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lisov135 [29]
3 years ago
8

Solve variable 3/4x-5=7

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
5 0

Answer:

x=16

Step-by-step explanation:

7+5=12

12 divided by 3/4 is 16

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Drawing Conclusions
maksim [4K]

Answer:

Some of the Exponents = -2 that is true, not 2.

Step-by-step explanation:

Let's check one at a time.

(a)The 6 without an exponent is equivalent to the 6 having a 0 exponent.

6^{0} =1 and 6^{1} = 6 (no exponent. 6 \neq 1 therefore this statement is False.

(b)The sum of the exponents is -2.

let's check , if the base is same we can add the exponents that is the exponent rule.(well established).

if we add exponents in the given expression we get.

6^{1} 6^{0} 6^{3} =6^{1+0+(-3)} =6^{-2}, therefore we can see that the sum of the exponents = -2 this is true.

(c) An equivalent expression is 65.6-7, lets evaluate our above expression, it is equal to \frac{1}{36} which we can see that \frac{1}{36}  \neq 65.6-7 ,therefore this statement is false as well.

3 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
You decide to bake a cake for your sister's birthday, but you discover you don't have enough eggs. Before you go to the store, y
zheka24 [161]

Answer:

I think it will c because I have some eggs at home

5 0
3 years ago
Jackson’s mother buys 4 packs of hamburger meat.Each pack contains 4/6 of a pound of meat.How much total meat did she buy?
wariber [46]

Answer:

8/3 total or 2 2/3

Step-by-step explanation:

4 x 4/6 is the same thing as...

4/1 x 4/6

Multiply straight across...

16/6

Simplify...

8/3 total or 2 2/3

:)

5 0
2 years ago
Sam lives near a lagoon in the Caribbean that is populated by flamingos. Sam decides to figure out approximately how many flamin
klasskru [66]

Answer:

about 330

Step-by-step explanation:

280 rounded is 330 and 30 is already rounded so you would add 30 plus 330

5 0
3 years ago
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