Tutors Answer Your Questions about Geometry Word Problems (FREE)
Question 1195721: A programmer is writing the code for a new interactive basketball game. She is using quadratic relations to model the path of the ball. During the game, when a ball is shot, the path it follows is modelled by the quadratic relation, h = - 0.2d2 + 3d + 6, where h represented the height of the ball above the ground and d represented the distance of the ball from the shooter.
Both distances are measured in feet.
a. How high was the ball when the shooter shot it?
b. What was the maximum height obtained by the ball?
c. A rim of a basketball net is 10 feet high. For what distance was the ball above the rim of
the basketball net?
d. How far would the shooter have to be away from the rim of the basketball net for the ball
to hit the rim of the basketball net and possibly go in?
e. Create a graphical model, using technology, to verify your calculations.
f. Create your own quadratic relation that would model the path of a shot from a distance of
15 feet that would hit the rim of the basketball net. Explain how you obtained your answer
I genuinely have no clue where to start on this, so even just a little help would be greatly appreciated :)
Click here to see answer by Boreal(15235)   |
Question 1195774: Kyle Shewfelt, from Calgary, AB, was the Olympic fl oor exercise champion in Athens in 2004. Gymnasts perform their routines on a 40-ft by 40-ft mat. They use the diagonal of the mat because it gives them greater distance to complete their routine. a) Use the tangent ratio to determine the angle of the gymnastics run relative to the sides of the mat.
Click here to see answer by ikleyn(52780)  |
Question 1195971: Graph f and the secant lines passing through the point P(4, 2) and Q(x, f(x)) for x-values of 1, 5, and 8.
Find the slope of each secant line. (Round your answers to three decimal places.)
line passing through
Q(1, f(x))
line passing through
Q(5, f(x))
line passing through
Q(8, f(x))
Click here to see answer by ikleyn(52780) |
Question 1196270: A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 30 ft is to be constructed.
Find a function that models the area of the window.
A(x) =
Find the dimensions of the window that admits the greatest amount of light. (Round your answers to one decimal place.)
x = ft
height = ft
Click here to see answer by math_tutor2020(3816) |
Question 1196270: A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 30 ft is to be constructed.
Find a function that models the area of the window.
A(x) =
Find the dimensions of the window that admits the greatest amount of light. (Round your answers to one decimal place.)
x = ft
height = ft
Click here to see answer by josgarithmetic(39617) |
Question 1196270: A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure below. A Norman window with perimeter 30 ft is to be constructed.
Find a function that models the area of the window.
A(x) =
Find the dimensions of the window that admits the greatest amount of light. (Round your answers to one decimal place.)
x = ft
height = ft
Click here to see answer by ikleyn(52780) |
Question 1196408: Find the acceleration of the specified object. (Hint: Recall that if a variable is changing at a constant rate, its acceleration is zero.)
A boat is pulled into a dock by means of a winch 24 feet above the deck of the boat (see figure). The winch pulls in rope at a rate of 5 feet per second. Find the acceleration (in ft/sec2) of the boat when there is a total of 25 feet of rope out. (Round your answer to three decimal places.)
Click here to see answer by ikleyn(52780) |
Question 1196409: An airplane is flying in still air with an airspeed of 400 miles per hour. The plane is climbing at an angle of 33°. Find the rate (in mi/hr) at which the plane is gaining altitude. (Round your answer to four decimal places.)
Click here to see answer by ikleyn(52780) |
Question 1197003: Two gardens are being fenced in. Both gardens will require the same amount of fencing (both gardens have the same perimeter in meters). One garden is in the shape of a square and the other is in the shape of an equilateral triangle. Each side of the triangle is 1 longer than each side of the square. Find the dimensions of the garden.
Click here to see answer by MathLover1(20849)  |
Question 1197003: Two gardens are being fenced in. Both gardens will require the same amount of fencing (both gardens have the same perimeter in meters). One garden is in the shape of a square and the other is in the shape of an equilateral triangle. Each side of the triangle is 1 longer than each side of the square. Find the dimensions of the garden.
Click here to see answer by ewatrrr(24785)  |
Question 1197011: A rectangular cube with sides measuring 4cm, is made with 1cm³ blocks. Two straight tunnels of 4 cubes each are taken out, as illustrated. All exposed surfaces are painted including inside the tunnels. How many small cubes have been painted on exactly 3 faces?
Please view the diagram/illustration as here on my google drive link:
https://drive.google.com/file/d/1YkGkoCOHEX0ZksF9r8UWdviXre3j3RDd/view?usp=sharing
Click here to see answer by math_tutor2020(3816) |
Question 1197011: A rectangular cube with sides measuring 4cm, is made with 1cm³ blocks. Two straight tunnels of 4 cubes each are taken out, as illustrated. All exposed surfaces are painted including inside the tunnels. How many small cubes have been painted on exactly 3 faces?
Please view the diagram/illustration as here on my google drive link:
https://drive.google.com/file/d/1YkGkoCOHEX0ZksF9r8UWdviXre3j3RDd/view?usp=sharing
Click here to see answer by ikleyn(52780) |
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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
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