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MArishka [77]
3 years ago
13

Explain why a set of points that defines a plane cannot be collinear

Mathematics
1 answer:
USPshnik [31]3 years ago
3 0

Answer:

Three non-collinear points determine a plane.

Step-by-step explanation:

This statement means that if you have three points not on one line, then only one specific plane can go through those points. The plane is determined by the three points because the points show you exactly where the plane is

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A firework is launched at the rate of 10 feet per second from a point on the ground 50 feet from an observer. to 2 decimal place
Kazeer [188]

The rate of change of the angle of elevation when the firework is 40 feet above the ground is 0.12 radians/second.

First we will draw a right angle triangle ΔABC, where ∠B = 90°

Lets, assume the height(AB) = h and base(BC)= x

If the angle of elevation, ∠ACB = α, then

tan(α) = \frac{AB}{BC} = \frac{h}{x}

Taking inverse trigonometric function, α = tan⁻¹ (\frac{h}{x}) .............(1)

As we need to find the rate of change of the angle of elevation, so we will differentiate both sides of equation (1) with respect to time (t) :

\frac{d\alpha}{dt}=[\frac{1}{1+ \frac{h^2}{x^2}}]*(\frac{1}{x})\frac{dh}{dt}

Here, the firework is launched from point B at the rate of 10 feet/second and when it is 40 feet above the ground it reaches point A,

that means h = 40 feet and \frac{dh}{dt} = 10 feet/second.

C is the observer's position which is 50 feet away from the point B, so x = 50 feet.

\frac{d\alpha}{dt}= [\frac{1}{1+ \frac{40^2}{50^2}}] *\frac{1}{50} *10\\ \\ \frac{d\alpha}{dt} = [\frac{1}{1+\frac{16}{25}}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt} = [\frac{25}{41}] *\frac{1}{5}\\   \\ \frac{d\alpha}{dt}= \frac{5}{41} =0.1219512

= 0.12 (Rounding up to two decimal places)

So, the rate of change of the angle of elevation is 0.12 radians/second.

5 0
3 years ago
Evaluate the expression for the given values of the variables.
vfiekz [6]

Answer:

A

Step-by-step explanation:

Substitute the given values into the expression

2a² + cb

= 2(5)² + 3(11)

= 2(25) + 33

= 50 + 33

= 83 → A

7 0
2 years ago
What is the slope of a line perpendicular to the line passing through (1, -3) and (-4, 7)?
andrezito [222]

Answer:

-2

Step-by-step explanation:

m=\frac{y2-y1}{x2-x1}

7 0
3 years ago
Is the number 5 prime, composite, or neither?
OlgaM077 [116]

Answer:

A number that is divisible only by itself and 1 

therefore 5 is a prime number

3 0
2 years ago
Read 2 more answers
1) Simplify the following ratios with steps:
serg [7]

Answer:

a 18.24

b 32ratio 48

c

d

Step-by-step explanation:

you have to do ur self itis very easy you can also search some parton Google ok bro

4 0
3 years ago
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