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:

Creep is the ratio of elongation to original length that occurs in materials over time. For a particular steel structure, for the first 5050 days the creep increases by \newline6×10−66\times10^{-6} per day. After the 5050th day, when the creep is \newline3×10−43\times10^{-4}, the creep triples every 6262 days. After the 236236 th day, how much less would the creep be if it had continued to grow linearly after the 5050 th day?\newlineChoose 11 answer:\newline(A) 1.1×10−31.1 \times10^{-3}\newline(B) 1.4×10−31.4 \times10^{-3}\newline(C) 6.7×10−36.7 \times10^{-3}\newline(D) 8.1×10−38.1 \times10^{-3}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 7right chevron icon
Volume of cubes and rectangular prisms: word problemsright chevron icon

Full solution

Q. Creep is the ratio of elongation to original length that occurs in materials over time. For a particular steel structure, for the first 5050 days the creep increases by \newline6×10−66\times10^{-6} per day. After the 5050th day, when the creep is \newline3×10−43\times10^{-4}, the creep triples every 6262 days. After the 236236 th day, how much less would the creep be if it had continued to grow linearly after the 5050 th day?\newlineChoose 11 answer:\newline(A) 1.1×10−31.1 \times10^{-3}\newline(B) 1.4×10−31.4 \times10^{-3}\newline(C) 6.7×10−36.7 \times10^{-3}\newline(D) 8.1×10−38.1 \times10^{-3}
  1. Calculate Total Creep: First, calculate the total creep after 5050 days due to the linear increase of 6×10−66\times10^{-6} per day.\newlineTotal creep after 5050 days = 5050 days ×\times 6×10−66\times10^{-6} per day
  2. Calculate 6262-Day Periods: Perform the calculation for the total creep after 5050 days.\newlineTotal creep after 5050 days = 50×6×10−6=3×10−450 \times 6\times10^{-6} = 3\times10^{-4}
  3. Calculate Creep After 236236 Days: Now, let's calculate the number of 6262-day periods that occur between the 5050th day and the 236236th day.\newlineNumber of 6262-day periods = (236−50)/62(236 - 50) / 62
  4. Calculate Linear Creep After 236236 Days: Perform the calculation for the number of 6262-day periods.\newlineNumber of 6262-day periods = (236−50)/62=186/62=3(236 - 50) / 62 = 186 / 62 = 3
  5. Find Difference in Creep: Since the creep triples every 6262 days, calculate the creep after the 236236th day.\newlineCreep after 236236 days = 3×10−4×333\times10^{-4} \times 3^3 (because it triples 33 times)
  6. Find Difference in Creep: Since the creep triples every 6262 days, calculate the creep after the 236236th day.\newlineCreep after 236236 days = 3×10−4×333\times10^{-4} \times 3^3 (because it triples 33 times)Perform the calculation for the creep after the 236236th day.\newlineCreep after 236236 days = 3×10−4×33=3×10−4×27=81×10−4=8.1×10−33\times10^{-4} \times 3^3 = 3\times10^{-4} \times 27 = 81\times10^{-4} = 8.1\times10^{-3}
  7. Find Difference in Creep: Since the creep triples every 6262 days, calculate the creep after the 236236th day.\newlineCreep after 236236 days = 3×10−4×333\times10^{-4} \times 3^3 (because it triples 33 times)Perform the calculation for the creep after the 236236th day.\newlineCreep after 236236 days = 3×10−4×33=3×10−4×27=81×10−4=8.1×10−33\times10^{-4} \times 3^3 = 3\times10^{-4} \times 27 = 81\times10^{-4} = 8.1\times10^{-3}Now, calculate the creep after 236236 days if it had continued to grow linearly at the rate of 6×10−66\times10^{-6} per day.\newlineLinear creep after 236236 days = 23623611
  8. Find Difference in Creep: Since the creep triples every 6262 days, calculate the creep after the 236236th day.\newlineCreep after 236236 days = 3×10−4×333\times10^{-4} \times 3^3 (because it triples 33 times)Perform the calculation for the creep after the 236236th day.\newlineCreep after 236236 days = 3×10−4×33=3×10−4×27=81×10−4=8.1×10−33\times10^{-4} \times 3^3 = 3\times10^{-4} \times 27 = 81\times10^{-4} = 8.1\times10^{-3}Now, calculate the creep after 236236 days if it had continued to grow linearly at the rate of 6×10−66\times10^{-6} per day.\newlineLinear creep after 236236 days = 3×10−4+(236−50)×6×10−63\times10^{-4} + (236 - 50) \times 6\times10^{-6}Perform the calculation for the linear creep after 236236 days.\newlineLinear creep after 236236 days = 3×10−4+186×6×10−6=3×10−4+1116×10−6=3×10−4+1.116×10−33\times10^{-4} + 186 \times 6\times10^{-6} = 3\times10^{-4} + 1116\times10^{-6} = 3\times10^{-4} + 1.116\times10^{-3}
  9. Find Difference in Creep: Since the creep triples every 6262 days, calculate the creep after the 236236th day.\newlineCreep after 236236 days = 3×10−4×333\times10^{-4} \times 3^3 (because it triples 33 times)Perform the calculation for the creep after the 236236th day.\newlineCreep after 236236 days = 3×10−4×33=3×10−4×27=81×10−4=8.1×10−33\times10^{-4} \times 3^3 = 3\times10^{-4} \times 27 = 81\times10^{-4} = 8.1\times10^{-3}Now, calculate the creep after 236236 days if it had continued to grow linearly at the rate of 6×10−66\times10^{-6} per day.\newlineLinear creep after 236236 days = 23623611Perform the calculation for the linear creep after 236236 days.\newlineLinear creep after 236236 days = 23623644Combine the terms to find the total linear creep after 236236 days.\newlineLinear creep after 236236 days = $\(3\)\times\(10\)^{\(-4\)} + \(1\).\(116\)\times\(10\)^{\(-3\)} = \(1\).\(416\)\times\(10\)^{\(-3\)}
  10. Find Difference in Creep: Since the creep triples every \(62\) days, calculate the creep after the \(236\)th day.\(\newline\)Creep after \(236\) days = \(3\times10^{-4} \times 3^3\) (because it triples \(3\) times)Perform the calculation for the creep after the \(236\)th day.\(\newline\)Creep after \(236\) days = \(3\times10^{-4} \times 3^3 = 3\times10^{-4} \times 27 = 81\times10^{-4} = 8.1\times10^{-3}\)Now, calculate the creep after \(236\) days if it had continued to grow linearly at the rate of \(6\times10^{-6}\) per day.\(\newline\)Linear creep after \(236\) days = \(236\)\(1\)Perform the calculation for the linear creep after \(236\) days.\(\newline\)Linear creep after \(236\) days = \(236\)\(4\)Combine the terms to find the total linear creep after \(236\) days.\(\newline\)Linear creep after \(236\) days = \(236\)\(7\)Finally, calculate how much less the creep would be if it had continued to grow linearly after the \(236\)\(8\)th day compared to the actual growth.\(\newline\)Difference in creep = Actual creep after \(236\) days - Linear creep after \(236\) days\(\newline\)Difference in creep = \(236\)\(1\)
  11. Find Difference in Creep: Since the creep triples every \(62\) days, calculate the creep after the \(236\)th day.\(\newline\)Creep after \(236\) days = \(3\times10^{-4} \times 3^3\) (because it triples \(3\) times)Perform the calculation for the creep after the \(236\)th day.\(\newline\)Creep after \(236\) days = \(3\times10^{-4} \times 3^3 = 3\times10^{-4} \times 27 = 81\times10^{-4} = 8.1\times10^{-3}\)Now, calculate the creep after \(236\) days if it had continued to grow linearly at the rate of \(6\times10^{-6}\) per day.\(\newline\)Linear creep after \(236\) days = \(3\times10^{-4} + (236 - 50) \times 6\times10^{-6}\)Perform the calculation for the linear creep after \(236\) days.\(\newline\)Linear creep after \(236\) days = \(3\times10^{-4} + 186 \times 6\times10^{-6} = 3\times10^{-4} + 1116\times10^{-6} = 3\times10^{-4} + 1.116\times10^{-3}\)Combine the terms to find the total linear creep after \(236\) days.\(\newline\)Linear creep after \(236\) days = \(3\times10^{-4} + 1.116\times10^{-3} = 1.416\times10^{-3}\)Finally, calculate how much less the creep would be if it had continued to grow linearly after the \(50\)th day compared to the actual growth.\(\newline\)Difference in creep = Actual creep after \(236\) days - Linear creep after \(236\) days\(\newline\)Difference in creep = \(8.1\times10^{-3} - 1.416\times10^{-3}\)Perform the calculation for the difference in creep.\(\newline\)Difference in creep = \(8.1\times10^{-3} - 1.416\times10^{-3} = 6.684\times10^{-3}\)
  12. Find Difference in Creep: Since the creep triples every \(62\) days, calculate the creep after the \(236\)th day.\(\newline\)Creep after \(236\) days = \(3\times10^{-4} \times 3^3\) (because it triples \(3\) times)Perform the calculation for the creep after the \(236\)th day.\(\newline\)Creep after \(236\) days = \(3\times10^{-4} \times 3^3 = 3\times10^{-4} \times 27 = 81\times10^{-4} = 8.1\times10^{-3}\)Now, calculate the creep after \(236\) days if it had continued to grow linearly at the rate of \(6\times10^{-6}\) per day.\(\newline\)Linear creep after \(236\) days = \(236\)\(1\)Perform the calculation for the linear creep after \(236\) days.\(\newline\)Linear creep after \(236\) days = \(236\)\(4\)Combine the terms to find the total linear creep after \(236\) days.\(\newline\)Linear creep after \(236\) days = \(236\)\(7\)Finally, calculate how much less the creep would be if it had continued to grow linearly after the \(236\)\(8\)th day compared to the actual growth.\(\newline\)Difference in creep = Actual creep after \(236\) days - Linear creep after \(236\) days\(\newline\)Difference in creep = \(236\)\(1\)Perform the calculation for the difference in creep.\(\newline\)Difference in creep = \(236\)\(2\)Round the difference in creep to the nearest option provided in the question.\(\newline\)Difference in creep \(236\)\(3\)

More problems from Volume of cubes and rectangular prisms: word problems

Question
A cylindrical soda can has a volume of 108π cm3108\pi\ \text{cm}^{3} and a height of 12cm12\text{cm}. What is the surface area of the soda can in square centimeters?\newlineChoose 11 answer:\newline(A) 18πcm218\pi\text{cm}^{2}\newline(B) 36πcm236\pi\text{cm}^{2}\newline(C) 72πcm272\pi\text{cm}^{2}\newline(D) 90πcm290\pi\text{cm}^{2}
Get tutor helpright-arrow

Posted 8 months ago

Question
A cake pan is in the shape of a right rectangular prism 20 cm20\,\text{cm} long by 20 cm20\,\text{cm} wide by 5 cm5\,\text{cm} high. The pan contains 1,000 cm31,000\,\text{cm}^3 of batter. Approximately how far is the cake batter from the top of the pan?\newline Choose 11 answer:\newline (A) 1 cm1\,\text{cm}\newline (B) 2.5 cm2.5\,\text{cm}\newline (C) 5 cm5\,\text{cm}\newline (D) 7 cm7\,\text{cm}
Get tutor helpright-arrow

Posted 8 months ago

Question
A contractor is to build a new structure at a farm for seed storage. It will have a rectangular base, which is 2020 feet wide by 3535 feet long, with walls of thickness tt feet. The structure is 9090 feet tall. Excluding the volume of the walls, which of the following functions best models the volume, VV, in cubic feet, inside the structure?
Get tutor helpright-arrow

Posted 7 months ago

Question
Rocio drops a ball from a height of 44 meters. Rocio observes that each time the ball bounces, it reaches a peak height which is \newline79%79\% of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height, \newlinehh, in meters, after \newlinebb bounces?\newlineChoose 11 answer:\newline(A) \newlineh=4⋅0.79(b−1)h=4\cdot0.79^{(b-1)}\newline(B) \newlineh=4⋅0.79bh=4\cdot0.79^{b}\newline(C) \newlineh=4−0.79⋅b2h=4-0.79\cdot b^{2}\newline(D) \newlineh=4⋅(1−0.79⋅b2)h=4\cdot(1-0.79\cdot b^{2})
Get tutor helpright-arrow

Posted 8 months ago

Question
Imani's grandmother's house is 55 miles west of her own house down Main Street. While at her grandmother's, Imani decides to ride her bike farther west down Main Street at 1010 miles per hour. Which equation best describes the distance, \newlinedd, in miles, Imani is from home after \newlinett hours?\newlineChoose 11 answer:\newline(A) d=5+10td=5+10t\newline(B) d=5−10td=5-10t\newline(C)d=5t+10d=5t+10\newline(D)d=5t−10d=5t-10
Get tutor helpright-arrow

Posted 8 months ago

Question
A piece of wood has a mass of m1m_1 grams and a volume of V1V_1 cubic centimeters. A second piece of wood has the same density ρ\rho and a volume of V2V_2. What is the mass, in grams, of the second piece of wood?
Get tutor helpright-arrow

Posted 9 months ago

Question
The function models RR, the revenue, in dollars, from selling a particular board game at a price of xx dollars. What is the revenue if the board game is sold at a price of 3030 dollars?\newlineChoose 11 answer:\newline(A) $500,000\$500,000\newline(B) $800,000\$800,000\newline(C) $900,000\$900,000\newline(D) $1,770,000\$1,770,000
Get tutor helpright-arrow

Posted 8 months ago

Question
Rocio drops a ball from a height of 44 meters. Rocio observes that each time the ball bounces, it reaches a peak height which is 79%79\% of the previous peak height, as shown. Which of the following equations correctly models the ball's peak height, hh, in meters, after bb bounces?\newlineChoose 11 answer:\newline(A) h=4⋅0.79(b−1)h=4\cdot0.79^{(b-1)}\newline(B) h=4⋅0.79bh=4\cdot0.79^{b}\newline(C) h=4−0.79⋅b2h=4-0.79\cdot b^{2}\newline(D) h=4⋅(1−0.79⋅b2)h=4\cdot(1-0.79\cdot b^{2})
Get tutor helpright-arrow

Posted 8 months ago

Question
What is the volume, in cubic inches, of a rectangular prism with a height of 77 inches, a width of 55 inches, and a length of 55 inches?\newlineAnswer: V=□ V=\square inches 3 ^{3}
Get tutor helpright-arrow

Posted 8 months ago

Question
A rectangular prism has a length of 22 inches, a height of 1616 inches, and a width of 1515 inches. What is its volume, in cubic inches?\newlineAnswer: V=□ V=\square inches 3 ^{3}
Get tutor helpright-arrow

Posted 8 months ago

View all (47)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant