Answer:
The rule of translation is 
.
The translated vector is 
.
Step-by-step explanation:
Let supposed that translation to the right is in the +x direction and translation downwards in the -y direction.
We procced to translate the operation into mathematic terms. A translation consists in a vectorial sum on a given vector. That is:
(Eq. 1)
Where:
- Original vector, dimensionless.
- Translation vector, dimensionless.
- Translated vector, dimensionless.
If we know that 
, then the rule of translation is described by:
(Eq. 2)
If 
, then the new location of A is:
The translated vector is .
Answer:
I am not exactly sure what the problem is asking. If the output of the equation f(x)= x+5 is 2 then the input would be -3.
Answer:
C. 2.8 miles per minute
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
... Tan = Opposite/Adjacent
In the relevant triangle, the side opposite the angle at the observer is the altitude of the airplane, 2 miles. The side adjacent is the horizontal distance to the airplane. At the first observation, that distance (d1) is ...
... tan(40°) = (2 mi)/d1
At the second observation, the horizontal distance to the airplane (d2) is ...
... tan(50°) = (2 mi)/d2
Solving for d1 and d2 and finding the difference (∆d), we have ...
... d1 = (2 mi)/tan(40°)
... d2 = (2 mi)/tan(50°)
... ∆d = d1 -d2 = (2 mi)(1/tan(40°) -1/tan(50°) ≈ 2·(1.1918 -0.8391) mi
... ∆d ≈ 2°0.3526 mi ≈ 0.7053 mi
This distance was flown by the plane in 15 seconds, so it will travel 4 times this distance in 60 seconds (1 minute).
... ∆d/∆t = (0.7053 mi)/(1/4 min) = 4·0.7053 mi/min ≈ 2.8 mi/min
Answer:
x = 7/12
Step-by-step explanation:
We start off by multiplying both sides by 4:
4(x-2) = 3(2-x)
Distribute the 4 and the 3:
4x - 8 = 6 - 3x
Bring all the terms with the x at the first side:
4x + 3x = 6 + 8
7x = 12
x = 7/12
Answer:
We will be using the Pythagorean theorem for the first 2 and SOH CAH TOA for the other 3.
a^2 + b^2 = c^2
sin(t) = b/c; cos(t) = a/c; tan(t) = b/a
#4) a^2 + 9^2 = (3sqrt(10))^2 #5 9^2 + 27^2 = c^2
a^2 + 81 = 90 81 + 729 = c^2
a^2 = 9 810 = c^2
a = 3 9sqrt(10) = c
#6 27 + 3 = 30 #9 cos(90) = 8/c
8/-0.45 = c
| 17 | = c [not the exact value]
#7 8^2 + b^2 = 17^2 #8 2^2 + 15^2 = c^2
64 + b^2 = 289 4 + 225 = c^2
b^2 = 225 229 = c^2
b = 15 [not the exact value] 15.3 = c [not the exact value]
Sorry if something doesn't make sense and felt kind of rushed. Feel free to comment down below my answer if you have any questions and I'll try to clarify it the best I can.
