Answer: ..................................................
Answer:
a.21 b. 1/24
Step-by-step explanation:
a. keep change flip
7/1 × 3/1
21/1
b. keep change flip
1/4 × 1/6
1/24
with speed of 18 feet per second the distance between the twins change.
<u>Step-by-step explanation:</u>
Here we have , Two twins are running away from their mother in opposite directions one with the speed of 10 feet per second and the other with the speed of 8 feet per second. We need to find How and with what speed does the distance between the twins change. Let's find out:
Two twins are running in opposite directions , Let us suppose one twin speed is denoted by
, i.e. 10 feet per second
⇒ ![v_1=10](https://tex.z-dn.net/?f=v_1%3D10)
Now , Speed of other twin is
, i.e. -8 feet per second . Minus sign shows the direction as this twin is moving in opposite direction :
⇒ ![v_2=-8](https://tex.z-dn.net/?f=v_2%3D-8)
Now, Difference in both speeds will give the change in speed between them :
⇒ ![v_1-v_2=10-(-8)](https://tex.z-dn.net/?f=v_1-v_2%3D10-%28-8%29)
⇒ ![v_1-v_2=18](https://tex.z-dn.net/?f=v_1-v_2%3D18)
Therefore , with speed of 18 feet per second the distance between the twins change.
Answer:
1. 1.685
2. 16.828
Step-by-step explanation:
1. log_5 15
To evaluate this logarithm you use the following formula:
![Log_ab=\frac{log_{10}b}{log_{10} a}](https://tex.z-dn.net/?f=Log_ab%3D%5Cfrac%7Blog_%7B10%7Db%7D%7Blog_%7B10%7D%20a%7D)
by replacing you obtain:
![log_5 15=\frac{log_{10} 15}{log_{10}5}=\frac{1.176}{0.698}=1.685](https://tex.z-dn.net/?f=log_5%2015%3D%5Cfrac%7Blog_%7B10%7D%2015%7D%7Blog_%7B10%7D5%7D%3D%5Cfrac%7B1.176%7D%7B0.698%7D%3D1.685)
hence, the answer is 1.685
2. -3ln(1/e4/5)
to solve this logarithm you use the following properties:
![ln(a^m)=m\ ln(a)\\\\ln(\frac{a}{b})=ln(a)-ln(b)\\\\ln(e^m)=m](https://tex.z-dn.net/?f=ln%28a%5Em%29%3Dm%5C%20ln%28a%29%5C%5C%5C%5Cln%28%5Cfrac%7Ba%7D%7Bb%7D%29%3Dln%28a%29-ln%28b%29%5C%5C%5C%5Cln%28e%5Em%29%3Dm)
![ln(1)=0](https://tex.z-dn.net/?f=ln%281%29%3D0)
By applying all these properties you obtain:
![-3ln(\frac{1}{\frac{e^4}{5}})=-3[ln(\frac{1}{e^4})-ln(5)]=-3[ln(1)-ln(e^4)-ln(5)]\\\\-3ln(\frac{1}{\frac{e^4}{5}})=-3[0-4-1.609]=16.828](https://tex.z-dn.net/?f=-3ln%28%5Cfrac%7B1%7D%7B%5Cfrac%7Be%5E4%7D%7B5%7D%7D%29%3D-3%5Bln%28%5Cfrac%7B1%7D%7Be%5E4%7D%29-ln%285%29%5D%3D-3%5Bln%281%29-ln%28e%5E4%29-ln%285%29%5D%5C%5C%5C%5C-3ln%28%5Cfrac%7B1%7D%7B%5Cfrac%7Be%5E4%7D%7B5%7D%7D%29%3D-3%5B0-4-1.609%5D%3D16.828)
hence, the answer is 16.282
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