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2 years ago

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9. Sonya opened a savings account with and deposits each week. Brad opened a savings account with and contributes each week. Aft

er how many weeks will account balance be twice as much as Sonya's What will i the balance be in each account then I I

1 answer:

Lapatulllka [165]2 years ago

8 0

It will take 6 weeks for Brad to get twice the amount as Sonya.
Sonya will have $260 dollars and Brad will have $360

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Compare each set of rational numbers.

Fed [463]

Hey.. don’t click on that link or any links on here !!! but i jus wanna say you didn’t attach an image of your question :).

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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

2 years ago

A textbook store sold a combined total of 368 psychology and sociology textbooks in a week. The number of psychology textbooks s

OLga [1]

Step-by-step explanation:

Total books = 368.

Sociology books = 92.

Psychology books = 3 times sociology books

= 3 x 92 = 276

Total = 276 + 92 = 368

3 0

2 years ago

Plz answer all corectly will mark brainlest plz answer within 1 hour

denis23 [38]

Answer:

for the first one I got y=-2x-2 the second part i got y=-x-1 or -1x-y-1=0 Correct me if I am wrong

Step-by-step explanation:

Use the slope formula

-4-4 =-8

/ =-2

1 - -3=4

2. The second part use this formula y-y1=m(x-x1)

y--4=-1(x-3)

y+4=-x+3

-4 -4

y+0=-x-1

y=-x-1 or -1x-y-1=0 I am not sure

6 0

2 years ago

What is the image point of (-8, 7) after a translation right 5 units and up 5 units?

aleksklad [387]

Answer:

(-3,12)

Step-by-step explanation:

4 0

2 years ago