1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Murljashka [212]
3 years ago
8

At time t=0 hours, a tank contains 3000 litres of water. Water leaks from the tank. At the end of every hour there is x% less wa

ter in the tank than at the start of the hour. The volume of water, in litres, in the tank at time t hours is Vt. Given that Vt=KtV0 V2=2881.2 work out the value of k and the value of x.
Mathematics
1 answer:
Margaret [11]3 years ago
5 0

Answer:

x = 2; K = 0.98

Step-by-step explanation:

At time, t = 0, Volume of Water = 3,000 litres

After t hours , the Volume of water in the tank = Vt

At the end of every hour there is a x% less water in the tank then at the start of the hour

After 1 hour, volume of water left Vt = V1

V1 = 3,000 - 3000 × (x/100)

V1 = 3,000 - 30x

After 2 hours, Volume of water left is V2

V2 = (3,000 - 30 x) - (3,000 - 30 x) × (x/100)

V2 = (3,000 - 30 x) - (3000x - 30x²)/100

V2 = {100(3000 - 30x) - x(3000 - 30x)} /100

V2 = {(3000 - 30x)(100 - x)}/100

Recall, V2 = 2881.2

Therefore

{(3000 - 30x)(100 - x)}/100 = 2881.2

(3000 - 30x)(100 - x) = 288120

300000 - 3000 x - 3000 x + 30 x² = 288120

30 x ² - 6000 x + 11880 = 0

Dividing both sides by 30

x² - 200 x + 396=0

Factorizing:

(x -198)(x-2) = 0

x = 198 or x = 2

Since the percentage by which the water reduces cannot be greater than 100, x = 2 is chosen.

Step 2: Solving for k

Given that Vt=KtV0

K = Vt/V0

At t = 1

V1 = 3000 - 30x

V1 = 3000 - 30 × 2

V1 = 3000 - 60

V1 = 2940

K = 2940/3000

K = 0.98

You might be interested in
On average 83.1% of welds performed by a particular welder are defective. if, in one day, the welder creates three welds. what i
Nuetrik [128]
Let p be 0.831 denote the percentage of defective welds and q be 0.169 denote the percentage of non-defective welds.

Using the binomial distribution, we want all three to be defective.
P(X = 3) = \binom{3}{3}(p)^{3}{q}^{3 - 3}
P(X = 3) = \binom{3}{3}(0.831)^{3}(1)
P(X = 3) = (0.831)^{3} \approx 0.573856191
4 0
3 years ago
⚠️Suppose you have two savings accounts, both with a principal of $200 and an interest rate of 3%, but one earns simple interest
Alika [10]

Answer: 60 I think

Step-by-step explanation: 200 dollar multiply by 0.03 then times 10.

3% is equal to 0.03 and by ten years means to multiply.

8 0
2 years ago
A 6-kilograms<br> bag of potting soil costs $4.08. What is the unit price?
Yanka [14]

Answer:

$0.68 or 68 cents

Step-by-step explanation:

4.08/6 = .68

5 0
2 years ago
Welp❌❌❌❌❗️⭕️welp welp
Harman [31]

Answer:

D

Step-by-step explanation:

:D

8 0
3 years ago
+3=17
aev [14]

Answer:

1

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • What is the arc length of a circle that has a 6-inch radius and a central angle that is 65 degrees? Use 3. 14 for pi and round y
    5·1 answer
  • Find the value of x round to the nearest tenth
    6·1 answer
  • draw a rectangle and another figure that is not a rectangle by tracing lines on a grid paper.describe how to find the perimeter
    15·1 answer
  • Your class built a tepee to use in the school play. The tepee has a diameter of 16 feet and a height of 13.5 feet. What is the v
    15·1 answer
  • Add the rational expressions
    15·1 answer
  • I will give you branilest!
    8·2 answers
  • A ball is thrown in air and it’s height, h(t) in feet, at any time, t in seconds, is represented by the equation h(t) =-t^2+7t.
    6·1 answer
  • Help meh im not smart with 6th grade math
    8·2 answers
  • Find the values of X and Y in the parallelogram.
    6·1 answer
  • Mandy used the input and output in this table to write ratios. She concluded that because they are not all equivalent, this is n
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!