20 points How on Earth do I do this?

Y=f(x)=9x^2+18x Axis= Vertex= Y-intercept = X-intercept=

svet-max [94.6K]

Sent a picture of the solution to the problem (s).

3 0

3 years ago

A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drain

MissTica

Answer:

(a) 60 kg; (b) 21.6 kg; (c) 0 kg/L

Step-by-step explanation:

(a) Initial amount of salt in tank

The tank initially contains 60 kg of salt.

(b) Amount of salt after 4.5 h

$\text{Let A = mass of salt after t min}\\\text{and }r_{i} = \text{rate of salt coming into tank}\\\text{and }r_{0} =\text{rate of salt going out of tank}$

(i) Set up an expression for the rate of change of salt concentration.

$\dfrac{\text{d}A}{\text{d}t} = r_{i} - r_{o}\\\\\text{The fresh water is entering with no salt, so}\\ r_{i} = 0\\r_{o} = \dfrac{\text{3 L}}{\text{1 min}} \times \dfrac {A\text{ kg}}{\text{1000 L}} =\dfrac{3A}{1000}\text{ kg/min}\\\\\dfrac{\text{d}A}{\text{d}t} = -0.003A \text{ kg/min}$

(ii) Integrate the expression

$\dfrac{\text{d}A}{\text{d}t} = -0.003A\\\\\dfrac{\text{d}A}{A} = -0.003\text{d}t\\\\\int \dfrac{\text{d}A}{A} = -\int 0.003\text{d}t\\\\\ln A = -0.003t + C$

(iii) Find the constant of integration

$\ln A = -0.003t + C\\\text{At t = 0, A = 60 kg/1000 L = 0.060 kg/L} \\\ln (0.060) = -0.003\times0 + C\\C = \ln(0.060)$

(iv) Solve for A as a function of time.

$\text{The integrated rate expression is}\\\ln A = -0.003t + \ln(0.060)\\\text{Solve for } A\\A = 0.060e^{-0.003t}$

(v) Calculate the amount of salt after 4.5 h

a. Convert hours to minutes

$\text{Time} = \text{4.5 h} \times \dfrac{\text{60 min}}{\text{1h}} = \text{270 min}$

b.Calculate the concentration

$A = 0.060e^{-0.003t} = 0.060e^{-0.003\times270} = 0.060e^{-0.81} = 0.060 \times 0.445 = \text{0.0267 kg/L}$

c. Calculate the volume

The tank has been filling at 6 L/min and draining at 3 L/min, so it is filling at a net rate of 3 L/min.

The volume added in 4.5 h is

$\text{Volume added} = \text{270 min} \times \dfrac{\text{3 L}}{\text{1 min}} = \text{810 L}$

Total volume in tank = 1000 L + 810 L = 1810 L

d. Calculate the mass of salt in the tank

$\text{Mass of salt in tank } = \text{1810 L} \times \dfrac{\text{0.0267 kg}}{\text{1 L}} = \textbf{21.6 kg}$

(c) Concentration at infinite time

$\text{As t $\longrightarrow \, -\infty,\, e^{-\infty} \longrightarrow \, 0$, so A $\longrightarrow \, 0$.}$

This makes sense, because the salt is continuously being flushed out by the fresh water coming in.

The graph below shows how the concentration of salt varies with time.

3 0

3 years ago

Find each of the numbers below.

iren [92.7K]

Answer:

opposite of -7 is 7 the oppositeof 3 is -3 oppositeof -4 is 4

8 0

3 years ago

A businessperson is charged a $4.96 monthly finance charge on a bill of $283.15.

gladu [14]

Answer:

1.75%

Step-by-step explanation:

The monthly interest rate is the interest amount divided by the base on which it is computed, expressed as a percentage.

$4.96/$283.15 × 100% ≈ 1.75172% ≈ 1.75%

3 0

2 years ago

I REALLY need help with these 3 questions plz!!!!

Tanzania [10]

Answer:

6. No. See explanation below.

7. 18 months

8. 16

Step-by-step explanation:

6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.

Let's find the GCF of 85 and 99:

85 = 5 * 17

99 = 3^2 + 11

5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.

Answer: No because the GCF of 85 and 99 is 1.

7.

We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.

6 = 2 * 3

9 = 3^2

LCM = 2 * 3^2 = 2 * 9 = 18

Answer: 18 months

We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.

Month Charlie Dasha

1 home home

2 home home

3 home home

4 home home

5 home home

6 trip home

7 home home

8 home home

9 home trip

10 home home

11 home home

12 trip home

13 home home

14 home home

15 home home

16 home home

17 home home

18 trip trip

Answer: 18 months

8.

First, we find the prime factorizations of 96 an 80.

96 = 2^5 * 3

80 = 2^4 *5

GCF = 2^4 = 16

Answer: 16

7 0

3 years ago