The line y=mx is tangent to the curve y^2 = X-C. Show that c = 1/ (4m^2)

Answers

Answer 1

Answer: Hello,
Let (a,b) the intersection of the tangent and the curve.
That point must be double.

So
b=m*a
b²=a-c
==>(ma)²-a+c=0
==>m²a²-a+c=0 roots must be equal
Δ=(-1)²-4*m²c=0 => 4m²c=1==>c=1/(4m²)

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What is the equation of the line with a slope m=5 and y intercept, b= -3

Answers

Plug the given info into the slope-intercept formula: y = mx + b, where m = the slope and b = the y-intercept.

y = 5x -3

find the area of a regular hexagon with an apothem 10.4 yards long and a side 12 yards long. round your answer to the nearest tenth. show all your work

Answers

The answer is 374.4 yards.

There are 2 ways to calculate the area of a a regular hexagon.
It is given:
apothem: b = 10.4 yards
side: a = 12 yards

1. The direct way is to use the formula for the regular hexagon without using an apothem:
$A= (3 √(3) )/(2) a^(2)$
where
A - the area of the hexagon
a - the side of the hexagon

Therefore:
$A= (3 √(3) )/(2) 12^(2)$
$A= (3 √(3) )/(2) 144$
$A= 374.4$

2. The indirect way is to sketch the hexagon with 3 diagonals and create 6 triangles. Then, it is necessary to calculate the area of one triangle and multiply it by 6. In this triangle, apothem is actually the height.
The area of the hexagon is:
A = 6 · A₁
where:
A - the area of the hexagon,
A₁ - the area of the triangle

$A_(1)= (a*h)/(2)$

where
h - height of the triangle.

Since apothem (b) of the hexagon is the height (h) of the triangle, then:
$A_(1)= (a*h)/(2)$
$A_(1)= (12*10.4)/(2)$
$A_(1)= 62.4$

Thus, the area of one triangle is 62.4 yards.

To calculate the area of the hexagon, we will multiply it by 6:
A = 6 · A₁
A = 6 · 62.4
A = 374.4 yards

In both cases, the result is 374.4 yards.The answer is

What is the least common denominator of 4 and 8

Answers

Answer: Least common multiple of 4 and 8 is 8

If 12 cows produce 70 gallons of milk, how many gallons of milk would 42 cows produce?A. 20
B. 245
C. 512
D. 840

Answers

This is a proportions question
12 42
------ = -------
70 ?

Cross multiply

70x42=2940
12x?=2940
294/12=245

42 cows can produce 245 gallons of milk.
So the answer is B.

Hope I helped!

Answer: 245 gallons

Step-by-step explanation: Set up a ratio, cows/gallons = 12/70 = 42/x, then cross multiply to get 12x = 70*42. Divide to get 245 gallons.

The locus of the equation xy + yz = 0 isA) a pair of perpendicular planes
B) a pair of parallel planes
C) a pair of straight lines
D) None of these

Answers

Answer:

it's A

Step-by-step explanation:

The locus represented by the equation xy+yz=0 is a pair of perpendicular planes

just graph it

What is (6 + 6 + 6) · (6² + 1²)?

Please don't tell the answer is the devil number.

Answers

(6+6+6)(36+1) = (18)(37) = 666. ... If you don't want an answer posted, there's a simple solution ... don't post the question ! And if it still mysterously somehow appears, then for heaven's sake, don't offer points as a reward for an answer. ... Finally ... devil's numbers belong in the Old Wives' Hooey category, not in the Mathematics one. They're not real.

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