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2 years ago

Explain how Cavalieri’s principle can be used to find the volume of any solid.

Mathematics

1 answer:

Kruka [31]2 years ago

8 0

Answer:

Cavalier's principle can be used to find the volume of any solid.

Step-by-step explanation:

Cavalier's Principle:

Cavalier introduced parallel planes and area to describe the relationship between solids.
Cavalier stated if two solids have the same height and equal areas of the base everywhere along the height then the solids have the same volume.

Suppose two regions are included between two parallel planes.
If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.
The formula for the volume of a prism is the area of the base times the height.

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Aryana wants to invest $43,000. She has two options. Option A gives her 6% compounded quarterly. Option B gives her 6% simple in

solmaris [256]

Answer:

Option A earns higher interest($84115.58)

the difference in interest between the two option is $197.9

Step-by-step explanation:

In the problem we are going to apply both the simple interest formula and compound interest formula and compare which has the best/higher returns

Given data

Principal P= $43,000

Rate r= 6%= 0.06

time t= 3years

n= 4 (applicable for compound interest compounded quarterly)

solving for option A gives her 6% compounded quarterly

the compound interest formula is

$A= P(1+\frac{r}{n} )^n^t\\A= 43000(1+\frac{0.06}{4} )^{4} ^*^3$

$A=43000(1+0.015)^{12} \\A=43000(1.015)^{12} \\A=43000*1.1956\\A= 51411.58$

Interest is $A-P= 51411.58-43000= 8411.58$ =$8411.58

solving for option B which gives her 6% simple interest annually

the simple interest formula is

$A=P(1+r)^{t} \\A=43000(1+0.06)^3\\A=43000(1.06)^3\\A=43000*1.191\\A= 51213.68$

Interest is $A-P=51213.68-43000= 8213.68$ = $8213.68

calculating the diference in interest between the two options we have

$8411.58-8213.68= 197.9$ = $197.9

Option A earns higher interest

8 0

3 years ago

There are 159 students to be grouped in math teams. Each team is to have the same number of students. Can each team have 3, 4, 5

Irina-Kira [14]

Answer:

3 students for each team

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

An Air Conditioner uses 850 Watts of electricity and local emissions from electricity produce 1.37 pounds of CO2 per kWh. If you

Zina [86]

Answer: 6,987,000 pounds fo CO₂ per kWh.

Step-by-step explanation: Quilowatt-hour (kWh) is a unit of energy that measures the amount of energy expended in 1 hour.

The AC uses 850 Watts, which in kW is 850,000 kW

If you leave the AC on for 6 hours, it will consume

850,000(6) = 5,100,000 kWh

Eletricity produces 1.37 pounds of CO₂ per kWh, then in 5,100,000 kWh:

1.37 $\frac{pounds}{kWh}$ .(5,100,000kWh) = 6,987,000 pounds

If you open a window for 6 hours, you would keep 6,987,000 pounds of CO₂ for entering the atmosphere.

7 0

2 years ago

A business was valued at £80000 at the start of 2013. In 5 years the value of this business raised to £95000. this is equivalent

Yuri [45]

the yearly increase of x% assumes is compounding yearly, so let's use that.

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\£95000\\ P=\textit{original amount deposited}\dotfill &\£80000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases}$

$95000=80000\left(1+\frac{~~ \frac{r}{100}~~}{1}\right)^{1\cdot 5}\implies \cfrac{95000}{80000}=\left( 1+\cfrac{r}{100} \right)^5 \\\\\\ \cfrac{19}{16}=\left( 1+\cfrac{r}{100} \right)^5\implies \sqrt[5]{\cfrac{19}{16}}=1+\cfrac{r}{100}\implies \sqrt[5]{\cfrac{19}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[5]{\cfrac{19}{16}}=100+r\implies 100\sqrt[5]{\cfrac{19}{16}}-100=r\implies 3.5\approx r$