The point (-1, -4) lies in the third quadrant
Answer:
$32.55
Step-by-step explanation:
The value of the expression is 98x
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}](https://tex.z-dn.net/?f=f%28x%29%3D230%280.886%29%5Ex%5C%5CWhere%2C%5C%20f%28x%29%5Crightarrow%20%5Ctextrm%7Bfish%20population%7D%5C%5Cx%5Crightarrow%20%5Ctextrm%7Bnumber%20of%20years%20passed%20after%201972%7D)
Now, when the fish population reaches 99 thousand, it means that
. Now, plugging in
in the above equation and solving for
. 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](https://tex.z-dn.net/?f=99%3D230%280.886%29%5Ex%5C%5C%5Cfrac%7B99%7D%7B230%7D%3D0.886%5Ex%5C%5C%5C%5C%5Ctextrm%7BTaking%20natural%20log%20on%20both%20sides%7D%5C%5C%5Cln%280.886%29%5Ex%3D%5Cln%28%5Cfrac%7B99%7D%7B230%7D%29%5C%5C%5C%5C%5Ctextrm%7BUsing%20log%20property%3A%20%7D%5Clog%20a%5Eb%3Db%5Clog%20a%5C%5Cx%5Cln%20%280.886%29%3D%5Cln%280.43%29%5C%5Cx%5Ctimes%20%28-0.12%29%3D-0.84%5C%5Cx%3D%5Cfrac%7B-0.84%7D%7B-0.12%7D%3D7%5C%20years)
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.
When two secant lines intersect each other outside a circle, the products of their segments are equal.
14(с + 14) = 10(10 + 20)
14с + 196 = 10 * 30
14с +196 = 300
14с = 300 - 196
14с = 104
с = 104/14
с ≈ 7.4