Answer:
No, with the guides in between the two ladders, it is not possible for the lower ends of the ladder to be up to 12 feet apart
Step-by-step explanation:
The given parameters are;
The length of two sides of the step ladder = 12 feet
The maximum value allowable for the included angle between the two 12 feet ladders = 58°
Therefore, the maximum value of the third side facing the included angle is given as follows;
let "a" represent the maximum value of the third side formed by the distance apart of the lower end of the ladder, by cosine rule, we have;
a² = 12² + 12² - 2 × 12 × 12 × cos(58°) = 135.383251901
∴ a = √(12² + 12² - 2 × 12 × 12 × cos(58°)) ≈ 11.64
The maximum value of the third side formed by the distance apart of the lower end of the ladder = a ≈ 11.64 feet < 12 feet
Therefore, it is not possible for the lower ends of the ladder to be up to 12 feet apart.
Hello :
let A(0,3,2) and (Δ) this line , v vector parallel to (<span>Δ).
M</span>∈ (Δ) : vector (AM) = t v..... t ∈ R
1 ) (Δ) parallel to the plane x + y + z = 5 : let : n an vector <span>perpendicular
to the plane : n </span>⊥ v .... n(1,1,1) so : n.v =0 means : n.vector (AM) = 0
(1)(x)+(1)(y-3)+(1)(z -2) =0 ( vector (AM) = ( x, y -3 , z-2 )
x+y+z - 5=0 ...(1)
2) (Δ) perpendicular to the line (Δ') : x = 1+t , y = 3 - t , z = 2t :
vector (u) ⊥ v .... vector(u) parallel to (Δ') and vector(u) = (1 , -1 ,1)
vector (u) ⊥ vector (AM) means :
(1)(x)+(-1)(y-3)+(2)(z -2) =0
x - y+2z - 1 = 0 ...(2)
so the system :
x+y+z - 5=0 ...(1)
x - y+2z - 1 = 0 ...(2)
(1)+(2) : 2x+3z - 6 =0
x = 3 - (3/2)z
subsct in (1) : 3 - (3/2)z +y +z - 5 =0
y = 1/2z +2
let : z=t
an parametric equations for the line (Δ) is : x = 3 - (3/2)t
y = (1/2)t +2
z=t
verifiy :
1) (Δ) parallel to the plane x + y + z = 5 :
(-3/2 , 1/2 ,1) <span>perpendicular to (1,1,1)
</span>because : (1)(-3/2)+(1)(1/2)+(1)(1) = -1 +1 = 0
2) (Δ) perpendicular to the line (Δ') :
(-3/2 , 1/2 ,1) perpendicular to (1,-1,2)
because : (1)(-3/2)+(-1)(1/2)+(1)(2) = -2 +2 = 0
A(0, 3, 2)∈(Δ) :
0 = 3-(3/2)t
3 = (1/2)t+2
2 =t
same : t = 2
-1 (5x 11) i hope that helps
Hello from MrBillDoesMath!
Answer:
+2
Discussion:
-8 (17 - 12) / ( -2 (8 - (-2)) ) -
= -8 ( 5) / ( -2 ( 8+2)) as 17 -12 = 5 and -(-2) = +2
= -40/ ( -2 (10))
= -40/(-20) =
= +2
which is the third choice.
Thank you,
MrB
Hello!
To solve this you use the equation to find the circumference of a circle which is
C is circumference
r is radius which is half the diameter
Put in the values you know and 3.14 for pi
C = 2 * 3.14 * 24
Multiply
C = 150.72
The answer is 150.72 centimeters
Hope this helps!
