Answer:
20
Step-by-step explanation:
Givens
Let child one = x
Let child two = y
Let child three = z
Equations
x^2 + y^2 + z^2 = 100
xy + xz + yz = 150
Solution
There's a trick here. The square of their weights added together is equal (with some modification) to the given conditions. Start by squaring (x+y+z).
(x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz
Take out 2 as a common factor from the last three terms.
(x + y + z)^2 = (x^2 + y^2 + z^2+ 2(xy + xz + yz) )
Substitute the given conditions into the equation. (x^2 + y^2 + z^2) = 100 and 2*(xy + xz + yz) = 2 * 150
(x + y + z)^2 = 100 + 2*150
(x + y + z)^2 = 100 + 300
(x + y + z)^2 = 400
Take the square root of both sides.
sqrt(x+y+z)^2 = sqrt(400)
x + y + z = 20
Note
This answer tells you nothing about the values of x y and z. On the other hand it does not ask for the values of x y and z.
Answer:
Part 1) 
Part 2) 
Part 3) 
Step-by-step explanation:
<u><em>The complete question is</em></u>
Consider this right triangle. 21 29 20 Write the ratio equivalent to: Sin B - CscA- Cot B
The picture of the question in the attached figure
Part 1) Write the ratio equivalent to: Sin B
we know that
In the right triangle ABC
----> by SOH (opposite side divided by the hypotenuse)
substitute the values
Part 2) Write the ratio equivalent to: Csc A
we know that
In the right triangle ABC
-----> by SOH (opposite side divided by the hypotenuse)
substitute the values
therefore
Part 3) Write the ratio equivalent to: Cot A
we know that
In the right triangle ABC
-----> by TOA (opposite side divided by the adjacent side)
substitute the values
therefore
Step-by-step explanation:
Pythagoras (for right-angled triangles) :
c² = a² + b²
c being the Hypotenuse, the side opposite of the right angle. and that would be here the diagonal.
c = diagonal = 10 ft
therefore, the width of the rectangle is 10/2 = 5 ft
10² = 5² + b²
100 = 25 + b²
b² = 75
b = length = sqrt(75) = 8.660254038... ft
Hyp^2 = 8^2 + 9^2
hyp^2 = 64 + 81
hyp^2 = 145
hot = 12 inch
