Answer is 426,700
Because the tens place is 4 and unless it’s 5 or above the hundreds place doesn’t go up (hopefully that makes sense)
Answer:
<em>The set of solutions will change</em>
<em>Observe the image attached</em>
Step-by-step explanation:
We have the following compound inequality
and ![x](https://tex.z-dn.net/?f=x%20%3C3)
This can be written as:
![-3](https://tex.z-dn.net/?f=-3%20%3Cx%20%3C3)
The expression "and" in this context means that the values of x must be greater than -3 and <em>at the same time</em> they must be less than 3.
Then the set of solution is given by <em>the intersection</em> of both inequalities: the interval (-3, 3)
If we change the expression "and" by the expression "or" then it is no longer necessary for both inequalities to be fulfilled at the same time. That is, x will be greater than -3 or less than 3. The set of solutions will be<em> the union</em> of both inequalities.
Therefore <em>the set of solutions will change</em> and it will be
x ∈ (-∞, 3) U (-3, ∞)
x ∈ (-∞, ∞)
Answer:
A and C
Step-by-step explanation:
A) y = (1/2)x + 2 {Compare with y =mx +b}
slope = (1/2)
C) y = -2x + 4
Slope = -2
![\dfrac{1}{2}*-2 = -1](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%2A-2%20%20%3D%20-1)
When product of two slopes is (-1), then the lines are perpendicular.
Answer:
![32.10\ \text{mph}](https://tex.z-dn.net/?f=32.10%5C%20%5Ctext%7Bmph%7D)
Step-by-step explanation:
Distance traveled by A in 4 hours = ![24\times 4=96\ \text{mi}=a](https://tex.z-dn.net/?f=24%5Ctimes%204%3D96%5C%20%5Ctext%7Bmi%7D%3Da)
Distance traveled by B in 4 hours = ![22\times 4=88\ \text{mi}=b](https://tex.z-dn.net/?f=22%5Ctimes%204%3D88%5C%20%5Ctext%7Bmi%7D%3Db)
Total distance between A and the initial point of B is ![40+96=136\ \text{mi}](https://tex.z-dn.net/?f=40%2B96%3D136%5C%20%5Ctext%7Bmi%7D)
Distance between A and B 4 hours later
![c=\sqrt{136^2+88^2}\ \text{mi}](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B136%5E2%2B88%5E2%7D%5C%20%5Ctext%7Bmi%7D)
From Pythagoras theorem we have
![(a+40)^2+b^2=c^2](https://tex.z-dn.net/?f=%28a%2B40%29%5E2%2Bb%5E2%3Dc%5E2)
Differentiating with respect to time we get
![2(a+40)\dfrac{da}{dt}+2b\dfrac{db}{dt}=2c\dfrac{dc}{dt}\\\Rightarrow (a+40)\dfrac{da}{dt}+b\dfrac{db}{dt}=c\dfrac{dc}{dt}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{(a+40)\dfrac{da}{dt}+b\dfrac{db}{dt}}{c}\\\Rightarrow \dfrac{dc}{dt}=\dfrac{(96+40)\times24+88\times 22}{\sqrt{136^2+88^2}}\\\Rightarrow \dfrac{dc}{dt}=32.10\ \text{mph}](https://tex.z-dn.net/?f=2%28a%2B40%29%5Cdfrac%7Bda%7D%7Bdt%7D%2B2b%5Cdfrac%7Bdb%7D%7Bdt%7D%3D2c%5Cdfrac%7Bdc%7D%7Bdt%7D%5C%5C%5CRightarrow%20%28a%2B40%29%5Cdfrac%7Bda%7D%7Bdt%7D%2Bb%5Cdfrac%7Bdb%7D%7Bdt%7D%3Dc%5Cdfrac%7Bdc%7D%7Bdt%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bdc%7D%7Bdt%7D%3D%5Cdfrac%7B%28a%2B40%29%5Cdfrac%7Bda%7D%7Bdt%7D%2Bb%5Cdfrac%7Bdb%7D%7Bdt%7D%7D%7Bc%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bdc%7D%7Bdt%7D%3D%5Cdfrac%7B%2896%2B40%29%5Ctimes24%2B88%5Ctimes%2022%7D%7B%5Csqrt%7B136%5E2%2B88%5E2%7D%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bdc%7D%7Bdt%7D%3D32.10%5C%20%5Ctext%7Bmph%7D)
So, the the distance between the ships at 4 PM is changing at ![32.10\ \text{mph}](https://tex.z-dn.net/?f=32.10%5C%20%5Ctext%7Bmph%7D)
Answer:
the answer is c and d
Step-by-step explanation:
C and D