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2 years ago

Q(-2, 3) and P (2, 1) Find the length of the segment. Simplify each radical,if possible

Mathematics

1 answer:

Montano1993 [528]2 years ago

7 0

9514 1404 393

Answer:

2√5

Step-by-step explanation:

The distance formula is useful for this.

d = √((x2 -x1)² +(y2 -y1)²)

d = √((2 -(-2))² +(1 -3)²) = √(4² +(-2)²) = √20

d = 2√5

The length of segment PQ is 2√5.

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2 years ago

Find an equation of the sphere that passes through the origin and whose center is (-2, 2, 3). Be sure that your formula is monic

Andrei [34K]

Answer:

$\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

Step-by-step explanation:

Given the center of sphere is: (-2, 2, 3)

Passes through the origin i.e. (0, 0, 0)

To find:

The equation of the sphere ?

Solution:

First of all, let us have a look at the equation of a sphere:

$(x-a)^2+(y-b)^2+(z-c)^2=r^2$

Where ( $x,y,z$ ) are the points on sphere.

$(a, b, c)$ is the center of the sphere and

$r$ is the radius of the sphere.

Radius of the sphere is nothing but the distance between any point on the sphere and the center.

We are given both the points, so we can use distance formula to find the radius of the given sphere:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Here,

$x_1 =0 \\y_1 =0 \\z_1 =0 \\x_2 =-2 \\y_2 =2 \\z_2 =3$

So, Radius is:

$r = \sqrt{(-2-0)^2+(2-0)^2+(3-0)^2}\\\Rightarrow r = \sqrt{4+4+9} = \sqrt{17}$

Therefore the equation of the sphere is:

$(x-(-2))^2+(y-2)^2+(z-2)^2=(\sqrt{17})^2\\\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

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4 years ago

Evaluate the expression -2cd if a = -8 b = 2 c = -5 d = 6

Elza [17]

Answer:

Step-by-step explanation:

Replace c and d with -5 and 6.

-2*-5*6

-2*-5=10

10*6=60

The expression is equal to 60.

-hope it helps

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3 years ago

Katie earned $1890 in 7 years on an investment at a 6% annual simple interest rate.

n200080 [17]

Her investment was $4500. To get this, you take 1890 and divide it by 7, giving you 270. This is 6% of 4500. To prove this, you would multiply 4500 by .06, giving the answer of 270, which can then be multiplied by 7 (years) to equal $1890.

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4 years ago

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