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2 years ago

Will someone please help me now i really need it and it’s due today and i don’t have it done

Mathematics

1 answer:

xxTIMURxx [149]2 years ago

6 0

Step-by-step explanation: 10*15

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Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).

aliya0001 [1]

Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

df/dx = 2(x - 6) + 2x = 0

2x - 12 + 2x = 0

4x = 12

x = 12/4

x = 3

Similarly,

df/dy = 2(y - 2) + 2y = 0

2y - 4 + 2y = 0

4y - 4 = 0

4y = 4

y = 4/4

y = 1

Now,from earlier;

z² = x² + y²

Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

7 0

3 years ago

Which amount is greater:50% of 40 or 40% of 50?

Rina8888 [55]

50% of 40 is 20, and 40% of 50 is 20, neither one is greater, they're equal

3 0

3 years ago

Read 2 more answers

Consider the graph of the function f(x)=2x.

77julia77 [94]

Given:

The parent function is:

$f(x)=2^x$

The other function is:

$g(x)=2f(x)$

To find:

The statement that describes a key feature of function g.

Solution:

We have,

$f(x)=2^x$

$g(x)=2f(x)$

Using these two functions, we get

$g(x)=2(2)^x$

Putting $x=0$ , we get

$g(x)=2(2)^{(0)}$

$g(x)=2(1)$

$g(x)=2$

The y-intercept of the function g at (0,2). So, option A is correct and option B is incorrect.

We know that $g(x)\to 0$ as $x\to -\infty$ and it will never intersect the line $y=0$ . It means the horizontal asymptote of the function g is

Therefore, the correct option is A.

3 0

2 years ago

Read 2 more answers

What is 5 units from -6?

Sedaia [141]

Answer:

Step-by-step explanation:

-6 + ___ = 5 is your format.

3 0

2 years ago

Read 2 more answers

Please help! Brainliest if you explain

My name is Ann [436]

Switch sides

4/5 (x+3)=y+6

Multiply both sides by 5

5*4/5 (x+3) = 5y+5*6

Simplify

4(x+3) = 57+30

Divide both sides by 4

4(x+3)/4 = 5y/4+ 30/4

Simplify

x+3 = 5y+30/4

Subtract 3 from both sides

x+3 - 3 = 5y+30/4 - 3

Simplify

x=5y+30/4 - 3

3 0

3 years ago