets us set up the following equation:

80+68+x = 180

Now, we can solve this equation. Our first step is to simplify the left side of the equation by adding together the constant terms.

148 + x = 180

Next, we should subtract 148 from both sides of the equation.

x = 180-148

x = 32

Therefore, the correct answer is x = 32 degrees.

Hope this helps!

Hellllllllllllllllllllllllllllllllllpppppppppppppppppppppppp whats the x

Answers

Easy buddy....

$2 x + 68 = 180$

Subtract the sides of the equation minus68

$2x = 180 - 68$

$2x = 112$

Divided the sides of the equation by2

$x = (112)/(2) = 56 \n$

So ;

$x = 56 \: degreees$

_________________________________

And we're done.

Thanks for watching buddy good luck.

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Find an equation of the circle that satisfies the given conditions. (Give your answer in terms of x and y.)Center

(4, −5)

and passes through

(7, 4)

Answers

Answer:

$(x-4)^2+(y+5)^2=90$

Step-by-step explanation:

The equation of a circle of radius r, centered at the point (a,b) is

$(x-a)^2+(y-b)^2=r^2$

We already know the center is at $(4,-5)$ , we are just missing the radius. To find the radius, we can use the fact that the circle passes through the point (7,4), and so the radius is just the distance from the center to this point (see attached image). So we find the distance by using distance formula between the points (7,4) and (4,-5):

radius $=√((7-4)^2+(4-(-5))^2)=√(3^2+9^2)=√(90)$

And now that we know the radius, we can write the equation of the circle:

$(x-4)^2+(y-(-5))^2=√(90)^2$

$(x-4)^2+(y+5)^2=90$

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The graph below shows the numbers of cups of apple juice that are mixed with different numbers of cups of lemon-lime soda to make servings of apple soda: A graph is shown. The values on the x axis are 0, 1, 2, 3, 4, 5. The values on the y axis are 0, 6, 12, 18, 24, 30. Points are shown on ordered pairs 0, 0 and 1, 6 and 2, 12 and 3, 18 and 4, 24. These points are connected by a line. The label on the x axis is Lemon -Lime Soda in cups. The title on the y axis is Apple Juice in cups. What is the ratio of the number of cups of apple juice to the number of cups of lemon-lime soda? 1:24 24:1 1:6 6:1

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Vitamin D is needed for the body to use calcium. An experiment is designed the effects of calcium and vitamin D supplements on the bones of first-year college students. The outcome measure is the total body mineral content (TBBMC), a measure of bone health. Three doses of calcium wil be used: 0, 200, and 400 mg/day. The doses of vitamin D will be 0, 50, and 100 international units (IU) per day. The calcium and vitamin D will be given in a single tablet. Al tablets including those with no calcium and no vitamin D will look identical. Subjects for the study will be 90 men and 90 women.a) What are the factors and the treatments for this experiment?b) Draw a picture explaining how you would randomize the 180 college students to the treatmentsc) Use a spreadsheet to carry out the randomization