C | math4u.vsb.cz

1003109402

Level:

Which of the given quadratic equations has the roots

x_{1} = 1 + i

and

x_{2} = (1 + i)^{2}

x^{2} - (1 + 3 i) x - 2 + 2 i = 0

x^{2} - (1 + 3 i) x - 2 - 2 i = 0

x^{2} - (1 + 3 i) x + 2 + 2 i = 0

x^{2} - (1 + 3 i) x + 2 - 2 i = 0

1003109401

Level:

Which of the given quadratic equations has the roots

x_{1} = 2 + i

and

x_{2} = 1 - 3 i

x^{2} - (3 - 2 i) x + 5 - 5 i = 0

x^{2} + (3 - 2 i) x + 5 - 5 i = 0

x^{2} - (3 + 2 i) x + 5 - 5 i = 0

x^{2} + (3 + 2 i) x + 5 - 5 i = 0

1003082308

Level:

Let

[x; y] \in N \times N

. Find all

[x; y]

, that satisfy

x (8 + 4 i) + y (1 - 4 i) + 5 = x (3 + i) + 6 (y - 2 i) + 9 i .

There is no

[x; y]

. (There is no solution.)

[1; 0]

[0; 1]

[- 1; 0]

[0; - 1]

1003082307

Level:

Let

z_{1} = x^{2} + 9 y i - 20 i

and

z_{2} = 7 x - 12 + y^{2} i

. Find all

[x; y] \in R \times R

such that

z_{1} = z_{2}

[x; y] \in {[3; 4], [3; 5], [4; 4], [4; 5]}

[x; y] \in {[4; 3], [4; 4], [5; 3], [5; 4]}

[x; y] \in {[- 3; - 4], [- 3; - 5], [- 4; - 4], [- 4; - 5]}

[x; y] \in {[- 4; - 3], [- 4; - 4], [- 5; - 3], [- 5; - 4]}

1003082306

Level:

Let

[x; y] \in R \times R

. Find all

[x; y]

that satisfy

(3 x + 2 y i) \cdot (3 x - 2 y i) + y^{2} i = 97 + 4 i .

[x; y] \in {[3; 2], [- 3; 2], [3; - 2], [- 3; - 2]}

[x; y] \in {[3; 2], [- 3; 2]}

[x; y] \in {[3; 2], [3; - 2]}

[x; y] \in {[3; 2], [- 3; - 2]}

1003082304

Level:

Let

x

and

y

be real numbers. Find the solution of the equation.

(5 + 2 i) x + (3 - 5 i) y = 124

x = 20, y = 8

x = 8, y = 20

x = - 20, y = - 8

x = - 8, y = - 20

1003107605

Level:

Evaluate the following integral on

(0; \infty)

\int \frac{7 x + 2}{15 x^{2} + 3 x} d x

\frac{2}{3} \ln x - \frac{1}{5} \ln (x + \frac{1}{5}) + c, c \in R

\ln \frac{\sqrt[3]{x^{2}}}{\sqrt[5]{x + 1}} + c, c \in R

\frac{2}{3} \ln x - \ln (5 x + 1) + c, c \in R

\ln \frac{\sqrt[3]{x^{2}}}{\sqrt[5]{x + 5}} + c, c \in R

1003107604

Level:

Evaluate the following integral on

(0; \infty)

\int \frac{- 2 x^{2} + 3 x + 2}{x^{3} + x^{2}} d x

\ln \frac{x}{x^{3} + 3 x^{2} + 3 x + 1} - \frac{2}{x} + c, c \in R

\ln x - \ln (x + 1)^{3} + c, c \in R

\ln \frac{x \cdot x^{2}}{(x + 1)^{3}} + c, c \in R

\ln \frac{x^{3}}{x^{3} + 3 x^{2} + 3 x + 1} - \frac{2}{x} + c, c \in R

1003107603

Level:

Evaluate the following integral on

(0; \infty)

\int \frac{3 x^{3} + 3 x^{2} - x + 1}{x^{2} + x} d x

1.5 x^{2} + \ln \frac{x}{x^{2} + 2 x + 1} + c, c \in R

\ln \frac{x}{(x + 1)^{2}} + 3 x + c, c \in R

\ln [x \cdot (x + 1)^{2}] + 3 x + c, c \in R

\ln \frac{(x + 1)^{2}}{x} + c, c \in R

1003107602

Level:

Evaluate the following integral on

(3; \infty)

\int \frac{7}{x^{2} + x - 12} d x

\ln \frac{x - 3}{x + 4} + c, c \in R

\ln [(x - 3) (x + 4)] + c, c \in R

\ln \frac{x + 4}{x - 3} + c, c \in R

\ln \frac{x + 6}{x - 2} + c, c \in R

« first
‹ previous
…
73
74
75
76
77
78
79
80
81
…
next ›
last »

C

1003109402

1003109401

1003082308

1003082307

1003082306

1003082304

1003107605

1003107604

1003107603

1003107602

Events

Akce

Interests

Zajímavosti

About portal

O portálu