The most difficult problems - page 4 of 5

Perimeter 7056
The perimeter of the rectangle is about cm. One side is three times smaller than the other. Express the lengths of both sides of the rectangle using its perimeter
Notation 7014
There is no 0 in the decimal notation in natural numbers, and there are even numbers or odd numbers, each at least once. Find the number of all k-digit natural numbers.
Kocourkov 7007
The train will run from Kockov to Drakov in 2 hours and 40 minutes, from Oslice to Kocourkov in 180 minutes, and from Kocourkov to Mokrov in 2 hours and 30 minutes. Which route will the train travel in the shortest and which in the longest time?
The position
The position of a body at any time T is given by the displacement function S=t³-2t²-4t-8. Find its acceleration at each instant time when the velocity is zero.
Domains of functions
F(x)=x²-7x and g(x)=5-x² Domain of (fg)(x) is. .. . . The domain of (f/g)(x). ..
Circle annulus
There are two concentric circles in the figure. The chord of the larger circle, 10 cm long, is tangent to the smaller circle. What does annulus have?
Commission 2
Mr gomez sells used cellphones. His commission for every cellphone sold is 20%. If his total sales is Php 33850, how much is his commission? Please, please, please show your solution.
Shuyen
Shuyen wanted to save some money. She deposited Php.300 in a bank which pays 0.5% interest per annum. After nine months, she needed the money to buy some gifts. How much will she be able to get if he withdraws all her money from the bank?
Real estate 2
A real estate agent sold a lot for Php.550,000. If his agency pays at 10% commission, how much commission will he or she receive?
Old laptop
The sale price of an old laptop is Php.11000. If 33 1/3% discount rate is given how much is the sale price of the laptop without the discount? Plese show your solution please. Php is Philippine peso
Rectangular 6892
How does one dimension of a rectangular garden depend on another if the garden has an area of 500 m²?
Cooperative 6873
The cooperative has n dairy cows. How many liters of milk would they increase per year if each dairy cow milked 2 liters per day more?
After 2
After we planted flowers in 2/5 of our garden, 24m remained unplanted. How many meters is the garden in total? If the total area of the garden is 1, the proportion of the remaining area is?
Inverse matrix
Find out inverse by Gauss elimination or by reduction method. A=[2/3. 1 -3. 1/3]
Cube root
Find cube root of 18
Square root 2
If the square root of 3m² +22 and -x = 0, and x=7, what is m?
Sum of two primes
Christian Goldbach, a mathematician, found out that every even number greater than two can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
Population growth
How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
Butter
At the Orville Redenbacher popcorn factory, there is a tank of artificial butter substitutes, which is 55 feet tall and 18 feet in diameter. How many gallons of artificial butter substitute can the tank contain?
Right triangle from axes
A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?

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