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2 years ago

Find the equation of the tangent to the circle x2 + y2 = 109 at point (-10,3)

Mathematics

1 answer:

konstantin123 [22]2 years ago

4 0

Answer:

10x - 3y = -109 .

Step-by-step explanation:

x^2 + y^2 = 109

Implicit Differentiation:

2x + 2y.y' = 0

y' = -2x/2y = -x/y

So at the point (-10,3) the gradient of the tangent is -(-10)/3 = 10/3.

Equation of the tangent:

y - y1 = m(x - x1)

y - 3 = 10/3(x + 10)

y - 3 = 10/3 x + 100/3

3y - 9 = 10x + 100

-109 + 3y = 10x

10x - 3y = -109

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what is the perimeter of the triangle. i do not know how to start this problem. any help will be greatly appreciated :))

xz_007 [3.2K]

Given:

Point F,G,H are midpoints of the sides of the triangle CDE.

$FG=9,GH=7,CD=24$

To find:

The perimeter of the triangle CDE.

Solution:

According to the triangle mid-segment theorem, the length of the mid-segment of a triangle is always half of the base of the triangle.

FG is mid-segment and DE is base. So, by using triangle mid-segment theorem, we get

$\dfrac{1}{2}DE=FG$

$DE=2(FG)$

$DE=2(9)$

$DE=18$

GH is mid-segment and CE is base. So, by using triangle mid-segment theorem, we get

$\dfrac{1}{2}CE=GH$

$CE=2(GH)$

$CE=2(7)$

$CE=14$

Now, the perimeter of the triangle CDE is:

$Perimeter=CD+DE+CE$

$Perimeter=24+18+14$

$Perimeter=56$

Therefore, the perimeter of the triangle CDE is 56 units.

7 0

2 years ago

What is the underlined sentence mean can someone explain

suter [353]

Step-by-step explanation:

1235

Now when we talk about place values we have ones tens hundreds thousands ten thousands and so on. So when you look at no.1 its place value is ones because 1 is the first value.

So 2 is in tens.

Now the difference of tens and hundreds is tens follows the 2 place value and hundreds the next.

HOPE ITS HELPFUL

8 0

2 years ago

Read 2 more answers

Plz help :( what is 10,000,000(20)^10 !?

Sergio [31]

Answer: 102,400,000,000,000,000,000

Step-by-step explanation:

First do 20^10 = 10,240,000,000,000.

Then, multiply 10,240,000,000,000 * 10,000,000 to get 102,400,000,000,000,000,000.

<em>Hope it helps <3</em>

7 0

3 years ago

I NEED HELPPPPPPPPPPPPPP ITS TIMED PLEASSE HURRY AND I WILL GIVE BRAINLIESTTTTT

luda_lava [24]

Answer:

4c + 6a < = 120 ...4(20) + 6(6) = 116 <== correct

4c + 4a < = 100....4(20) + 4(6) = 104 <== incorrect

first answer choice

5 0

2 years ago

Read 2 more answers

What is the solution to 3 times the square root of 4 minus 2 times the square root of 4? A. 0 B. 1 C. 2 D. 3

olasank [31]

For this case we have the expression:

"the square root of 4" is represented algebraically as:

$\sqrt {4}$

Then, we can express the given statement as:

$3 \sqrt {4} -2 \sqrt {4} =$

They are similar terms, we can subtract:

$3 \sqrt {4} -2 \sqrt {4} = \sqrt {4} = \sqrt {2 ^ 2}$

By definition of power properties we have that:

$\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a$

Then the expression is reduced to:

$\sqrt {2 ^ 2} = 2$

Answer:

$3 \sqrt {4} -2 \sqrt {4} = 2$

8 0

3 years ago