The lenght of a rectangle is 27 cm and its width is 15 cm. *

Mathematics

2 answers:

valentina_108 [34]3 years ago

5 0

Answer:

Step-by-step explanation:

So should I find area or perimeter?

son4ous [18]3 years ago

4 0

Not sure what I should do with this information, but the area is 405 square cm.

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Determine whether the planes are parallel, perpendicular or neither. 2x â 4y + 3z = 5, x + 8y + 10z = 3

dexar [7]

The given two planes 2x + 4y + 3z = 5 and x + 8y + 10z = 3 are perpendicular to each other.

According to the given question.

We have two planes

2x - 4y + 3z = 5

and,

x + 8y + 10z = 3

Since, two planes are perpenicular if

$a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0$

Where $a_{1}$ , $b_{1}$ and $c_{1}$ and $a_{2}$ , $b_{2}$ and $c_{2}$ are the direction ratios of planes.

And the two planes are parallel to each other if

$\frac{a_{1} }{a_{2} } =\frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }$

Here, the direction ratios of plane 2x + 4y + 3z = 5 are 2, -4, and 3 and the direction ratios of plane x + 8y + 10z = 3 are 1, 8, and 10

Now,

2(1) + (-4)(8) + 3(10)

= 2 - 32 + 30

= 0

Since, the sum of the product of the direction ratios of the two palnes is 0. Therefore, the given two planes 2x + 4y + 3z = 5 and x + 8y + 10z = 3 are perpendicular to each other.

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1 year ago

The function h(x) = x2 + 14x + 41 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. S

Solnce55 [7]

Part A:

 

The first thing of completing the square is writing the expression as which expands to .

We have the first two terms exactly alike with the function we start with: and but we need to add/subtract from the last term, 49, to obtain 41. 

So, the second step is to subtract -8 from the expression 

The function in finalizing the square form is
 

Part B:

The vertex is acquired by equating the expression in the bracket from part A to zero

 
 

It means the curve has a turning point at x = -7

This vertex is a minimum since the function will make a U-shape.
A quadratic function can either make U-shape or ∩-shape depends on the value of the constant that goes with . When is (+), the curve is U-shape. When (-), the curve is ∩-shape

Part C:

The symmetry line of the curve will go through the vertex, hence the symmetry line is 

This function is shown in the diagram below