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3 years ago

Solve equation for 0 < x < 2pi

Mathematics

1 answer:

77julia77 [94]3 years ago

6 0

$\sqrt2\cos x-1=0$
$\sqrt2\cos x=1$
$\cos x=\dfrac1{\sqrt2}$

This occurs twice in the interval $0\le x\le2\pi$ , when $x=\dfrac\pi4$ and $x=\dfrac{3\pi}4$ .

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On a coordinate plane, the segment with endpoints (10, 40) and (70, 120) is

OlgaM077 [116]

Answer:

The length of the resulting segment is 500.

Step-by-step explanation:

Vectorially speaking, the dilation is defined by following operation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation.

$P(x,y)$ - Original point.

$k$ - Scale factor.

$P'(x,y)$ - Dilated point.

First, we proceed to determine the coordinates of the dilated segment:

( $P(x,y) = (10, 40)$ , $Q(x,y) = (70, 120)$ , $O(x,y) = (0,0)$ , $k = 5$ )

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$

$P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]$

$P'(x,y) = (50,200)$

$Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]$

$Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]$

$Q'(x,y) = (350, 600)$

Then, the length of the resulting segment is determined by following Pythagorean identity:

$l_{P'Q'} = \sqrt{(350-50)^{2}+(600-200)^{2}}$

$l_{P'Q'} = 500$

The length of the resulting segment is 500.

3 0

3 years ago

Which one doesn’t belong? Why? Explain. please help me

USPshnik [31]

Hi again! I'm assuming that the straight line, which I believe is for y = -2 doesn't belong because everything else has two lines, I mean like it reflects off a certain point on the x or y axis but b) [as I like to call it] doesn't reflect on another axis.

6 0

3 years ago

What is 500 percent as a decimal and a fraction please help.

andreyandreev [35.5K]

A percent mean per 100 so 500% is 500/100
which is 5, and I guess you could use 500/100 and then just divide each by 100 to get the fraction 5/1.
so 5.0 as a decimal
5/1 as a fraction

7 0

3 years ago

Read 2 more answers

I’ve noticed here are around 4 ways to solve a Quadratic Equation. Factoring, Completing the square, The quadratic Formula, and

valentina_108 [34]

Answer:

See explanation

Step-by-step explanation:

Usually, I just find the quadratic formula the easiest to go, but here are some tips to tell if which you should use.

1. First see if you can get integer values for the roots to multiply to c and add to b.

This is the easiest way to solve a quadratic equation, and I always check for whether I can easily find the roots by multiply two numbers for c and adding them for b.

For instance, the Quadratic $x^2 + 5x + 6$

I can easily see that 2 and 3 are the roots here - as $2\cdot3=6$ and $2+3=5$ . If you can do this and receive integer values, then great! I'd definitely stick with this.

2. See if you can complete the square

If you have a quadratic which is a perfect square, you'll be able to tell if c is a perfect square, and b is twice that number. This will be easiest. <em>Any quadratic equation can be solved by completing the square</em><em>, </em>but I personally stick to this method only if I can tell it's a perfect square quadratic.

3. Stick to the Quadratic Formula

If all else fails, go with the Quadratic formula. It's not that hard and it gets the job done. I would highly discourage going with graphing, as it takes too much time and it's quite a hassle unless you have a graphing calculator.

I really hope this helped!

5 0

4 years ago

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What is the remainder when (x3 + 1) is divided by (x2 – x + 1)? x + 1 x 2 0

mariarad [96]

Answer:

x+1

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers