Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs 62.5lb//ft^(3). a. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full? b. If the water is pumped to ground level with a (10/11)-horsepower (hp) motor (work output 500ft-lb//sec), how long will it take to empty the tank (to the nearest minute)? c. Show that the pump in part (b) will lower the water level 10ft (halfway) during the first 18 minutes of pumping. d. What are the answers to parts (a) and (b) in a location where water weighs 62.31lb//ft^(3)?62.61lb//ft^(3)? a. Set up an integral to find the work done. W= ◻ How much work does it take to empty the tank? ◻ ◻ b. How long will it take to empty the tank? ◻ minutes (Round to the nearest minute as needed.) c. How much work does it take to lower the water level halfway? ◻ ◻

The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs 62.5lb/ft3 62.5 \mathrm{lb} / \mathrm{ft}^{3} .\newlinea. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full?\newlineb. If the water is pumped to ground level with a (1010/1111)-horsepower (hp) motor (work output 500ft−lb/sec) 500 \mathrm{ft}-\mathrm{lb} / \mathrm{sec}) , how long will it take to empty the tank (to the nearest minute)?\newlinec. Show that the pump in part (b) will lower the water level 10ft 10 \mathrm{ft} (halfway) during the first 1818 minutes of pumping.\newlined. What are the answers to parts (a) and (b) in a location where water weighs 62.31lb/ft3?62.61lb/ft3? 62.31 \mathrm{lb} / \mathrm{ft}^{3} ? 62.61 \mathrm{lb} / \mathrm{ft}^{3} ? \newlinea. Set up an integral to find the work done.\newlineW= \mathrm{W}= \newline□ \square \newlineHow much work does it take to empty the tank?\newline□ \square \newline□ \square \newlineb. How long will it take to empty the tank?\newline□ \square minutes (Round to the nearest minute as needed.)\newlinec. How much work does it take to lower the water level halfway?\newline□ \square \newline□ \square

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve quadratic equations: word problemsright chevron icon

Full solution

Q. The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs 62.5lb/ft3 62.5 \mathrm{lb} / \mathrm{ft}^{3} .\newlinea. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full?\newlineb. If the water is pumped to ground level with a (1010/1111)-horsepower (hp) motor (work output 500ft−lb/sec) 500 \mathrm{ft}-\mathrm{lb} / \mathrm{sec}) , how long will it take to empty the tank (to the nearest minute)?\newlinec. Show that the pump in part (b) will lower the water level 10ft 10 \mathrm{ft} (halfway) during the first 1818 minutes of pumping.\newlined. What are the answers to parts (a) and (b) in a location where water weighs 62.31lb/ft3?62.61lb/ft3? 62.31 \mathrm{lb} / \mathrm{ft}^{3} ? 62.61 \mathrm{lb} / \mathrm{ft}^{3} ? \newlinea. Set up an integral to find the work done.\newlineW= \mathrm{W}= \newline□ \square \newlineHow much work does it take to empty the tank?\newline□ \square \newline□ \square \newlineb. How long will it take to empty the tank?\newline□ \square minutes (Round to the nearest minute as needed.)\newlinec. How much work does it take to lower the water level halfway?\newline□ \square \newline□ \square
  1. Determine Tank Dimensions and Water Weight: Determine the dimensions of the tank and the weight of the water. Assume the tank is a rectangular prism with dimensions 20 ft20 \, \text{ft} (length) ×10 ft\times 10 \, \text{ft} (width) ×20 ft\times 20 \, \text{ft} (depth). The weight of water is given as 62.5 lb/ft362.5 \, \text{lb/ft}^3.
  2. Calculate Volume of Water: Calculate the volume of water in the tank when full. Volume = length×width×depth=20 ft×10 ft×20 ft=4000 ft3\text{length} \times \text{width} \times \text{depth} = 20 \, \text{ft} \times 10 \, \text{ft} \times 20 \, \text{ft} = 4000 \, \text{ft}^3.
  3. Calculate Total Weight of Water: Calculate the total weight of the water in the tank. Total weight =volume×density=4000 ft3×62.5 lb/ft3=250,000 lb.= \text{volume} \times \text{density} = 4000 \, \text{ft}^3 \times 62.5 \, \text{lb/ft}^3 = 250,000 \, \text{lb}.
  4. Set up Integral for Work Done: Set up the integral for work done to pump the water to ground level. Work WW = ∫020(weight of water per layer×distance to pump) dx\int_{0}^{20} (\text{weight of water per layer} \times \text{distance to pump}) \, dx, where xx is the depth from the top.
  5. Simplify Integral: Simplify the integral. Assume each layer of water is 1 ft1 \, \text{ft} thick, so the weight of each layer is 62.5 lb/ft3×200 ft2=12,500 lb62.5 \, \text{lb/ft}^3 \times 200 \, \text{ft}^2 = 12,500 \, \text{lb}. The distance to pump each layer is x ftx \, \text{ft}. W=∫020(12,500 lb×x ft) dxW = \int_{0}^{20} (12,500 \, \text{lb} \times x \, \text{ft}) \, dx.
  6. Calculate Integral: Calculate the integral. W=12,500 lb∫020x dx=12,500 lb×[x22]020=12,500 lb×(200)=2,500,000 ft-lb.W = 12,500 \, \text{lb} \int_{0}^{20} x \, dx = 12,500 \, \text{lb} \times \left[\frac{x^2}{2}\right]_{0}^{20} = 12,500 \, \text{lb} \times (200) = 2,500,000 \, \text{ft-lb}.

More problems from Solve quadratic equations: word problems

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 2 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 2 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 3 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 3 months ago

View all (232)