C | math4u.vsb.cz

1103021901

Level:

What is the slope of a staircase if the height of a stair is

15 cm

and the depth of a stair is

30 cm

{26.57}^{\circ}

{63.43}^{\circ}

30^{\circ}

60^{\circ}

1103256903

Level:

In isosceles triangle

A B C

| A B | = 8 cm

| B C | = | A C | = 6 cm

. Determine what percentage of the triangle area is a circle that is inscribed in it. Round the result to full percentages.

56 %

48 %

62 %

64 %

1103256902

Level:

The cucumber field has the shape of an isosceles right triangle. The length of its legs is

12 m

. Rotary sprinklers placed in its vertices have a reach of

6 m

. Find the area of the field that is not sprinkled with water. Round the result to two decimal places.

15.45 m^{2}

41.10 m^{2}

16.29 m^{2}

15.25 m^{2}

1103256901

Level:

The farmer tied two goats on the meadow. The distance of the stakes

K_{1}

K_{2}

to which the goats are tied is

5 m

and the ropes have lengths of

3 m

and

4 m

. What is the area of the grassland which is common for both goats? Round the result to two decimal places.

6.64 m^{2}

0.57 m^{2}

0.35 m^{2}

1.52 m^{2}

1003085910

Level:

The solution set of the inequality

{tg}^{3} x + {tg}^{2} x - tg x - 1 < 0

for

x \in (- \frac{π}{2}; \frac{π}{2})

is:

(- \frac{π}{2}; \frac{π}{4})

(\frac{π}{2}; \frac{7 π}{4})

(- \frac{π}{2}; \frac{3 π}{4})

(- \frac{π}{2}; \frac{π}{2})

1003085909

Level:

The solution set of the inequality

| tg x | < 1

for

x \in (- \frac{π}{2}; \frac{π}{2})

is:

(- \frac{π}{4}; \frac{π}{4})

(- \frac{π}{2}; \frac{π}{2})

(0; \frac{π}{4})

(- \frac{π}{2}; - \frac{π}{4})

1003085908

Level:

The solution set of the inequality

cotg (3 x - \frac{π}{4}) \geq - 1

for

x \in [0; \frac{π}{2}]

is:

{0} \cup (\frac{π}{12}; \frac{π}{3}] \cup (\frac{5 π}{12}; \frac{π}{2}]

[0; \frac{π}{3}]

(\frac{π}{12}; \frac{π}{3}]

(0; \frac{π}{2}]

1003085907

Level:

The solution set of the inequality

| \sin x | \geq 0.5

for

x \in [0; 2 π]

is:

[\frac{π}{6}; \frac{5 π}{6}] \cup [\frac{7 π}{6}; \frac{11 π}{6}]

[0; \frac{5 π}{6}] \cup [\frac{7 π}{6}; \frac{11 π}{6}]

[\frac{π}{6}; \frac{11 π}{6}]

[0; \frac{π}{6}] \cup [\frac{5 π}{6}; \frac{11 π}{6}]

1003085906

Level:

The solution set of the inequality

\cos 3 x > \frac{\sqrt{3}}{2}

for

x \in (0^{\circ}; 180^{\circ})

is:

(0^{\circ}; 10^{\circ}) \cup (110^{\circ}; 130^{\circ})

(330^{\circ}; 360^{\circ})

(110^{\circ}; 120^{\circ})

(0^{\circ}; 30^{\circ})

1003085905

Level:

The solution set of the inequality

| cotg x | \leq \sqrt{3}

for

x \in R

is:

⋃_{k \in Z} [\frac{π}{6} + k π; \frac{5 π}{6} + k π]

⋃_{k \in Z} [\frac{π}{6} + k π; \frac{π}{2} + k π]

⋃_{k \in Z} [\frac{π}{2} + k π; \frac{5 π}{6} + k π]

⋃_{k \in Z} [k π; (k + 1) π]

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