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dimulka [17.4K]

3 years ago

12

Derive the equation from the parabola with a focus at (0,1) and a directrix of y=-1

1 answer:

Lady bird [3.3K]3 years ago

3 0

Answer:

y = (x^2)/4

Step-by-step explanation:

The vertex of this parabola is halfway between the focus (0,1) and the directrix y = -1. Thus, the vertex is at (0,0). The variable p represents the distance between focus and vertex, which is 1.

Thus, adapting the general formula for the equation of a parabola, we have:

4(1)y=x^2, or 4y = x^2, or y = (x^2)/4.

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Someone help me pls,I need the value of both x and y

zlopas [31]

Answer
Y=10 x=9
Explanation
Y= 16-6
X= 13-4

5 0

1 year ago

The length of a rectangular garden is 6 more than its width. If the perimeter is 32 feet, what is the width and the area of the

PolarNik [594]

Answer:

${\fbox{ \sf{Width \: of \: a \: rectangular \: garden \: = 5 \: feet}}}$

$\boxed{ \sf{ \: Area \: of \: a \: rectangular \: garden = 55 {ft}^{2}}}$

Step-by-step explanation:

$\star$ Let the width of a rectangular garden be 'w'

$\star$ Length of a rectangular garden = 6 + w

$\star$ Perimeter of a rectangular garden = 32 feet

<u> $\longrightarrow$ </u><u> </u><u>Finding </u><u>the</u><u> </u><u>width</u><u> </u><u>of</u><u> </u><u>a</u><u> </u><u>rectangular</u><u> </u><u>garden</u> :

$\boxed{ \sf{ \: Perimeter \: of \: a \: rectangle \: = \: 2(length + width}}$

$\mapsto{ \text{32 = 2(6 + w + w)}}$

$\text{Step \: 1 \: : Collect \: like \: terms}$

Like terms are those which have the same base

$\mapsto{ \text{32 = 2(6 + 2w) }}$

$\text{Step \: 2 \: : Distribute \: 2 \: through \: the \: parentheses}$

$\mapsto{ \text{32 = 12 + 4w}}$

$\text{Step \: 3 \: : Swap \: the \: sides \: of \: the \: equation}$

$\mapsto{ \text{4w + 12 = 32}}$

$\text{Step \: 4 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}$

$\mapsto{ \text{4w = 32 - 12}}$

$\text{Step \: 5 \: : Subtract \: 12 \: from \: 32}$

$\mapsto{ \sf{4w = 20}}$

$\text{Step \: 6 \: : Divide \: both \: sides \: by \: 4}$

$\mapsto{ \sf{ \frac{4w}{4} = \frac{20}{4}}}$

$\text{Step \: 7 \: : Calculate}$

$\mapsto{ \text{w = 5}}$

Width of a rectangular garden = 5 feet

$\longrightarrow$ <u>Substituting </u><u>/</u><u> </u><u>Replacing </u><u>the </u><u>value </u><u>of </u><u>w </u><u>in </u><u>6</u><u> </u><u>+</u><u> </u><u>w </u><u>in </u><u>order </u><u>to </u><u>find</u><u> </u><u>the</u><u> </u><u>length</u><u> </u><u>of</u><u> </u><u>a</u><u> </u><u>rectangular </u><u>garden</u>

$\mapsto{ \sf{Length = 6 + w = 6 + 5 = \bold{11 \: feet} }}$

$\longrightarrow$ <u>Finding</u><u> </u><u>the</u><u> </u><u>area</u><u> </u><u>of</u><u> </u><u>a</u><u> </u><u>rectangular</u><u> </u><u>garden</u><u> </u><u>having</u> <u>length of 11 feet and</u><u> </u><u>width</u><u> </u><u>of</u><u> </u><u>5</u><u> </u><u>feet</u> :

$\boxed{ \sf{Area \: of \: a \: rectangle = length \:∗ \: width}}$

$\mapsto{ \text{Area \: = \: 11 \: ∗ \: 5}}$

$\mapsto{ \sf{Area \: = 55 \: {ft}^{2} }}$

Area of a rectangular garden = 55 ft²

Hope I helped!

Best regards! :D

~ $\sf{TheAnimeGirl}$

6 0

3 years ago

What is an equation of the line?

Harman [31]

Your answer is going to be B.y-2=-3/8(x+4)

5 0

3 years ago

3/2000 as a decimal

Anarel [89]

<span>Decimal</span>

<span>
</span>

<span>3/2000 = 0.0015</span>

4 0

3 years ago

A blacksmith blends one alloy of silver that is 35% silver and another that is 95% silver. To the nearest ton, how much of the a

hammer [34]

Answer:

Let x be the unknown quantity of 50% silver.

Look at the silver concentrations... This will be 0.5x of actual silver,

Added to 5% silver in 500g or 0.05(500)g of actual silver

Totaling to (500+x)g of 20% silver which will have 0.2(500+x)g of silver

Your equation is:

0.5x + 0.05(500) = 0.2(500+x)

Solve for x to find the grams of 50% silver used

Step-by-step explanation:

sana maka tulong po sorry po kung mali

5 0

3 years ago