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mrs_skeptik [129]
3 years ago
7

Evaluate the determinant for the following matrix: A. –42 B. –36 C. 12 D. 10

Mathematics
1 answer:
Gemiola [76]3 years ago
6 0
Missing information, you didn't provide the matrix
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Point A. (1,6)
point B.(7,8)
point C (6,3)
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This takes too long!!!!!!!!
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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
I WILL GIVE BRAINLIEST TO WHOEVER IS CORRECT
babymother [125]

So I believe that the position the triangle is sitting in is the original position that the question started with correct? (Wasn't sure if you moved it before the screenshot or not)

So for all three points of the triangle, move each of them 6 units to the left since the rule has (x-6). If it was x+6, it should be 6 units to the right then.

After you move it 6 units to the left, move the points (all three) 4 units down since (y-4) means moving in the y-direction downward!

That should be the new place for the triangle to be positioned.

Hope this helps!

6 0
3 years ago
7. Find an equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4.
bagirrra123 [75]

The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5

<h3>How to find the equation of a line?</h3>

The equation of a line can be represented as follows:

y = mx + b

where

  • m = slope
  • b = y-intercept

Therefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4

Hence,

perpendicular lines follows the rule below:

m₁m₂ = -1

Hence,

5x - 3y = 4

5x - 4 = 3y

y = 5/ 3 x - 4 / 3

m₁ = 5 / 3

5/3 m₂ = -1

m₂ = - 3 / 5

Hence,

using (-4, 5)

5 = - 3 / 5 (-4) + b

5 = 12 / 5 + b

b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5

Therefore,

y = -3 / 5 x + 13 / 5

learn more on equation of a line here: brainly.com/question/10727767

#SPJ1

6 0
2 years ago
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