Answer:
The barge can carry up to 94 railroad cars.
Step-by-step explanation:
Create an inequality to represent the weight of the barge to the max weight.
24 + 4r ≤ 400
Solve for r:
4r ≤ 400 - 24
4r ≤ 376
4r ≤ 376/4
r ≤ 94
Answer:
x=-2.5
Step-by-step explanation:
4x+(7-3)5=10
4x+(4)5=10
4x+20=10
subtract 20 from each side
4x=-10
divide each side by 4
x=-2.5
Answer:
77. 
Proved
78. ![\sec^{4}x \tan^{2} x = \sec^{2}x [\tan^{2}x + \tan^{4}x ]](https://tex.z-dn.net/?f=%5Csec%5E%7B4%7Dx%20%5Ctan%5E%7B2%7D%20x%20%3D%20%5Csec%5E%7B2%7Dx%20%5B%5Ctan%5E%7B2%7Dx%20%2B%20%5Ctan%5E%7B4%7Dx%20%5D)
Proved
79. ![\cos^{3} x\sin^{2} x = [\sin^{2}x - \sin^{4}x] \cos x](https://tex.z-dn.net/?f=%5Ccos%5E%7B3%7D%20x%5Csin%5E%7B2%7D%20x%20%3D%20%5B%5Csin%5E%7B2%7Dx%20-%20%5Csin%5E%7B4%7Dx%5D%20%5Ccos%20x)
Proved.
80. 
Proved.
Step-by-step explanation:
77. Left hand side
= 
= 
= ![\cot^{4}x [\csc^{2}x - 1]](https://tex.z-dn.net/?f=%5Ccot%5E%7B4%7Dx%20%5B%5Ccsc%5E%7B2%7Dx%20-%201%5D)
{Since we know, 
}
= 
= Right hand side (Proved)
78. Left hand side
= 
= ![\sec^{2} x [1 + \tan^{2}x] \tan^{2} x](https://tex.z-dn.net/?f=%5Csec%5E%7B2%7D%20x%20%5B1%20%2B%20%5Ctan%5E%7B2%7Dx%5D%20%5Ctan%5E%7B2%7D%20x)
{Since 
}
= ![\sec^{2}x [\tan^{2}x + \tan^{4}x ]](https://tex.z-dn.net/?f=%5Csec%5E%7B2%7Dx%20%5B%5Ctan%5E%7B2%7Dx%20%2B%20%5Ctan%5E%7B4%7Dx%20%5D)
= Right hand side (Proved)
79. Left hand side
= 
= ![\cos x[1 - \sin^{2} x] \sin^{2} x](https://tex.z-dn.net/?f=%5Ccos%20x%5B1%20-%20%5Csin%5E%7B2%7D%20x%5D%20%5Csin%5E%7B2%7D%20x)
{Since 
}
= ![[\sin^{2}x - \sin^{4}x] \cos x](https://tex.z-dn.net/?f=%5B%5Csin%5E%7B2%7Dx%20-%20%5Csin%5E%7B4%7Dx%5D%20%5Ccos%20x)
= Right hand side
80. Left hand side
= 
= ![[\sin^{2}x + \cos^{2}x]^{2} - 2\sin^{2} x \cos^{2}x](https://tex.z-dn.net/?f=%5B%5Csin%5E%7B2%7Dx%20%2B%20%5Ccos%5E%7B2%7Dx%5D%5E%7B2%7D%20-%202%5Csin%5E%7B2%7D%20x%20%5Ccos%5E%7B2%7Dx)
{Since }
= ![1 - 2\cos^{2} x[1 - \cos^{2}x ]](https://tex.z-dn.net/?f=1%20-%202%5Ccos%5E%7B2%7D%20x%5B1%20-%20%5Ccos%5E%7B2%7Dx%20%5D)
= 
= Right hand side. (Proved)
Fix you some claculations?
Step-by-step explanation:
Firstly, notice that this shape is composed of ³/₄ of a circle and ¹/₂ of a square;
The lower left part is the ¹/₂ square, with only 2 sides (a left and lower side) of length 3 units;
The perimeter of this part of the shape is simply the sum of the two sides:
3 + 3 = 6
The remaining part is the ³/₄ circle, which has a radius of 3 units;
The circumference of a circle is found by the formula:
πd
d = diameter = 2 × radius
We only have ³/₄ of the circle, however, so we only have ³/₄ the circumference:
³/₄ × π(2(3)) = ³/₄ × 6π
= ⁹/₂π (or, equally, 4.5π)
So the total perimeter is the sum of the perimeter of the ¹/₂ square and the ³/₄ circle:
4.5π + 6
