All categories

2 years ago

Find three different surfaces that contain the curve r(t) = t^2 i + lnt j + (1/t)k

Mathematics

1 answer:

Viefleur [7K]2 years ago

7 0

solution:

Consider the curve: r(t) = t²i +(int)j + 1/t k

X= t² , y = int ,z = 1/t

Using, x = t², z = 1/t

X = (1/z)²

Xz²= 1

Using y = int, z= 1/t

Y = in│1/z│

Using x = t², y = int

Y = int

= in(√x)

Hence , the required surface are,

Xz² = 1

Y = in│1/z│

Y= in(√x)

You might be interested in

in triangleABC the side lengths are b=13, ac=21 and bc=x. write a compound inequality the represents the range of possible value

tankabanditka [31]

Answer:

8 < x < 34

Step-by-step explanation:

ab = 13, ac = 21, bc = x

The longest side of a triangle must be less than the sum of the other two sides.

If 21 is the longest side:

21 < 13 + x

8 < x

If x is the longest side:

x < 13 + 21

x < 34

Therefore, 8 < x < 34.

3 0

2 years ago

The graph of y=3x^2-3x-1 is shown. Use the graph to find estimates for the solutions of i)3x^2-3x+2=2 ii) 3x^2-3x-1=x+1

AlexFokin [52]

Answer:

i) (0, 2) and (1, 2), ii) (0.333, 1.333) and (1, 2).

Step-by-step explanation:

i) Let be $y=3\cdot x^{2}-3\cdot x -1$ , if $3\cdot x^{2}-3\cdot x +2 = 2$ , which is equivalent to the following system of equations:

$y = 3\cdot x^{2}-3\cdot x +2$

$y = 2$

Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0, 2) and (1, 2)

ii) Let be $y=3\cdot x^{2}-3\cdot x -1$ , if $3\cdot x^{2}-3\cdot x +2 = x+1$ , which is equivalent to the following system of equations:

$y = 3\cdot x^{2}-3\cdot x +2$

$y = x+1$

Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0.333, 1.333) and (1, 2)

7 0

2 years ago

Triangle XYZ was dilated using the rule DO,0.25 (x, y) → (0.25x, 0.25y). The image is shown in the diagram. What are the coordin

yaroslaw [1]

I was able to find the image associated with this question, in which the coordinates of point Z are given as (-2,-1).

We know that the coordinates of a point are multiplied by the scale factor to give the new coordinates. Since these coordinates result after the dilation, we divide them by the scale factor to obtain the original coordinates as such:

-2/0.25 , -1/0.25

(-8 , -4)

8 0

2 years ago

Read 2 more answers

A toy company produces rubber balls that have a radius of 1.7 cm. A sphere has a radius of 1.7 centimeters. What is the volume o

kow [346]

Answer: 1 ) 20.58 cm^3

2 ) $0.09

3 ) $ 0.41

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Andrea has a yard shaped like parallelogram ABCD. The garden area, parallelogram EFGB, has an area of 105 ft2004-05-02-04-00_fil

Lynna [10]

The area of a parallelogram is simply calculated using the formula:

A = b * h

Where,

b = length of the base = 45 ft

h = height which is perpendicular to the base = 21 ft

Using the formula, we calculate the total area of the yard.

A = b* h

A = 45 ft * 21 ft

A = 945 ft^2

Now we don’t want to sod the Garden area for the most obvious reason. The garden has an Area of 105 ft^2, we subtract this to the total area giving us,

Area to sod = 945 ft^2 – 105ft^2

5 0

2 years ago