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3 years ago

Is the square root of 81 natural whole integer rational irrational or real ?

Mathematics

1 answer:

Alika [10]3 years ago

6 0

Answer:

It is natural

Step-by-step explanation:

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Which is the better buy? 5-pack of toaster pastries for $4.13 or 9-pack of toaster pastries for $7.56

kolbaska11 [484]

Answer: The answer is 9-pack of toaster pastries for $7.56

Step-by-step explanation:

Basicly it would be more expensive if you bought 9 for the first option but less for the other.

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3 years ago

HELP HELP PLEASE!! D: Determine the missing side length!! PLEASE NO CAP!!

charle [14.2K]

Answer:

missing side length = 9

Step-by-step explanation:

$c^{2} = a^{2} + b^{2}$

a = 6

b = 7

c = missing side

$c^{2} = 6^{2} + 7^{2}$

$c^{2} = 36 + 49$

$c^{2} = 85$

$\sqrt{c^{2} } = \sqrt{85}$

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3 years ago

A car is traveling at a speed of 79 feet per second. (a) what is its speed in kilometers per hour?

AysviL [449]

79 ft/s = 0.0240792 km/s

0.0240792 x 60 = 1.444752 km/minute
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Ans: 86.69 km/h

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3 years ago

Please Help! This is a trigonometry question.

liraira [26]

$\large\begin{array}{l} \textsf{From the picture, we get}\\\\ \mathsf{tan\,\theta=\dfrac{2}{3}}\\\\ \mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{2}{3}}\\\\ \mathsf{3\,sin\,\theta=2\,cos\,\theta}\qquad\mathsf{(i)} \end{array}$

$\large\begin{array}{l} \textsf{Square both sides of \mathsf{(i)} above:}\\\\ \mathsf{(3\,sin\,\theta)^2=(2\,cos\,\theta)^2}\\\\ \mathsf{9\,sin^2\,\theta=4\,cos^2\,\theta}\qquad\quad\textsf{(but }\mathsf{cos^2\theta=1-sin^2\,\theta}\textsf{)}\\\\ \mathsf{9\,sin^2\,\theta=4\cdot (1-sin^2\,\theta)}\\\\ \mathsf{9\,sin^2\,\theta=4-4\,sin^2\,\theta}\\\\ \mathsf{9\,sin^2\,\theta+4\,sin^2\,\theta=4} \end{array}$

$\large\begin{array}{l} \mathsf{13\,sin^2\,\theta=4}\\\\ \mathsf{sin^2\,\theta=\dfrac{4}{13}}\\\\ \mathsf{sin\,\theta=\sqrt{\dfrac{4}{13}}}\\\\ \textsf{(we must take the positive square root, because }\theta \textsf{ is an}\\\textsf{acute angle, so its sine is positive)}\\\\ \mathsf{sin\,\theta=\dfrac{2}{\sqrt{13}}} \end{array}$

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$\large\begin{array}{l} \textsf{From (i), we find the value of }\mathsf{cos\,\theta:}\\\\ \mathsf{3\,sin\,\theta=2\,cos\,\theta}\\\\ \mathsf{cos\,\theta=\dfrac{3}{2}\,sin\,\theta}\\\\ \mathsf{cos\,\theta=\dfrac{3}{\diagup\!\!\!\! 2}\cdot \dfrac{\diagup\!\!\!\! 2}{\sqrt{13}}}\\\\ \mathsf{cos\,\theta=\dfrac{3}{\sqrt{13}}}\\\\ \end{array}$

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$\large\begin{array}{l} \textsf{Since sine and cosecant functions are reciprocal, we have}\\\\ \mathsf{sin\,2\theta\cdot csc\,2\theta=1}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{sin\,2\theta}\qquad\quad\textsf{(but }}\mathsf{sin\,2\theta=2\,sin\,\theta\,cos\,\theta}\textsf{)}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{2\,sin\,\theta\,cos\,\theta}}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{2\cdot \frac{2}{\sqrt{13}}\cdot \frac{3}{\sqrt{13}}}} \end{array}$

$\large\begin{array}{l} \mathsf{csc\,2\theta=\dfrac{~~~~1~~~~}{\frac{2\cdot 2\cdot 3}{(\sqrt{13})^2}}}\\\\ \mathsf{csc\,2\theta=\dfrac{~~1~~}{\frac{12}{13}}}\\\\ \boxed{\begin{array}{c}\mathsf{csc\,2\theta=\dfrac{13}{12}} \end{array}}\qquad\checkmark \end{array}$

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$\large\textsf{I hope it helps.}$

Tags: trigonometry trig function cosecant csc double angle identity geometry

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3 years ago

PLEASE HELP ASAP PLEASE ANSWER CORRECTLY WILL GET BRAINLIEST

Xelga [282]

Answer:

True

Step-by-step explanation:

Each x input has 1 y output

5 0

2 years ago

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