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3 years ago

A square desktop has an area of 324 square inches. What is the length of one side of the desktop

1 answer:

8 0

Question: The area of a square is 324 square inches. What is the length of one side of the square?
The formula for finding area of squares is:

Length x Width

Squares have 4 sides, and all sides measure the same. If the area is 324 square units, that means the length and width are the same.

x X x=x2

X2=324

x squared(x²) is equal to 324. To find x, you have to do the opposite of squaring, which is finding the square root.

x2= 324 —> square root of 324=x

To find x, you have find the square root of 324.

Square root of 324 is 8

The length of one side is 18 inches
Check:
The formula for finding area is:

Length x Width

The length and width gotten was 18. Put that into the formula:

18 x 18

Multiply:

18 x 18= 324

That means the answer is correct. Your answer is 18 inches.
If you have any questions, feel free to ask in the comments! :)

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How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

$y=-\frac{3}{2}$

3 0

1 year ago

Which number in the monomial 125x^18y^3z^25 needs to be changed to make it a perfect cube

Oksana_A [137]

Hi,

You just have to change z^25 to z^24 or z^27.

$125x^{18}y^3z^{24}=(5x^6*y*z^8)^3$

4 0

3 years ago

Read 2 more answers

PLEASE HELPPPPPP EASY

lianna [129]

The answer to your question is D

5 0

2 years ago

What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3.

Studentka2010 [4]

Hello,

y+2=1/3*(x-1) ==>3y+6=x-1==>x-3y-7=0

Answer C

8 0

3 years ago

Read 2 more answers

3) Solve the problem using your graphing calculator. Round all para meter values to the nearest hundredth.

Mama L [17]

Answer:

mmm, well, not much we can do per se, you'd need to use a calculator.

I'd like to point out you'd need a calculator that has regression features, namely something like a TI83 or TI83+ or higher.

That said, you can find online calculators with "quadratic regression" features, which is what this, all you do is enter the value pairs in it, to get the equation.

Step-by-step explanation:

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2 years ago