Math Formulas

Algebra → Exponential equations and inequalities → Exponential equations

MR-357

We write a cone on the sphere. The center of the sphere divides the height of the cone into two sections such that the longer section equals the geometric mean of the shorter section and the total height. Determine the volume ratio of the sphere to the cone.

MR-401 / 2.

The second member of a geometric series is 6, the third member is 18. Enter the fifth member of the series!

MR-517 / 2.

If 1 kg of salami is 2800 HUF, how much will cost 35 dkg salami?

MR-403 / 3.

Members of a six-person table company: Anna, Balázs, Cili, Dezső, Egon and Fruzsina. Each of them knows exactly three other people in the company. Cili knows Dezső and Egon, and Anna doesn't know either Balázs or Dezső.

Illustrate the familiar relationships of the company with a graph! (All acquaintances are mutual.)

MR-404 / 5.

In the assignment instructions below, enter the letter that assigns 0 to 4 and 2 to 0!

$A : x \mapsto 2 x + 4 B : A : x \mapsto 2 x - 4 C : x \mapsto - 2 x + 4 D : x \mapsto - 2 x - 4$

MR-382 / 6.

Solve the following equation on the set of real numbers!
Round your answer to three decimal places!

$2^{x} = 10$

MR-396 / 7.

Enter the logical value (true or false) of the following statements.

A: If a number is divisible by 6 and 8, it can also be divisible by 48.
B: If every digit of a positive integer is divisible by 3, then the number can also be divisible by 3.
C: The largest common divisor of 48 and 120 is 12.

MR-383 / 8.

The fourth member of the arithmetic series is 7, and the fifth is -5.
Determine the first member of the series!

MR-523 / 8.

The fourth member of the arithmetic series is 7, and the fifth is -5.
Determine the first member of the series!

MR-413 / 9.

The 1 liter milk box of Bocitej Kft. Has the shape of a square rectangular column. The box is filled to the brim with milk.
How tall is the box if the base square is 7 cm? Explain your solution!

MR-525 / 10.

Draw the graph of the function $x \to |x - 2| - 3$ on interval [–3; 6]!

MR-416 / 11.

Plot the line below as |x|

MR-387 / 12.

The class organizes a lottery with three numbers from numbers: 1, 2, 3, 4, 5 . Tom markes 2, 3 and 5 number on the coupon.
Calculate the probability that Tom will have a total win!

MR-368 / 12.

Determine the true value of the following expressions:

$p \equiv \frac{3 + 2 x}{3} - \frac{2 - 3 x}{4} = \frac{29}{24}; x = 0, 5$

$q \equiv 3 (5 - y) - 2 (y - 1) = 1 + 3 y; y = 2$ Then determine the true value of the following two terms:

a) $(p \lor q) \land p$

b) $(p \land q) \lor p$

MR-527 / 12.

The class organizes a lottery with three numbers from numbers: 1, 2, 3, 4, 5 . Tom markes 2, 3 and 5 number on the coupon.
Calculate the probability that Tom will have a total win!

MR-358 / 13.

Solve the following equation on the set of real numbers!

$7 - 2 (x + 5) = \frac{x + 6}{4} + \frac{x + 2}{2}$

MR-545 / 13.

MR-529 / 14.

Length of the sides of cyclic trapezoid are: AB = 5 cm, BC = 2,5 cm, CD = 2 cm and DA = 2,5 cm.

a) Calculate the angles of the trapezoid!
b) Determine the ratio of ABC and ACD triangles!
c) The inner angles of the trapezoid are marked with an arc of 5 mm radius. Calculate the sum of the four arc lengths!

MR-227 / 15.

MR-421 / 16.

There are two points on the coordinate plane: A (2; 6) and B (4; -2).
a) Write the equation of the perpendicular to the section AB.
b) Write down the equation of the circle centered on A through B.
Given y equals is a 3 x straight line and {formula_3698} a circle.
c) Give the coordinates of the line and the circle with their coordinates.

MR-229 / 17.

MR-532 / 17.

MR-230 / 18.

MR-533 / 18.

MR-371 / 31.

Set S is given undefined. Determine the elements of A i B sets.

$A = \{x | x \in S \land \frac{2 x}{12 - x} \in S\}$ undefined

Determine the elements of the fallowing sets undefined

MR-162 / 156.

MR-192 / 192.

Calculate the following expression for α=30°.

$\frac{4 - s i n α}{1 - s i n α} - \frac{25}{4 c o s^{2} α} + \frac{2}{1 + s i n α}$

MR-249 / 249.

Determine the first derivative of the function below:

$y = \ln \sin^{2} x$

MR-273 / 273.

MR-302 / 302.779

Solve the following system of equations:

$\begin{matrix} x^{2} + y^{2} = 29 \\ x + y = 7 \end{matrix}$

MR-334 / 334.

Solve the following equation:

$\log_{10} (x^{2} + 19) - \log_{10} (x - 8) = 2$

MR-343 / 343.

Calculate the area of the parallelogram if its altitudes are 3 and $2 \sqrt{3}$ cm, and the angle $between tham is$ 60°!

MR-349 / 349.

The area of the rhombus is 100 cm², while its sharp angle is 30°. Calculate the diagonals of the rhombus!

MR-366 / 366.

Solve the following inequality on the set of real numbers!

$x^{2} - x - 2 < 0$

MR-367 / 588.

Vektori $\vec{a}$ i $\vec{b}$ obrazuju ugao $ψ = \frac{π}{6}$ . Ako je $|\vec{a}| = \sqrt{3}$ i $|\vec{b}| = 1$ izračunati ugao između vektora $\vec{p} = \vec{a} + \vec{b}$ i $\vec{q} = \vec{a} - \vec{b}$ .

MR-200 / 1069.a

Solve the exponential equation:

$2^{x - 3} = 16$

MR-202 / 1070.a

Solve the following exponential equation:

$16^{\frac{1}{x}} = 4^{\frac{x}{2}}$

MR-204 / 1071.b

Solve the following exponential equation:

$4^{x + 1} + 4^{x} = 320$

MR-205 / 1073.

Solve the following exponential equation:

$2^{x - 1} - 2^{x - 3} = 3^{x - 2} - 3^{x - 3}$

MR-208 / 1076.a

$5^{x} - 5^{3 - x} = 20$

MR-242 / 1175.

Simplify the following expression:

$\cos^{2} x - \cos^{4} x + \sin^{4} x$