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11111nata11111 [884]
3 years ago
12

Solve the equation r²-4s+s²=8r+2s=28​

Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
5 0

Answer:

{r}^{2}  - 4s +  {s}^{2}  = 8r + 2s = 28 \\  \\ r =  \frac{24}{5 }  - i   \frac{ \sqrt[4]{129} }{5}  \\ \: s =  \frac{58}{5}  +    i \frac{ \sqrt[2]{129} }{5 }  \\  \\ r =  \frac{24}{5}  + i  \frac{ \sqrt[4]{129} }{5}  \\ s =  \frac{58}{5}  - i \frac{ \sqrt[2]{129} }{5}

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How to prove this using trig identities?
Pavlova-9 [17]

Step-by-step explanation:

tanB + cotB = (sinB)/(cosB) + (cosB)/(sinB)

 

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                       = 1/[(cosB)(sinB)]

 

                        = (1/cosB)(1/sinB)

 

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7 0
3 years ago
A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a
laila [671]

Complete Question

A survey is planned to estimate the proportion of voters who support a proposed gun control law. The estimate should be within a margin of error of ±5% with 90% confidence, and we do not have any prior knowledge about the proportion who might support the law. How many people need to be included in the sample?

Round your answer up to the nearest integer.

sample size = _____

Answer:

The sample size is n = 271    

Step-by-step explanation:

From the question we are told that  

   The margin of error is  E = 5% = 0.05

Generally given that there was no prior knowledge about the proportion of who might support the law, we will assume the sample proportion to be  

     \^ p =  0.5

From the question we are told the confidence level is  90% , hence the level of significance is    

      \alpha = (100 - 90 ) \%

=>   \alpha = 0.05

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.645

Generally the sample size is mathematically represented as  

    n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )

=>   n = [\frac{1.645 }{0.05} ]^2 * 0.5 (1 - 0.5 )

=>   n = 271    

5 0
3 years ago
Sort the polynomials according to whether they are prime or non prime
gladu [14]

Answer:

Prime Polynomials:

12x^2-3x+4x-7

6x^3-5x^2+2x-14

Non-Prime Polynomials:

12x^4-18x^2+8x^2-12

6x^3+9x^2+10x+15

5 0
3 years ago
The vertices of a triangle are A(0,0),B(3,8) and C(9,0). What is the area of this triangle?
Svetradugi [14.3K]

Answer:

9

Step-by-step explanation:

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

Fill in the numbers for each corresponding letter combination within the formula.

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Subtract the numbers within the parentheses.

0 from 8 = 8, 0 from 0 = 0 and 8 from 10 = 2.

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0 by 8 = 0, 3 by 0 = 0 and 9 by 2 = 18.

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5 0
2 years ago
HELP! BRAINLIEST!
love history [14]

Given that,

Charge q₁ = -0.004 C

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Distance between charges, d = 3 m

To find,

The electrostatic force between charges.

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So, 12000  N of electrostatic force is produced.

5 0
3 years ago
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