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atroni [7]
1 year ago
6

Is 4.55 and 1.23456 a rational number

Mathematics
1 answer:
kaheart [24]1 year ago
7 0

Problem

Is 4.55 and 1.23456 a rational number

Solution

4.55 can be written as:

455/100 so then it could be a rational number

For the second number we have: 1.23456

And we can write this number as:

123456/100000

So then is also ratioanl

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5. How does the length of the long leg compare to the length of the short leg?
Oliga [24]

Answer:

measure it bro lol

Step-by-step explanation:

4 0
3 years ago
write the factored form for a quadratic equation with x-intercepts of -6 and -2 and the point (-3,-6) is on the parabola
kenny6666 [7]
F(x)=a(x-x1)(x-x2)
F(x)=a(x- - 6)(x- -2)
F(x)=a(x+6)(x+2)
-6=a(-3+6)(-3+2)
-6=a(3)(-1)
-6=-3a
2=a

Equation: f(x)=2(x+6)(x+2)
6 0
3 years ago
1. Evaluate each expression when x = -2 and y = 3.
borishaifa [10]
a) 3(-2) + 4(3) = -6 + 12 = 6

b) 2(-2) -3(3) +5 = -4 -9 + 5 = -8

c) 4(-2) -(3) = -8 -3 = -11

d) -(-2) -2(3) = 4 -6 = -2

e) (1/2)(-2) +(3) = -1 +3 = 2

f) (2/3)(3) -(1/2)(-2) = 2 + 1 = 3
5 0
3 years ago
How to know if a function is periodic without graphing it ?
zhenek [66]
A function f(t) is periodic if there is some constant k such that f(t+k)=f(k) for all t in the domain of f(t). Then k is the "period" of f(t).

Example:

If f(x)=\sin x, then we have \sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x, and so \sin x is periodic with period 2\pi.

It gets a bit more complicated for a function like yours. We're looking for k such that

\pi\sin\left(\dfrac\pi2(t+k)\right)+1.8\cos\left(\dfrac{7\pi}5(t+k)\right)=\pi\sin\dfrac{\pi t}2+1.8\cos\dfrac{7\pi t}5

Expanding on the left, you have

\pi\sin\dfrac{\pi t}2\cos\dfrac{k\pi}2+\pi\cos\dfrac{\pi t}2\sin\dfrac{k\pi}2

and

1.8\cos\dfrac{7\pi t}5\cos\dfrac{7k\pi}5-1.8\sin\dfrac{7\pi t}5\sin\dfrac{7k\pi}5

It follows that the following must be satisfied:

\begin{cases}\cos\dfrac{k\pi}2=1\\\\\sin\dfrac{k\pi}2=0\\\\\cos\dfrac{7k\pi}5=1\\\\\sin\dfrac{7k\pi}5=0\end{cases}

The first two equations are satisfied whenever k\in\{0,\pm4,\pm8,\ldots\}, or more generally, when k=4n and n\in\mathbb Z (i.e. any multiple of 4).

The second two are satisfied whenever k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}, and more generally when k=\dfrac{10n}7 with n\in\mathbb Z (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when k is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

Let's verify:

\sin\left(\dfrac\pi2(t+20)\right)=\sin\dfrac{\pi t}2\underbrace{\cos10\pi}_1+\cos\dfrac{\pi t}2\underbrace{\sin10\pi}_0=\sin\dfrac{\pi t}2

\cos\left(\dfrac{7\pi}5(t+20)\right)=\cos\dfrac{7\pi t}5\underbrace{\cos28\pi}_1-\sin\dfrac{7\pi t}5\underbrace{\sin28\pi}_0=\cos\dfrac{7\pi t}5

More generally, it can be shown that

f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))

is periodic with period \mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n).
4 0
3 years ago
7 What is the value of the expression -3x^2 y +4x when x = -4 and y = 2
love history [14]
<span> -3x^2 y +4x 
</span><span> =-3(-4)^2 (2) + 4(-4)
=-96-16
=-112</span>
7 0
3 years ago
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