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lutik1710 [3]
3 years ago
9

You’re baking a circular cake for a party. Your cake can be any size you want. What will the radius of your cake be and how many

slices will you be able to cut?

Mathematics
1 answer:
REY [17]3 years ago
7 0
What will the radius of your cake be?

This is a problem of geometry. Given that the cake is circular, the greater the cake the greater the radius of it. So, as shown in the figure 1, the radius will be the distance from the center to any extreme point of the circle.

How many slices will you be able to cut?

The total area of a circle is given by:

A= \pi  r^{2}

We need to fin how many slices will be cut, so let's calculate the area of the circular sector which can be obtained simply applying rule of three, so:

A_{cs}= \pi r^{2}( \frac{\theta}{2\pi})= \frac{r^{2}\theta}{2}

Let's name n the number of slices, if we divide the total area by n this result, each area  must equal, then:

\frac{\pi r^{2}}{n}=\frac{r^{2}\theta}{n}

Finally, we will be able to cut:

n= \frac{2\pi}{\theta} Slices

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Find the equation of the line: parallel to 3x−y=11 through (−2, 0).
stepan [7]

Answer:

I believe it is:

slope-intercept form: y=3x+6

standard form: -3x+y=6 or 3x-y=-6

point slope-form: y-0=3(x+2)

Step-by-step explanation:

First, I put 3x-y=11 into slope-intercept form:

Subtract 3x from both sides: 3x-3x-y=11-3x

That becomes -y=-3x+11

Divide both sides by -1: -y/-1=(-3x+11)/-1

That becomes y=3x-11\

Then, the definition of a parallel line is having the same slope but different y-intercepts, so I dropped the -11 as the y-intercept, and I rewrote the equation as y=3x+b, where b is the y-intercept.

Now, I have to find the y-intercept of the parallel line, so I plug the coordinates (-2,0) into the equation for x and y to solve for the y-intercept

Write the equation out with what you have so far: y=3x+b

Substitute the coordinates (-2,0) in for x and y: 0=3(-2)+b

That becomes 0=-6+b

Add 6 to both sides: 0+6=-6+6+b

That becomes 6=b, which means that 6 is your y-intercept.

Finally, you have gathered everything you need to write the parallel line in equation format.

The parallel line's equation is

in slope-intercept form: y=3x+6

in standard form: -3x+y=6 or 3x-y=-6

in point-slope form: y-0=3(x+2)

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What is x equal to ? 7x+3=2x-4
Amanda [17]
<h3><u>Explanation</u></h3>
  • Solve for x-term by making the x-term as the subject.

7x +3 = 2x - 4 \\ 7x - 2x =  - 4 - 3 \\ 5x =  - 7 \\ x =  \frac{ - 7}{5}  \longrightarrow -  \frac{7}{5}

  • Answer Check by substituting the value of x in the equation.

7 ( -  \frac{7}{5} )+ 3 = 2( -  \frac{7}{5} ) - 4 \\  -  \frac{49}{5}  + 3 =  -  \frac{14}{5}  - 4 \\  -  \frac{49}{5}  +  \frac{15}{5}  =  -  \frac{14}{5}  -  \frac{20}{5}  \\  -  \frac{34}{5}  =  -  \frac{34}{5}

The equation is true for the value of x. Therefore the answer is x = -7/5

<h3><u>Answer</u></h3>

<u>\large \boxed{x =  -  \frac{7}{5} }</u>

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3 years ago
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