Answer:
x=32
Step-by-step explanation:
Since we know all the angels are equal to 60, you can pick whichever angel you wish and set it equal to 60 to find the value of x
Answer:
261 cm²
Step-by-step explanation:
To find the surface area of a square pyramid, you must first recognize all of the shapes.
There are four triangles and one square.
- To find the area of a square, multiply the side by itself twice.
- To find the area of a triangle, multiply the base and the height, then multiply the product by 1/2.
The triangles have a base of 9 and a height of 10.
Multiply the product by 1/2.
There are four triangles.
The area of all three triangles is 180 centimeters; the area of a single triangle is 45 centimeters.
There square has sides of 9 centimeters.
The area of the square is 81 centimeters.
Lastly, we add the areas of the shapes.
Therefore, the surface area of this square prism is 261 cm².
You can use this layout to find the surface area of a square pyramid.
Answer:
7. Always, Veritcal Angle therom
8. Never true, it will never add up to 180 degrees
9. Never true, it will never add up to 90 degrees
10. Never true, Angle 8 and 5 are not vertical with one anouther.
11. Sometimes
12. Yes it is possible.
1.8, Problem 37: A lidless cardboard box is to be made with a volume of 4 m3
. Find the
dimensions of the box that requires the least amount of cardboard.
Solution: If the dimensions of our box are x, y, and z, then we’re seeking to minimize
A(x, y, z) = xy + 2xz + 2yz subject to the constraint that xyz = 4. Our first step is to make
the first function a function of just 2 variables. From xyz = 4, we see z = 4/xy, and if we substitute
this into A(x, y, z), we obtain a new function A(x, y) = xy + 8/y + 8/x. Since we’re optimizing
something, we want to calculate the critical points, which occur when Ax = Ay = 0 or either Ax
or Ay is undefined. If Ax or Ay is undefined, then x = 0 or y = 0, which means xyz = 4 can’t
hold. So, we calculate when Ax = 0 = Ay. Ax = y − 8/x2 = 0 and Ay = x − 8/y2 = 0. From
these, we obtain x
2y = 8 = xy2
. This forces x = y = 2, which forces z = 1. Calculating second
derivatives and applying the second derivative test, we see that (x, y) = (2, 2) is a local minimum
for A(x, y). To show it’s an absolute minimum, first notice that A(x, y) is defined for all choices
of x and y that are positive (if x and y are arbitrarily large, you can still make z REALLY small
so that xyz = 4 still). Therefore, the domain is NOT a closed and bounded region (it’s neither
closed nor bounded), so you can’t apply the Extreme Value Theorem. However, you can salvage
something: observe what happens to A(x, y) as x → 0, as y → 0, as x → ∞, and y → ∞. In each
of these cases, at least one of the variables must go to ∞, meaning that A(x, y) goes to ∞. Thus,
moving away from (2, 2) forces A(x, y) to increase, and so (2, 2) is an absolute minimum for A(x, y).
My guess would be less than $25
