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3 years ago

Write the expression a2b3c2d in expanded form.

Mathematics

1 answer:

Zanzabum3 years ago

8 0

Answer:

a*2+b*2+c*2+d

Step-by-step explanation:

If i's meant to be Pythagorean theorem, a*a+b*b=c*c

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For the function given state the period f(t) =6sin(3t-pi/6)-1

lapo4ka [179]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\
% function transformations for trigonometric functions
\begin{array}{rllll}
% left side templates
f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}}
\\\\
f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\
f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}}

\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks}\\
\quad \textit{horizontally by amplitude } |{{ A}}|\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{function period or frequency}\\
\qquad \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\
\qquad \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)
\end{array}$

now, with that template in mind, let's take a peek at yours

$\bf \begin{array}{lllcclll}
f(t)=&6sin(&3t&-\frac{\pi }{6})&-1\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}\\\\
-----------------------------\\\\
period\qquad \cfrac{2\pi }{B}\iff\cfrac{2\pi }{3}$

8 0

3 years ago

The intercepts of the circle (x-1)^2 + (y-2)^2 = 10 are ?

IRISSAK [1]

y-intercept: Let x = 0 and solve for y:

(x-1)^2 + (y-2)^2 = 10 => (-1)^2 + y^2 - 4y + 4) = 10

=> 1 + y^2 - 4y + 4 = 10, or y^2 - 4y -5 = 0

The solutions of this quadratic are y = 5 and y = -1.

Thus, the y-intercepts are (0, 5) and (0, -1).

Now find the x-intercepts: Let y = 0 and solve the resulting equation for x:

(x-1)^2 = 10 - (-2)^2, or (x-1)^2 = 10 - 4 = 6.

Taking the sqrt of both sides, x - 1 = plus or minus sqrt(6), or:

x = 1 +√6 and x = 1 - √6, so that the x-intercepts

are (1+√6, 0) and (1-√6, 0).

8 0

4 years ago

Slope of (17,11)(5,0)

stepladder [879]

Hello from MrBillDoesMath!

Answer:

m = 11/12

Discussion:

Slope of line = m = (change in y) / (change in x)

= ( 11 - 0) / (17-5)

= 11/12

Thank you,

MrB

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4 years ago

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What is 7/10 as a decimal and a percent?

AlekseyPX

7 / 10 = 0.70 = 70%

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4 years ago

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Scientific notation<br> 54,268.8

stealth61 [152]

5.4 x 10^4... Hope this helped!

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3 years ago