Step-by-step explanation:
Solution
(s) = 100m
(t) = 72.54s
(v) = ??
We have,
v = s÷t
v = 100 ÷ 72.54
v = 1.37 m/s
Hence, the velocity of the swimmer is 1.37 m/s
[this is how I personally have to do it but not sure about you]
Answer:
a) 0.2098
b) 0.036
c) 0.1866
d) 0.9849
Step-by-step explanation:
Image is color coordinated for each part below,
Learn more about Probability here: brainly.com/question/13604758
Answers: 16 states and ![\frac{16}{50}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B50%7D)
Explanation:
Question A involves finding the number of states that do not have a store operated by company A. This can be easily found by subtracting the number of states where the company operates stores, which is 34 states, from the total of states, which is 50.
50 - 34 = 16
This means 16 states do not have a store operated by this company
Question B involves writing a fraction to represent the number of states that do not have a store operated by the company. A fraction includes a numerator (top number) that represents the parts selected (number of states without a store: 16), and a denominator, which is the total of parts (total of states: 50). Thus, the fraction is
. Moreover, this can be simplified as
by dividing both numbers by the seame number (2).
a) If the motorcycle starts from rest, then we have an initial speed equal to zero (V0 = 0), with this we can choose a formula that does not contain the initial speed, now we also know that what it asks us is the time that it takes a certain speed to pass, so the formula we will use will be:
![\bf{\displaystyle d=\frac{a{{t}^{2}}}{2}}](https://tex.z-dn.net/?f=%5Cbf%7B%5Cdisplaystyle%20d%3D%5Cfrac%7Ba%7B%7Bt%7D%5E%7B2%7D%7D%7D%7B2%7D%7D)
Clearing "t"
![\boldsymbol{\sf{t=\sqrt{\dfrac{2d}{a} } } }](https://tex.z-dn.net/?f=%5Cboldsymbol%7B%5Csf%7Bt%3D%5Csqrt%7B%5Cdfrac%7B2d%7D%7Ba%7D%20%20%7D%20%20%7D%20%7D)
The distance is in Kilometers, we first need to pass this distance in meters, so we'll need to do our conversion:
![\boldsymbol{\sf{1.6\not{km}*\dfrac{1000 \ m}{1\not{km}}=1600 \ m } }](https://tex.z-dn.net/?f=%5Cboldsymbol%7B%5Csf%7B1.6%5Cnot%7Bkm%7D%2A%5Cdfrac%7B1000%20%5C%20m%7D%7B1%5Cnot%7Bkm%7D%7D%3D1600%20%5C%20m%20%20%7D%20%7D)
1.6 km = 1600m
Substituting our data into the formula:
![\boldsymbol{\sf{t=\sqrt{\dfrac{2d}{a} }=\sqrt{\dfrac{2(1600 \ m) }{9.45 \ \frac{m}{s^2} } }=84.32 \ s } }](https://tex.z-dn.net/?f=%5Cboldsymbol%7B%5Csf%7Bt%3D%5Csqrt%7B%5Cdfrac%7B2d%7D%7Ba%7D%20%20%7D%3D%5Csqrt%7B%5Cdfrac%7B2%281600%20%5C%20m%29%20%7D%7B9.45%20%5C%20%5Cfrac%7Bm%7D%7Bs%5E2%7D%20%20%7D%20%20%7D%3D84.32%20%5C%20s%20%20%20%7D%20%7D)
So the motorcycle will take 84.32 seconds to travel 1600 meters.
b) Since we are asked to obtain the speed in the time it took for the 1600 meters, we are going to use the following formula.
![\boldsymbol{\sf{V_{f}=at }}](https://tex.z-dn.net/?f=%5Cboldsymbol%7B%5Csf%7BV_%7Bf%7D%3Dat%20%7D%7D)
Substituting our data:
![\boldsymbol{\sf{V_{f}=at=\left(0.45 \ \dfrac{m}{\not{s^{2}} }\right)(84.23 \ s)=37.94 \ \dfrac{m}{s} }}](https://tex.z-dn.net/?f=%5Cboldsymbol%7B%5Csf%7BV_%7Bf%7D%3Dat%3D%5Cleft%280.45%20%5C%20%5Cdfrac%7Bm%7D%7B%5Cnot%7Bs%5E%7B2%7D%7D%20%7D%5Cright%29%2884.23%20%5C%20s%29%3D37.94%20%5C%20%5Cdfrac%7Bm%7D%7Bs%7D%20%20%20%7D%7D)
In order to express the final result of the speed, in terms of km/h, we would only apply the conversion factors.
![\boldsymbol{\sf{V_{f}=37.94\dfrac{\not{m}}{\not{s}}*\dfrac{1 \ km}{1000\not{m}}*\dfrac{3600\not{s}}{1 \ h}=136.58 \ \dfrac{km}{h} }}](https://tex.z-dn.net/?f=%5Cboldsymbol%7B%5Csf%7BV_%7Bf%7D%3D37.94%5Cdfrac%7B%5Cnot%7Bm%7D%7D%7B%5Cnot%7Bs%7D%7D%2A%5Cdfrac%7B1%20%5C%20km%7D%7B1000%5Cnot%7Bm%7D%7D%2A%5Cdfrac%7B3600%5Cnot%7Bs%7D%7D%7B1%20%5C%20h%7D%3D136.58%20%5C%20%5Cdfrac%7Bkm%7D%7Bh%7D%20%20%20%20%20%7D%7D)
Answer:
3.2
Step-by-step explanation:
x² + xy = 20
Take the derivative with respect to time:
2x dx/dt + x dy/dt + y dx/dt = 20
(2x + y) dx/dt + x dy/dt = 20
Given x = -5, y = 1, and dx/dt = -4:
(2(-5) + 1) (-4) + (-5) dy/dt = 20
(-10 + 1) (-4) − 5 dy/dt = 20
36 − 5 dy/dt = 20
5 dy/dt = 16
dy/dt = 3.2