Graph this function: y

Lilit [14]

$\bf log_{{ a}}(xy)\implies log_{{ a}}(x)+log_{{ a}}(y)\\\\
and\qquad \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
ln(a+3)+ln(a-3)=ln(16)\implies ln[(a+3)(a-3)]=ln(16)
\\\\\\
ln[a^2-3^2]=ln(16)\impliedby \textit{removing ln() from both sides}
\\\\\\
a^2-9=16\implies a^2=16+9\implies a^2=25
\\\\\\
a=\pm\sqrt{25}\implies a=\pm 5$

7 0

3 years ago

Using sum or difference formulas, find the exact value of sin(165∘)

Nikitich [7]

$\bf \textit{Sum and Difference Identities}
\\ \quad \\
sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})\\\\
-------------------------------\\\\$

$\bf sin(165^o)\implies sin(120^o+45^o)
\\\\\\
sin(120^o)cos(45^o)~+~cos(120^o)sin(45^o)\implies \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}~+~\cfrac{-1}{2}\cdot \cfrac{\sqrt{2}}{2}
\\\\\\
\cfrac{\sqrt{6}}{4}~-~\cfrac{\sqrt{2}}{4}\implies \cfrac{\sqrt{6}-\sqrt{2}}{4}$

6 0

3 years ago

What are the x and y-intercepts of the line described by this equation? -6x+3y=18.9?

Naddika [18.5K]

The "x" intercept is found when you plug in "0" for "y"
-6x + 3(0) = 18.9
-6x = 18.9 (Divide both sides by -6)
x = - 3.15
(-3.15, 0) is your x-intercept

Now plug in "0" for the x
-6(0) + 3y = 18.9
3y = 18.9 (Divide both sides by 3)
y = 6.3
(0, 6.3) is your y - intercept

5 0

4 years ago

The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each f

WITCHER [35]

Answer:

Part 1) $A=36(\pi-2)\ cm^2$