Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
Answer:
The slope of f(x) is equal to the slope of g(x).
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
step 1
Find the slope of the function f(x)
we have the points
(0,-1) and (3,1)
substitute in the formula
step 2
Find the slope of the function g(x)
take two points of the given table
(0,2) and (3,4)
substitute in the formula
step 3
Compare the slopes
therefore
The slope of f(x) is equal to the slope of g(x).
Answer:
Permanent Magnets and Electromagnets: What are the Differences? A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. ... An electromagnet is made from a coil of wire which acts as a magnet when an electric current passes through it.
Step-by-step explanation:
Answer:
f
Step-by-step explanation:
A right angled triangle has one angle equal to 90°
an obtuse angle triangle has one angle greater tan 90°
a) An o and right-angled triangle btuse angled triangle can have one angle equal.
b) R and O are not equivalent by definition
c) subset of R and Oare not all triangles as R and O are categories of all triangles. R and O are subset of all triangles
d) Acute triangles have all acute angles. So subset of R and O can't be all acute traingles
e) All triangles with two acute angles are may or may not have third angle as obtuse angle or 90° angle
f) none of the above
To answer this item, we have 4 as the speed of the kayaker in still water and the speed of current be y.
When the karayaker moves upstream or against the current, his speed would be 4 - y. Further, if he moves downstream or with the current, the total speed would be 4 + y. The time utilized for the travel is equal to the ratio of the distance and the speed.
Total time = 9/(4 - y) + 9/(4 + y) = 6
We multiply the equation by (4-y)(4+y)
9(4-y) + 9(4 + y) = 6(4-y)(4+y)
Simplifying,
72 = 96 - 6y²
Transposing all the constants to only one side of the equation and rearranging,
6y² = 96 - 72
y² = 4
y = 2
Hence, the speed of the river's current is 2 miles/hr. <em>The answer is letter B.) 2 miles/hour.</em>
