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4 years ago

Find the missing angle

Mathematics

1 answer:

m_a_m_a [10]4 years ago

7 0

The answer would be 180 or a little more i would need a protractor to be exactly right<span />

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Let d represent the distance from the center of the sphere x 2 + y 2 + z 2 − 6 x + 2 y = − 6 to the plane y = 2.

MrRissso [65]

Answer:

$A=-10$ and $2$

Step-by-step explanation:

The given sphere is $x^2 + y^2 + z^2 -6x + 2y =-6$

This can be rearranged as $(x-3)^2 -9+ (y+1)^2 -1 + (z-0)^2=-6$

$\Rightarrow (x-3)^2 + (y+1)^2 + (z-0)^2=4\\$

On comparing with the standard equation of a circle $(x-x_0)^2 + (y-y_0)^2 + (z-z_0)^2=r^2$ , with center $(x_0,y_0,z_0)$ and radius $r$ .

The center of the given circle is $( 3, -1 ,0)$ .

Now, as the perpendicular distance, $d$ , of a point $(x_0,y_0,z_0)$ from a plane $ax+by+cz=p$ is

$d= \left | \frac {xx_0+yy_0+zz_0-p}{\sqrt {a^2+b^2 +c^2}} \right|$ .

$\Rightarrow d= \left | \frac {0\times 3+1\times (-1)+0-2}{\sqrt {1^2}} \right|$ [ as the given plane is y=2]

$\Rightarrow d=3 \; \cdots (i)$

Similarly, the other equation of the circle, $x^2 + y^2 + z^2 + Ay + 6z = 2,$ can be rearranged as $(x-0)^2 + (y+\frac {A}{2})^2 + (z+3)^2=11+\frac {A^2}{4}.$

Here, the center for this circle is $\left( 0, -\frac {A}{2}, -3\rigfht).$

From the given condition, the distance of the center from the plane $y=2$ is $d$ .

$\Rightarrow \left | \frac {0+1 \times \left (-\frac {A}{2}\right)+0\times (-3)-2}{\sqrt {1^2}} \right|=3$ [from equation (i) ]

$\Rightarrow \left | -\frac {A}{2}-2\right|=3$

$\Rightarrow \frac {A}{2}+2=\pm 3$

$\Rightarrow \frac {A}{2}=-2\pm 3$

$\Rightarrow A=2\times (-2-3)$ and $2\times (-2+3)$

$\Rightarrow A=-10$ and $2$ .

4 0

3 years ago

What is cos 30°?<br> 60<br> 2<br> 30<br> 90*

REY [17]

It’s 90 or 60 I believe

7 0

4 years ago

Read 2 more answers

What is the gradient of the line 3x+y=4

algol13

Answer:

<h2>The slope is - 3</h2>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

The equation is 3x+y = 4

To find the slope of the line we must first write the equation in the general form above

Make y the subject

That's

y = - 3x + 4

Comparing with the general equation above

Slope of the line = - 3

Hope this helps you

3 0

4 years ago

HELP ASAP MARKING BRAINLIEST

lesya [120]

I hoped this helped! +*♡

6 0

3 years ago

which of these situations can be represented with an inter that, when combined with the opposite of -7, makes 0: you walk down 7

kobusy [5.1K]

Answer:

When you ear $7 from your chores.

Step-by-step explanation:

Say you owe your friend $7 from that box of candy that they bot you at the movies. You now have -$7 until you gain that money back. So, you did all of your chores, and you made $7! Now you have enough money to pay your friend back. You are now left with $0.

-$7 + $7 = $0

3 0

4 years ago