I need help please???

Find the unit vectors that are parallel to the tangent line to the parabola y = x2 at the point (2, 4).

skelet666 [1.2K]

Answer:

The unit vectors are:

$\vec u_1 = \left\\\vec u_2 = \left$

Step-by-step explanation:

Unit vectors that are a parallel to the tangent line have the same slope than the tangent line, thus we can find the slope of the tangent line, find directional vectors and then their corresponding unit vectors.

Finding the slope of the tangent line.

We can find the first derivative of the curve, which represents the slope of the tangent line of the curve at that point.

$y = x^2 \\ y'=2x$

At x = 2 we have

$y'= 2(2)\\y'= 4\\$

Thus we have slope m = 4, then the parallel unit vector has slope m = 4/1

Finding unit vectors.

From the slope m = 4/1, we can write it as a direction vector with x =1 and y = 4. Notice also that x = -1 and y = -4 would have given as as well slope m = 4 too.

$\vec u =$

Then in order to find the unit vector on that direction we can use the formula

$\hat u =\cfrac{\vec u}{|\vec u|}$

So finding the magnitude we get

$|\vec u |= \sqrt{(1)^2+(4)^2}\\|\vec u| = \sqrt{17}$

Then one unit vector that is parallel to the tangent line is

$\vec u_1 = \left$

And the second unit vector is

$\vec u_2 = \left$

The negative sign on both x and y components just tell us that we are aiming on the opposite direction as the first unit vector, yet both have the same value of the slope.

6 0

3 years ago

If n = 4, then 9 8 ÷ 9 n is equal to _____.

Gre4nikov [31]

Your solution would be 2.7222(repeating)

4 0

4 years ago

What is the mean absolute deviation?

Lostsunrise [7]

Answer:

0.8 cm

Step-by-step explanation:

The formula for MAD is attached in the picture.

x_i are the values (data)

x bar is the mean

n is the number of numbers (data)

For figuring out MAD, basically, we subtract the mean from each of the values respectively and take the absolute value and SUM for all of the numbers in the data set. Then we divide by n, the number of numbers.

Let's do this:

MAD = $\frac{|2-3|+|2-3|+|2-3|+|2-3|+|3-3|+|3-3|+|3-3|+|4-3|+|4-3|+|5-3|}{10}\\=\frac{1+1+1+1+0+0+0+1+1+2}{10}\\=\frac{8}{10}=0.8$

MAD is 0.8

6 0

3 years ago

Volume finding help volume

riadik2000 [5.3K]

1. This is a rectangular prism (box), therefore its volume is written as V = w l h where w is the width, l is the length, and h is the height.
w = 2 1/4 (2.25) m
l = 3 m
h = 8 1/4 (8.25) m
V = w l h
V = 2.25×3×8.25
V = 55.69 m³

2. This is a cube, as shown by the measurements all being equal. Its volume is written as V = a³ where a is the length of any side.
a = 3 1/4 (3.25) in
V = a³
V = 3.25³
V = 33.33 in³

# 3 through 8 are all rectangular prisms (boxes), whose volume is written as V = w l h

3.
w = 2 1/3 (2.33) ft
l = 9 1/4 (9.25) ft
h = 4 ft
V = w l h
V = 2.33×9.25×4
V = 86.21 ft³

4.
w = 3.7 in
l = 10.3 in
h = 2.4 in
V = w l h
V = 3.7×10.3×2.4
V = 91.46 in³

5.
w = 4 in
l = 7 in
h = 5 in
V = w l h
V = 4×7×5
V = 140 in³

6.
w = 5 in
l = 3.6 in
h = 4.2 in
V = w l h
V = 5×3.6×4.2
V = 75.6 in³

7.
w = 2.2 cm
l = 6.6 cm
h = 3 cm
V = w l h
V = 2.2×6.6×3
V = 43.56 cm³

8.
w = 2.1 m
l = 4.2 m
h = 12.2 m
V = w l h
V = 2.1×4.2×12.2
V = 107.60 m³

9. This is a cube again, therefore its volume is written as V = a² where a is the length of any side.
a = 2.3 ft
V = a³
V = 2.3³
V = 12.17 ft³

10. A rectangular box (prism) 12.7 cm long, 7.1 cm wide, and 3 cm high.
V = w l h
V = 7.1×12.7×3
V = 270.51 cubic cm (cm³)

11. A cube 11 1/4 (11.25) inches long.
V = a³
V = 11.25³
V = 1423.83 cubic inches (in³)

12. A rectangular box (prism) 9.8 feet long, 4 feet wide, and 2 1/2 (2.5) feet high.
V = w l h
V = 4×9.8×2.5
V = 98 cubic feet (ft³)

Use the formula V=bh or V=l×w×h (V = w l h) to find the volume of each.

1. Area of base: 8 × 3 = 24 square units
Height: 4 1/2 (4.25) units
V = bh
V = 24×4.25
V = 102 cubic units

2. V = l×w×h
V = bh
V = 3.6×5×4.2
V = 75.6 cubic inches

3. V = bh
b = lw
l = 4 ft
w = 2 1/2 (2.5) ft
b = 4×2.5
b = 10
h = 7
V = bh
V = 10×7
V = 70 cubic feet

4. A rectangular box 6.8 feet long, 4 feet wide, and 2 feet high.
(is it just me, or does that one sound like the dimensions of a coffin???)
V = l×w×h
V = 6.8×4×2
V = 54.4 cubic feet

5. A cube 3 1/2 (3.5) inches long. Draw a picture and label it. Tell how it can help you find the volume.
V = bh
b = l×w
b = 3.5×3.5
b = 12.25
h = 3.5
V = 12.25×3.5
V = 42.88 cubic inches
Drawing attached.

7 0

3 years ago

Masha had 200 scoops of ice cream and Liz had 180 scoops. What is the ratio of the ice cream they have?

s2008m [1.1K]

It depends. If its the ratio of Masha to Liz, it is 10:9. If it is Liz to Masha, its 9:10. If it is Masha to the total, it is 10:19. If it is Liz to the total, it is 9:19. Hope this helps!

5 0

3 years ago

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