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3 years ago

Between which two consecutive integers does the square root of 53 lie

Mathematics

2 answers:

Fittoniya [83]3 years ago

6 0

53<span> is </span>between<span> 49 and 64</span>

choli [55]3 years ago

4 0

The square root of 53 will lie between 7 and 8.

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Find the exact value of tan (arcsin (two fifths)). For full credit, explain your reasoning.

Hitman42 [59]

$\bf sin^{-1}(some\ value)=\theta \impliedby \textit{this simply means}
\\\\\\
sin(\theta )=some\ value\qquad \textit{now, also bear in mind that}
\\\\\\
sin(\theta)=\cfrac{opposite}{hypotenuse}\qquad 
\qquad 
% tangent
tan(\theta)=\cfrac{opposite}{adjacent}\\\\
-------------------------------\\\\$

$\bf sin^{-1}\left( \frac{2}{5} \right)=\theta \impliedby \textit{this simply means that}
\\\\\\
sin(\theta )=\cfrac{2}{5}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}\qquad \textit{now let's find the adjacent side}
\\\\\\
\textit{using the pythagorean theorem}\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad 
\begin{cases}
c=hypotenuse\\
a=adjacent\\
b=opposite\\
\end{cases}$

$\bf \pm \sqrt{5^2-2^2}=a\implies \pm\sqrt{21}=a
\\\\\\
\textit{we don't know if it's +/-, so we'll assume is the + one}\quad \sqrt{21}=a\\\\
-------------------------------\\\\
tan(\theta)=\cfrac{opposite}{adjacent}\qquad \qquad tan(\theta)=\cfrac{2}{\sqrt{21}}
\\\\\\
\textit{and now, let's rationalize the denominator}
\\\\\\
\cfrac{2}{\sqrt{21}}\cdot \cfrac{\sqrt{21}}{\sqrt{21}}\implies \cfrac{2\sqrt{21}}{(\sqrt{21})^2}\implies \cfrac{2\sqrt{21}}{21}
$

7 0

3 years ago

Write an equation that passes through (0, 20) and (4, 80) ??

trapecia [35]

Answer:

M= 15

Step-by-step explanation:

Hope it’s right

7 0

3 years ago

Based on the diagram, what is the value of x?

Fynjy0 [20]

Hope this helps! feel free to clarify

8 0

3 years ago

Each student at some college has a mathematics requirement M (to take at least one mathematics course) and a science requirement

Furkat [3]

all students = 150

M = 60

S = 45

M and S = 25

(a) At least one of the two requirements:

M or S = M + S - (M and S) = 60 + 45 - 25 = 80

(b) Exactly one of the two requirements:

(M or S) - (M and S) = 80 - 25 = 55

(all students) - (M or S) = 150 - 80 = 70

8 0

3 years ago

Here are three different recipes for orangey- pineapple juice. Two of these mixtures taste the same and one tastes different.

LekaFEV [45]

Answer:

recipe 1 and recipe 2 will taste the same while recipe 3 will taste different

Step-by-step explanation:

Let's look at the Mix ratio

for recipe 1 the mix ratio is 2:3

recipe 2 ratio is 2:3

and recipe 3 ratio is 3:4

5 0

3 years ago