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Luba_88 [7]
3 years ago
6

Write the standard equation of the ellipse with center at the origin, and vertices at (-4,0), (4,0), (0, -3), and (0,3).

Mathematics
1 answer:
levacccp [35]3 years ago
5 0

9514 1404 393

Answer:

  (a)  x^2/16 +y^2/9 = 1

Step-by-step explanation:

The form for the equation of an ellipse centered at the origin is ...

  (x/(semi-x-axis))^2 +(y/(semi-y-axis))^2 = 1

The vertex values tell you the semi-x-axis is 4 units, and the semi-y-axis is 3 units. Then you have ...

  (x/4)^2 +(y/3)^2 = 1

  x^2/16 +y^2/9 = 1

__

In case you don't remember that form, you can try any of the points in the equations. The equation that works will quickly become apparent.

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What is the value 10 years from now of $200 deposited in an account earning 12% interest?
Rzqust [24]

Answer:$440

Step-by-step explanation:

Principal(p)=$200

Rate(r)=12%

Time(t)=10years

Simple interest=(pxrxt) ➗ 100

Simple interest =(200x12x10) ➗ 100

Simple interest=24000 ➗ 100

Simple interest=240

Total amount=p + simple interest

Total amount =200+240

Total amount =440

5 0
3 years ago
Read 2 more answers
HELP PLEASE!!!
Marina CMI [18]

Answer:

The maximum profit of $  10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) -C(x)

       = -31.72x^2 + 2,030x -( -126.96x + 26,391)

Distribute the minus sign

       = -31.72x^2 + 2,030x+126.96x - 26,391

 Combine like terms

      =   -31.72 x^2 + 2156.96 x - 26391

This is a parabola.  It is facing downwards.  The maximum profits is at the vertex ( where the max is)

vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34

Evaluate P(x) at x=34 to determine the profit

P(34) =  -31.72 (34)^2 + 2156.96 (34) - 26391

          -36668.32+73336.64-26391

          10277.32

8 0
3 years ago
Read 2 more answers
What is the circumference and the area of this circle​
alexira [117]
<h2>circumference = 50.24cm</h2><h2>area = 200.96cm²</h2>

Step-by-step explanation:

radius (r) = 8cm

circumference = 2π×r

= 2 × 3.14 × 8

= 50.24cm

area = π × r²

= 3.14 × 8 × 8

= 200.96cm²

<h2>MARK ME BRAINLIST</h2>
3 0
3 years ago
An increase in which of the following causes GDP to decrease?
Svetradugi [14.3K]

Answer:

B

Step-by-step explanation:

The GDP measures the market value of all goods and services produced in an economy (country or region) in a specific period of time. The GDP formula is:

GDP= Consumption (C)+ Investment (I)+ Government expenditure (G)+ (Exports - Imports) (Net exports)  

Notice that if exports increase, GDP will increase too. Also, if investment increases GDP will increase. Notice that imports have a negative sign, then if they increase, GDP will decrease.

5 0
3 years ago
1. whats the midpoint between (7,3) and (-3,-1)
Elanso [62]

Answer:

(2, 1 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( \frac{x_{1}+x_{2}  }{2}, \frac{y_{1}+y_{2}  }{2} )

Here (x₁, y₁ ) = (7, 3) and (x₂, y₂ ) = (- 3, - 1) , then

midpoint = ( \frac{7-3}{2}, \frac{3-1}{2} ) = ( \frac{4}{2}, \frac{2}{2} ) = (2, 1 )

5 0
3 years ago
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