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Reptile [31]
4 years ago
5

1. Practicando: expresa en lenguaje algebraico.

Mathematics
1 answer:
Natasha_Volkova [10]4 years ago
8 0

Answer:

Part 1) 3n

Part 2) 4n

Part 3) \frac{2}{3}n

Step-by-step explanation:

<u><em>The question in English is</em></u>

Expressed in algebraic language.

Symbolically write the following expressions:

Three times a number:

Four times a number:

Two-thirds of a number

Let

n ----> the number

Part 1) we have

Three times a number:

we know that

The algebraic expression is equal to multiply 3 by the number n

so

3n

Part 2) we have

Four times a number:

we know that

The algebraic expression is equal to multiply 4 by the number n

so

4n

Part 3) we have

Two-thirds of a number

we know that

The algebraic expression is equal to multiply the fraction 2/3 by the number n

so

\frac{2}{3}n

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A fan is marked up 40% on the original price. The original price was $20. What is the new price of the fan before sales tax?
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Step-by-step explanation:

40% of 20 is 8

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4 years ago
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7 0
4 years ago
What is the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compare
Elena-2011 [213]

Answer:

38.9 square inches.

Step-by-step explanation:

We are asked to find the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees.

We will use area of sector formula to solve our given problem as:

\text{Area of sector}=\frac{\theta}{360}\times \pi r^2, where, r represents radius and theta represents central angle.

Let us find area of sector with central angle 140 degree and radius 3 inch.

\text{Area of sector}=\frac{138}{360}\times \pi (3)^2

\text{Area of sector}=\frac{138}{360}\times 9\pi

\text{Area of sector}=10.83849

Now, we will find area of sector with central angle 114 degree and radius 5 inch and multiply by 2 as:

\text{Area of sector}=2(\frac{114}{360}\times \pi (5)^2)

\text{Area of sector}=2(\frac{114}{360}\times 25\pi)

\text{Area of sector}=\frac{114}{360}\times 50\pi

\text{Area of sector}=49.74188

Let us find difference of area as shown below:

\text{Difference of areas}=49.74188-10.83849

\text{Difference of areas}=38.90339

\text{Difference of areas}\approx 38.9

Therefore, the difference in area covered is approximately 38.9 square inches.

8 0
3 years ago
7. By using binomial expansion show that the value of (1.01)^12 exceed the value of (1.02)^6 by 0.0007 correct to four decimal p
BlackZzzverrR [31]

Binomial expansion is used to factor expressions that can be expressed as the power of the sum of two numbers.

The proof that (1.01)^12 exceeds (1.02)^6 by 0.0007 is\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }

The expressions are given as:

\mathbf{(1.01)^{12}\ and\ (1.02)^6}

A binomial expression is represented as:

\mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}

Express 1.01 as 1 + 0.01

So, we have:

\mathbf{(1.01)^{12} = (1 + 0.01)^{12}}

Apply the above formula

\mathbf{(1.01)^{12} = ^{12}C_0 \times 1^{12 - 0} \times 0.01^0 + .........  .......... +  ^{12}C_{12} \times 1^{12 - 12} \times 0.01^{12} }}

\mathbf{(1.01)^{12} = 1 \times 1 \times 1 + .........  .......... +  1 \times 1 \times 10^{-24} }}

\mathbf{(1.01)^{12} = 1  + .........  .......... +  10^{-24} }}

This gives

\mathbf{(1.01)^{12} = 1.1268\ (approximated)}

Similarly,

Express 1.02 as 1 + 0.02

So, we have:

\mathbf{(1.02)^6 = (1 + 0.02)^6}

Apply \mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}

\mathbf{(1.02)^6 = ^6C_0 \times 1^{6 - 0} \times 0.02^0 +  ^6C_1 \times 1^{6 - 1} \times 0.02^1 +.............. + ^6C_6 \times 1^{6 - 6} \times 0.02^6 }\mathbf{(1.02)^6 = 1 \times 1 \times 1 +  6 \times 1 \times 0.02 +.............. + 1 \times 1 \times 6.4 \times 10^{-11} }

\mathbf{(1.02)^6 = 1 +  0.12 +.............. + 6.4 \times 10^{-11} }

This gives

\mathbf{(1.02)^6 = 1.1261\ (approximated) }

Calculate the difference as follows:

\mathbf{(1.01)^{12} - (1.02)^6 \approx 1.1268 - 1.1261 }

\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }

The above equation means that:

(1.01)^12 exceed the value of (1.02)^6 by 0.0007

Read more about binomial expansions at:

brainly.com/question/9554282

7 0
3 years ago
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