The volume of a box like this is found by multiplying the length times the width times the height. We are told that the length is 8 more inches than the width, so the width is w and the length is w + 8. If we cut away 3 square inches from each corner, the height when we fold up those corners is going to be 3. The volume is given as 27, so our formula looks like this:
. When we do that multiplication, we have
. We need to solve for w so we can then solve for h. Move the 27 over and set the quadratic equal to 0.
. We can then factor out a 3 to make the job easier:
. Now we can factor to solve for w. The 2 numbers that add up to 8 and multiply to -9 are 9 and -1. So (w+9) = 0, (w-1) = 0, or 3 = 0. Of course 3 doesn't equal 0, so that's out. w + 9 = 0 so w = -9. w - 1 = 0 so w = 1. There are 2 things in math that can never EVER be negative and those are time and distance/length. So -9 is out. That means that w = 1. But don't forget that there was 6 inches cut off each side, so the width is 1 + 3 + 3 which is 7. The length is w + 8 which means that the length is 7 + 8 or 15. Those are the dimensions of the rectangle before it was cut.
Answer:
Total area is 198.6cm²
Step-by-step explanation:
This problem bothers on the mensuration of flat shapes.
Step one
From the given figure the two semi circles left and right can be resolved as a whole (a complete circle) with diameter d 10cm
Radius r = 10/2= 5cm
Area of circle A= πr²
A= 3.142*5²
A= 3.142*25
A= 78.55
A= 78.6cm²
Step two
The remaining part of the shape is a rectangle with length (22-10)= 12cm
I.e the 10 is as a result of the radius of the two semi circles = r+r= 5+5=10
The rectangle has a width of 10cm
Area of rectangle A=12*10= 120cm²
Hence the total surface area of the shape
Total area = 120+78.6
Total area = 198.6cm²
Answer: 31 degrees
Step-by-step explanation: Angle ABD and BDC are alternate interior angles, meaning that they are congruent. Therefore, the measure of angle ABD is 31 degrees.
Answer:
2236.77 feets
Step-by-step explanation:
From the attached picture, we are to find x, which is the vertical depth of the submarine.
Using trigonometry based on the illustration in the diagram:
Sinθ = opposite / hypotenus
Sinθ = x (depth of submarine) / distance from ship (4000)
Hence,
Sinθ = x / 4000
θ = 34°
Sin34 = x / 4000
0.5591929 * 4000 = x
2236.7716 = x
Hence, depth of submarine = 2236.77 feets
