math question

[Penguin1]

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taken from sample ada test..

9) a rectangular room is 3 meters wide, 4 meters long and 2 meters high. How far is it from the northeast corner at the floor to the southwest corner at the ceiling? (the answer is square root 29)

10) A person travels to work at an average speed of 40 mph, and reutns home at 60mph. Which of the following, in mph, is the average speed for the entire trip? (answer 48)

35) What is the maximum number of 3-inch squares (squares that are three inches on a side) that can be cut from a sheet of tin 19 x 23 inches? ( answer 42)


i have no idea how these came about.. help? thanks!!

 

[PinkStripe]

9) In order to solve number 9, it would be easiest to draw the rectangle in 3D. Once you draw the lines as instructed, from the Southwest corner in the top and the Northeast corner in the bottom, you get a triangle. The base of the triangle is the length determined by doing the pythagorean theorem and finding the length of the hypotenuse to be the 25 of the square at the bottom.

.3^2 + 4^2 = c^2
c = 5
.
Then you must perform the Pythagorean theorem to find the length of the desired distance that the question is asking for.

.2^2 + 5^2 = c^2
c = . .&#8730;29 <--- The answer!

Hope this helps!
.

 

[PinkStripe]

10) Are you sure the answer isn't 50mph.

40 + 60 = 100
100/2 = 50

 

[PinkStripe]

35) I approached this problem by first sketching a 2D rectangle and added the dimensions, 19 on one side, and 23 on the other. 3 goes into 19 a maximum of 6 times, and 3 goes into 23 a maximum of 7 times.

6 x 7 = makes the maximum area 42

 

[Penguin1]

whoa... pinkstripe w/ your glittery pink tooth... you are simply the best. thanks for all the help!! i really appreciate it.

and yeah question ten for some reason is 48. i also got 50, but i guess i'm just glad you got the same thing. ahha 😛

 

[sonofastunna]

for question 9 you should memorize the easy formula. the formula is sqrt(a^2+b^2+c^2) where a,b, and c are the 3 sides.

 

[Penguin1]

for question 9 you should memorize the easy formula. the formula is sqrt(a^2+b^2+c^2) where a,b, and c are the 3 sides.

oh, sick. when do you apply it? whenever you have a triangle in a 3d rectangle?

 

[sonofastunna]

oh, sick. when do you apply it? whenever you have a triangle in a 3d rectangle?

whenever you are given dimensions for a rectangular solid and asked for the distance between the 2 opposite vertices. (this is a very common question that you will likely see in many mock exams)

 

[Streetwolf]

10) Are you sure the answer isn't 50mph.

40 + 60 = 100
100/2 = 50

Think about it. The distance both ways is the same. Keeping that in mind, the driver spends LESS TIME driving home at 60 mph than going to work at 40 mph. It makes sense that the average speed is under 50 because a longer amount of time on the road is at 40 mph.

Now for the math... Average speed = total distance over total time.

In this case you don't get a distance... you only get that the distance is the SAME. So you can choose any distance.

Choose a random distance. Choose a distance that's easy to work with. So choose 120 miles since 40 and 60 both go into it. So on the way there it takes 3 hours. The way back takes 2 hours. In total the driver travels 240 miles (120 each way) over 5 hours. That's 48 mph.

 

[Penguin1]

thanks sonofastunna... your parents must be stunnas.


thanks streetwolf.... you are... ugh.. definitely the wolf of the street. hahah 🙂

 

[sonofastunna]

Runs in the family lol