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4 years ago

How do you write 1 tenth as a decimal

Mathematics

2 answers:

Bingel [31]4 years ago

8 0

"one tenth" as a decimal is 0.1 .

Nutka1998 [239]4 years ago

3 0

0.1 is the ansewer to the question

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N is a rational number.m is an irrational number.n2 cannot be an irrational number? why or why not

Korolek [52]

If n is rational, it means that

$n\in\mathbb{Q}\Rightarrow n=\frac{p}{q},\quad p\in\mathbb{Z},\quad q\in\mathbb{Z}^*$

Therefore when we do n² we can write it as

$n^2=\frac{p^2}{q^2},\quad p\in\mathbb{Z},\quad q\in\mathbb{Z}^*$

Remember that the product of two integer numbers is also an integer, therefore we can guarantee that

$p^2\in\mathbb{Z}\text{ and }q^2\in\mathbb{Z}^*$

Then we can confirm that n² is the quotient of two integers and the denominator is not zero, therefore, n² is always rational, it cannot be an irrational number

8 0

1 year ago

Find an exact value.

Westkost [7]

Answer:

$\displaystyle \cos\left(-\frac{7\,\pi}{12}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}$ .

Step-by-step explanation:

Convert the angle $\displaystyle \left(-\frac{7\, \pi}{12}\right)$ to degrees:

$\displaystyle \left(-\frac{7\, \pi}{12}\right) = \left(-\frac{7\, \pi}{12}\right) \times \frac{180^\circ}{\pi} = -105^\circ$ .

Note, that $\left(-105^\circ\right)$ is the sum of two common angles: $\left(-45^\circ\right)$ and $\left(-60^\circ\right)$ .

$\displaystyle \cos\left(-45^\circ\right) = \cos\left(45^\circ\right) = \frac{\sqrt{2}}{2}$ .
$\displaystyle \cos\left(-60^\circ\right) = \cos\left(60^\circ\right) = \frac{1}{2}$ .

$\displaystyle \sin\left(-45^\circ\right) = -\sin\left(45^\circ\right) = -\frac{\sqrt{2}}{2}$ .
$\displaystyle \sin\left(-60^\circ\right) = -\sin\left(60^\circ\right) = -\frac{\sqrt{3}}{2}$ .

By the sum-angle identity of cosine:

$\cos(A + B) = \cos(A)\cdot \cos(B) - \sin(A) \cdot \sin(B)$ .

Apply the sum formula for cosine to find the exact value of $\cos\left(-105^\circ \right)$ .

$\begin{aligned}\cos\left(-105^\circ \right) &= \cos\left(\left(-45^\circ\right) + \left(-60^\circ\right)\right) \\ &= \cos\left(-45^\circ\right) \cdot \cos\left(-60^\circ\right)\right) - \sin\left(-45^\circ\right) \cdot \sin\left(-60^\circ\right)\right) \\ &= \frac{\sqrt{2}}{2} \times \frac{1}{2} - \left(-\frac{\sqrt{2}}{2}\right)\times \left(-\frac{\sqrt{3}}{2}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}\end{aligned}$ .

$\displaystyle \left(-\frac{7\, \pi}{12}\right) = \left(-\frac{7\, \pi}{12}\right) \times \frac{180^\circ}{\pi} = -105^\circ$ . In other words, $\displaystyle \left(-\frac{7\, \pi}{12}\right)$ and $\left(-105^\circ\right)$ correspond to the same angle. Therefore, the cosine of $\displaystyle \left(-\frac{7\, \pi}{12}\right)\!$ would be equal to the cosine of $\left(-105^\circ\right)\!$ .

$\displaystyle \cos\left(-\frac{7\,\pi}{12}\right) = \cos\left(-105^\circ\right) = \frac{\sqrt{2} - \sqrt{6}}{4}$ .

3 0

3 years ago

Find the distance between points (0,-8) and (3,-2)

kompoz [17]

$\bf~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3-0]^2+[-2-(-8)]^2}\implies d=\sqrt{(3-0)^2+(-2+8)^2} \\\\\\ d=\sqrt{3^2+6^2}\implies d = \sqrt{9+36}\implies d=\sqrt{45}\implies d\approx 6.71$

7 0

3 years ago

Read 2 more answers

A customer at the mall is shopping for holiday gifts, and is considering having them wrapped. He can get them wrapped at the dep

ycow [4]

It would include 25 gifts for the cost the same amount either way

<em><u>Solution:</u></em>

Let "a" be the number of gifts to be wrapped

He can get them wrapped at the department store, which charges $2 per gift

Therefore,

Cost at department store: 2(number of gifts)

Cost at department store: 2a

The customer can pay his niece a flat fee of $50 to wrap all of his gifts

Cost at his niece: 50

He has a certain number of small packages, it would cost the same amount either way

Therefore,

Cost at department store = Cost at his niece

2a = 50

Divide both sides by 2

a = 25

Thus it would include 25 gifts for the cost the same amount either way

6 0

3 years ago

What is the area of these

Andrews [41]

Answer:

A. 27 ft. B. 12 ft. C. 28 ft. D. 15 ft. E. 35 ft. F. 75 ft.

Step-by-step explanation:

area of a triangle is equal to A= 1/2 BH (In other words just multiply the two numbers aka base times height then divide by two)

6 0

3 years ago