Answer:both are in thousandths place,in the thousandths place both have 4 as a value
Step-by-step explanation:
One prism with a volume of 2400 might have a rectangular base with a length of 4 and a width of 5, as well as a height of 120.
V = l x w x h
V = 4 x 5 x 120
V = 2400
This prism would essentially look like a really tall rectangle, since the height is such a large number. I wouldn't accurately represent the units on graph paper, if I were you. Just label the sides with the numbers I gave you.
Another prism with a volume of 2400 might be a rectangular prism with a length of 8, a width of 10, and a height of 30.
V = l x w x h
V= 8 x 10 x 30
V = 2400
This would also be a tall rectangle, although it isn't as tall. Keep in mind that l x w x h is only the volume formula for a rectangular prism. I only used rectangular prisms because they would be the easiest for this example. A triangular prism has a different volume formula.
Answer:
KL= 63
Step-by-step explanation:
JK=7x+9 , JL=114 , KL=9x+9 ( if the points are on the same line and point J at the end point and K in the middle)
*J_______________________K___________________________L
JL=JK+KL
114=7x+9+9x+9
114-18=16 x
16x=98
x=98/16=6
KL= 9x+9
KL=9(6)+9
KL= 63
![\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]](https://tex.z-dn.net/?f=%5Crightarrow%20z%5E4%3D-625%5C%5C%5C%5C%5Crightarrow%20z%3D%28-625%2B0i%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5C%5C%5C%5C%5Crightarrow%20x%2Biy%3D%28-625%2B0i%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5C%5C%5C%5C%20x%3Dr%20%5Ccos%20A%5C%5C%5C%5Cy%3Dr%20%5Csin%20A%5C%5C%5C%5Cr%20%5Ccos%20A%3D-625%5C%5C%5C%5C%20r%20%5Csin%20A%3D0%5C%5C%5C%5Cx%5E2%2By%5E2%3D625%5E%7B2%7D%5C%5C%5C%5Cr%5E2%3D625%5E%7B2%7D%5C%5C%5C%5C%7Cr%7C%3D625%5C%5C%5C%5C%20%5Ctan%20A%3D%5Cfrac%7B0%7D%7B-625%7D%5C%5C%5C%5C%20%5Ctan%20A%3D0%5C%5C%5C%5C%20A%3D%5Cpi%5C%5C%5C%5C%5Crightarrow%20z%3D%20%5B625%28%5Ccos%20%282k%20%5Cpi%2Bpi%29%20%2Bi%20%5Csin%20%282k%5Cpi%2B%20%5Cpi%29%5D%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5C%5C%5C%5Ck%3D0%2C1%2C2%2C3%2C4%2C....%5C%5C%5C%5C%5Crightarrow%20z%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B%282k%20%5Cpi%2Bpi%29%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B%282k%5Cpi%2B%20%5Cpi%29%7D%7B4%7D%5D%20)
![\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]](https://tex.z-dn.net/?f=%5Crightarrow%20z_%7B0%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7Bpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B%5Cpi%29%7D%7B4%7D%5D%5C%5C%5C%5C%5Crightarrow%20z_%7B1%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B3%5Cpi%7D%7B4%7D%5D%5C%5C%5C%5C%20%5Crightarrow%20z_%7B2%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%5D%5C%5C%5C%5C%20%5Crightarrow%20z_%7B3%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B7%5Cpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B7%5Cpi%7D%7B4%7D%5D)
Argument of Complex number
Z=x+iy , is given by
If, x>0, y>0, Angle lies in first Quadrant.
If, x<0, y>0, Angle lies in Second Quadrant.
If, x<0, y<0, Angle lies in third Quadrant.
If, x>0, y<0, Angle lies in fourth Quadrant.
We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is
![\rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]](https://tex.z-dn.net/?f=%20%5Crightarrow%20z_%7B2%7D%3D%28625%29%5E%7B%5Cfrac%7B1%7D%7B4%7D%7D%5B%5Ccos%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%20%2Bi%20%5Csin%20%5Cfrac%7B5%5Cpi%7D%7B4%7D%5D)
Step-by-step explanation:
First, the pizza is 18 inches in diameter, so
and, because the radium is half of the diameter,
<u>Note that the units are inches.</u>
Using the equation
where a is the area of a circle, we know that the area of the whole pizza is approx.254.5 square inches. Divide by 8 to find the area of 1/8 of a pizza. Each slice will have an area of approx. 32 square inches. For a precise result, the answer is
where a(s) is the area of a slice of pizza, and s is the total number of slices, given they are equal in size.
