Answer:
c=
−4
3
s−t+
−4
3
Step-by-step explanation:
Let's solve for c.
3s+2t−3c−7s−5t=4
Step 1: Add 4s to both sides.
−3c−4s−3t+4s=4+4s
−3c−3t=4s+4
Step 2: Add 3t to both sides.
−3c−3t+3t=4s+4+3t
−3c=4s+3t+4
Step 3: Divide both sides by -3.
−3c
−3
=
4s+3t+4
−3
c=
−4
3
s−t+
−4
3
Answer:
d=-5
Step-by-step explanation:
-4d-37=7d +18
move the terms to its correct side
-4d-7d=18+37
calculate the like terms together.
-11d=55
divide both sides by -11. both of the negavtive (-11) will cancel out and become d on the left and on the right 55 will be divided by -11 = -5. the 5 is negative because there's a negative -11 if there were a postive 11 it will be 5 instead of D=-5
Answer with Step-by-step explanation:
We are given that
u+ v and u-v are orthogonal
We have to prove that u and v must have the same length.
When two vector a and b are orthogonal then
![a\cdot b=0](https://tex.z-dn.net/?f=a%5Ccdot%20b%3D0)
By using the property
![(u+v)\cdot (u-v)=0](https://tex.z-dn.net/?f=%28u%2Bv%29%5Ccdot%20%28u-v%29%3D0)
We know that
![(a+b)\cdot (a-b)=\mid a\mid^2-\mid b\mid^2](https://tex.z-dn.net/?f=%28a%2Bb%29%5Ccdot%20%28a-b%29%3D%5Cmid%20a%5Cmid%5E2-%5Cmid%20b%5Cmid%5E2)
![\mid u\mid ^2-\mid v\mid^2=0](https://tex.z-dn.net/?f=%5Cmid%20u%5Cmid%20%5E2-%5Cmid%20v%5Cmid%5E2%3D0)
![\mid u\mid^2=\mid v\mid^2](https://tex.z-dn.net/?f=%5Cmid%20u%5Cmid%5E2%3D%5Cmid%20v%5Cmid%5E2)
Magnitude is always positive
When power of base on both sides are equal then base will be equal
Therefore,
![\mid u\mid=\mid v\mid](https://tex.z-dn.net/?f=%5Cmid%20u%5Cmid%3D%5Cmid%20v%5Cmid)
Hence, the length of vectors u and v must have the same length.
Answer:
∠6=58°
Step-by-step explanation:
∠3=∠6=58°
Answer:
1. More magnets are longer than 2 1/2
2. 10 magnets measure in whole numbers and 5 magnets between 2 whole numbers
3. Because the shortest magnet is 1 inch and the longest magnet is 4 inches.
Step-by-step explanation:
1. There are 7 magnets that are longer than 7 1/2 and only 6 magnets that are shorter than 2 1/2. (The 2 magnets that are exactly 2 1/2 are neither longer nor shorter therefore they do not apply to the question.)