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3 years ago

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Mathematics

1 answer:

kenny6666 [7]3 years ago

4 0

Answer:

(4,-1)

Step-by-step explanation:

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Find the value of k for which the line y = kx + 6 is a tangent to the curve x^2 + y^2 – 10x + 8y = 84

guajiro [1.7K]

Answer:

k = 1/2

Step-by-step explanation:

input y = kx +6 into the equation of the curve x² + y² – 10x + 8y = 84

x² + (kx + 6)² - 10x + 8(kx + 6) = 84

expand:

x² + k²x² + 12kx + 36 - 10x + 8kx + 48 = 84

simplify by collecting like terms:

x² + k²x² + 20kx - 10x + 84 = 84

subtract 84 on both sides to bring it to the left:

x² + k²x² + 20kx - 10x + 84 - 84 = 0

x² + k²x² + 20kx - 10x = 0

factorise out x:

x²(1 + k²) + x(20k - 10) = 0

using the discriminant b² - 4ac where b is 20k - 10, a is 1 + k² and c is 0, substitute them in the formula b² - 4ac:

b² - 4ac

(20k - 10)² - 4(1 + k²)(0) = 0

the part highlighted in bold is gone because it's all multiplied by 0, so we are left with (20k - 10)² = 0

(20k - 10)² is the same as

(20k - 10)(20k - 10)

equate both to 0

20k - 10 = 0 and 20k - 10 = 0

add 10 on both sides

20k = 10 and 20k = 10

divide 20 on both sides

k = 10/20 and k = 10/20 which are both the same

10/20 is simplified to 1/2

k = 1/2

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2 years ago

Solve forx: (x – 3)/ 3 =4

Nezavi [6.7K]

Answer:

x = 15

Step-by-step explanation:

=> x - 3 = 12

=> x = 15

8 0

3 years ago

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HELP i dont get it<br> this is so harddddd

Lady bird [3.3K]

B. the line is going up so it’s going to be positive not negative. the b value is gonna be negative 1 instead of positive because it crosses the y axis closer to -1 than it does 1

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3 years ago

If $525 is 40% of my take home pay for 1 week how much to I make in a week

Vlada [557]

Answer: 525=2/5 so 1/5=262.5 and multiply that by 3 is 787.5 2/5 plus 3/5 is 100% so you would make 787.5

Step-by-step explanation:

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3 years ago

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Trigonometry: <br>1) Work out the bearing from B to C. <br>2) Calculate the bearing of D from B

kakasveta [241]

Answer:

see below

Step-by-step explanation:

a bearing is the angle in degrees measured clockwise from north.

Triangle ABC is a right triangle

Tan C = opp side / hyp

tan C = AB / CA

tan C = 30/30

tan C = 1

taking the inverse tan

tan ^ -1 tan C = tan ^ -1 ( 1)

C = 45 degrees

This is 90+45 degrees from North

135 degrees from north

Tan B = opp side / hyp

tan B = AD/BA

tan B = 45/30

tan B = 3/2

taking the inverse tan

tan ^ -1 tan B = tan ^ -1 ( 3/2)

D = 56.30993247

Add 180 degrees

180+56.30993247

236.3099325 from north

7 0

3 years ago