Answer:
The expression 3p⁵ ₓ 8p³ / 2p can be simplified to 12p⁷.
Step-by-step explanation:
To simplify:
3p⁵ ₓ 8p³ / 2p
= (3 ₓ 8)(p⁵ ₓ p³) / 2p
= 24p⁸ / 2p
= 12p⁷
Answer:
$26
Step-by-step explanation:
To find your answer, simply plug in Francesca's time and Phil's time to your cost equation.
Francesca can be represented by the following equation:
![c=6.5(2)\\c=13](https://tex.z-dn.net/?f=c%3D6.5%282%29%5C%5Cc%3D13)
Phil can be represented by the following equation:
![c=6.5(6)\\c=39](https://tex.z-dn.net/?f=c%3D6.5%286%29%5C%5Cc%3D39)
As such, Francesca pays $13 and Phil pays $39. Next, since you want to find how much more Phil paid, all you have to do is subtract 13 from 39. That will give you $26.
Answer:
a)
, b)
, c)
, d) ![\Delta U_{k} = 4.5\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%204.5%5C%2CJ)
Step-by-step explanation:
a) The spring constant is calculated by using this expression:
![k = \frac{F}{x}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7BF%7D%7Bx%7D)
![k = \frac{30\,N}{0.1\,m}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B30%5C%2CN%7D%7B0.1%5C%2Cm%7D)
![k = 300\,\frac{N}{m}](https://tex.z-dn.net/?f=k%20%3D%20300%5C%2C%5Cfrac%7BN%7D%7Bm%7D)
b) The work needed to compress the spring from its initial position is:
![\Delta U_{k} = \frac{1}{2}\cdot k \cdot (x_{f}^{2}-x_{o}^{2})](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20k%20%5Ccdot%20%28x_%7Bf%7D%5E%7B2%7D-x_%7Bo%7D%5E%7B2%7D%29)
![\Delta U_{k} = \frac{1}{2}\cdot (300\,\frac{N}{m} )\cdot [(-0.3\,m)^{2}-(0\,m)^{2}]](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%28300%5C%2C%5Cfrac%7BN%7D%7Bm%7D%20%29%5Ccdot%20%5B%28-0.3%5C%2Cm%29%5E%7B2%7D-%280%5C%2Cm%29%5E%7B2%7D%5D)
![\Delta U_{k} = 13.5\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%2013.5%5C%2CJ)
c) The work needed to stretch the spring is:
![\Delta U_{k} = \frac{1}{2}\cdot (300\,\frac{N}{m} )\cdot [(0.2\,m)^{2}-(0\,m)^{2}]](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%28300%5C%2C%5Cfrac%7BN%7D%7Bm%7D%20%29%5Ccdot%20%5B%280.2%5C%2Cm%29%5E%7B2%7D-%280%5C%2Cm%29%5E%7B2%7D%5D)
![\Delta U_{k} = 6\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%206%5C%2CJ)
d) The work need to stretch the spring is:
![\Delta U_{k} = \frac{1}{2}\cdot (300\,\frac{N}{m} )\cdot [(0.2\,m)^{2}-(0.1\,m)^{2}]](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%28300%5C%2C%5Cfrac%7BN%7D%7Bm%7D%20%29%5Ccdot%20%5B%280.2%5C%2Cm%29%5E%7B2%7D-%280.1%5C%2Cm%29%5E%7B2%7D%5D)
![\Delta U_{k} = 4.5\,J](https://tex.z-dn.net/?f=%5CDelta%20U_%7Bk%7D%20%3D%204.5%5C%2CJ)
Answer: The answer is everytime you mutiply in by 0.6
Step-by-step explanation:
The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the number of hamburger sold and y represent the number of cheeseburgers sold, hence:
x + y = 460 (1)
Also:
y = 3x (2)
From both equations:
x = 115, y = 345
The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.
Find out more on equation at: brainly.com/question/2972832
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