The answer: 35 pages .
_________________________________________________<span>Explanation:
_____________________________________________________
You would MULTIPLY:
_______________________________
</span> → <span>(5/8) *(56) = (</span>5/8) *(56/1) = ? <span>
_______________________________
</span> → (5/8) *(56/1) = ? ;
<span>_______________________________
</span>→ Cancel the "8" to a "1", and change the "56" to "7" ; since "8*7 =56".
→ Now, rewrite as: 5/1 *7/1 ; = 35/1 = 35; which is the correct answer.
______________________________________________________
Answer: Choice C![a-7 \le 5](https://tex.z-dn.net/?f=a-7%20%5Cle%205)
(a-7 is less than or equal to 5)
and
![a-7 \ge -5](https://tex.z-dn.net/?f=a-7%20%5Cge%20-5)
(a-7 is greater than or equal to -5)
----------------------------------------------------
Explanation:
![|a-7| \le 5](https://tex.z-dn.net/?f=%7Ca-7%7C%20%5Cle%205)
is the same as
![-5 \le a-7 \le 5](https://tex.z-dn.net/?f=-5%20%5Cle%20a-7%20%5Cle%205)
We can use the rule that if
![|x| \le k](https://tex.z-dn.net/?f=%7Cx%7C%20%5Cle%20k)
then
![-k \le x \le k](https://tex.z-dn.net/?f=-k%20%5Cle%20x%20%5Cle%20k)
where k is any positive number
After we get
![-5 \le a-7 \le 5](https://tex.z-dn.net/?f=-5%20%5Cle%20a-7%20%5Cle%205)
, we break it down into two pieces. The first piece is
![-5 \le a-7](https://tex.z-dn.net/?f=-5%20%5Cle%20a-7%20)
while the second piece is
![a-7 \le 5](https://tex.z-dn.net/?f=a-7%20%5Cle%205)
Flip the two sides of
![-5 \le a-7](https://tex.z-dn.net/?f=-5%20%5Cle%20a-7%20)
to get
![a-7 \ge -5](https://tex.z-dn.net/?f=a-7%20%5Cge%20-5)
So we have
![a-7 \le 5](https://tex.z-dn.net/?f=a-7%20%5Cle%205)
and
![a-7 \ge -5](https://tex.z-dn.net/?f=a-7%20%5Cge%20-5)
That's why
the answer is choice CSide Note: we must use the connector "and" instead of "or". Both parts of
![a-7 \le 5](https://tex.z-dn.net/?f=a-7%20%5Cle%205)
and
![a-7 \ge -5](https://tex.z-dn.net/?f=a-7%20%5Cge%20-5)
need to be true, instead of just one part only. This is why we can rule out choice B due to the "or" connector.
The perimeter in this case is:
y + 2x = 5000
The area is:
A = x * y
We rewrite the area:
A = x * (5000-2x)
A = 5000x-2x ^ 2
We derive:
A '= 5000-4x
We equal zero and clear x:
0 = 5000-4x
4x = 5000
x = 5000/4
x = 1250
We look for the other dimension:
y = 5000-2x
y = 5000-2 (1250)
y = 5000-2500
y = 2500
Then, the area will be:
A = (2500) * (1250)
A = 3125000 m ^ 2
Answer:
The largest area that can be enclosed is:
A = 3125000 m ^ 2
Answer:
![r = \dfrac{-3 - \sqrt{57}}{6},\dfrac{-3 + \sqrt{57}}{6}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7B-3%20-%20%5Csqrt%7B57%7D%7D%7B6%7D%2C%5Cdfrac%7B-3%20%2B%20%5Csqrt%7B57%7D%7D%7B6%7D)
Step-by-step explanation:
We are given the following in the question:
![y = e^{rx}](https://tex.z-dn.net/?f=y%20%3D%20e%5E%7Brx%7D)
It is a solution to the differential equation
![3y''+3y'-4y=0](https://tex.z-dn.net/?f=3y%27%27%2B3y%27-4y%3D0)
![y' = \dfrac{dy}{dx} = \dfrac{d(e^{rx})}{dx} = re^{rx}\\\\y'' = \dfrac{d(y')}{dx} = \dfrac{d(re^{rx})}{dx} = r^2e^{rx}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cdfrac%7Bd%28e%5E%7Brx%7D%29%7D%7Bdx%7D%20%3D%20re%5E%7Brx%7D%5C%5C%5C%5Cy%27%27%20%3D%20%5Cdfrac%7Bd%28y%27%29%7D%7Bdx%7D%20%3D%20%5Cdfrac%7Bd%28re%5E%7Brx%7D%29%7D%7Bdx%7D%20%3D%20r%5E2e%5E%7Brx%7D)
Putting the values in the differential equation we get,
![3(r^2e^{rx}) + 3(re^{rx})-4e^{rx} = 0\\(3r^2+3r-4)e^{rx} = 0\\e^{rx}\neq 0\\3r^2+3r-4 = 0\\\\r = \dfrac{-3\pm \sqrt{9-4(3)(-4)}}{6}\\\\r =\dfrac{-3\pm \sqrt{57}}{6}\\\\r =\dfrac{-3 - \sqrt{57}}{6},\dfrac{-3 + \sqrt{57}}{6}](https://tex.z-dn.net/?f=3%28r%5E2e%5E%7Brx%7D%29%20%2B%203%28re%5E%7Brx%7D%29-4e%5E%7Brx%7D%20%3D%200%5C%5C%283r%5E2%2B3r-4%29e%5E%7Brx%7D%20%3D%200%5C%5Ce%5E%7Brx%7D%5Cneq%200%5C%5C3r%5E2%2B3r-4%20%3D%200%5C%5C%5C%5Cr%20%3D%20%5Cdfrac%7B-3%5Cpm%20%5Csqrt%7B9-4%283%29%28-4%29%7D%7D%7B6%7D%5C%5C%5C%5Cr%20%3D%5Cdfrac%7B-3%5Cpm%20%5Csqrt%7B57%7D%7D%7B6%7D%5C%5C%5C%5Cr%20%3D%5Cdfrac%7B-3%20-%20%5Csqrt%7B57%7D%7D%7B6%7D%2C%5Cdfrac%7B-3%20%2B%20%5Csqrt%7B57%7D%7D%7B6%7D)