![\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh\qquad \begin{cases} B=\textit{area of the base}\\ h=height \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20pyramid%7D%5C%5C%5C%5C%0AV%3D%5Ccfrac%7B1%7D%7B3%7DBh%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0AB%3D%5Ctextit%7Barea%20of%20the%20base%7D%5C%5C%0Ah%3Dheight%0A%5Cend%7Bcases%7D)
now, the first one, on the far-left.... can't see the height.. but I gather you do, now as far as its Base area, well, the bottom is just a 12x12 square, so the area of its base is just 12*12
now, the middle pyramid, has a height of 6, the base is also a square, 8x8, so the Base area is just 8*8
now the last one on the far-right
has a height of 8, the Base is a Hexagon, with sides of 6
Answer:
8/27 cups
Step-by-step explanation:
Nima uses 2/3 cups of peanuts to make a recipe of 2 1/4 = 9/4 cups of trail mix. If we want to find how many cups of peanuts are there per cup of trail mix, we can do a rule of three:
If 9/4 cups of trail mix need 2/3 cups of peanuts, 1 cup of trail mix need X cups of peanuts:
9/4 cups of trail mix -> 2/3 cups of peanuts
1 cup of trail mix -> X cups of peanuts
9/4 / 1 = 2/3 / X
9/4 = 2/(3*X)
3*X*9 = 4*2
27*X = 8
X = 8/27 cups
Answer:
Minimum value of function
is 63 occurs at point (3,6).
Step-by-step explanation:
To minimize :
![C=x+10y](https://tex.z-dn.net/?f=C%3Dx%2B10y)
Subject to constraints:
![x\leq 3---(1)\\y\leq 9---(2)\\x+y\geq 9----(3)\\x\geq 0\\y\geq 0](https://tex.z-dn.net/?f=x%5Cleq%203---%281%29%5C%5Cy%5Cleq%209---%282%29%5C%5Cx%2By%5Cgeq%209----%283%29%5C%5Cx%5Cgeq%200%5C%5Cy%5Cgeq%200)
Eq (1) is in blue in figure attached and region satisfying (1) is on left of blue line
Eq (2) is in green in figure attached and region satisfying (2) is below the green line
Considering
, corresponding coordinates point to draw line are (0,9) and (9,0).
Eq (3) makes line in orange in figure attached and region satisfying (3) is above the orange line
Feasible region is in triangle ABC with common points A(0,9), B(3,9) and C(3,6)
Now calculate the value of function to be minimized at each of these points.
![C=x+10y](https://tex.z-dn.net/?f=C%3Dx%2B10y)
at A(0,9)
![C=0+10(9)\\C=90](https://tex.z-dn.net/?f=C%3D0%2B10%289%29%5C%5CC%3D90)
at B(3,9)
![C=3+10(9)\\C=93](https://tex.z-dn.net/?f=C%3D3%2B10%289%29%5C%5CC%3D93)
at C(3,6)
![C=3+10(6)\\C=63](https://tex.z-dn.net/?f=C%3D3%2B10%286%29%5C%5CC%3D63)
Minimum value of function
is 63 occurs at point C (3,6).
Answer:
a=-22
Step-by-step explanation:
Multiply both sides of the negative equation by (-2) to get the equation:
a-4=13(-2)
then simplify to get:
a-4=-26
then isolate the variable by addig 4 to both sides of the equation to get:
a=-26+4
simplify to get:
a=-22