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2 years ago

) tan C с 45 36 to 27 А

Mathematics

1 answer:

Sliva [168]2 years ago

5 0

Answer:

36. 1193 or 33.12 degrees rounded

Step-by-step explanation:

Tan = opp/adj

Tan C = 27/37

Tan inverse (.729 . . .) = C

= 36. 1193 or 33.12 degrees rounded

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Gordon Rosel went to his bank to find out how long it will take for $2,500 to amount to $3,090 at 6% simple interest. Calculate

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It will take 4 years

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3 years ago

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Annie, Brianna & Carly are selling fruit boxes to raise money for their soccer team. All together the girls have sold 105 bo

GaryK [48]

Step-by-step explanation:

Annie = x

Brianna = y

Carly = z

Now,

x + y + z = 105 ...(1)

Carly has sold ten more than three times Brianna's sales.

z = 10 + 3y ...(2)

Brianna sold five more than Annie.

y = 5 + x ...(3)

Now,

z = 10 + 3y

z = 10 + 3(5 + x)

z = 10 + 15 + 3x

z = 25 + 3x

Now,

x + y + z = 105

x + (5 + x) + 25 + 3x = 105

5x + 30 = 105

5x = 105 - 30

5x = 75

5x/5 = 75/5

x = 15

So,

y = 5 + x

y = 5 + 15

y = 20

Now,

z = 25 + 3x

z = 25 + 3(15)

z = 25 + 45

z = 70

Thus,

Annie Sold 15 boxes

Brianna Sold 20 boxes

Carly Sold 70 boxes

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2 years ago

How to know if a function is periodic without graphing it ?

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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 $\mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n)$ .

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2 years ago

Write an expression with (-1) as its base that will product a negative product

algol [13]

Base of the exponential equation should be (-1).

And finally the product or result should also be a negative number.

Let us take a variable for n natural numbers.

(Note: All positive whole numbers are called natural numbers that is 1,2,3,4,5,....).

In order to get the expression, we need to find the expession for odd natural numbers.

We know,

The expession for odd natural numbers is given by = 2n-1.

Where n= 1,2,3,4,5...

If we have an odd exponent of a negative number, it always gives a negative number.

We got, base = -1 ( a negative number) and

exponent = (2n-1) ........... expression for odd number.

Therefore, we could write final exponential expression that would give a negative for all natural numbers.

$(-1)^{2n-1}$

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3 years ago

a childrens book has dimensions 20cm by 24cm what scale factor should be used to make a enlarged version that has dimensions 25c

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A scale factor of 1.25, also written as 1 1/4 should be used

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3 years ago