Uhm..
From what I can understand the height:width ratio is 3:4 so if the width is ten then you will be increasing the ratio by 2.5. So all you have to do is multiply 3 by 2.5.
The height is 7.5cm
Answer:
B. (1,5) and (5.25, 3.94)
Step-by-step explanation:
The answer is where the 2 equations intersect.
We need to solve the following system of equations:
y = -x^2 + 6x
4y = 21 - x
From the second equation:
x = 21 - 4y
Plug this into the first equation:
y = -(21 - 4y)^2 + 6(21 - 4y)
y = -(441 - 168y + 16y^2)+ 126 - 24y
y = -441 + 168y - 16y^2 + 126 - 24y
16y^2 + y - 168y + 24y + 441 - 126 = 0
16y^2 - 143y + 315 = 0
y = [-(-143) +/- sqrt ((-143)^2 - 4 * 16 * 315)]/ (2*16)
y = 5, 3.938
When y = 5:
x = 21 - 4(5) = 1
When y = 3.938
x = 21 - 4(3.938) = 5.25.
The volume of the remaining solid can be calculated by subtracting the volume of the cylindrical hole from the volume of the original box.
1- getting volume of original box:
We have:
length of box = 24 cm
width of box = 16 cm
height of box = 16 cm
Since the box has a rectangular shape, therefore:
volume of box = length * width * height
volume of box = 24 * 16 * 16 = 6144 cm^3
2- getting the volume of cylindrical hole:
We have:
radius of hole = 4 cm
height of hole = 24 cm (as it goes along the hole length of the original box)
Volume pf cylinder = pi * r^2 * h
volume of cylinder = pi * (4)^2 * 24 = 1206.371579 cm^3
3- getting volume of remaining solid:
volume of remaining solid = volume of box - volume of cylinder
volume of remaining solid = 6144 - 1206.371579 = 4937.628421 cm^3
Answer:
D
Step-by-step explanation:
12 cm,
Simply use Pythagora's theorem. The square of the hypotenuse = the sum of the squares of the other two sides
So, you get the square of the missing side by subtracting 5 squared from 13 squared, which gives 144.
Square root of 144 is the length of the missing side, i.e. 12 cm.