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3 years ago

Explain how to use a basic fact and a pattern to find 6 ✖ 100

Mathematics

2 answers:

PtichkaEL [24]3 years ago

7 0

Ummm....did you mean like what is the answer to 6x100?

Umnica [9.8K]3 years ago

3 0

A basic fact is 6x1, which everyone knows is 6. Because 6x1=6, we can use a pattern of either counting by six 100 times, or adding two zeroes at the end, which is the "zero trick".
Another example of the zero trick is 70x100, because all you have to do is 7x1=7 and then add the three zeroes at the end, which gets you 7,000.

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A cylinder’s volume must be 850 cubic feet while the radius of the cylinder cannot exceed 6 feet. What is the smallest possible

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3 years ago

In RST, R = 23* and S = 136*. Which list has the sides of RST in order from shortest to longest?

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RS,ST,TR IS THE ANSWER

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3 years ago

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Delphine has to place 64 bottles of water on a banquet table. it must have a way to fill a rectangular. what are the possible ar

tangare [24]

Answer:

Since $64= 2^6$ , you have the following arrangements.

Optional: $64 \times 1$ (and it's mirror version $1 \times 64$ , if you want to consider a long strip of bottles a rectangle. Technically it is, but it's open to interpretation.

$32 \times 2$ and it's mirror $2 \times 32$ ;

$16 \times 4$ and it's mirror $4 \times 16$ ;

Optional: $8 \times 8$ . Since a square is a rectangle with extra limitations.

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2 years ago

Given the circle with the equation (x + 1)2 + y2 = 36, determine the location of each point with respect to the graph of the cir

kati45 [8]

$\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad 
radius=\stackrel{}{ r}\\\\
-------------------------------\\\\
(x+1)^2+y^2=36\implies [x-(\stackrel{h}{-1})]^2+[y-\stackrel{k}{0}]^2=\stackrel{r}{6^2}~~~~
\begin{cases}
\stackrel{center}{(-1,0)}\\
\stackrel{radius}{6}
\end{cases}$

so, that's the equation of the circle, and that's its center, any point "ON" the circle, namely on its circumference, will have a distance to the center of 6 units, since that's the radius.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{1})\qquad \qquad 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(1-0)^2}\implies d=\sqrt{(-1+1)^2+1^2}
\\\\\\
d=\sqrt{0+1}\implies d=1$

well, the distance from the center to A is 1, namely is "inside the circle".

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6})\\\\\\
\stackrel{distance}{d}=\sqrt{[-1-(-1)]^2+(6-0)^2}\implies d=\sqrt{(-1+1)^2+6^2}
\\\\\\
d=\sqrt{0+36}\implies d=6$

notice, the distance to B is exactly 6, and you know what that means.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
(\stackrel{x_1}{-1}~,~\stackrel{y_1}{0})\qquad 
C(\stackrel{x_2}{4}~,~\stackrel{y_2}{-8})
\\\\\\
\stackrel{distance}{d}=\sqrt{[4-(-1)]^2+[-8-0]^2}\implies d=\sqrt{(4+1)^2+(-8)^2}
\\\\\\
d=\sqrt{25+64}\implies d=\sqrt{89}\implies d\approx 9.43398$

notice, C is farther than the radius 6, meaning is outside the circle, hiking about on the plane.

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3 years ago

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Rama09 [41]

Standard form is just another way of saying "how to write a number in a regular form".

Ex. Standard form is any number.

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3 years ago