A boat heading out to sea starts out at Point A, at a horizontal distance of 639 feet from a lighthouse/the shore. From that point, the boat's crew measures the angle of elevation to the lighthouse's beacon-light from that point to be 11 degrees . At some later time, the crew measures the angle of elevation from point B to be . Find the 3 degrees distance from point A to point B. Round your answer to the nearest foot if necessary .

Evaluting the limand directly at x = 0 yields the indeterminate form 0/0, so we have a candidate for L'Hopital's rule. We get

[tex]\displaystyle\lim_{x\to0}\frac{\sqrt{1+x+x^2}-1}{\tan(5x)} = \lim_{x\to0}\frac{\frac{1+2x}{2\sqrt{1+x+x^2}}}{5\sec^2(5x)} = \frac{1+2\times0}{2\sqrt{1+0+0^2}\times5\sec^2(5\times0)} = \boxed{\dfrac{1}{10}}[/tex]

If you don't know about L'Hopital's rule, or are otherwise not allowed to use it, you can instead rely on algebraic manipulation and a well-known limit,

[tex]\displaystyle\lim_{x\to0}\frac{\sin(ax)}{ax}=\lim_{x\to0}\frac{ax}{\sin(ax)}=1[/tex]

where a ≠ 0. We write

[tex]\displaystyle\frac{\sqrt{1+x+x^2}-1}{\tan(5x)} = \frac{5x}{\sin(5x)}\times\frac{\cos(5x)}5\times\frac{\sqrt{1+x+x^2}-1}x[/tex]

The limit of a product is equal to the product of limits:

[tex]\displaystyle\lim_{x\to0}\frac{\sqrt{1+x+x^2}-1}{\tan(5x)} = \left(\lim_{x\to0}\frac{5x}{\sin(5x)}\right)\times\left(\lim_{x\to0}\frac{\cos(5x)}5\right)\times\left(\lim_{x\to0}\frac{\sqrt{1+x+x^2}-1}x\right)[/tex]

The first limit is 1 and the second limit is 1/5. For the remaining limit, multiply through the fraction by the conjugate of the numerator:

[tex]\dfrac{\sqrt{1+x+x^2}-1}x\times\dfrac{\sqrt{1+x+x^2}+1}{\sqrt{1+x+x^2}+1} = \dfrac{\left(\sqrt{1+x+x^2}\right)^2-1^2}{x\left(\sqrt{1+x+x^2}+1\right)} \\\cdots= \dfrac{x+x^2}{x\left(\sqrt{1+x+x^2}+1\right)} \\\cdots= \dfrac{1+x}{\sqrt{1+x+x^2}+1}[/tex]

The remaining limand is continuous at x = 0, and its limit is

[tex]\displaystyle\lim_{x\to0}\frac{1+x}{\sqrt{1+x+x^2}+1}=\frac{1+0}{\sqrt{1+0+0^2}+1}=\frac12[/tex]

and hence the original limit is again 1 × 1/5 × 1/2 = 1/10.

Answer:

a.3.4x

Step-by-step explanation:

A monomial only had one term

mono is the prefix for one

the answer is [tex]x^{2} \sqrt{x} \leq \geq \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \pi x^{2} \sqrt{x} \frac{x}{y} \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left \{ {{y=2} \atop {x=2}} \right.[/tex]random but marter than einstein

Answer:

7.85 in³

Step-by-step explanation:

π · r² · h

3.14  · 0.5² · 10

7.85 in³

Answer:                                                                    

14 and 1

Explanation:

14 + 14 + 1 + 1 = 30

14 x 1 = 14

The perimeter is the sum of all 4 sides. Divide the perimeter in half fo the some of one length and one width:

Length + width = 15

Area is length x width

Find 2 numbers that when added equal 15 but when multiplied equal 14

15 + 0 = 15, 15 x 0 = 0

14 + 1 = 15, 14 x 1 = 14

The answer is 14 ft long by 1 ft wide

The answer is 2990.8 yd

Formula for SA of cylinder: 2*pi*r*h+2*pi*r^2

Formula for radius: diameter/2

Plug the radius, 17, height, 11, and pi, 3.14, into the formula above.

= 2990.8 yd

Answer:

Step-by-step explanation:

It's 5

Answer:

10

Step-by-step explanation:

( 1 / 20 ) x ( 1 / 8 ) x 1600

= ( 1 / 20 x 8 ) x 1600

= ( 1 / 160 ) x 1600

= 1600 / 160

Answer:10

Step-by-step explanation:

1/20 x 1/8 x 1600 = 10

= 10

Answer:

David had x amount of M&M's. He then ate 15 of them for snack. Now David only has 35 M&M's left. How many M&M's did David have in the beginning?

Step-by-step explanation:

Answer:

X= 20

Step-by-step explanation:

Hannah has 35 marbles. Hannah gives away 15 marbles. How many marbles does Hannah have left? Solve the equation X- 15=35.

Answer:

32 Years, 7 Months, 2 Days old

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

The angle in the bottom right is 120

Call is y

y+60 = 180

y = 180-60

y =120

Opposite angles in a parallelogram are equal so the upper left angle is 120

Call the 3x +z = 120

We also know that 2x+90 +z = 180 since it forms a straight line

Subtract 90 from each side

2x+z = 90

Using 3x+z = 120 and 2x+z =90 and subtracting the second equation

3x+z = 120  

-2x-z =-90

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

x = 30

Answer:

2590.33

Step-by-step explanation:

...............

Answer:

According to me it should be Option B, 15.31

Hope this helps!

The expected value for the age of a randomly chosen student is,

⇒  15.38

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that:

Total number of students,

⇒ n = 1500,

And, Age : 13, 14, 15, 16, 17, 18

Probability : 0.01, 0.25, 0.27, 0.30, 0.16, 0.01

Now,

We can Calculate the expected value as shown below,

E = 13 × 0.01 + 14 × 0.25 + 15 × 0.27 + 16 × 0.30 + 17 × 0.16 + 18 × 0.01

E = 0.13 + 3.5 + 4.05 + 4.8 + 2. 72 + 0.18

E = 15.38

Therefore, The expected value for the age of a randomly chosen student is 15.

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Answer:

70

Step-by-step explanation:

Tangent Chord Angle = 1/2Intercepted Arc

? = 1/2(140)

? = 70

Answer: if its asking for that angle its 70 cause thats the only one that would fit

Step-by-step explanation:

Answer:

option D

Step-by-step explanation:

18 1/5 + 22 2/5 +40 1/5

Answer:

Step-by-step explanation:

X * 3^2 +2 = 47

X * 9 + 2 = 47

9X = 47 - 2

9x = 45

x = 45 : 9

X = 5

Answer:

[tex]3+\dfrac{n}{2}[/tex]

Step-by-step explanation:

Let the number is n.

ATQ,

The quotient of a number and two​ means n/2

Something is increased means plus.

It means,

The required expression is : [tex]3+\dfrac{n}{2}[/tex]. Hence, this is the required solution.

The square of z varies inversely as the square root of e. If z=36 when w=16, then value of z is 24 when w=81.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The square of z varies inversely as the square root of e.

If z=36 when w=16

The value of z when w is 81 we need to find

z²=k/√e

where k is a proportionality constant

36²=k/√16

36²=k/4

Apply cross multiplication

1296(4)=k

5184=k

Now let us find when k is 5184 and w is 81

z²=5184/9

z²=576

Take square root on both sides

z=24

Hence, the value of z is 24 when w is 81.

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it wouldnt let me type the answer-

Answer:

c

Step-by-step explanation:

Answer:

[tex]t = \sqrt{ {(5x - 2) {}^{2} + (6x + 7)}^{2} } [/tex]

Answer:

a²+2a-8

Step-by-step explanation:

Answer:

A sample of 801 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

25% of U.S. homes have a direct satellite television receiver.

This means that [tex]\pi = 0.25[/tex]

How large a sample is necessary to estimate the true population of homes which do with 95% confidence and within 3 percentage points?

This is n for which M = 0.03. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.25*0.75}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2[/tex]

[tex]n = 800.3[/tex]

Rounding up:

A sample of 801 is needed.

Answer:

A. y = cos(x) - 2

Step-by-step explanation:

The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.

However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.

Answer:

2

Step-by-step explanation:

find the slope of a line from a graph following those steps

-pick any two points on the graph that belong to the line,

for example (1,1) and (2,3)

-find out how did you get from one point to the other

to get from (1,1) to (2,3) I went 2 up (rise) and 1 to the right (run)

slope= rise /run = 2/1 =2

Few things to keep in mind:

-To find the slope, always move vertical first (y-axis) and than horizontal( x-axis) , because m=change in y/change in x

-For vertical movement, moving up is positive , moving down is negative

For horizontal movement, moving right is positive , moving left is negative

Answer:

(0,-2)

Step-by-step explanation:

It would be (0,-2) because that is the only one in the solution range,. Solution range is everything above the intersection that is not outside line.

The solution of graphed equations is (-4, 2 1/2).

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

From the graph, we have the following highlights.

The x-coordinate of the point of intersection is close to 4

The y-coordinate of the point of intersection is close to 2 1/2.

So, the coordinates can be estimated to be -4 and 2 1/2

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Answer:

[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

Since both fractions have a different denominator, we need to look for a common denominator.

[tex]\frac{1}{3}=\frac{3}{9}[/tex]   Multiply 3 in both numerator and denominator

[tex]\frac{5}{9} -\frac{3}{9} =\frac{2}{9}[/tex]    

Hence, 2/9 is the answer

Answer:

3,1 I'm pretty sure lol....

Answer:

X = 2

Step-by-step explanation:

44 + 104 + (18+7x) = 180

Simplify