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Alexxx [7]
3 years ago
11

Given the directrix of y = 6 and focus of (0, 4), which is the equation of the parabola?\

Mathematics
1 answer:
Yuliya22 [10]3 years ago
5 0

Answer:

The directrix is y=6 and focus is (0,4)

The equation of the parabola is,

20-4y=x²

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-8x + 7y=-16<br> 4x + y=-28
topjm [15]

Answer:

x=-5

y=-8

Step-by-step explanation:

let first equation be equation 1

let second equation be equation 2

so we gather the like terms

5 0
3 years ago
The total amount of money (in cents) in x nickels, (x+5) dimes and 2x quarters
Scorpion4ik [409]

\\&#10;\text{Suppose you have x nickels, (x+5) dimes and 2x quarters}\\&#10;\\&#10;\text{we know that the value of 1 quarter is}=\$ 0.25=\text{ 25 cents}\\&#10;\\&#10;\text{value of 1 dime}=\$0.10=10 \text{ cents}\\&#10;\\&#10;\text{value of 1 Nickel}=\$ 0.05=5 \text{ cents}\\&#10;\\&#10;\text{so the total amount of money in cents is}\\&#10;\\&#10;=5(x)+10(x+5)+25(2x)\\&#10;\\&#10;=5x+10x+50+50x\\&#10;\\&#10;=65x+50

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7 0
3 years ago
27.9km to the nearest km
yuradex [85]

Answer: It rounds to <u>28 km</u>

Explanation:

The units or ones digit is "7". The next digit over (9) is five or larger. This means we bump the 27 up to 28. Everything after the 7 is ignored.

So we could have something like 27.999871212512 and we still follow the same idea of focusing on the 27, bumping it up to 28, and everything else gets ignored.

The reason for this is because 27.9 is much closer to 28 than it is to 27. Draw out a number line to help see this. Split the region from 27 to 28 into 10 equal pieces. The 9th little piece represents 27 & 9/10 aka 27.9

Refer to the number line diagram below.

8 0
2 years ago
How to find area and perimiter of a 30/60/90 triangle
Travka [436]
The perimeter would be 15+5 \sqrt{2} and the area would be 12.5 \sqrt{2} .
3 0
3 years ago
I'm have some issues with the problem shown in the screenshot and would love some help.
KiRa [710]

The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;

  • Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.

  • Maximum volume of the box is approximately 1048.6 in.³

<h3>How can the dimensions and volume of the box be calculated?</h3>

The given dimensions of the cardboard are;

Width = 18 inches

Length = 35 inches

Let <em>x </em>represent the side lengths of the cut squares, we have;

Width of the box formed = 18 - 2•x

Length of the box = 35 - 2•x

Height of the box = x

Volume, <em>V</em>, of the box is therefore;

V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x

By differentiation, at the extreme locations, we have;

\frac{d V }{dx}  =  \frac{d( 4 \cdot \:  {x}^{3}  - 106 \cdot \:  {x}^{2}  + 630\cdot \:  {x} )  }{dx} = 0

Which gives;

\frac{d V }{dx}  =12\cdot \:  {x}^{2}  -  212\cdot \:  {x} + 630 = 0

6•x² - 106•x + 315 = 0

x  =  \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6}

Therefore;

x ≈ 4.55, or x ≈ -5.55

When x ≈ 4.55, we have;

V = 4•x³ - 106•x² + 630•x

Which gives;

V ≈ 1048.6

When x ≈ -5.55, we have;

V ≈ -7450.8

The dimensions of the box that gives the maximum volume are therefore;

  • Width ≈ 18 - 2×4.55 in. = 8.89 in.

  • Length of the box ≈ 35 - 2×4.55 in. = 24.89 in.

  • Height = x ≈ 4.55 in.

  • The maximum volume of the box, <em>V </em><em> </em>≈ 1048.6 in.³

Learn more about differentiation and integration here:

brainly.com/question/13058734

#SPJ1

7 0
1 year ago
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