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2 years ago

I need help woth question and my test

Mathematics

2 answers:

Maksim231197 [3]2 years ago

8 0

Answer:

28.26 $cm^2$

Step-by-step explanation:

The area of the quarter circle is the area of the circle / 4. Thus, the area is $\frac{\pi r^2}{4}$ = $\frac{3.14*6^2}{4}$ = 28.26 square centimeters

alisha [4.7K]2 years ago

8 0

Answer:

28.26

Step-by-step explanation:

Volume of a Circle = 3.14 * radius * radius

So, Volume of a quarter of a circle = Volume of a circle / 4

---------------------------------------------------------------------

Volume of quarter of circle = (6*6*3.14)/4

= 28.26

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Find the greatest solution for x+y when x^2+y^2 = 7, x^3+y^3=10

damaskus [11]

Answer:

Step-by-step explanation:

set

$f(x,y)=x+y\\$

constrain:

$g(x,y)=x^2+y^2 = 7\\h(x,y)=x^3+y^3=10$

Partial derivatives:

$f_{x}=1\\f_{y} =1 \\g_{x}=2x \\g_{y}=2y\\h_{x}=3x^2 \\h_{y}=3y^2$

Lagrange multiplier:

$grad(f)=a*grad(g)+b*grad(h)\\$

$\left[\begin{array}{ccc}1\\1\end{array}\right]=a\left[\begin{array}{ccc}2x\\2y\end{array}\right]+b\left[\begin{array}{ccc}3x^2\\3y^2\end{array}\right]$

4 equations:

$1=2ax+3bx^2\\1=2ay+3by^2\\x^2+y^2=7\\x^3+y^3=10$

By solving:

$a=4/9\\b=-2/27\\x+y=4$

Second mathod:

Solve for x^2+y^2 = 7, x^3+y^3=10 first:

$x=\frac{1}{2} -\frac{\sqrt{13}}{2} \ or \ y=\frac{1}{2} +\frac{\sqrt{13}}{2} \\x=\frac{1}{2} +\frac{\sqrt{13}}{2} \ or \ y=\frac{1}{2} -\frac{\sqrt{13}}{2} \\x+y=-5\ or\ 1 \or\ 4$

The maximum is 4

6 0

2 years ago

A school gym has an area of 2400 square feet. For a pep rally there are 700 people in the gym. How many square feet are availabl

Fantom [35]

All we need to do is 2400/700 = 3.43 (rounded) square ft. per person

8 0

2 years ago

Read 2 more answers

Is -28 greater than or less than -162

vivado [14]

Answer:

Any number which is on left side on the line number is less than the number which is on right hand side relative to that number.

As -28 is on the right hand side of the line number, and -162 is heading towards left hand side relative to -28.

Therefore, -28 is greater than -162.

Step-by-step explanation:

To determine:

Is -28 greater than or less than -162?

Solution Steps:

In mathematics, a number line is considered to be a straight line with numbers placed at equal intervals along its length.

A number line could be extended infinitely in any direction i..e -∞ to +∞.

A number is usually represented horizontally.

Any number which is on left side on the line number is less than the number which is on right hand side relative to that number.

As -28 is on the right hand side of the line number, and -162 is heading towards left hand side relative to -28.

Therefore, -28 is greater than -162.

In other words,

$-28>-162\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$