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navik [9.2K]
3 years ago
10

What is the solution to the system of equations?

Mathematics
1 answer:
Llana [10]3 years ago
3 0

Solution in attachment.

<h3>x = -6, y = 9, z = -3</h3>

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5) Placido pulls a rope attached to a wagon through a pulley at a rate of q m/s. With dimension as in Figure 5:
Damm [24]

The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.

(a) \ \mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = q -\dfrac{x}{\sqrt{x^2+ 5.76}}

(b) When <em>x </em>= 0.6 and q = 0.5 m/s, the speed of the wagon is approximately <u>0.243 m/s</u>.

Reasons:

(a) The distance from the cart to the pulley, <em>r</em> is given by Pythagoras's

theorem as follows;

r = √((3 - 0.6)² + x²) = √(2.4² + x²)

The speed of the wagon = \mathbf{\dfrac{dx}{dt}}

The speed of the rope, q = \mathbf{\dfrac{dr}{dt}}

By chain rule, we have;

\dfrac{dr}{dt} = \mathbf{\dfrac{dr}{dx} + \dfrac{dx}{dt}}

\dfrac{dr}{dx} = \dfrac{x}{\sqrt{x^2+ 5.76}}

Therefore;

\dfrac{dr}{dt} = q =\dfrac{x}{\sqrt{x^2+ 5.76}}+ \dfrac{dx}{dt}

\mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = \underline{ q -\dfrac{x}{\sqrt{x^2+ 5.76}}}

(b) The speed of the wagon when <em>x</em> = 0.6 if q = 0.5 m/s is given as follows;

\dfrac{dx}{dt} = 0.5 -\dfrac{0.6}{\sqrt{0.6^2+ 5.76}} =\sqrt{\dfrac{1}{17} } \approx 0.243

The speed of the wagon when <em>x </em>= 0.6 and q = 0.5 m/s, \dfrac{dx}{dt} ≈ <u>0.243 m/s</u>

Learn more here:

brainly.com/question/17081984

4 0
2 years ago
If you flip three fair coins, what is the probability that youll get all three heads
Leona [35]

Answer:

12.5

Step-by-step explanation:

100/2=50/2=25/2=12.5

8 0
3 years ago
Jayden recently learned that the atmosphere is made of gases. Which is NOT a way in whichgases are helpful to life on Earth?A.It
snow_lady [41]

Answer:

A. It provides carbon monoxide to help plants grow.

Step-by-step explanation:

The only incorrect option is that carbon monoxide is required by plant, but the correct statement would be carbon dioxide is required my plants, for its growth, which helps to perform the process of photosynthesis.

The rest of the statements are correct.

As, the atmosphere acts as a blanket, which protects the earth from the harmful rays of the sun.

And, atmosphere constitute of various gases, which enables the living organisms to breath.

And, the atmosphere protects from any meteors entering from space.  

3 0
3 years ago
Find the value of z ANSWER IS NOT 12. NO LINKS OR SPAMS! THANK YOU!!!!!!​
alexgriva [62]

Answer:

12√3

Step-by-step explanation:

sin 30 =1/2

sin30=a/24. sin=opposit side/Hypotenuse

a is the opposite side of 30

1/2=a/24

a=12

now take pythagoras theroem

24^2=z^2+12^2

576=z^2+144

z^2=576-144

z^2=432

z=√432

z=√144*3

z=12√3

4 0
3 years ago
Is -3y = 5x + 4 perpendicular
aivan3 [116]

Answer:

no it is not perpedicular

Step-by-step explanation:

I plugged the equation into a graphing calculator and the line does not appear to be perpendicular

5 0
3 years ago
Read 2 more answers
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