<span><span>DO use multiplication sign '*' (the STAR) symbol. For the simplifier, xy is NOT the same as x*y or yx. Simplifier thinks that xy is a separate variable. Good example: x*y-y*(x+2). Bad example: xy-y(x+2).</span>DO use '*' when multiplying a variable by an expression in parentheses: x*(x+2). Otherwise, my simplifier will think that you are trying to use a function and will become confused.Use parentheses liberally to avoid any ambiguity. (x+y)/(x-y) is NOT the same as x+y/x-y. x+y/x-y means x+(y/x)-y.</span>Operations<span>Use '*' (STAR) for multiplication. 2*3 is legal, 2x3 will be misunderstood.Use '^' (CARET) for power. 2^3 means 2 to degree of 3, or 8.Use '/' (FORWARD SLASH) for divisionOnly '(' and ')' (parentheses) are allowed for grouping terms. Curly or square brackets are used for other purposes.</span>
Operation priority: + and - have lowest priority, * and / h
Good Examplesx*y-x*(y+2) <-- '*' is used for multiplications
a^b*3 <-- means (a to the degree of b) multiplied by 3
Bad examples<span>xy-yx <-- variable xy and variable yx are different variables
y(x-2) <-- simplifier will think that it is function y of x-2.</span>
5 milligrams are equal to .005 grams.
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:
a
Step-by-step explanation:
The equation of a proportional relationship is
y = kx ← k is the constant of proportionality
Divide both sides by x
= k
To find k use any ordered pair from the table
Using (2, 
) , then
k = 
= 2 × 
= 
Answer:
I think it's -2
Step-by-step explanation:
