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3 years ago

Find an equation of the tangent plane to the surface at the point . Question 14 options: a) b) c) d) e)

Mathematics

1 answer:

sesenic [268]3 years ago

7 0

This question is incomplete, the complete question is;

Find an equation of the tangent plane to the surface z=1y²−1x² at the point (-4, 3, -7).

z = .....................

Note: Your answer should be an expression of x and y; e.g. 3x - 4y + 6.

Answer:

Z = 8x + 6y + 7

Step-by-step explanation:

Given that z = 1y² - 1x²

with points (-4, 3, -7)

Z = y² - x²

Equation of tangent plane to the surface Z = f(x,y) at the points ( x₀,y₀,z₀) is

Z - Z₀ = fx (x₀,y₀)(x-x₀) + fy (x₀y₀)(y-y₀)

therefore

Z = f(x,y) = y² - x²

fx = -2x, fx (-4, 3, -7) = -2(-4) = 8

fy = -2y, fy ( -4, 3, -7 ) = 6

Z + 7 = 8(x+4) + 6(y-3)

Z + 7 = 8x + 32 + 6y - 18

Z + 7 = 8x + 6y + 14

Z = 8x + 6y + 14 - 7

Z = 8x + 6y + 7

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An angle measures 40.2° more than the measure of its complementary angle. What is the measure of each angle?

vampirchik [111]

<h3>Solving for the measurements of Complementary Angles</h3><h3>Answer:</h3>

$24.9^{\circ}$ and $65.1^{\circ}$

<h3>Step-by-step explanation:</h3>

Recall that Angles that are complementary to each other add up to $90^{\circ}$ .

Let $a$ be the measure of the complementary angle.

If an angle is $40.2^{\circ}$ more than its complementary angle, the measure of that angle is $a +40.2$ . The sum of both angles are expressed $a +(a +40.2)$ but since the have to add to $90$ as they are complementary, $a +(a +40.2) = 90$ .

Solving for $a$ :

$a +(a +40.2) = 90 \\ a +a +40.2 = 90 \\ 2a +40.2 = 90 \\ 2a +40.2 -40.2 = 90 -40.2 \\ 2a = 49.8 \\ \frac{2a}{2} = \frac{49.8}{2} \\ a = 24.9$

Since the other angle measures $a +40.2$ , we can plug in the value of $a$ to find the measure of the angle.

Evaluating $a +40.2$ :

$a +40.2 \\ 24.9 +40.2 \\ 65.1$

The measure of the angles are $24.9^{\circ}$ and $65.1^{\circ}$

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