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4 years ago

13

Find the exact solutions of the problem algebraically: tan 2x-cot x=0

1 answer:

Eva8 [605]4 years ago

5 0

Tan 2x - cot x = 0
2tan x / (1 - tan^2 x) - 1/tan x = 0
2tan^2 x - (1 - tan^2 x) = 0
2tan^2 x - 1 + tan^2 x = 0
3tan^2 x - 1 = 0
tan^2 x = 1/3
tan x = + or - 1/√3

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Tom has 2 1/2 times as many cards as Harry. Together they have 98 cards. How many cards do they each have?

USPshnik [31]

Answer:

Tom has 70 cards, and Harry has 28 cards.

Step-by-step explanation:

Let h = number of cards Harry has.

Then the number of cards Tom has is 2 1/2 * h = 2.5h.

Together they have 2.5h + h = 3.5h number of cards.

Together they have 98 cards.

3.5h = 98

h = 98/3.5

h = 28

Harry has 28 cards.

Tom has 2.5h = 2.5 * 28 = 70

Answer: Tom has 70 cards, and Harry has 28 cards.

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3 years ago

A box contains 2 red marbles , 3 green marbles , and 3 blue marbles

krek1111 [17]

Answer:

the box contains a total of 8 marbles .

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Step-by-step explanation:

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5 0

4 years ago

Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 10 right angle0,−10 in the directions

quester [9]

Solution :

Let $v_0$ be the unit vector in the direction parallel to the plane and let $F_1$ be the component of F in the direction of $v_0$ and $F_2$ be the component normal to $v_0$ .

Since, $|v_0| = 1,$

$(v_0)_x=\cos 60^\circ= \frac{1}{2}$

$(v_0)_y=\sin 60^\circ= \frac{\sqrt 3}{2}$

Therefore, $v_0 = \left$

From figure,

$|F_1|= |F| \cos 30^\circ = 10 \times \frac{\sqrt 3}{2} = 5 \sqrt3$

We know that the direction of $F_1$ is opposite of the direction of $v_0$ , so we have

$F_1 = -5\sqrt3 v_0$

$=-5\sqrt3 \left$

$= \left$

The unit vector in the direction normal to the plane, $v_1$ has components :

$(v_1)_x= \cos 30^\circ = \frac{\sqrt3}{2}$

$(v_1)_y= -\sin 30^\circ =- \frac{1}{2}$

Therefore, $v_1=\left< \frac{\sqrt3}{2}, -\frac{1}{2} \right>$

From figure,

$|F_2 | = |F| \sin 30^\circ = 10 \times \frac{1}{2} = 5$

∴ $F_2 = 5v_1 = 5 \left< \frac{\sqrt3}{2}, - \frac{1}{2} \right>$

$=\left$

Therefore,

$F_1+F_2 = \left< -\frac{5\sqrt3}{2}, -\frac{15}{2} \right> + \left< \frac{5 \sqrt3}{2}, -\frac{5}{2} \right>$

$= = F$

3 0

3 years ago

HELP AAAAAAAAAAAAAAAAAAA<br> Name all the factors of 12.

rjkz [21]

I think it’s 1 2 3 4 6

3 0

3 years ago

Read 2 more answers

A triangle has one angle that measures 56° and one angle that measures 63º.

crimeas [40]

<h2>sum of a triangle= 180°</h2>

63+56=119
180-119=61
ans=61°

7 0

3 years ago