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2 years ago

How do you solve simultaneous equations

Mathematics

1 answer:

Sladkaya [172]2 years ago

7 0

Step 1: Multiply each equation by a suitable number so that the two equations have the same leading coefficient.

Step 2: Subtract the second equation from the first.

Step 3: Solve this new equation for y.

Step 4: Substitute y = 2 into either Equation 1 or Equation 2 above and solve for x.

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You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta

vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

$\cos 2\theta = 0$

$2\theta = \cos^{-1}0$

$\theta = \frac{1}{2}\cdot \cos^{-1} 0$

$\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)$ , for all $i \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

y: 1 -1 1 -1

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

6 0

2 years ago

Use the law of sines to find the value of w.

Lunna [17]

Option B: 4.0 cm is the value of w

Explanation:

It is given that $\angle W= 39$ , $\angle U=31$ , $VW=3.3$ and $UV=w$

Using the law of sines, we have,

$\frac{sin U}{3.3} =\frac{sin W}{w}$

Substituting the values, we have,

$\frac{\sin 31}{3.3}=\frac{\sin 39}{w}$

Cross multiplying, we get,

$(sin31) w=3.3( \sin 39)$

Simplifying, we have,

$0.515w=2.077$

Dividing both sides by 0.515, we have,

$w=4.0$

Thus, the value of w is 4.0 cm

Hence, Option B is the correct answer.

4 0

2 years ago

Read 2 more answers

Carloshas1.2 meters of wood if cut into 3 equal pieces how many mm each

sdas [7]

1.2 ÷ 3 = 0.4 meters each
0.4 meters = 40 cm
40 cm = 400 mm

therefore,
Carlos must cut each piece of wood 400 mm each.

Hope this helps and have a great day! :D

5 0

2 years ago

Which numbers are in order from least to greatest?

mixas84 [53]

Answer:

Step-by-step explanation:

5 0

2 years ago

PLS HELP ASAP PLSSS IT DETECTS IF ITS RIGHT OR WRONG HELPPP

timurjin [86]

Answer:

y= 250 - 2x

Step-by-step explanation:

She spends $2 per bottle, which is my it's 2x.

She has a total of 250, and she spends $2 per bottle, so you subtract 2x from 250, which leaves the equation at y = 250 - 2x

3 0

2 years ago