All categories

3 years ago

Find a unit vector parallel to and normal to the graph of f(x) at the indicated point. f(x) = sqrt(25-x^2) point (3,4)

1 answer:

4 0

y = sqrt(25-x^2) at point (3,4)

The derivative gives us the slope at 3 to be:
-2x
------------ at x=3: -3/4
2sqrt(25-x^2)

so we have a vector that is parallel to the slope of the tangent line is: <4,-3>

the mag = 5 so; unit tangent = <4/5 , -3/5>

since perpendicular lines have a -1 product between slopes we get the normal to be... <3/5,4/5>

It is <4,-3> because it is rise over run. Rise is y component of vector and run is x component of vector.

You might be interested in

Hãy nêu định lý pytago

Natasha_Volkova [10]

The text of the Pythagorean Theorem The Pythagorean Theorem states: “The sum of the squares of the lengths of the two sides of the right triangle, which are the shortest sides in a right-angled triangle, is equal to the square of the length of the hypotenuse, which is the longest side of the triangle.”

And in symbols: Pythagorean theorem = ( A² + B² = C²)

where ;

● A, B: the two sides of a right triangle ABC.

● C: The hypotenuse of a right triangle is ABC, which is the longest side.

It should be noted that the inverse of the theory is also true; Since the triangle to which the Pythagorean theorem applies, namely: A² + B² = C², is necessarily a right-angled triangle.

<h3>In Vietnamese ( Bằng tiếng việt) ;</h3>

Nội dung của Định lý Pitago Định lý Pitago phát biểu: “Tổng bình phương độ dài hai cạnh của tam giác vuông, là cạnh ngắn nhất của tam giác vuông, bằng bình phương độ dài của cạnh huyền, là cạnh dài nhất của tam giác. "

Và trong các ký hiệu: Định lý Pitago = (A² + B² = C²)

ở đâu ;

● A, B: hai cạnh của tam giác vuông ABC.

● C: Cạnh huyền của tam giác vuông ABC là cạnh dài nhất.

Cần lưu ý rằng điều ngược lại của lý thuyết cũng đúng; Vì tam giác áp dụng định lý Pitago, cụ thể là: A² + B² = C², nhất thiết phải là tam giác vuông.

I hope I helped you^_^

6 0

3 years ago

On a coordinate plane, 2 exponential fuctions are shown. Function f (x) decreases from quadrant 2 into quadrant 1 and approaches

Gala2k [10]

Answer:

$g(x)=6(3)^x$

Step-by-step explanation:

We are given that

$f(x)=6(\frac{1}{3})^x$

Function f decreases from quadrant 2 to quadrant 1 and approaches y=0

It cut the y- axis at (0,6) and passing through the point (1,2).

Function g(x) approaches y=0 in quadrant 2 and increases into quadrant 1.

It passing through the point (-1,2) and cut the y-axis at point (0,6).

Reflection across y- axis:

Rule of transformation is given by

$(x,y)\rightarrow (-x,y)$

Using the rule then we get

$g(x)=6(\frac{1}{3})^{-x}=6(3)^x$

By using

$x^{-a}=\frac{1}{x^a}$

Substitute x=-1

$g(-1)=6\times (\frac{1}{3})=2$

Substitute x=0

$g(0)=6$

Therefore, $g(x)=6(3)^x$ is true.

8 0

3 years ago

Read 2 more answers

Uhm yeah can i get a brain dump momment

luda_lava [24]

Answer: 5 the gcf is 5

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

if angle 1 and angle 2 are vertical angles, angle 2 and angle 3 are complementary angles and the measure of angle 3 is 56 degree

dimulka [17.4K]

Answer:

34º

Step-by-step explanation: so basically you know a complementary angle is 2 angles that make a straight line and a vertical angle crosses which means 2 angles are congruent to each other so I drew a line that bisected the angle by drawing a line that cut through the right angle and i extended a line down from the right angle so now I have a vertical angle and a complementary so from here I labeled each angle <1 <2 <3 If I know angle 3 is 56º then I know 56 plus __ equals 90º I then subtracted 56 from 90 and I got 34 and since I am trying to figure out what angle 1 is I know that angle 1 and 2 are vertical angles therefore I know they are congruent to each other so <1 = 34º

6 0

3 years ago

Geometry Help i don't understand! 20 points!!

Shkiper50 [21]

1. Given
2.Given
3.Alternate Interior Angles
4. Alternate Exterior ANgles

6 0

3 years ago