Identify the center and radius of a circle with aquation (x+9)^2+(y+6)^2=9

the pitch, or frequency, of a vibrating string varies directly with the square root of the tension. if a string vibrates at a fr

Naily [24]

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\begin{array}{llll}
\stackrel{frequency}{f}\textit{ of a vibrating string varies directly}\\
\qquad \qquad \textit{with the square root of the tension }\stackrel{tension}{t}
\end{array}$

$\bf f=k\sqrt{t}\quad \textit{we also know that }
\begin{cases}
f=300\\
t=8
\end{cases}\implies 300=k\sqrt{8}
\\\\\\
\cfrac{300}{\sqrt{8}}=k\implies \cfrac{300}{\sqrt{2^2\cdot 2}}=k\implies \cfrac{300}{2\sqrt{2}}=k\implies \cfrac{150}{\sqrt{2}}=k
\\\\\\
\textit{and we can \underline{rationalize} it to }\cfrac{150\sqrt{2}}{2}\implies 75\sqrt{2}=k$

$\bf thus\qquad f=\stackrel{k}{75\sqrt{2}}\sqrt{t}\implies \boxed{f=75\sqrt{2t}}\\\\
-------------------------------\\\\
\textit{now, when t = 72, what is \underline{f}?}\qquad f=75\sqrt{2(72)}$

5 0

3 years ago

Read 2 more answers

The number of students in a chess club decreased from 14 to 12. What is the percent decrease? Round your answer to the nearest p

Zolol [24]

Answer:

14.2857% decrease

≈ 14.3% decrease

Step-by-step explanation:

nearest tenths : 14.3%

nearest hundredths : 14.29%

nearest thousandths : 14.286%

I hope my answer is correct, I provided more options because I wasn't sure what nearest percent wanted.

Hope this helps!

8 0

2 years ago

4xsquared - 9=0? could anyone help me solve this quadratic equation by FACTORING?

Verizon [17]

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-------------------------------\\\\
4x^2-9=0\implies 2^2x^2-3^2=0\implies (2x)^2-3^2=0
\\\\\\\
[(2x)-3][(2x)+3]=0\implies 
\begin{cases}
2x-3=0\\
2x=3\\
x=\frac{3}{2}\\
------\\
2x+3=0\\
2x=-3\\
x=-\frac{3}{2}
\end{cases}$

7 0

3 years ago

Which of the following expressions is equal to -4x^2-36

liubo4ka [24]

Answer:

Step-by-step explanation:

-4x^2-36 can be rewritten as -4(x^2 + 9). The quantity in parentheses does not have real roots, but does have the imaginary roots ±3i.

Next time, please share the possible answer choices.

6 0

2 years ago

Which polynomial represents the area of the rectangle? 3x-5= x+1

maxonik [38]

Answer: 3x² - 2x - 5

Step-by-step explanation:

The area of a rectangle is simply length * width. Thus, simply multiply them, and FOIL.

(3x - 5) (x + 1)

3x ^2 + 3x - 5x - 5

Combine like terms

3x² - 2x - 5

Hope it helps :) and let me know if you want me to elaborate.

4 0

2 years ago