From the moment the friend passes the bicyclist, his friend covers a distance over time t of (3.63 m/s)*t.
The bicyclist covers a distance of 1/2*(2.11 m/s^2)*t^2. They meet when these distances are equal:
3.63 t = 1.055 t^2 ==> 1.055 t^2 - 3.63 t = 0
==> t = 0 s or t = 3.44 s
1] Given that the value of x has been modeled by f(x)=12500(0.87)^x, then:
the rate of change between years 1 and 5 will be:
rate of change is given by:
[f(b)-f(a)]/(b-a)
thus:
f(1)=12500(0.87)^1=10875
f(5)=12500(0.87)^5=6230.3
rate of change will be:
(6230.3-10875)/(5-1)
=-1161.2
rate of change in years 11 to 15 will be:
f(11)=12500(0.87)^11=2701.6
f(15)=12500(0.87)^15=1,547.74
thus the rate of change will be:
(1547.74-2701.6)/(15-11)
=-288
dividing the two rates of change we get:
-288/-1161.2
-=1/4
comparing the two rate of change we conclude that:
The average rate of change between years 11 and 15 is about 1/4 the rate between years 1 and 5.
The answer is D]
2] Given that the population of beavers decreases exponentially at the rate of 7.5% per year, the monthly rate will be:
monthly rate=(n/12)
where n is the number of months
=7.5/12
=0.625
This is approximately equal to 0.65%. The correct answer is A. 0.65%
Answer:
<em>There are 72 crayons in the box</em>
Step-by-step explanation:
<u>Fractions</u>
To solve this problem we'll manage numbers as fractions to keep the precision up to the end of it.
Lynn has a box of crayons. It's given 4/9 of the crayons are blue. The remaining crayons are:
![1-\frac{4}{9}=\frac{5}{9}](https://tex.z-dn.net/?f=1-%5Cfrac%7B4%7D%7B9%7D%3D%5Cfrac%7B5%7D%7B9%7D)
From that portion, 65% are red, or equivalently, 35% are yellow.
We write 35% as a fraction:
![\displaystyle 35\%=\frac{35}{100}=\frac{7}{20}](https://tex.z-dn.net/?f=%5Cdisplaystyle%2035%5C%25%3D%5Cfrac%7B35%7D%7B100%7D%3D%5Cfrac%7B7%7D%7B20%7D)
Thus, the portion of yellow crayons is:
![\displaystyle \frac{7}{20}\cdot \frac{5}{9}=\frac{7}{36}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B7%7D%7B20%7D%5Ccdot%20%5Cfrac%7B5%7D%7B9%7D%3D%5Cfrac%7B7%7D%7B36%7D)
This fraction of x crayons is equal to 14, thus:
![\displaystyle x=\frac{14}{\frac{7}{36}}=14\cdot\frac{36}{7}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B14%7D%7B%5Cfrac%7B7%7D%7B36%7D%7D%3D14%5Ccdot%5Cfrac%7B36%7D%7B7%7D)
x = 72
There are 72 crayons in the box
Reorder 2 cos (2y) and sin (2y)
= sin (2y)(2 cos(2y))
Remove parenthesis
= sin (2y) * 2 cos (2y)
Reorder sin (2y) and 2
= 2 * sin (2y) cos (2y)
Apply the sine double-angle identity
= sin (2(2y))
Now multiply 2 by 2
<u>= sin (4y) </u>
Answer:
Hey :)
Step-by-step explanation:
I dont know how to do emoji on laptop