Answer:
25. rational
26. irrational
Step-by-step explanation:
A rational number is a number that can be written as a fraction. It may have decimals that end or repeating decimals.
An irrational number cannot be written as a fraction. It's decimals continue on and do not repeat.
25.
When you multiply two rational numbers, the product is rational. The square root of 16 is 4, which is rational because it is a whole number. 4/7 is written as a fraction so it is rational.
26.
The square root of 2 is an irrational number because its decimals go on and do not repeat. 7 is a whole number so it is rational. Subtracting a irrational number from a rational number gives an irrational number.
It is the first one for sure! Hope this helps
Answer:
y=9
Step-by-step explanation:
4y-7=29
(add 7 to both sides)
4y=36
(divide both sides by 4)
y=9
The answer to the question is true
Answer:
A = √29
Step-by-step explanation:
The short of it is that ...
A² = 2² + 5² = 29
A = √29
_____
<u>Amplitude</u>
If you expand the second form using the sum-of-angles formula, you get ...
Asin(ωt +φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Comparing this to the first form, you find ...
c₂ = 2 = Acos(φ)
c₁ = 5 = Asin(φ)
The Pythagorean identity can be invoked to simplify the sum of squares:
(Asin(φ))² + (Acos(φ))² = A²(sin(φ)² +cos(φ)²) = A²·1 = A²
In terms of c₁ and c₂, this is ...
(c₁)² +(c₂)² = A²
A = √((c₁)² +(c₂)²) . . . . . . . formula for amplitude
_____
<u>Phase Shift</u>
We know that tan(φ) = sin(φ)/cos(φ) = (Asin(φ))/(Acos(φ)) = 5/2, so ...
φ = arctan(c₁/c₂) . . . . . . . formula for phase shift*
φ = arctan(5/2) ≈ 1.19029 radians
___
* remember that c₁ is the coefficient of the cosine term, and c₂ is the coefficient of the sine term.
