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3 years ago

Describe the difference between collinear points and coplanar lines..

1 answer:

8 0

Notice the word LINE in COLLINEAR. Collinear points are points that lie ON A LINE. Any two points are always collinear because you can always connect them with a straight line.
Notice the word PLANE in COPLANAR. A group of points that lie IN THE SAME PLANE are coplanar. Any two or three points are always coplanar.
I hope you get the answer you needed.

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A piece of solid, spherical glass has a circumference of 18.84 centimeters. The sphere is cut in half, creating two identical he

julsineya [31]

We know that

the sphere is divided into two hemispheres
the two hemispheres are equals

if Tran computes the amount of paint needed to cover the sphere
therefore
Tran computes the amount of paint needed to cover both hemispheres.

the answer is
Tran found the minimum amount of paint needed to cover both hemispheres.

[surface area of sphere]=4*pi*r²
[surface area of each hemisphere]=2*pi*r²

circumference=18.84 cm------> 2*pi*r------> r=18.84/(2*pi)------> 3cm
[surface area of each hemisphere]=2*pi*3²---------> 56.52 cm²

surface area of sphere=2*56.52=113.04 cm²

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4 years ago

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Jada is solving the equation shown below.

Vikentia [17]

Answer:

Distribute -1/2 over (x - 4)

Divide both sides of the equation by -2

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3 years ago

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What is the volume of a prism

Cerrena [4.2K]

To find the volume of a prism, the formula is V = B*h

Volume = Base*Height

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3 years ago

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Solve the matrix and prove that it is equal 0

Art [367]

Step-by-step explanation:

$\underline{ \underline{ \text{Given}}} :$

$\tt{ {A}^{T} = \begin{bmatrix} 2 & - 4 \\ 4 & 3 \\ \end{bmatrix}}$

$\underline{ \underline { \text{To \: Find}}} :$

$\sf{ {A}^{2} - 5A+ 22I= 0}$

$\underline{ \underline{ \text{Solution}}} :$

The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by $\sf{ {A}^{T}}$ . Again , Interchange it's rows and columns in order to find ' A '.

$\tt{A = \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix}}$

Now , LEFT HAND SIDE ( L.H.S )

$\tt{ {A}^{2} - 5A+ 22I}$

Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.

⟼ $\begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} - 5 \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} + 22 \times \begin{bmatrix} 1 & 0 \\ 0 & 1\\ \end{bmatrix}$

⟼ $\begin{bmatrix} 2 \times 2 + 4 \times ( - 4)& 2 \times 4 + 4 \times 3 \\ - 4 \times 2 + 3 \times ( - 4) & - 4 \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} 4 + ( - 16) & 8 + 12 \\ - 8 + ( - 12) & - 16 + 9 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} - 12 & 20\\ - 20& - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} - 22 & 0 \\ 0& - 22 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} - 22 + 22 & 0 + 0 \\ 0 + 0 & - 22 + 22 \\ \end{bmatrix}$

⟼ $\begin{bmatrix} 0 & 0\\ 0 & 0 \\ \end{bmatrix}$

⟼ $\sf{0}$

RIGHT HAND SIDE ( R.H.S ) : 0

L.H.S = R.H.S [ Hence , proved ! ]

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3 years ago

Three consecutive odd integers have a sum of 33

KATRIN_1 [288]

Three consecutive integers that add up to 33 are 2 above and lower than a middle number. This means that the average of these 3 numbers will be the same. Therefore, 33/3=11 as the average. Therefore 11 is the middle number, 9 is 2 below (a consecutive odd integer) and 13 is 2 above (a third consecutive odd integer). Therefore the 3 numbers are 9, 11, and 13.

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3 years ago

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