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Georgia [21]
2 years ago
10

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 isA-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: <u>Quilowatt</u>-<u>hour</u> <u>(kWh)</u> 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

4 0
2 years ago
20.
Alik [6]

Answer:

After 3 seconds

Step-by-step explanation:

Given

h(t) = -16t^2 + 96t

Required

Seconds to attain maximum height

The maximum of a quadratic function y = ax^2 + bx + c is calculated using:

x = -\frac{b}{2a}

So, we have:

t = -\frac{b}{2a}

Where:

a = -16 and b = 96

So:

t = -\frac{96}{2 * -16}

t = -\frac{96}{-32}

Cancel out negatives

t = \frac{96}{32}

t = 3

5 0
2 years ago
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