Answer: Sup. 4x is da slope
Step-by-step explanation: Hope dis helps u bro
slope = y2 -y1 ÷ x2 - x1
slope = -18 - (-2) ÷ -15 - (-11)
slope = -16 ÷ -4
slope = 4x
Salt flows in at a rate of (5 g/L)*(3 L/min) = 15 g/min.
Salt flows out at a rate of (x/10 g/L)*(3 L/min) = 3x/10 g/min.
So the net flow rate of salt, given by
in grams, is governed by the differential equation,
![x'(t)=15-\dfrac{3x(t)}{10}](https://tex.z-dn.net/?f=x%27%28t%29%3D15-%5Cdfrac%7B3x%28t%29%7D%7B10%7D)
which is linear. Move the
term to the right side, then multiply both sides by
:
![e^{3t/10}x'+\dfrac{3e^{t/10}}{10}x=15e^{3t/10}](https://tex.z-dn.net/?f=e%5E%7B3t%2F10%7Dx%27%2B%5Cdfrac%7B3e%5E%7Bt%2F10%7D%7D%7B10%7Dx%3D15e%5E%7B3t%2F10%7D)
![\implies\left(e^{3t/10}x\right)'=15e^{3t/10}](https://tex.z-dn.net/?f=%5Cimplies%5Cleft%28e%5E%7B3t%2F10%7Dx%5Cright%29%27%3D15e%5E%7B3t%2F10%7D)
Integrate both sides, then solve for
:
![e^{3t/10}x=50e^{3t/10}+C](https://tex.z-dn.net/?f=e%5E%7B3t%2F10%7Dx%3D50e%5E%7B3t%2F10%7D%2BC)
![\implies x(t)=50+Ce^{-3t/10}](https://tex.z-dn.net/?f=%5Cimplies%20x%28t%29%3D50%2BCe%5E%7B-3t%2F10%7D)
Since the tank starts with 5 g of salt at time
, we have
![5=50+C\implies C=-45](https://tex.z-dn.net/?f=5%3D50%2BC%5Cimplies%20C%3D-45)
![\implies\boxed{x(t)=50-45e^{-3t/10}}](https://tex.z-dn.net/?f=%5Cimplies%5Cboxed%7Bx%28t%29%3D50-45e%5E%7B-3t%2F10%7D%7D)
The time it takes for the tank to hold 20 g of salt is
such that
![20=50-45e^{-3t/10}\implies t=\dfrac{20}3\ln\dfrac32\approx2.7031\,\mathrm{min}](https://tex.z-dn.net/?f=20%3D50-45e%5E%7B-3t%2F10%7D%5Cimplies%20t%3D%5Cdfrac%7B20%7D3%5Cln%5Cdfrac32%5Capprox2.7031%5C%2C%5Cmathrm%7Bmin%7D)
Hello :),
(a+b)²=a²+2ab+b²
(x+6)²=x²+2× x × 6+6²=x²+12x+36
Answer:
The answer for log(ab²) is x + 2y.
Step-by-step explanation:
You have to apply Logarithm Law,
![log(a) + log(b) \: ⇒ \: log(a \times b)](https://tex.z-dn.net/?f=%20log%28a%29%20%20%2B%20%20%20log%28b%29%20%5C%3A%20%20%E2%87%92%20%5C%3A%20%20log%28a%20%5Ctimes%20b%29%20)
![log( {a}^{n} ) \: ⇒ \: n log(a)](https://tex.z-dn.net/?f=%20log%28%20%7Ba%7D%5E%7Bn%7D%20%29%20%20%5C%3A%20%E2%87%92%20%5C%3A%20n%20log%28a%29%20)
In this question, you have to seperate it out :
![log(a {b}^{2} ) = log(a) + log( {b}^{2} )](https://tex.z-dn.net/?f=%20log%28a%20%7Bb%7D%5E%7B2%7D%20%29%20%20%3D%20%20log%28a%29%20%20%2B%20%20log%28%20%7Bb%7D%5E%7B2%7D%20%29%20)
![log( {b}^{2} ) = 2 log(b)](https://tex.z-dn.net/?f=%20log%28%20%7Bb%7D%5E%7B2%7D%20%29%20%20%3D%202%20log%28b%29%20)
![let \: log(a) = x](https://tex.z-dn.net/?f=let%20%5C%3A%20%20log%28a%29%20%20%3D%20x)
![let log(b) = y](https://tex.z-dn.net/?f=let%20log%28b%29%20%20%3D%20y)
![log(a {b}^{2} ) = log(a) + 2 log(b)](https://tex.z-dn.net/?f=%20log%28a%20%7Bb%7D%5E%7B2%7D%20%29%20%20%3D%20%20log%28a%29%20%20%2B%202%20log%28b%29%20)
![log(a {b}^{2} ) = x + 2y](https://tex.z-dn.net/?f=%20log%28a%20%7Bb%7D%5E%7B2%7D%20%29%20%20%3D%20x%20%2B%202y)
Answer:
72 cm^3
Step-by-step explanation:
find the volume of the big block and the volumem of the smaller block and subtract it
(8 x 2 x 5) - (2 x 2 x2)
= 80 cm^3 - 8 cm^3
= 72cm^3