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BARSIC [14]
2 years ago
13

Consider the spiral given by c(t) = (e2t cos(2t), e2t sin(2t)). Show that the angle between c and c' is constant. c'(t) = _____L

et θ be the angle between c and c'. Using the dot product rule we have the following. c(t) · c'(t) = c(t) · c'(t) cos(θ) 2e4t =________ cos(θ)

Mathematics
1 answer:
Tcecarenko [31]2 years ago
8 0

Answer:

angle is 45° which is constant

Step-by-step explanation:

We use formula for two vectors <u>a </u>and <u>b</u>    to calculate angle θ between them by formula

cos θ =  <u>a .</u> <u>b</u>  / magnitude of <u>a </u>  ×  magnitude of <u>b</u>

<u>Please see the attached file</u>

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What digit makes each number divisible by nine?<br><br> _7,302
Alborosie

Answer:

Not completely sure but hopefully these will help.

Step-by-step explanation:

I'm kind of confused what you're asking for. If you could clarify that would be great. If you're trying to make it divisible by 9, you can either do 3, 6 or 9. If you want the first two digits: 2,5,8. Please clarify so I can help

8 0
3 years ago
From your conclusions in part E, how many triangles can be constructed based on the given conditions?
cricket20 [7]

What are the given conditions?

6 0
3 years ago
Read 2 more answers
16x 2 + 8x - 15 Mathematics?
Gala2k [10]
If you're factoring, your answer is

(4x - 3)(4x + 5)

You'll work it out this way:

16x^2 + 8x - 15

Since there's no GCF here, you multiply the first and third terms, giving you -240. Your next step is to find two numbers that have a sum of 8 and a product of -240. These numbers are 20 and -12. Plug those in and you've got:

16x^2 + 20x - 12x - 15

From here you divide it into two binomials. These are (16x^2 + 20x) and (-12x - 15).
When you take out the greatest common factors (4x and -3), they become:

4x(4x + 5) - 3(4x + 5)

Then you group what's outside of the parentheses together (4x - 3)
And bring what's inside of the parentheses down (4x + 5).
This brings your answer to

(4x - 3)(4x + 5)
5 0
3 years ago
The length of a rectangle exceeds the breadth by 8 cm. Find the area of the rectangle, if its perimeter is 180 cm
sergiy2304 [10]

Answer:

2009cm^2

Step-by-step explanation:

Given data

let the length be L

and the width be w

so

w= x

L=x+8

P= 180cm

P= 2L+2W

180= 2(x+8)+2(x)

180= 2x+16+2x

collect like terms

180= 4x+16

180-16= 4x

164= 4x

x= 164/4

x=41

W= 41cm

L= 41+8

L= 49cm

A= L*W

A=49*41

A=2009cm^2

Hence the area is 2009cm^2

3 0
2 years ago
Draw place value disks on the place value chart 0.7 ÷ 4
Mama L [17]
Change 0.7 to 7/10 and 4 to 1/4,so it'll be 7/10x1/4, then find least common denominator, 40.change fractions to 28/40x10/40=280/40=70
4 0
3 years ago
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