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3 years ago

The number of subscribers y to a website after t years is shown by the equation below:

Mathematics

2 answers:

damaskus [11]3 years ago

7 0

Answer: A. It increased by 75% every year.

choli [55]3 years ago

5 0

$\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}
\end{cases}\\\\
-------------------------------\\\\
y=50(1.75)^t\implies 
\begin{array}{llllll}
y=&50(&1+&0.75)&^t\\
\uparrow &\uparrow &&\uparrow &\uparrow \\
A&I&&r&t
\end{array}\qquad \cfrac{r}{100}=0.75
\\\\\\
r=100\cdot 0.75\implies \boxed{r=75\%}$

the amount is a positive "r", rate, thus is a growth equation, so it increased.

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Samir bought 3 pounds of cement to repair the cracks in his sidewalk.Each crack needs to be filled with 2 ounces of cement. Will

drek231 [11]

Answer: He will divide to convert pounds to ounces.

Step-by-step explanation:

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3 years ago

At what point on the curve x^2 + y^2 = 9 is the tangent line vertical?

Gemiola [76]

x² + y² = 9 is the equation of a circle with center (0, 0) and radius 3.

This puts the vertices at (-3, 0), (3, 0), (0, -3), and (0, 3).

When is the tangent line vertical? <em>when it passes through the x-axis.</em>

Answer: (-3, 0), (3, 0)

7 0

2 years ago

Find the x- and y-intercepts of the graph of the given equation.<br> -4x + 3y = -3.6

tino4ka555 [31]

Answer:

x intercept is (0.9,0)

y intercept is (0,-1.2)

Step-by-step explanation:

3 0

3 years ago

What is the volume of the rectangular prism? please answer fast!!

oee [108]

Answer:

360in cubed

Step-by-step explanation:

the formual for the volume is v=(L)(W)(H)

so you substitute the measurements into the formula, so you would have V=(6)(6)(10), now you can either solve this in the calculator or you can solve on paper and do 6 times 6, which equals 36, then multiply 36 by ten, and you will arrive at the answer 360in cubed

8 0

3 years ago

If cos theta= -8/17 and theta is in quadrant 3, what is cos2 theta and tan2 theta

Karo-lina-s [1.5K]

$\bf cos(\theta)=\cfrac{adjacent}{hypotenuse}\qquad 
\begin{array}{llll}
\textit{now, hypotenuse is always positive}\\
\textit{since it's just the radius}
\end{array}
\\\\\\
thus\qquad cos(\theta)=\cfrac{-8}{17}\cfrac{\leftarrow adjacent=a}{\leftarrow hypotenuse=c}$

since the hypotenuse is just the radius unit, is never negative, so the - in front of 8/17 is likely the numerator's, or the adjacent's side

now, let us use the pythagorean theorem, to find the opposite side, or "b"

$\bf c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite
\end{cases}
\\\\\\
\pm\sqrt{17^2-(-8)^2}=b\implies \pm\sqrt{225}=b\implies \pm 15=b$

so... which is it then? +15 or -15? since the root gives us both, well
angle θ, we know is on the 3rd quadrant, on the 3rd quadrant, both, the adjacent(x) and the opposite(y) sides are negative, that means, -15 = b

so, now we know, a = -8, b = -15, and c = 17
let us plug those fellows in the double-angle identities then

$\bf \textit{Double Angle Identities}
\\ \quad \\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\
cos(2\theta)=
\begin{cases}
cos^2(\theta)-sin^2(\theta)\\
\boxed{1-2sin^2(\theta)}\\
2cos^2(\theta)-1
\end{cases}
\\ \quad \\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-----------------------------\\\\
cos(2\theta)=1-2sin^2(\theta)\implies cos(2\theta)=1-2\left( \cfrac{-15}{17} \right)^2
\\\\\\
cos(2\theta)=1-\cfrac{450}{289}\implies cos(2\theta)=-\cfrac{161}{289}$

$\bf tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\implies tan(2\theta)=\cfrac{2\left( \frac{-15}{-8} \right)}{1-\left( \frac{-15}{-8} \right)^2}
\\\\\\
tan(2\theta)=\cfrac{\frac{15}{4}}{1-\frac{225}{64}}\implies tan(2\theta)=\cfrac{\frac{15}{4}}{-\frac{161}{64}}
\\\\\\
tan(2\theta)=\cfrac{15}{4}\cdot \cfrac{-64}{161}\implies tan(2\theta)=-\cfrac{240}{161}$

6 0

3 years ago