1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
BaLLatris [955]
3 years ago
13

A basketball gymnasium is 25 meters high, 80 meters wide and 200 meters long. We want to connect two strings, one from each of t

he two corners above one basket to the diagonally opposite corners of the gym floor. (a) Find the center of the gymnasium? (b) What is the length of the strings? (c) (What angle is formed by the strings as they cross?
Mathematics
1 answer:
Rudiy273 years ago
7 0

Answer:

a) the centre is at (12.5 m, 40 m , 100 m ) with respect to our position

b) the length of the strings S will be 216.85 m

c) the angle that is formed by the strings is  1.23 rad

Step-by-step explanation:

assuming that we stand on one of the corners on the floor , so our coordinates are (0,0,0)  , then the coordinates of the center of the gymnasium   are found through

x center = (25 + 0)/2 = 12.5 m

y center = (80+ 0)/2 = 40 m

z center = (200+ 0)/2 = 100 m

then the centre is at (12.5 m, 40 m , 100 m ) with respect to our position

b) the length of the strings S will be the modulus of the vector that points from our position to the diagonally opposite corners

|S| = √(25²+80²+200²) = 216.85 m

c) the angle can be found through the dot product of the vectors that represent the strings S₁ and S₂

S₁ =(25,80,10)

S₂ =(-25,80,100)

then

S₁*S₂ = 25*(-25) +80*80 + 100*100 = 15775

but also

S₁*S₂ = |S₁||S₂| cos θ = |S|² * cos θ

S₁*S₂ =  |S|² * cos θ

cos θ= S₁*S₂/|S|²

θ= cos ⁻¹ ( S₁*S₂/|S|² ) = cos ⁻¹ [15775/(25²+80²+200²)] = 1.23 rad

You might be interested in
What number is the opposite of the number 0
Klio2033 [76]

Answer:

it is the second one, number zero does not have an opposite

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Juanita borrowed $600 to purches a computer
4vir4ik [10]

Answer:

Juanita borrowed $600 to purchase a computer

Step-by-step explanation:

Grammer

7 0
3 years ago
Read 2 more answers
Write 0.000000364 in standard form
Thepotemich [5.8K]

Answer:

yes

Step-by-step explanation:

this number is a decimal

5 0
3 years ago
If 675 is 3/4 what is the the other 1/4 and how did you get it ?
SashulF [63]

Answer:

225

Step-by-step explanation:

If you divide 675 you'll get 225. 225 times 4 will be 900. But 225 times 3 will be 674. So each 1/4 will be 225.

6 0
3 years ago
Read 2 more answers
15=x/3 +7 equation to words
emmasim [6.3K]
15 is equal to x divided by 3 plus 7
5 0
3 years ago
Other questions:
  • -12 + 18. = 70<br><br> complete the square
    13·1 answer
  • Olivia ordered cupcakes and a layer cake. Together she paid $52. She paid $12 more on the layer cake than on the cupcakes. What
    7·1 answer
  • the cost of a plane ticket from pheonix to dallas cost $120 last week. This week, the same ticket will cost $165. What is the pe
    5·1 answer
  • Find n (write in simplest radical form)
    9·1 answer
  • What’s seven more than the quotient of a number and 2 is 10
    9·1 answer
  • What is the remainder when f(x) = x^4 -8x^2 + 10x + 22 is divided by x + 3
    9·1 answer
  • Find the value of k
    15·1 answer
  • In a recent survey, 10 percent of the participants rated Pepsi as being "concerned with my health." PepsiCo's response included
    12·1 answer
  • HELPPPPPPP PLZZZZZZZZZZZZ
    7·1 answer
  • O. The number of for attending football match this week was 12% more more than last week. if 728 people attended this week's mat
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!