Select TWO expressions that contain a coefficient of 4.

The number of a particular fish in thousands x years after 1972 can be modeled by f(x)=230(0.886)x. Estimate the year when the n

sashaice [31]

Answer:

The year is 1979.

Step-by-step explanation:

Given:

The function relating fish population and number of years since 1972 is:

$f(x)=230(0.886)^x\\Where,\ f(x)\rightarrow \textrm{fish population}\\x\rightarrow \textrm{number of years passed after 1972}$

Now, when the fish population reaches 99 thousand, it means that $f(x)=99$ . Now, plugging in $f(x)=99$ in the above equation and solving for $x$ . This gives,

$99=230(0.886)^x\\\frac{99}{230}=0.886^x\\\\\textrm{Taking natural log on both sides}\\\ln(0.886)^x=\ln(\frac{99}{230})\\\\\textrm{Using log property: }\log a^b=b\log a\\x\ln (0.886)=\ln(0.43)\\x\times (-0.12)=-0.84\\x=\frac{-0.84}{-0.12}=7\ years$

Therefore, the year after 7 years passed since 1972 is given as:

1972 + 7 = 1979.

So, the year when the number of fish reaches 99 thousand is 1979.

8 0

3 years ago

What type of traingle is a 45-45-90 triangle

Alexxandr [17]

Answer:

isosceles triangle

Step-by-step explanation:

An isosceles triangle has both two equal sides and two equal angles.

8 0

3 years ago

Convert: 6y + y² = x² from rectangular to polar form.

11Alexandr11 [23.1K]

$\bf \textit{Double Angle Identities}
\\ \quad \\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\\\
cos(2\theta)=
\begin{cases}
\boxed{cos^2(\theta)-sin^2(\theta)}\\
1-2sin^2(\theta)\\
2cos^2(\theta)-1
\end{cases}\\\\\\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-------------------------------\\\\$

$\bf 6y+y^2=x^2\implies \cfrac{6y}{x^2}+\cfrac{y^2}{x^2}=1\implies \cfrac{6rsin(\theta )}{[rcos(\theta )]^2}+\cfrac{[rsin(\theta )]^2}{[rcos(\theta )]^2}=1
\\\\\\
\cfrac{6rsin(\theta )}{r^2cos^2(\theta )}+\cfrac{r^2sin^2(\theta )}{r^2cos^2(\theta )}=1\implies 
\cfrac{6sin(\theta )}{rcos^2(\theta )}+\cfrac{sin^2(\theta )}{cos^2(\theta )}=1$

$\bf \cfrac{6sin(\theta )}{rcos^2(\theta )}=1-\cfrac{sin^2(\theta )}{cos^2(\theta )}\implies \cfrac{6sin(\theta )}{1-\frac{sin^2(\theta )}{cos^2(\theta )}}=rcos^2(\theta )
\\\\\\
\cfrac{6sin(\theta )}{cos^2(\theta )\left[ 1-\frac{sin^2(\theta )}{cos^2(\theta )} \right]}=r\implies \cfrac{6sin(\theta )}{cos^2(\theta )-sin^2(\theta )}=r
\\\\\\
\cfrac{6sin(\theta )}{cos(2\theta )}=r$

5 0

3 years ago

I am between 24 and 34 . you say my name when you count by twos from zero. you say my name when you count by fives from zero. wh

jonny [76]

The answer is 30

2 * 15 = 30
5 * 6 = 30
30 is between 24 and 34

4 0

3 years ago

Represent the set of numbers as decimals on the number line {5 3/10, 5 1/10, 5 and if you answer more than needed thank you

Alina [70]

Answer:

(0.53 > 0.51) both less than 1 while 5 is greater than both

Step-by-step explanation:

$\frac{53}{10} = .53, \frac{51}{10} = .51.$ and 5

the number line has two sides, with the left side for negative numbers while the right side is for positive numbers.

-5 -4 -3 -2 -1 -.53 -.51 0 .51 .53 1 2 3 4 5

By studying the number line above all decimal numbers greater than 0 but less than 1 are from 0, .1, .2,.........,.98, .99, 1.00 which is also the same as 1 because all numbers greater than 1 has an invisible point at its right side like 2., 3. which also means 2, 3 while negative number are all less than 0

7 0

3 years ago