Answer:
x = 52, A.
Step-by-step explanation:
The two angles across from each other are both acute angles, which means that considering their positioning, they're gonna equal the same in degrees. If the question were asking to find the value of x on one of the obtuse angles, your answer would be B, considering both of those lines would equal 180 degrees.
Hope that helps!
9.42 Units
Step-by-step explanation:
Since the angle shown is 90 degrees we can deduce that the rest of the arc is 270 degrees therefore we can make the fraction:
270/360; 360 being the total angle measurement of a circle
270/360 simplifies to 3/4
The fraction represents how much of the circle that arc covers
Now we have to find the circumference which would be
2(3.14)r
r = 2 therefore: 2(3.14)2 = 12.56
Now that we have the circumference of the WHOLE circle we multiply it by 3/4 to find out the arc length
Which gives us 9.42
Answer:
C. 5
Step-by-step explanation:
first expression 5 × (9-3) = 30
second one 45 - 3x
to make it 30 = 30
x should be = 5
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:
Step-by-step explanation:
This is <em>a separable differential equation</em>. Rearranging terms in the equation gives
Integration on both sides gives
where 
is a constant of integration.
The steps for solving the integral on the right hand side are presented below.
Therefore,
Multiply both sides by 
By taking exponents, we obtain
Isolate 
.
Since 
when 
, we obtain an initial condition 
.
We can use it to find the numeric value of the constant .
Substituting 
for and 
in the equation gives
Therefore, the solution of the given differential equation is
