Find the surface area

Answers

Answer 1

Answer: Surface Area formula of a cylinder:
S.A = 2 × Area of base + Perimeter of base × Height of prism
= 2 $\pi$ r² + 2 $\pi$ rh
= 2 $\pi$ (10)² + 2 $\pi$ (10)(100)
{We took 10 ft as the radius because the diameter is 20 ft, so the radius is half the diameter}
= 200 $\pi$ + 2000 $\pi$
= 2200 $\pi$ ft² (in terms of $\pi$ )
= 6911.5 ft² (to the nearest tenth)

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One positive number is 5 less than twice a second number, and their product is 117. Find the two numbers.

Answers

x,y - the numbers

one positive number is 5 less than twice a second number

(1) x - 5 = 2y

their product is 117

(2) xy = 117

(1) x - 5 = 2y add 5 to both sides

x = 2y + 5 substitute it to (2)

(2y + 5)y = 117 use distributive property

(2y)(y) + (5)(y) = 117

2y² + 5y = 117 subtract 117 from both sides

2y² + 5y - 117 = 0

2y² + 18y - 13y - 117 = 0

2y(y + 9) - 13(y + 9) = 0

(y + 9)(2y - 13) = 0 ↔ y + 9 = 0 ∨ 2y - 13 = 0

y + 9 = 0 subtract 9 from both sides

y = -9

2y - 13 = 0 add 13 to both sides

2y = 13 divide both sides by 2

y = 6.5

substitute the values of y to (1)

x = 2(-9) + 5 = -18 + 5 = -13 < 0

x = 2(6.5) + 5 = 13 + 5 = 18

Answer: x = 18 and y = 6.5

Using the right triangle below find the cosine of angle A.

Answers

For the given triangle, the cosine of angle A equals $(1)/(2)$ .

Step-by-step explanation:

Step 1; In the given triangle, the opposite side has a length of 9 units, the adjacent side has a length of 3√3 units while the hypotenuse of the triangle measures 6√3 units. To calculate the cosine of angle A we divide the adjacent side by the hypotenuse side.

cos A = $(adjacent side)/(hypotenuse)$ .

Step 2; Length of the adjacent side = 3√3 units.

Length of the hypotenuse side = 6√3 units.

cos A = 3√3 / 6√3

cos A = $(1)/(2)$ .

To check we also have A = 60° and cos 60° = $(1)/(2)$ .

870 is 30% of what number

Answers

I got 2,900. What I did was divide 870 by 3 to get 10%. Then i multiplied it by 10 to get 100%, which is 2,900

your answer is 29 divide 870 divided by 30

What is 2/5 simplified?

Answers

2/5 van not be simiplified because 2 and 5 dont have a common factor lower than them

Write the steps for how to use a number line to multiply a 2-digit number by 20. give an example

Answers

To obtain the multiplication of $2$ digits number by $20$ first jump two times the $2$ digit number then jump $10$ times by the result we get in step 1.

Further explanation:

A straight line that has all real numbers is known as number line.

The steps involve in multiplying 2-digit number by $20$ are as follows.

1. First multiply the two digit number by 2 and the get the result.

2. Multiply the result by $10$ to obtain the final result.

For example we have to multiply $15$ by $20$ on the number line.

Following are the steps involve in multiply $15$ by $20$ on the number line.

Step 1

Multiply 15 by 2 as,

$\begin{gathered}A = 15 \cdot 2 \n= 30 \n \end{gathered}$

Make 2 jumps of 15 to get 30.

Step 2

Multiply $30$ to $10$ to obtain the final result.

$\begin{gathered}B = 30 \cdot 10 \n = 300 \n \end{gathered}$

Now make 10 jumps of 30 to get $300$ .

To obtain the multiplication of 2 digits number by $20$ first jump two times the 2 digit number then jump $10$ times by the result we get in step 1.

Kindly refer to the image attached to the question.

Learn more:

1. Problem on multiplication brainly.com/question/573729

2. Problem on division brainly.com/question/545132

3. Problem on lines brainly.com/question/8554769

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Number line

Keywords: two digit number, number line, twenty, multiply, add, jump, examples, multiplication.

Final answer:

To multiply a 2-digit number by 20 using a number line, draw a number line, plot your 2-digit number, make jumps of 20 units equal to your 2-digit number. The end point is the product.

Explanation:

To use a number line to multiply a 2-digit number by 20, follow these steps:

First, draw a number line. You can start at 0 and end at a number that is more than the product of your multiplication.
Plot your 2-digit number on the number line.
Start from your plotted point, and make jumps of 20 units each. The number of jumps should be equal to the quantity of your 2-digit number.
The point where you land, after making the necessary jumps, is the product of your multiplication.

For example, if you want to multiply 3 by 20: plot 3 on your number line, jump 3 points of 20 units each from point 3. You will land at 60, which is the product of 3 and 20.