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Nookie1986 [14]

3 years ago

11

A pole that is 3.3 m tall casts a shadow that is 1.29 m long. At the same time, a nearby tower casts a shadow that is 36.75 m lo

ng. How tall is the tower?

1 answer:

Ilia_Sergeevich [38]3 years ago

4 0

Check the picture below.

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Car is moving on a circle on a plane. At time t (seconds), its x-coordinate is given by x(t) = 10 sin(200t + 3) + 30 while its y

Aleks [24]

Answer:

we have centre of circle as (30,40) and radius = 1

Step-by-step explanation:

Given that a car is moving on a circle on a plane.

At time t (seconds),

$x(t) = 10 sin(200t + 3) + 30$

and

$y(t) = 10 cos(200t + 3) + 40$

$x-30 = 10 sin(200t + 3) \\y-40 = 10 cos(200t + 3) + 40$

when we square and add both the equations we get

$(x-30)^2 + (y-40)^2 = 1$

(since sin square + cos square = 1 always)

i.e. we have centre of circle as (30,40) and radius = 1

3 0

3 years ago

43 divided by 4759 and 69 divided by 6267

Goshia [24]

43÷4759=0.0090355117 and 69÷6267=0.0110100527 is your answers

6 0

4 years ago

A jury pool consists of 35 people, 17 men and 18 women. Compute the probability that a randomly selected jury of 12 people is al

Lelechka [254]

Answer:

17/35

Step-by-step explanation:

Prob.

=DC/SS(desired chance/sample space)

=17/35

7 0

3 years ago

Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos

Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$P_{1} = (- 1, 4)$

$P_{2} = (6, 2)$ and

$P_{3} = (4, - 5)$

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $(x_1, y_1)$ and $(x_2, y_2)$ is:

$\sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+} \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}}$

Length between $P_1$ and $P_{2}$ , (Side 1) :

$(x_1, y_1) = (- 1, 4)$ and

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2$

$= \sqrt{7^2 + 2^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}}$

Length of Side 1 = $\sqrt{\textbf{53}}$ units.

Distance between $P_1$ and $P_2$ , (Side 2):

$(x_1, y_1) = (-1, 4)$

$(x_2, y_2) = (4, - 5)$

Distance = $\sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2$

$= \sqrt{ 25 + 81 }$

$= \sqrt{\textbf{106}}$

Length of Side 2 = $\sqrt{\textbf{106}}$ units.

Distance between $P_2$ and $P_3$ , Side 3 :

$(x_1, y_1) = (4, 5)$

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}$

Length of Side 3 = $\sqrt{\textbf{53}}$ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$\bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2$

i.e, 53 + 53 = 106

Hence, the triangle is a right - angled triangle as well.

7 0

4 years ago

2.1 million deaths per year. What is the quantity of deaths per minute

tino4ka555 [31]

<span>If approximately 2.3 million people die per year in the US, this is equivalent to deaths per minute. Round to the nearest hundredth.
of minutes in a year
365*24*60
of deaths per minute = 2.3x10^6/(365*24*60) = 4.38 deaths/minute</span>

6 0

3 years ago