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bagirrra123 [75]
2 years ago
12

An observer on the ground is x meters from the base of the launch pad of a rocket, which is at the same level as the observer. A

few seconds after the rocket takes off vertically, the observer sees its tip at an angle of q° from the horizontal. How far above the ground is the tip of the rocket at that instant? Assume that the ground is level.. a) x/ tan q. b) x/sin q. cx tan q. d) x cos q.
Mathematics
2 answers:
Firlakuza [10]2 years ago
5 0
This can be solved using trigonometric functions. The distance x serves as one leg of a triangle, and makes an angle q with the hypotenuse. The distance from the tip of the rocket to the ground make up the other leg of the triangle. So solving this:

tan q = y / x

Where: y = distance from the tip of the rocket to the ground

Therefore, y = x tan q

Among the choices, the correct answer is C.
SVETLANKA909090 [29]2 years ago
3 0

Answer:C

Step-by-step explanation:

You might be interested in
In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that
attashe74 [19]

Answer:

(a) The probability of more than one death in a corps in a year is 0.1252.

(b) The probability of no deaths in a corps over 7 years is 0.0130.

Step-by-step explanation:

Let <em>X</em> = number of soldiers killed by horse kicks in 1 year.

The random variable X\sim Poisson(\lambda = 0.62).

The probability function of a Poisson distribution is:

P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,...

(a)

Compute the probability of more than one death in a corps in a year as follows:

P (X > 1) = 1 - P (X ≤ 1)

             = 1 - P (X = 0) - P (X = 1)

             =1-\frac{e^{-0.62}(0.62)^{0}}{0!}-\frac{e^{-0.62}(0.62)^{1}}{1!}\\=1-0.54335-0.33144\\=0.12521\\\approx0.1252

Thus, the probability of more than one death in a corps in a year is 0.1252.

(b)

The average deaths over 7 year period is: \lambda=7\times0.62=4.34

Compute the probability of no deaths in a corps over 7 years as follows:

P(X=0)=\frac{e^{-4.34}(4.34)^{0}}{0!}=0.01304\approx0.0130

Thus, the probability of no deaths in a corps over 7 years is 0.0130.

6 0
2 years ago
Select the expressions that are equivalent to 18m - 12.
krok68 [10]

Answer:

All the expressions other than option E, is equivalent to the expression 18m - 12.

Step-by-step explanation:

A. 6m - 4 + 6m -4 + 6m - 4

or 6m+6m+6m -4 -4 -4

or 18m -12

B. 12m + 6 - 6m -6

or 12m - 6m + 6 - 6

or 6m

C.6(3m - 2)

or 18m - 12

D.3(6m - 4)

or 18m - 12

E. 24n - 4² + 8 -6m

This option can not satisfy the given expression as it contains another variable as n.

4 0
2 years ago
Sydney earns a yearly salary of $32,000. Sydney's salary is equal to 40% of her boss' yearly salary. What is the yearly salary o
Oliga [24]

Answer: $80,000

Step-by-step explanation:

40%___$32,000

100%___X=$80,000

(100*32,000)/40 = 80,000

6 0
2 years ago
Rectangle TUVW is on a coordinate plane at T (a, b), U (a + 2, b + 2), V (a + 5, b − 1), and W (a + 3, b − 3). What is the slope
masya89 [10]

Answer:

The correct option is;

A 1

Step-by-step explanation:

The given rectangle TUVW has coordinates T(a, b), U (a + 2, b + 2), V ( a + 5, b - 1) and W (a + 3, b - 3).

Given that the coordinates of T and U are T (a, b), and U (a + 2, b + 2), we have;

The slope, m of the line TU is is found by the following relation;

Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

Where we put (x₁, y₁) = (a, b) and (x₂, y₂) = (a + 2, b + 2), we have;

m = ((b + 2) - b)/((a + 2) - a) = 2/2 = 1

Whereby the slope of a line parallel to another line are equal, we have that the slope of the line parallel to the line that contains the side TU is also 1.

7 0
2 years ago
Read 2 more answers
Which statements are true regarding triangle LMN? Check all that apply.
dimaraw [331]

Answer:

NM = x

LM = x\sqrt{2}

tan (45) = 1

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

                                        LM^{2} =LN^{2} +NM^{2}

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

                                        sin (\theta) = \frac{opposite}{hypotenuse}

                                        cos (\theta) = \frac{adjacent}{hypotenuse}

                                    tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}

Step 3: Verifying all the possible answers

A: Since, LN = x and using tan (45) =1

we can calculate

                                              tan (\theta)= \frac{opposite}{adjacent}

                                           tan (45)= \frac{NM}{x} =1

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to x\sqrt{2\\}.

C: Using Pythagoras Theorem

                                        LM^{2} =LN^{2} +NM^{2}

                                           LM^{2} =x^{2} +x^{2}

                                              LM^{2} =2x^{2}

                                         LM = \sqrt{2x^{2}} = x\sqrt{2}

It can also be proved using trigonometric relation

                                           cos (45) = \frac{x}{LM}

                                            LM = \frac{x}{cos (45)}

As, \frac{1}{cos (45)}= \sqrt{2}

Therefore

                                            LM = x\sqrt{2}

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

                                              tan (\theta)= \frac{opposite}{adjacent}

                                           tan (45)= \frac{x}{x} =1

Therefore, tan (45) = 1  and not equal to \frac{\sqrt{2} }{2}

3 0
2 years ago
Read 2 more answers
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