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Elis [28]
3 years ago
7

2(4x – 3) ≥ –3(3x) + 5x?

Mathematics
1 answer:
tatyana61 [14]3 years ago
8 0
Treat the 'more than or equal to' sign as a '=' then work it out like an ordinary algebraic equation.    
2(4x-3) = -3(3x)+5x
8x-6 = -9x+5x
-6 = -9x+5x-8x
-6 = -12x
-6/-12 = x
1/2 = x
Then swap the '=' back for the other sign. This works for all of the '<' type signs
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Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)2 = 16 in the manner described. (En
ArbitrLikvidat [17]

Answer:

a) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t, b) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t, c) x = 4\cdot \cos \left(t+\frac{\pi}{2}  \right), y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right).

Step-by-step explanation:

The equation of the circle is:

x^{2} + (y-1)^{2} = 16

After some algebraic and trigonometric handling:

\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = 1

\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = \cos^{2} t + \sin^{2} t

Where:

\frac{x}{4} = \cos t

\frac{y-1}{4} = \sin t

Finally,

x = 4\cdot \cos t

y = 1 + 4\cdot \sin t

a) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t.

b) x = 4\cdot \cos t, y = 1 + 4\cdot \sin t.

c) x = 4\cdot \cos t'', y = 1 + 4\cdot \sin t''

Where:

4\cdot \cos t' = 0

1 + 4\cdot \sin t' = 5

The solution is t' = \frac{\pi}{2}

The parametric equations are:

x = 4\cdot \cos \left(t+\frac{\pi}{2}  \right)

y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right)

7 0
3 years ago
6) (after 2.3) Consider the infinite system of linear equations in two variables given by ax + by = 0 where (a, b) moves along t
Paraphin [41]

Answer:

Step-by-step explanation:

Given infinite system of linear equations is ax + by = 0

when (a,b) moves along unit circle in plane.

a) system having unique system (0, 0)

Since two of equation in thus system will be

1.x+0.y=0\\x=0

and

0.x+1.y=0\\y=0

It is clear that x = 0, y= 0 is the only solution

b) Linear independent solution in this system gives some set of solutions

1.x+0.y=0\\\x=0

and

0.x+1.y=0\\y=0

Vector form is

\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] =I

c) for this equation if add 0x +0y = 0 to system , Nothing will change

Because [0,0] satisfies that equation

d) If one of the equation is ax + by = 0.00001

where 0.00001 is small positive number

so, the system will be inconsistent

Therefore, the system will have no solution.

6 0
3 years ago
Sophie found the volume of the figure below by using the steps shown.
Westkost [7]

Answer: it's C Sophie used the wrong height for the pyramid

It's Right cause I took the test.

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
1 1/2 x -2= <br> PROCESS !!!!
trasher [3.6K]
11/2x=2
2/11(11/2)x=2(2/11)
x=4/11
7 0
2 years ago
The u.s. department of health and human services collected sample data for 772 males between the ages of 18 and 24. that sample
soldier1979 [14.2K]
The 99% confidence interval for the true mean is given by:

\bar{x}\pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}

where: 

\bar{x} is the sample mean = 69.7
\sigma is the standard deviation = 2.8
z_{\alpha/2} is the test statistics = 2.58 for for 99% confidentce interval.
n is the sample size = 772.

Therefore, the 99% confidence interval is:

69.7\pm2.58\left( \frac{2.8}{\sqrt{772}} \right)=69.7\pm2.58(0.1008) \\  \\ =69.7-0.26\leq\mu\leq69.7+0.26 \\  \\ =69.44\leq\mu\leq69.96
6 0
2 years ago
Read 2 more answers
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