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kogti [31]
2 years ago
12

Who knows how to do this I TRULY NEED HELP

Mathematics
1 answer:
Stella [2.4K]2 years ago
6 0

Answer:

sorry i cant help , not smart enough ,but i wish i was tho

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

5 0
2 years ago
What is 1.04 to the 1/12 power
LiRa [457]
1.04 ^ 1/12 = 0.086666666
or
1.04 ^ 1/12 = 13/150
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3 years ago
2 times the square root of 27 minus the square root of 48
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3 years ago
What is the undefined variable in this equation (6x2 +3x) ÷ (3x) simplified 3x + 1
ozzi
X is the undefined variable hope it helps

4 0
3 years ago
What is 3.245 rounded to the nearest thousandth
kramer
3.25 is rounded to the nearest thousandth 
8 0
3 years ago
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