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3 years ago

1) 52 + 33=| 2) 26 = 42 = 3) 72 - 2015 4) 32 x 22=

Mathematics

1 answer:

inna [77]3 years ago

5 0

1) 52 + 33= 85

2) 26 + 42 = 68 or 26 - 42 = - 16

3) 72 - 2015 = =1943

4) 32 x 22 = 704

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Square root of 2tanxcosx-tanx=0

kobusy [5.1K]

If you're using the app, try seeing this answer through your browser: brainly.com/question/3242555

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Solve the trigonometric equation:

$\mathsf{\sqrt{2\,tan\,x\,cos\,x}-tan\,x=0}\\\\ \mathsf{\sqrt{2\cdot \dfrac{sin\,x}{cos\,x}\cdot cos\,x}-tan\,x=0}\\\\\\ \mathsf{\sqrt{2\cdot sin\,x}=tan\,x\qquad\quad(i)}$

Restriction for the solution:

$\left\{ \begin{array}{l} \mathsf{sin\,x\ge 0}\\\\ \mathsf{tan\,x\ge 0} \end{array} \right.$

Square both sides of (i):

$\mathsf{(\sqrt{2\cdot sin\,x})^2=(tan\,x)^2}\\\\ \mathsf{2\cdot sin\,x=tan^2\,x}\\\\ \mathsf{2\cdot sin\,x-tan^2\,x=0}\\\\ \mathsf{\dfrac{2\cdot sin\,x\cdot cos^2\,x}{cos^2\,x}-\dfrac{sin^2\,x}{cos^2\,x}=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left(2\,cos^2\,x-sin\,x \right )=0\qquad\quad but~~cos^2 x=1-sin^2 x}$

$\mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\cdot (1-sin^2\,x)-sin\,x \right]=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2-2\,sin^2\,x-sin\,x \right]=0}\\\\\\ \mathsf{-\,\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}\\\\\\ \mathsf{sin\,x\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}$

Let

$\mathsf{sin\,x=t\qquad (0\le t$

So the equation becomes

$\mathsf{t\cdot (2t^2+t-2)=0\qquad\quad (ii)}\\\\ \begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{2t^2+t-2=0} \end{array}$

Solving the quadratic equation:

$\mathsf{2t^2+t-2=0}\quad\longrightarrow\quad\left\{ \begin{array}{l} \mathsf{a=2}\\ \mathsf{b=1}\\ \mathsf{c=-2} \end{array} \right.$

$\mathsf{\Delta=b^2-4ac}\\\\ \mathsf{\Delta=1^2-4\cdot 2\cdot (-2)}\\\\ \mathsf{\Delta=1+16}\\\\ \mathsf{\Delta=17}$

$\mathsf{t=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{2\cdot 2}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{4}}\\\\\\ \begin{array}{rcl} \mathsf{t=\dfrac{-1+\sqrt{17}}{4}}&\textsf{ or }&\mathsf{t=\dfrac{-1-\sqrt{17}}{4}} \end{array}$

You can discard the negative value for t. So the solution for (ii) is

$\begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{t=\dfrac{\sqrt{17}-1}{4}} \end{array}$

Substitute back for t = sin x. Remember the restriction for x:

$\begin{array}{rcl} \mathsf{sin\,x=0}&\textsf{ or }&\mathsf{sin\,x=\dfrac{\sqrt{17}-1}{4}}\\\\ \mathsf{x=0+k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=arcsin\bigg(\dfrac{\sqrt{17}-1}{4}\bigg)+k\cdot 360^\circ}\\\\\\ \mathsf{x=k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=51.33^\circ +k\cdot 360^\circ}\quad\longleftarrow\quad\textsf{solution.} \end{array}$

where k is an integer.

I hope this helps. =)

3 0

2 years ago

The phone company NextFell has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of mon

zaharov [31]

The equation in the form y = mx + b is y = 0.35x + 36.

<h3>How to represent a linear equation?</h3>

The equation formed from the expression is a linear equation and should be expressed in the slope intercept form.

y = mx + b

where

m = slope
b = y-intercept

Therefore,

y = mx + b

where

x = the number of monthly minutes used
y = the total monthly of the Next fell plan

using the coordinates, let's find m

(470, 200.5)(590, 242.5)

Hence,

m = 242.5 - 200.5 / 590 - 470

m = 42 / 120

m = 0.35

Therefore,

y = 0.35x + b

200.5 = 0.35(470) + b

200.5 - 164.5 = b

b = 36

Finally, the equation in the form y = mx + b is y = 0.35x + 36.

learn more on linear equation here: brainly.com/question/24223023

#SPJ1

7 0

1 year ago

The proper angle for a ladder is about 75 ∘ 75∘ from the ground. suppose you have a 14 foot ladder. how far from the house shoul

jonny [76]

We just use the sinus rule to calculate this

a / sin alpha = b / sin beta

Alpha is the 90 degree angle from the wall to the floor
beta is the angle from the top of the ladder to the wall,
wich is 90 degrees - 75 degrees (triangle has 180 degrees angles, one is 90 degrees), so beta = 15 degrees

14 foot / sin 90 = b / sin 15
sin 90 = 1
we move the sin15 over to the other side

14 foot x sin 15 = b
b = 3.62 foot

5 0

3 years ago

Which is greater 1/10 or .09 why?

lesantik [10]

Answer:

1/10

Step-by-step explanation:

Decimal Form:

0.09

0.1

Fraction Form:

9/100

1/10

Percentage Form:

10%

Hope that helps :-)

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2 years ago

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zhannawk [14.2K]

Answer:

Step-by-step explanation:

Since a die has six faces, 6 outcomes are possible

Since a coin has two faces, 2 outcomes are possible

Multiply the chances together and you get 12

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2 years ago