6) Evaluate for x = 3:<br> 3•4x/2

Solve this please show your work <3

Nookie1986 [14]

Given:

The expression is

$\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=$

To find:

The simplified form of the expression.

Solution:

We have,

$\sqrt[3]{48}=\sqrt[3]{8\cdot \_\_}=$

The expression $\sqrt[3]{48}$ can be written as

$\sqrt[3]{48}=\sqrt[3]{8\cdot 6}$

$\sqrt[3]{48}=\sqrt[3]{8}\cdot \sqrt[3]{6}$ $[\because \sqrt[3]{ab}=\sqrt[3]{a}\sqrt[3]{b}]$

$\sqrt[3]{48}=2\cdot \sqrt[3]{6}$

$\sqrt[3]{48}=2\sqrt[3]{6}$

Therefore, $\sqrt[3]{48}=\sqrt[3]{8\cdot 6}=2\sqrt[3]{6}$ .

5 0

3 years ago

Classwork 12.1 surface area

s344n2d4d5 [400]

Answer:

6) LA = 90 units² and SA = 202 units²

7) LA = 377 units² and SA = 477.5 units²

8) LA = 208 units² and SA = 232 units²

9) LA = 455 units² and SA = 591 units²

Step-by-step explanation:

* Lets revise the rules of lateral area and surface area

- Lateral area of the solid = perimeter of its base × its height

- Surface area = lateral area + 2 × area of its base

* Now lets solve the problems

6) The solid is a rectangular prism

- Its base is a rectangle with dimensions 8 units and 7 units

- Its height is 3 units

∵ Perimeter of the rectangle = 2(L + W)

∴ Perimeter of the base = 2(8 + 7) = 2(15) = 30 units

∴ LA = 30 × 3 = 90 units²

∵ Area of the rectangle = L × W

∴ Area of the base = 8 × 7 = 56 units²

∴ SA = 90 + 2 × 56 = 90 + 112 = 202 units²

7) The solid is a cylinder

- Its base is a circle with diameter 8 units

∴ Its radius = 8 ÷ 2 = 4 units

- Its height is 15 units

∵ The perimeter of the circle is 2πr

∴ The perimeter of the base = 2π(4) = 8π

∴ LA = 8π(15) = 120π = 376.99 ≅ 377 units²

∵ The area of the circle = πr²

∴ The area of the base = π(4)² = 16π

∴ SA = 120π + 2 × 16π = 120π + 32π = 152π = 477.5 units²

6) The solid is a triangular prism

- Its base is a triangle with sides 5 , 5 , 6 units and height 4 units

- Its height is 13 units

∵ Perimeter of the triangle is the sum of the 3 sides

∴ Perimeter of the base = 5 + 5 + 6 = 16 units

∴ LA = 16 × 13 = 208 units²

∵ Area of the triangle = 1/2 × base × height

∴ Area of the base = 1/2 × 6 × 4 = 12 units²

∴ SA = 208 + 2 × 12 = 208 + 24 = 232 units²

9) The solid is a prism

- Its base is an isosceles trapezium with parallel bases 7 units and 10

units, 2 non-parallel bases 9 units and height 8 units

- Its height is 13 units

∵ Perimeter of the trapezium is the sum of its sides

∴ Perimeter of the base = 7 + 10 + 9 + 9 = 35 units

∴ LA = 35 × 13 = 455 units²

∵ Area of the trapezium = 1/2(b1 + b2) × h

∴ Area of the base = 1/2(7 + 10) × 8 = 68 units²

∴ SA = 455 + 2 × 68 = 455 + 136 = 591 units²

6 0

3 years ago

Find the area of a triangle with a base length of 3 units and a height of 4 units.

svetlana [45]

Answer:

$6$ square units

Step-by-step explanation:

The area of a triangle can be calculated by multiplying the triangle's base by its height, and then dividing the result by $2$ . As an algebraic expression, this would be $\frac{bh}{2}$ , where $b$ is the triangle's base and $h$ is the triangle's height. In this case, we know that $b=3$ and $h=4$ . Therefore, the area of this triangle is $\frac{3*4}{2} =\frac{12}{2} =6$ square units. Hope this helps!