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2 years ago

What is the volume of the composite figure? Express the

Mathematics

2 answers:

Agata [3.3K]2 years ago

5 0

Answer:

312 πmm^2

Step-by-step explanation:

On edg

Papessa [141]2 years ago

3 0

Answer:

$V=312\pi\ mm^{3}$

Step-by-step explanation:

we know that

The volume of the composite figure is equal to the volume of a semi-sphere plus the volume of the cone

$V=\frac{4}{6}\pi r^{3} +\frac{1}{3} \pi r^{2} h$

we have

$r=6\ mm$

$h=14\ mm$

substitute

$V=\frac{4}{6}\pi (6)^{3} +\frac{1}{3} \pi (6)^{2} (14)$

$V=144\pi +168\pi$

$V=312\pi\ mm^{3}$

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write a function g whose graph represents a translation 2 units to the right followed by a horizontal stretch by a factor or 2 o

Alenkinab [10]

$\bf f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}\\\\
f(x)=&{{ A}} \left|{{ B }}x+{{ C}} \right|+{{ D}}
\\\\
--------------------\\\\$

$\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\
\left. \qquad \right. \textit{reflection over the y-axis}$

$\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{ D}}\\
\left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\
\left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}$

with that template in mind, let's see,

$\bf f(x)=|x| \implies \begin{array}{lllccll}
f(x)=&1|&1x&+0|&+0\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

so, to shift it to the right by 2 units, simply set C = 2.
to stretch it by 2, set A = 1/2.

the smaller A is, the wider it opens, the larger it is, the more it shrinks.

5 0

3 years ago

Solve the quadratic equation 3x^2 - 9x + 1 = 0 Give answer to 3 significant figures

Orlov [11]

Answer:

Either, (9+√69)/6 or (9-√69)/6

Step wise:

3x²-9x+1=0-------------------(i)

comparing equation onw with (ax²+bx+c=0), we get,

a=3, b=-9, c=1

now,

using Quadratic Formula,

(-b±√b²-4ac)/2a=x

{-(-9)±√(-9)²-4.3.1}/2.3=x

(9±√81-12)/6=x

(9±√69)/6=x

Taking +(ve) sign Taking -(ve) sign

(9+√69)/6=0 (9-√69)/6=0

∴(9+√69)/6=0 ∴(9-√69)/6=0

[∵They cannot be further solved]

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3 years ago

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Dmitrij [34]

The answer is 78 because when you add all the numbers it equals 780 and you need to divide the end sum by the amount of numbers added to get it. So in the end there were 10 numbers added to equal 780 so 780\10 equals 78

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UNO [17]

Answer:

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Step-by-step explanation: can you elaborate

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