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3 years ago

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A flag staff is fixed at one corner of a rectangular room of side 20×10m.The angle of elevation on the top of the flag from oppo

site corner of the room is found 30.Find the height is flag staff.

1 answer:

Vedmedyk [2.9K]3 years ago

7 0

Answer:

The height is 12.9m

Step-by-step explanation:

First we have to find the distance from the corner of the flag to the opposite corner, for this we will use Pythagoras

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

h² = s1² + s2²

h² = 10² + 20²

h² = 100 + 400

h² = 500

h = √500

h = 22.36

Now that we know this measurement we can calculate the height of the flagpole

well to start we have to know the relationship between angles, legs and the hypotenuse

α = 30

a: adjacent = 22.36

o: opposite = ?

h: hypotenuse

sin α = o/h

cos α= a/h

tan α = o/a

we see that it has (angle, adjacent, opposite)

is the tangent

tan α = o/a

tan 30 = o/22.36

tan30 * 22.36 = o

12.9 = o

The height is 12.9m

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Assume that a procedure yields a binomial distribution with a trial repeated n = 5 times. Use some form of technology to find th

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Answer:

$P(X = 0) = 0.0263$

$P(X = 1) = 0.1407$

$P(X = 2) = 0.3012$

$P(X = 3) = 0.3224$

$P(X = 4) = 0.1725$

$P(X = 5) = 0.0369$

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$n = 5, p = 0.517$

Distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{5,0}.(0.517)^{0}.(0.483)^{5} = 0.0263$

$P(X = 1) = C_{5,1}.(0.517)^{1}.(0.483)^{4} = 0.1407$

$P(X = 2) = C_{5,2}.(0.517)^{2}.(0.483)^{3} = 0.3012$

$P(X = 3) = C_{5,3}.(0.517)^{3}.(0.483)^{2} = 0.3224$

$P(X = 4) = C_{5,4}.(0.517)^{4}.(0.483)^{1} = 0.1725$

$P(X = 5) = C_{5,5}.(0.517)^{5}.(0.483)^{0} = 0.0369$

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3 years ago

Aline with a slope of 2 passes through the point (3,9).

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Answer:

WAP

Step-by-step explanation:

ddhghfd WAP

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3 years ago

An internet site requires a password with 2 digits (numbers) and 3 letters. How many possible passwords are there?

Llana [10]

Answer:

1,757,600

Step-by-step explanation:

26x26x26x10x10 = 1,757,600

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2 years ago

Find the largest prime divisor of $15^6 - 7^6$<img src="https://tex.z-dn.net/?f=Find%20the%20largest%20prime%20divisor%20of%20%2

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Answer:

Largest prime factor of the given expression is <em>379.</em>

Step-by-step explanation:

Given the expression:

$15^6 - 7^6$

To find:

The largest prime factor of the given expression.

Solution:

First of all, let us factorize the given expression.

$15^6 - 7^6\\\Rightarrow (15^3)^2 - (7^3)^2\\\\\text{Using } x^{2} -y^2 = (x+y) (x-y)\\\\\Rightarrow (15^3+7^3)(15^3-7^3)$

Let us learn two formula:

$x^3+y^3 = (x+y)(x^2+y^2-xy)$

$x^3-y^3 = (x-y)(x^2+y^2+xy)$

Applying the above formula in the expression written above:

$(15^3+7^3) = (15+7)(15^2+7^2-15\times 7)\\\Rightarrow 22(225+49-105 ) = 2 \times 11 \times 169 \\\Rightarrow 2 \times 11\times 13\times 13\\\Rightarrow 2 \times 11\times 13^2$ ...... (1)

Similarly:

$(15^3-7^3) = (15-7)(15^2+7^2+15\times 7)\\\Rightarrow 8(225+49+105 ) = 2^3 \times 379$ ........ (2)

Multiplying the expressions from (1) and (2) to get the result:

$\therefore 15^6 - 7^6 = 2^4 \times 11 \times \underline{\bold{379}} \times 13 ^2$

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2 years ago

The lateral area of a cone is 400 pi cm^2. The radius is 10 cm. Find the slant height to the nearest tenth.

natka813 [3]

ANSWER

The slant height is 40cm.

EXPLANATION

The lateral area of a cone is given by:

$Area= \pi \: r \: l$

where r=10cm is the radius of the circle and l is the slant height.

It was also given that, the lateral area is 400π cm²

We substitute the values to get,

$400\pi = \pi \times \: 10 \times \: l$

We now divide both sides by 10π.

This implies that,

$\frac{400 \pi}{10\pi} = l$

$40 = l$

Hence the slant height is 40cm.

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3 years ago