Question

Задача №1 Сумма длин всех ребер прямоугольного параллелепипеда равна 96см два его измерения 7 и 12см Найдите об объем парелелепипеда. Задача №2 Расстояние 240км моторная лодка проходит по течению реки 8 ч а против течения за 10ч Найдите скорость течения реки и собственную скорость лодки. Задача №3 Самолет долетел из одного города в другой за 3 часа За первый час он пролетел 30% всего пути во вторую 60% пути оставшегося а третью остальные 558км Найдите расстояние между городами Задача №4 Расстояние между двумя станциями равно 14.4км С этих станций в одном направлении одновременно двигались два поезда Позади двигался поезд со скоростью 59.3км / ч за 3 часа 12 мин после начала движения он догнал поезд который шел впереди Найдите скорость поезда который шел впереди Задача №5 Саша его сестра Лена и их отец собрали 48кг клубники Саша собрал в 3 раза больше чем Аленка а отец столько сколько Аленушка и Саша вместе Сколько кг клубники собрала Аленка? Задача №6 Ширина прямоугольного параллелепипеда равна 6 см длина на 12см больше ширины и составляет 60% от высоты Вычислить площадь поверхности параллелепипеда Спасибо большое) Писать только ПравильнО!)

Answer 1

#1
4(7+12+c)=96
28+48+c=96
c=96-76
c=20(см)-c
V=abc
V=7*12*20=7*240=1680см³
#2
V лодки-x
V течения-y
{(x+y)8=240
{(x-y)10=240
{8x+8y=240|*10
{10x-10y=240|*8
+{80x+80y=2400
+{80x-80y=1920
160x=4320|:160
x=27
27*8+8y=240
8y=240-216
8y=24|:8
y=3
#3
S-x
0,3x+(x-0,3x)0,6+558=x
0,3x+0,42x-x=-558
-0,28x=-558|:(-0,28)
x≈1993(km)
#4
V2-x
(x-59,3)3,2=14,4
3,2x-189,76=14,4
3,2x=14,4+189,76
3,2x=204,16|:3,2
x=63,8(км/ч)
#5
Алена-x
Саша- 3x
отец-(x+3x)
x+3x+x+3x=48
8x=48|:8
x=6(л)
#6
S=2(ab+ac+bc)
a=6+12=18cm
c=18:6/10=18*10/6=30cm
S=2(18*6+18*30+6*30)=2(108+540+180)=
2*828=1656cm²

Answer 2

Problem 1: Finding the volume of a rectangular parallelepiped

To find the volume of a rectangular parallelepiped, we need to multiply the lengths of its three edges. In this case, the sum of the lengths of all the edges is given as 96 cm, and two of the dimensions are given as 7 cm and 12 cm.

Let's assume the third dimension is x cm. We can set up the equation:

2(7 + 12 + x) = 96

Simplifying the equation, we get:

2(19 + x) = 96 38 + 2x = 96 2x = 96 - 38 2x = 58 x = 58/2 x = 29

Therefore, the third dimension of the rectangular parallelepiped is 29 cm.

Now, we can calculate the volume by multiplying the three dimensions:

Volume = 7 cm * 12 cm * 29 cm = 2436 cm³

So, the volume of the rectangular parallelepiped is 2436 cm³.

Problem 2: Finding the speed of the river current and the speed of the motorboat

To find the speed of the river current and the speed of the motorboat, we can use the formula:

Speed of the motorboat = (Total distance traveled) / (Total time taken)

Let's assume the speed of the river current is x km/h, and the speed of the motorboat is y km/h.

Given: - Distance traveled with the current = 240 km - Time taken with the current = 8 hours - Distance traveled against the current = 240 km - Time taken against the current = 10 hours

Using the formula, we can set up the following equations:

240 km = (y + x) km/h * 8 hours 240 km = (y - x) km/h * 10 hours

Simplifying the equations, we get:

8(y + x) = 240 10(y - x) = 240

Solving these equations simultaneously, we find:

y + x = 30 y - x = 24

Adding the two equations, we get:

2y = 54 y = 54/2 y = 27

Substituting the value of y into one of the equations, we find:

27 - x = 24 x = 27 - 24 x = 3

Therefore, the speed of the river current is 3 km/h and the speed of the motorboat is 27 km/h.

Problem 3: Finding the distance between two cities

To find the distance between two cities, we can use the information given in the problem.

Given: - The plane traveled for 3 hours. - In the first hour, it covered 30% of the total distance. - In the second hour, it covered 60% of the remaining distance. - In the third hour, it covered the remaining 558 km.

Let's assume the total distance between the cities is x km.

Using the given information, we can set up the following equation:

0.3x + 0.6(0.7x) + 558 = x

Simplifying the equation, we get:

0.3x + 0.42x + 558 = x 0.72x + 558 = x 0.72x - x = -558 -0.28x = -558 x = -558 / -0.28 x = 1992

Therefore, the distance between the two cities is 1992 km.

Problem 4: Finding the speed of the train

To find the speed of the train, we can use the information given in the problem.

Given: - The distance between the two stations is 14.4 km. - The train traveling behind another train at a speed of 59.3 km/h catches up to it after 3 hours and 12 minutes.

Let's assume the speed of the train ahead is x km/h.

Using the given information, we can set up the following equation:

59.3 km/h * 3.2 hours = 14.4 km + x km/h * 3.2 hours

Simplifying the equation, we get:

189.76 km = 14.4 km + 3.2x 189.76 km - 14.4 km = 3.2x 175.36 km = 3.2x x = 175.36 km / 3.2 x = 54.8 km/h

Therefore, the speed of the train ahead is 54.8 km/h.

Problem 5: Finding the amount of strawberries collected by Alenka

To find the amount of strawberries collected by Alenka, we can use the information given in the problem.

Given: - Sasha, Lena, and their father collected a total of 48 kg of strawberries. - Sasha collected 3 times more than Alenka. - Their father collected as much as Alenka and Sasha together.

Let's assume the amount of strawberries collected by Alenka is x kg.

Using the given information, we can set up the following equation:

x + 3x + (x + 3x) = 48

Simplifying the equation, we get:

8x = 48 x = 48 / 8 x = 6

Therefore, Alenka collected 6 kg of strawberries.

Problem 6: Finding the surface area of a rectangular parallelepiped

To find the surface area of a rectangular parallelepiped, we can use the information given in the problem.

Given: - The width of the parallelepiped is 6 cm. - The length is 12 cm more than the width. - The length is 60% of the height.

Let's assume the width of the parallelepiped is x cm.

Using the given information, we can find the length and height:

Length = x + 12 cm Height = (100/60) * (x + 12) cm = (5/3) * (x + 12) cm

The surface area of a rectangular parallelepiped is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we get:

Surface Area = 2(x + 12)(6) + 2(x + 12)(5/3)(x + 12) + 2(6)(5/3)(x + 12)

Simplifying the equation, we get:

Surface Area = 12(x + 12) + 10(x + 12)(x + 12) + 20(x + 12)

Surface Area = 12x + 144 + 10(x^2 + 24x + 144) + 20x + 240

Surface Area = 12x + 144 + 10x^2 + 240x + 1440 + 20x + 240

Surface Area = 10x^2 + 272x + 1824

Therefore, the surface area of the parallelepiped is 10x^2 + 272x + 1824 cm².