Answer:
a^2+b^2=c^2
Step-by-step explanation:
Based on the pythagorean theorem for right triangle, if you plug in 3 for a, 4 for b, and 5 for c, the equation will be made true, making it a right triangle.
3^2 + 4^2 = 5^2
9 + 16 = 25
The z-score is given by:
Z-score=(x-μ)/σ
where:
μ=mean
σ=std deviation
From the information:
mean for 20-29 year old man is μ=69.669 and std deviation is σ=3.23
mean for 20-29 year old woman is μ=64.564 and the std deviation is σ=3.83
the z-score for 75 inch men is:
z-man=(75-69.669)/3.23=1.651
the z-core for 70 inch woman:
z-woman=(70-64.564)/3.83
=1.42
From the above we conclude that the z-score for the man is relatively larger than that of the women, this means that the man is taller.
The answer is A.
Answer:
See explanations below
Step-by-step explanation:
Given the following complex numbers in polar form:
w = 2(cos(90°) + i sin (90°))
sin 90 = 1
cos 90 = 0
Substitute into the formula:
w = 2(0+i(1))
w = 2(0)+2i
w = 0+2i
Hence the value of w in rectangular form is 0+2i
For z:
z =√2(cos(225°) + i sin(225°))
z = √2(-1/√2+ i (-1/√2))
z = -√2/√2 - √2(-1/√2)i
z = -1+ 1i
Hence the value of z in rectangular coordinate is -1+ 1i
For w + z:
w + z = 0+2i + (-1+1i)
w+z = 0+2i-1+i
w+z = -1+3i
Write w+z in polar form
Get the modulus
|w+z| = √(-1)²+3²
|w+z| = √1+9
|w+z| = √10
Get the modulus
theta = tan^-1(-3)
theta = -71.56
theta = 180 - 71.56
theta = 108.43
The expression in polar form is z = √10(cos108.43+isin108.43)
Answer:
(x - 10)² + y² = 29
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k) = (10, 0), thus
(x - 10)² + (y - 0)² = r²
The radius is the distance from the centre to a point on the circle
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (10, 0) and (x₂, y₂ ) = (5, 2)
r =
=
= =
Thus
(x - 10)² + (y - 0)² = ( )², that is
(x - 10)² + y² = 29 ← equation of circle
Answer:
18/3 =6/1 and 12/2=6 so both answers should be 6