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1003086002

Level:

The equation

(\sin x + \cos x)^{2} = 1.5

has two solutions on the interval

(0^{\circ}; 90^{\circ})

. The larger one is:

75^{\circ}

15^{\circ}

30^{\circ}

65^{\circ}

1003086001

Level:

The arithmetic mean of all

x \in [0^{\circ}; 360^{\circ}]

satisfying the equation

\sin 2 x = \sin x

is:

180^{\circ}

240^{\circ}

360^{\circ}

270^{\circ}

1003032508

Level:

Find the term that does not contain

x

and

y

(constant term) in the expansion of

(x + y)^{4} (\frac{1}{x} + \frac{1}{y})^{4}

70

2

36

0

1003032507

Level:

Express

v_{1}

from the formula

v = \frac{v_{1} v_{2} (d_{1} + d_{2})}{d_{1} v_{2} + d_{2} v_{1}}

v_{1} = \frac{v d_{1} v_{2}}{v_{2} d_{1} + v_{2} d_{2} - v d_{2}}

v_{1} = \frac{v v_{2} d_{1}}{v d_{2} - v_{2} d_{1} - v_{2} d_{2}}

v_{1} = \frac{v v_{2} (d_{1} + d_{2})}{d_{1} v_{2} + d_{2} v}

v_{1} = \frac{v (d_{1} v_{2} + d_{2} v_{1})}{v_{2} (d_{1} + d_{2})}

1003032506

Level:

In a parallel circuit the total resistance

R

of three components with the resistances

R_{1}

R_{2}

R_{3}

is given by the formula

\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

. Express

R_{1}

from this formula.

R_{1} = \frac{R R_{2} R_{3}}{R_{2} R_{3} - R (R_{2} + R_{3})}

R_{1} = \frac{R - R_{2} - R_{3}}{R R_{2} R_{3}}

R_{1} = R - \frac{R_{2} R_{3}}{R_{2} + R_{3}}

R_{1} = \frac{R_{2} R_{3} - R (R_{2} + R_{3})}{R R_{2} R_{3}}

1003032505

Level:

Factoring the polynomial

x^{4} + 4

you get:

(x^{2} - 2 x + 2) (x^{2} + 2 x + 2)

(x^{2} + 2) (x^{2} - (- 2))

{(x + \sqrt{2})}^{4}

(x^{2} - \sqrt{2} x + 2) (x^{2} + \sqrt{2} x + 2)

1003032503

Level:

The polynomial

3 x^{5} + p x^{3} - (p - 1) x^{2} + 5 x - 9

is divisible by the binomial

x^{2} - 1

p

is equal to:

- 8

- 16

4

6

1003032502

Level:

Let the polynomial

(x - 2)^{5} - (x + 2)^{5}

be expressed in the form

a_{5} x^{5} + a_{4} x^{4} + a_{3} x^{3} + a_{2} x^{2} + a_{1} x + a_{0}

. Give the sum of

a_{5} + a_{4} + a_{3} + a_{2} + a_{1}

- 180

- 244

- 242

- 212

1003086108

Level:

The solution set of the equation

1 + \sin x \cdot \cos 2 x = \sin x + \cos 2 x

for

x \in R

is:

⋃_{k \in Z} {\frac{π}{2} + 2 k π; k π}

⋃_{k \in Z} {\frac{π}{2} + 2 k π}

⋃_{k \in Z} {k π}

⋃_{k \in Z} {2 k π}

1003086107

Level:

The solution set of the equation

2 {tg}^{2} x + 4 \cos^{2} x = 7

for

x \in R

is:

⋃_{k \in Z} {\frac{π}{3} + k π; \frac{2 π}{3} + k π}

⋃_{k \in Z} {\frac{π}{3} + 2 k π; \frac{2 π}{3} + 2 k π}

⋃_{k \in Z} {\frac{π}{3} + k π}

⋃_{k \in Z} {\frac{2 π}{3} + k π}

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