Real numbers + equation - practice problems - last page
Number of problems found: 38
- 2x cone
Circular cone height 84 cm was cut plane parallel with the base. The volume of these two small cones is the same. Calculate the height of the smaller cone. - Circle
Write the equation of a circle that passes through the point [0,6] and touches the X-axis point [5,0]: (x-x_S)²+(y-y_S)²=r² - Observer
The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from another end of the fence? - Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm², and if a: b: c = 12:7:18
- Rectangle
In rectangle ABCD with sides, |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio (|PB|)/(|DP|). - Equations: 80499
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - Circle
From the equation of a circle: -x² -y² +16x -4y -59 = 0 Calculate the coordinates of the center of the circle S[x0, y0] and the radius of the circle r. - Medians
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 25 cm and tb=30 cm. - Pool
If water flows into the pool by two inlets, fill the whole for 20 hours. The first inlet filled the pool 8 hour longer than the second. How long does the pool take to fill with two inlets separately?
- Euclid1
The right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c? - Hypotenuse and height
In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both triangle legs. - Pumps
The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than the second one. How many minutes is filled with the first pump? - Right Δ
A right triangle has the length of one leg 72 cm and the hypotenuse 90 cm size. Calculate the height of the triangle. - Short cut
Imagine that you are going to a friend. That path has a length 120 meters. Then turn doprava and go other 630 meters, and you are at a friend's. The question is, how much will the journey be shorter if you go direct across the field?
- Resistors
Two parallel resistors connected in series give the resulting resistance $R1Ω and $R2Ω. Determine the resistance of these resistors. - When will I be a millionaire?
Barry monthly send 280 euros to the bank, which he deposits bear interest of 2.1% p. A. Calculate how many months must Barry save to save 1000000 euros? Inflation, interest rate changes, or bank failures are ignored. - Server
Calculate how many average minutes the web server is unavailable a year if the availability is 99.9%. - Spherical cap
From the sphere with a radius of 11 was a truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere?
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