Find the vertex, focus, directrix, and focal width of the parabola: -1/40x^2=y

Answers

Answer 1

Answer: for
(x-h)^2=4p(y-k)
vertex is (h,k)
distance from vertex to directix=p=distance from vertex to focus
|4p|=focal width

remember, focus is on the side of the parabola where it opens and directix is at the back
when p is negative, it opens down
when p is positive, it opens up

look at equation
-1/40(x-0)^2=(y-0)
times -40 to both sides
(x-0)^2=-40(y-0)
(x-0)^2=4(-10)(y-0)
vertex=(0,0)
p=-10,it's negative so it opens down

focus is 10 units below vertex (y direction)
focus=(0,-10)

diretix is 10 above
directix is y=10

focal width=|4p|=|4(-10)|=|-40|=40

vertex=(0,0)
focus=(0,-10)
directix is y=10
focal width=40 units

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A number is multiplied by 8 , and that product is added to 2 . the sum is equal to the product of 2 and 21 . find the number.

Answers

number—> x
8x+2=2*21
8x=40
x=5

A table is rectangular and its length is twice its width. Find the dimensions of the table if it occupies 18 ft2 of floor space.

Answers

the dimensions of the table width would be 2 feet and the length would be 4 feet.

The answer would be length is 6, and width would be 3.
How to find the answer:
First you make combinations that multiply to 18 (because area is length times width)
2 x 9
3 x 6
6 x 3
9 x 2
since the last two are basically the same as the first two, you can get rid of those.
2 x 9
3 x 6
since 3 is half of 6 (and 2 isn't half of 9),
3 x 6 is the answer.
Hope this helps.

A student bought a pair of sunglasses in the USA.He paid $35.50
In England, an identical pair of sunglasses costs £26.99
The exchange rate is £1 = $1.42
In which country were the sunglasses cheaper, and by how much?

Answers

You almost have it!!!

all you do is multiply 26.99*1.42

this equals 38.33 dollars

35.50 is less than 38.33

thus, USA is cheaper than England.

can some one please help my with 1 &2? there’s supposed to be only 1 false but i can’t figure it out

Answers

Answer:

The third one one number 1 is false

The second one on number 2 is true

What's the formula to perimeter

Answers

The formula is:

Perimeter = (the distance all the way around the outside of the figure) .

How to calculate the distance all the way around the outside of the figure
is different for every shape.

A few of them are:

Square . . . . . 4 x the length of one side

Rectangle . . . . . (2) x (length + width)

Circle . . . . . (2 pi) x (radius)

etc.

$The\ perimeter\ of\ any\ polygon\ is\ the\ sum\ of\ the\ lengths \nof\ all\ its\ sides\ (a,\ b,\ c,\ d,\ ...)\n\ntriangle:\ \ \ P=a+b+c\n\nequilateral\ triangle:\ \ \ P=3a \n\nrectangle:\ \ \ P=2a+2b \n\nsquare:\ \ \ P=4 a\n\ndiamond :\ \ \ P=4a\n\ntrapez:\ \ \ P=a+b+c+d\n\nisosceles trapezoid:\ \ \ P=a+b+2c\ \ \ \ \ (c-arm length)\n\nany\ polygon:\ \ \ P=a+b+c+d+...\n----------------\nThe\ perimeter\ of\ a\ circle:\ \ \ P=2 \pi r\ \ \ \ \ (r-radius\ or\ a\ circle)$

What is the area of the kitchen floor in this floor plan?A-24 sq meters
B-28 sq meters
C-35 sq meters
D-42 sq meters

Answers

Answer: The correct option is (C) 35 sq. meters.

Step-by-step explanation: We are given to find the area of the kitchen floor in the floor plan shown in the figure.

From the figure, we see that

the kitchen is in the form of a rectangle with length 7 meters and breadth 5 meters.

We know that

the area of a rectangle with length l units and breadth b units is given by

$A=l* b.$

For the rectangular kitchen, we have

length, l = 7 meters

and

breadth, b = 5 meters.

Therefore, the area of the kitchen floor in the floor plan is given by

$A=l* b=7* 5=35~\textup{sq. meters}.$

Thus, option (C) is CORRECT.

First you would figure out the dimensions, which are 7 ft by 5 ft. Then, multiply those together, which equals 35 sq ft. The answer to your question is C - 35 sq ft. Hope this helps!

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