Simplify. 32 + 16 + 8 A) 4 + 6 2 B) 6 + 4 2 C) 10 + 2 D) 10 2

6. In a toy factory, 200 wooden closed cylinders of diameter 35 mm and height 7 cm have to be painted. What is the total surface

Pachacha [2.7K]

Answer:

6) About 19,244.75 square centimeters.

7) About 4895 containers.

Step-by-step explanation:

Question 6)

We need to paint 200 wooden closed cylinders of diameter 35 mm and height 7 cm. And we want to find the total surface area that needs to be painted.

First, since the diameter is 35 mm, this is equivalent to 3.5 cm.

The radius is half the diameter, so the radius of each cylinder is 1.75 cm.

Recall that the surface area of a cylinder is given by the formula:

$\displaystyle \text{SA}=2\pi r^2+ 2\pi rh$

Where r is the radius and h is the height.

Therefore, the surface area of a single cylinder will be:

$\displasytyle \text{SA}=2(3.142)(1.75)^2+2(3.142)(1.75)(7) = 96.22375\text{ cm}^2$

Then the total surface area for 200 cylinders will be:

$\displaystyle \text{SA}_{\text{total}}=200(96.22375)=19244.75\text{ cm}^2$

Question 7)

We know that the tank has a diameter of 2.4 m and a height of 6.4 m.

Since its diamter is 2.4 m, then its radius is 1.2 m.

Find the total volume of the tank. The volume for a cylinder is given by:

$\displaystyle V=\pi r^2h$

Since r = 1.2 and h = 6.4:

$\displaystyle V=(3.142)(1.2)^2(6.4)=28.956672\text{ m}^3$

Each container has a base radius of 8.2 cm and a height of 28 cm.

So, the radius of each container is 0.082 m and the height is 0.28 m.

Then the volume of each container is:

$\displaystyle V=(3.142)(0.082)^2(0.28)=0.005915506\text{ m}^3$

Then to find the number of containers that can be filled by the tank, we can divide the two values. Hence:

$\displaystyle C=\frac{28.956672}{0.005915506}=4895.045466\approx 4895$

Thus, approximately 4895 containers can be filled.

5 0

2 years ago

Read 2 more answers

Today, everything at a store is on sale. The store offers a 20% discount. The regular price of a shirt is $14. What is the disco

USPshnik [31]

Answer:

$11.20

Step-by-step explanation:

The regular price of the T-Shirt is $14 dollars. The discount is 20% off.

20 percent of 14:

14 * 0.2 = 2.80

You would save $2.80.

14 - 2.80 = 11.20

The discount price should be $11.20.

Hope this helps.

4 0

3 years ago

HELP PLEASE!

olasank [31]

Answer

Find out the Area of a triangle .

To proof

Formula

Area of Triangle

$= \frac{1}{2}\times( {x_1(y_{2}-y_{3}) +x_{2}(y_{3} - y_{1})+x_{3}(y_{1}-y_{2})})$

Now vertices are D(3, 3) , E(3, −1) , and F(−2, −5) .

$= \frac{1}{2} (3\times(-1 +5) + 3\times(-5-3)-2\times(3+1))$

Solving the above

$= \frac{1}{2}(3\times4+3\times-8 -2\times4)$

$=\frac{1}{2} (12-24-8)\\ =\frac{1}{2} (-32+12)\\=\frac{1}{2} (-20)$

= -10 units²

(Neglected the negative sign as area cannot be negative.)

= 10 units ²

Area of a triangle is 10 units ²

Hence proved

6 0

3 years ago

In a school auditorium, the number of chairs in a row is the same as the number of rows of chairs. There are 7033 students in th

mafiozo [28]

Same number of rows to chairs in a row would form a square.

Use the total number of students as the area

Find the number or rows by taking the square root of student:

The square root of 7033 is 83.86

Round up to 84

Total seats would be rows x seats per row:

84 x 84 = 7,056 total seats

7056 seats - 7033 students = 23 empty seats

3 0

2 years ago

Hi. Please I need help with these questions.

ElenaW [278]

Answer:

Q 12 roots of the equation

$2x^{2} -6+1=0 \\= (x-\frac{\sqrt{10} }{2})(x+\frac{\sqrt{10} }{2})\\$

∝ = $\frac{\sqrt{10} }{2}$

β = $-\frac{\sqrt{10} }{2}$

no matter if u oppose the root

(i) 2( $\frac{\sqrt{10} }{2}$ ) $(-\frac{\sqrt{10} }{2} )^{2}$ +2 $(\frac{\sqrt{10} }{2} )^{2}$ ( $-\frac{\sqrt{10} }{2}$ )+2(

(ii)( $(\frac{\sqrt{10} }{2})^{2}$ - 3 ( $\frac{\sqrt{10} }{2}$ )( $-\frac{\sqrt{10} }{2}$ ) + ( $(-\frac{\sqrt{10} }{2})^{2}$ ) = $\frac{25}{2}$

Q 13 roots of equation

$4x^{2} -3x-4=0\\\alpha = -0.693\\\beta = 1.443$

the roots of the second equation are

x1 = 1/3(-0.693) = -0.231

x2 = 1/3(1.443) = 0.481

the equation is

(x+0.231)(x-0.481)=0

$x^{2}-\frac{1}{4} x-\frac{1}{9}$

4 0

3 years ago