Questions on Word Problems: Geometry answered by real tutors!

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Question 1202178: construction crew wants to hoist a heavy beam so that it is standing up straight. They
tie a rope to the beam, secure the base, and pull the rope through a pulley to raise one end
A of the beam from the ground. When the beam makes an angle of 40o with the ground, the
top of the beam is 8 ft above the ground.
The construction site has some telephone wires crossing it.. The workers are concerned
that the beam may hit the wires. When the beam makes an angle of 60o with the ground,
the wires are 2 ft above the top of the beam. Will the beam clear the wires on its way to
standing up straight? Explain your answer
Thank you

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Question 1202452: Twenty four students
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Question 1202453: nyard and Barley's circus is in town, and Lorena is going with her father. When Lorena and her father arrive at the performance, they can choose from six entrances to the ground floorof the main arena. There are two stairways and one elevator that go to the balcony. How many different paths can Lorena and her father take from outside the arena to the balcony?
Click here to see answer by ikleyn(52780) About Me 
Question 1202453: nyard and Barley's circus is in town, and Lorena is going with her father. When Lorena and her father arrive at the performance, they can choose from six entrances to the ground floorof the main arena. There are two stairways and one elevator that go to the balcony. How many different paths can Lorena and her father take from outside the arena to the balcony?
Click here to see answer by greenestamps(13200) About Me 
Question 1202453: nyard and Barley's circus is in town, and Lorena is going with her father. When Lorena and her father arrive at the performance, they can choose from six entrances to the ground floorof the main arena. There are two stairways and one elevator that go to the balcony. How many different paths can Lorena and her father take from outside the arena to the balcony?
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Question 1202487: Word Problems involving Optimization (Derivatives)
A poster must have a printed area of 781.25 cm^2. It will have top and bottom margins that are 5 cm each and side margins that are 4 cm each. If all the dimensions of the printed area are at least 25 cm but at most 35 cm, what are the dimensions of the whole poster with the smallest total area? Show your solution.

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Question 1202487: Word Problems involving Optimization (Derivatives)
A poster must have a printed area of 781.25 cm^2. It will have top and bottom margins that are 5 cm each and side margins that are 4 cm each. If all the dimensions of the printed area are at least 25 cm but at most 35 cm, what are the dimensions of the whole poster with the smallest total area? Show your solution.

Click here to see answer by ikleyn(52780) About Me 
Question 1202487: Word Problems involving Optimization (Derivatives)
A poster must have a printed area of 781.25 cm^2. It will have top and bottom margins that are 5 cm each and side margins that are 4 cm each. If all the dimensions of the printed area are at least 25 cm but at most 35 cm, what are the dimensions of the whole poster with the smallest total area? Show your solution.

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Question 1202486: Word Problems involving Optimization (Derivatives)
A poster must have a printed area of 781.25 cm^2. It will have top and bottom margins that are 5 cm each, and side margins that are 4 cm each. If all the dimensions of the printed area are at least 25 cm but at most 35 cm, what are the dimensions of the whole poster with the smallest total area? Show your solution.

Click here to see answer by mananth(16946) About Me 
Question 1202486: Word Problems involving Optimization (Derivatives)
A poster must have a printed area of 781.25 cm^2. It will have top and bottom margins that are 5 cm each, and side margins that are 4 cm each. If all the dimensions of the printed area are at least 25 cm but at most 35 cm, what are the dimensions of the whole poster with the smallest total area? Show your solution.

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Question 1202527: The largest truck commonly received is 20m long and can hold 26 pallets of goods. The owner doesn't like to receive partial shipments. The receiving bay therefore needs to be bigger than the area of pallets. You decide to make two rows of 13 pallets each. A forklift is used to move pallets and it requires a width of 2,85m to operate in. Each pallet is 1.25m long and 1.25m wide. What size would the receiving bay area be for two pf palltes and space between rows?
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Question 1202806: The length of a rectangle is three more than triple the width. If the perimeter is 94 inches, find the dimensions
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Question 1202986: The largest truck commonly received is 20m long and can hold 26 pallets of goods. The owner doesn't like to receive partial shipments. The receiving bay therefore needs to be bigger than the area of pallets. You decide to make two rows of 13 pallets each. A forklift is used to move pallets and it requires a width of 2,85m to operate in. Each pallet is 1.25m long and 1.25m wide. What size would the receiving bay area be for two pf palltes and space between rows?
Click here to see answer by greenestamps(13200) About Me 
Question 1202986: The largest truck commonly received is 20m long and can hold 26 pallets of goods. The owner doesn't like to receive partial shipments. The receiving bay therefore needs to be bigger than the area of pallets. You decide to make two rows of 13 pallets each. A forklift is used to move pallets and it requires a width of 2,85m to operate in. Each pallet is 1.25m long and 1.25m wide. What size would the receiving bay area be for two pf palltes and space between rows?
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Question 1203117: How to calculate the size of the receiving bay area for two rows of pallets and space bottom rows?
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Question 1203297: The length of a rectangle is 10 more than three times it with. The perimeter of the triangle is 108. Find the dimensions of the triangle.
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Question 1203360: A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 11,925π ft^3
Click here to see answer by josgarithmetic(39617) About Me 
Question 1203360: A large grain silo is to be constructed in the shape of a circular cylinder with a hemisphere attached to the top (see the figure). The diameter of the silo is to be 30 feet, but the height is yet to be determined. Find the height h of the silo that will result in a capacity of 11,925π ft^3
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Question 1203439: You must order a new rope for the flagpole. To find out what length of rope is needed, you observe that the pole casts a shadow of 9.2 meters on the ground. The angle of elevation of the sun is 32 . How tall is the flagpole? (Round your answer to the nearest tenth, as necessary.)
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Question 1203442: The sonar of a navy cruiser, sailing on the surface of the ocean, detects a submarine that is 4000 feet (measured in a straight line distance) from the cruiser. The angle of depression from the cruiser to the submarine is 31.2 °.
How deep is the submarine? Round to the nearest tenth.

What is its horizontal distance from the navy cruiser to the submarine? Round to the nearest tenth.

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Question 1203442: The sonar of a navy cruiser, sailing on the surface of the ocean, detects a submarine that is 4000 feet (measured in a straight line distance) from the cruiser. The angle of depression from the cruiser to the submarine is 31.2 °.
How deep is the submarine? Round to the nearest tenth.

What is its horizontal distance from the navy cruiser to the submarine? Round to the nearest tenth.

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Question 1203492: The perimeter of the rectangular playing field is 538 yards. The length of the field is 6 yards less than quadruple the width. What are the dimensions of the playing​ field?
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Question 1203492: The perimeter of the rectangular playing field is 538 yards. The length of the field is 6 yards less than quadruple the width. What are the dimensions of the playing​ field?
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Question 1203596: My rectangular soccer field site has a length equal to one and a half times its width. Find its area in terms of its length x.
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Question 1204089: A 40ft boom on a crane is attached to the crane platform at point D. A cable is attached to the end of the boom at point B and to a 12 ft A-frame at point A anchored by the counterweight. If angle BDA os 85.2 degrees, find the length of the cable to the nearest 10th foot.
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Question 1204184: sara has 80000 to invest. she invests part a5 %. a fourth this amount at 6%, and the blance at 7%.Her total annual income from interest is 4700. FInd the amount invested at each rate
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Question 1204409: A mountain is 11,986 feet above sea​ level, and a valley is 263 feet below sea level. What is the difference in elevation between the mountain and the​ valley?
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Question 1204409: A mountain is 11,986 feet above sea​ level, and a valley is 263 feet below sea level. What is the difference in elevation between the mountain and the​ valley?
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Question 1204433: What is the maximum number of bottles, each of diameter 10 cm, that can be packed into a box with a square base measuring 1000 cm by 1000 cm? The link below shows a diagram of the closest packing method provided by the textbook.
https://ibb.co/KqVSGkL

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Question 1204467: Ms.Ikelyn,
I asked a question here: https://www.algebra.com/tutors/students/your-answer.mpl?question=1204433
To which you responded (with a helpful!) lesson about a TWIN problem. However, I am confused and need help. What is that "shift" term? And can you break it down simpler?
Thank you Ma'am

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Question 1204771: In the triangle shown here: https://ibb.co/Ch9FTZT, DB = DC , DE = CE and
∠DAE = 42°. Find the measure of ∠ACB.

I understand Mr.Greenstamps posted a solution, but it was a "Here's a hint, now you solve it!" But my IQ is far too low to solve it despite all the information he gave. Please help.

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Question 1204771: In the triangle shown here: https://ibb.co/Ch9FTZT, DB = DC , DE = CE and
∠DAE = 42°. Find the measure of ∠ACB.

I understand Mr.Greenstamps posted a solution, but it was a "Here's a hint, now you solve it!" But my IQ is far too low to solve it despite all the information he gave. Please help.

Click here to see answer by greenestamps(13200) About Me 

Question 1204770: How many scalene triangles have perimeter less than 16 and sides of integral length?
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Question 1204849: Find the largest angle in a triangle with sides 6.0 cm, 7.0 cm and 8.0 cm.
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Question 1204848: At a point A on level ground, the angle of elevation to the top of a shed is 20° . If a person walked 30.0 m away from point A, from the shed, to point B, the angle of elevation decreases by 12°. Find the height of the shed.
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Question 1204848: At a point A on level ground, the angle of elevation to the top of a shed is 20° . If a person walked 30.0 m away from point A, from the shed, to point B, the angle of elevation decreases by 12°. Find the height of the shed.
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Question 1204853: In the diagram below, circle with centre O has a radius of 5 cm. Segment AT is tangent to the circle. AO = 13 cm, and AX = XY (this length is labeled m). Find the length of m.
https://ibb.co/6HKJNjR

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Question 1204857: In the diagram, BE = 45 cm and AC = DC . Find the length of BC, in cm.
https://ibb.co/5rmVZ26

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Question 1204855: In the diagram to the left, ∆ABC is isosceles, and ∆MPQ is equilateral.
Find the area, in cm^2 of ∆MPQ.

https://ibb.co/F89dt0X

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Question 1204856: Equilateral triangle ABC has sides of 22 cm. A circle of radius 5 cm inside it is tangent to sides AB & AC. Find the distance from the circle's centre to side BC, in cm.
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Question 1204851: In the diagram on the right, AB is the diameter of the circle, and E is the
centre. Find the measure of angle D, in degrees.
https://ibb.co/SxjJWg5

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Question 1204851: In the diagram on the right, AB is the diameter of the circle, and E is the
centre. Find the measure of angle D, in degrees.
https://ibb.co/SxjJWg5

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Question 1204851: In the diagram on the right, AB is the diameter of the circle, and E is the
centre. Find the measure of angle D, in degrees.
https://ibb.co/SxjJWg5

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Question 1204916: How many distinct line segments are formed by connecting 20 collinear points?
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Question 1204915: In the diagram, EFGH is a rhombus formed by connecting the mid-points of the sides of the rectangle ABCD. The rectangle is circumscribed by the circle with centre 0. Find the area, in cm² of the rhombus if OF = 15 cm, and JH = 6 cm.
https://ibb.co/p3zy0T8

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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020