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2 years ago

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Answer two questions about Equations AAA and BBB:\begin{aligned} A.&&5x&=3x \\\\ B.&&5&=3 \end{aligned}A

.B.5x5=3x=31) How can we get Equation BBB from Equation AAA?

1 answer:

max2010maxim [7]2 years ago

6 0

Answer:

mulitply and divide by both sides

and yes

Step-by-step explanation:

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Look at the graph. What is ?

shepuryov [24]

Answer:

no picture.

Step-by-step explanation:

no picture

4 0

2 years ago

Simplify <img src="https://tex.z-dn.net/?f=%5Csqrt%20-25" id="TexFormula1" title="\sqrt -25" alt="\sqrt -25" align="absmiddle" c

garik1379 [7]

Answer:

5<em>i</em>

Step-by-step explanation:

= $\sqrt{-1 * 25}$
= $\sqrt{-1}\sqrt{25}$
= $\sqrt{-1}$ * 5

Rule: $\sqrt{-1}$ = <em>i</em>

So you get <em>i </em>* 5<em> </em>=<em> </em>5<em>i</em>

5 0

2 years ago

Find all solutions of each equation on the interval 0 ≤ x < 2π.

Korvikt [17]

Answer:

$x = 0$ or $x = \pi$ .

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

$\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}$ .

$\displaystyle \sec{x} = \frac{1}{\cos{x}}$ .

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, $\sin^{2}{x} = 1 - \cos^{2}{x}$ . Therefore, for the square of tangents,

$\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}$ .

This equation will thus become:

$\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2$ .

To simplify the calculations, replace all $\cos^{2}{x}$ with another variable. For example, let $u = \cos^{2}{x}$ . Keep in mind that $0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1$ .

$\displaystyle \frac{1 - u}{u^{2}} + \frac{2}{u} - \frac{1 - u}{u} = 2$ .

$\displaystyle \frac{(1 - u) + u - u \cdot (1- u)}{u^{2}} = 2$ .

Solve this equation for $u$ :

$\displaystyle \frac{u^{2} + 1}{u^{2}} = 2$ .

$u^{2} + 1 = 2 u^{2}$ .

$u^{2} = 1$ .

Given that $0 \le u \le 1$ , $u = 1$ is the only possible solution.

$\cos^{2}{x} = 1$ ,

$x = k \pi$ , where $k\in \mathbb{Z}$ (i.e., $k$ is an integer.)

Given that $0 \le x < 2\pi$ ,

$0 \le k$ .

$k = 0$ or $k = 1$ . Accordingly,

$x = 0$ or $x = \pi$ .

8 0

2 years ago

Read 2 more answers

What is the slope of the line?

sineoko [7]

Answer:

3/4

Step-by-step explanation:

You can do this two different ways. Both include picking two points where the line crosses a corner. I'm using (0,-1) and (4,2). Now here you can either use

Slope= $\frac{Rise}{Run}$

or $\frac{y2-y1}{x2-x1}$

If you use the first one start at point (0,-1) and go to point (4,2) and count how many it goes up (rise) and then put that over how many it goes to the right (run).

If you use the second one then plug in the numbers.

y2=second y point

y1=first y point

x2=second x point

x1=first x point

$\frac{2-(-1)}{4-0}$ Now just solve.

$\frac{3}{4}$

4 0

3 years ago

Find an equation of the circle and sketch it if it has: Center on y=4, tangent x-axis at (–2, 0)

Digiron [165]

Answer:

$(x+2)^2+(y-4)^2=16$

OK, lets start by drawing a basic graph (the first one) so we can visualize.

We already know that the y coordinate of the circle's center is $4$ .

We know that the circle is tangent to the $X$ axis at $(-2,0)$

That means the x coordinate of the center has to be $-2$ , as the tangent is a point on the edge of the circle that touches a line at exactly one point.

The radius is the distance from the center of the circle to its edge. We know the center's location now, it is $(-2, 4)$ and a point on the edge of the circle (the tangent point) which is $(-2,0)$ . so the distance between the points is 4 which is the radius (you can use the distance formula, but it's quite oblivious.)

We can imagine the circle should look like this (the second one):

Now we can piece together an equation

The equation of a circle is $(x-h)^2+(y-k)^2=r^2$ where $(h,k)$ is the center and $r$ is the radius. When we put the numbers in: we get $(x-(-2))^2+(y-(4))^2=4^2$ which can be simplified into $(x+2)^2+(y-4)^2=16$ which is the answer.

Step-by-step explanation:

4 0

3 years ago