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irinina [24]
3 years ago
13

What is the y-intercept of y = -2x+6

Mathematics
1 answer:
nikitadnepr [17]3 years ago
3 0

Answer:

6

Step-by-step explanation:

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Which expression is equivalent to 4r2/514.3V5r8, if x=0?
san4es73 [151]

Step-by-step explanation:

I think it would be c if not D

8 0
2 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
On a coordinate plane, 2 triangles are shown. The first triangle has points S (3, 5), R (5, 0), and Q (1, 0). The second triangl
enyata [817]

Answer:

<u>B. (x, y) → (–x, –y).</u>

Step-by-step explanation: This is the correct answer on <u>Edge 2021</u>, just did the assignment. Hope this helps ^-^.

6 0
2 years ago
A single-engine plane is flying at 30 mph in the direction N 60° E. A wind is blowing from west to east at 15 mph
Ksivusya [100]

Answer:

C on Edge 2020

Step-by-step explanation:

The graph where the 60 degree angle is touching the y axis and air is above ground

7 0
3 years ago
Read 2 more answers
Please help ASAP<br><br><br>Simplify <img src="https://tex.z-dn.net/?f=%5Csqrt%7B.64x%5E2%7D" id="TexFormula1" title="\sqrt{.64x
Brilliant_brown [7]
Answer: 4/5x

Explanation: simply the expression, then convert it and calculate your answer.
3 0
3 years ago
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