Volume of cube = side^3
= 15^3
= 3375
Volume of pyramid= length x width x height/3
= 15 x 15 x 9
= 675
Total volume = 3375 + 675
= 4050 cubic feet
Answer:
ok so S=soda C=chips and G=gum
Step-by-step explanation:
From the information,
s+3=c
(1/2)c=g
from this P=s+c+g
P=s+(s+3)+((s+3)/2)
P=5/2s+9/2
Theres no real name for a shape with uneven sides. I just realized that. A four sided figure is a quadrilateral. Or irregular polygon/quadrilateral. A four sided shape with no even sides.
Answer:
20 minutes( 0.3333 hours) after they leave the station will they be 50 km apart, if the Two trains on opposite tracks leave the same station at the same time.
Step-by-step explanation:
One train travels at an average speed of 80 km/hr and the other travels at an average speed of 70 km/hr.
Answer:
For h= 25, b in the plane spanned by a1 and a2
Step-by-step explanation:
![a1= \left[\begin{array}{c}1\\2\\-1\end{array}\right] \\a2 = \left[\begin{array}{c}-7\\-7\\2\end{array}\right] \\\\b = \left[\begin{array}{c}3\\-22\\h\end{array}\right]](https://tex.z-dn.net/?f=a1%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C2%5C%5C-1%5Cend%7Barray%7D%5Cright%5D%20%5C%5Ca2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-7%5C%5C-7%5C%5C2%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5Cb%20%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%5C%5C-22%5C%5Ch%5Cend%7Barray%7D%5Cright%5D)
we have to find value of h for which b in the plane spanned by a1 and a2.
For this the linear systems given by the following augmented matrix must be consistent.
![\left[\begin{array}{cc|c}1&-7&3\\2&-7&-22\\-1&2&h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%26-7%263%5C%5C2%26-7%26-22%5C%5C-1%262%26h%5Cend%7Barray%7D%5Cright%5D)
Reduce the augmented matrix into row echelon form:
![R_{2} - 2R_{1} , R_{3} + R_{1}\\\\\left[\begin{array}{cc|c}1&-7&3\\0&7&-28\\-0&-5&h+3\end{array}\right]\\\\7R_{3}+5R_{2}\\\\\left[\begin{array}{cc|c}1&-7&3\\0&7&-28\\-0&0&7h-175\end{array}\right]](https://tex.z-dn.net/?f=R_%7B2%7D%20-%202R_%7B1%7D%20%2C%20R_%7B3%7D%20%2B%20R_%7B1%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%26-7%263%5C%5C0%267%26-28%5C%5C-0%26-5%26h%2B3%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C7R_%7B3%7D%2B5R_%7B2%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Cc%7D1%26-7%263%5C%5C0%267%26-28%5C%5C-0%260%267h-175%5Cend%7Barray%7D%5Cright%5D)
For system to be consistent:
