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Nikitich [7]
2 years ago
11

How much times longer is Jupiter’s orbit than earth’s orbit?

Mathematics
1 answer:
GarryVolchara [31]2 years ago
3 0

Answer:

Jupiter's orbit is 5 times longer than earths

Step-by-step explanation:

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Please help my<br> home work is due tomorrow
bekas [8.4K]
Why is everything due tomorrow xD. Also im sorry but I dont understand this either.
5 0
3 years ago
How many ways can two students be chosen from a group of four?<br><br> 4<br> 6<br> 14<br> 10
taurus [48]

Answer:

6

Step-by-step explanation:

8 0
3 years ago
3. Let A, B, C be sets and let ????: ???? → ???? and ????: ???? → ????be two functions. Prove or find a counterexample to each o
Fiesta28 [93]

Answer / Explanation

The question is incomplete. It can be found in search engines. However, kindly find the complete question below.

Question

(1) Give an example of functions f : A −→ B and g : B −→ C such that g ◦ f is injective but g is not  injective.

(2) Suppose that f : A −→ B and g : B −→ C are functions and that g ◦ f is surjective. Is it true  that f must be surjective? Is it true that g must be surjective? Justify your answers with either a  counterexample or a proof

Answer

(1) There are lots of correct answers. You can set A = {1}, B = {2, 3} and C = {4}. Then define f : A −→ B by f(1) = 2 and g : B −→ C by g(2) = 4 and g(3) = 4. Then g is not  injective (since both 2, 3 7→ 4) but g ◦ f is injective.  Here’s another correct answer using more familiar functions.

Let f : R≥0 −→ R be given by f(x) = √

x. Let g : R −→ R be given by g(x) = x , 2  . Then g is not  injective (since g(1) = g(−1)) but g ◦ f : R≥0 −→ R is injective since it sends x 7→ x.

NOTE: Lots of groups did some variant of the second example. I took off points if they didn’t  specify the domain and codomain though. Note that the codomain of f must equal the domain of

g for g ◦ f to make sense.

(2) Answer

Solution: There are two questions in this problem.

Must f be surjective? The answer is no. Indeed, let A = {1}, B = {2, 3} and C = {4}.  Then define f : A −→ B by f(1) = 2 and g : B −→ C by g(2) = 4 and g(3) = 4. We see that  g ◦ f : {1} −→ {4} is surjective (since 1 7→ 4) but f is certainly not surjective.  Must g be surjective? The answer is yes, here’s the proof. Suppose that c ∈ C is arbitrary (we  must find b ∈ B so that g(b) = c, at which point we will be done). Since g ◦ f is surjective, for the  c we have already fixed, there exists some a ∈ A such that c = (g ◦ f)(a) = g(f(a)). Let b := f(a).

Then g(b) = g(f(a)) = c and we have found our desired b.  Remark: It is good to compare the answer to this problem to the answer to the two problems

on the previous page.  The part of this problem most groups had the most issue with was the second. Everyone should  be comfortable with carefully proving a function is surjective by the time we get to the midterm.

3 0
3 years ago
Write the equation for function g(x)
iragen [17]

Answer:

g(x) = (x + 2)^2 + 1

Step-by-step explanation:

From the graph/image that you have provided said translated shift of

f(x) -> g(x)

f(x) = x^2 , g(x) = a(x -h)^2 +k

h is shift right/left

k is shift up/down.

It appears that the shift is left 2 and up 1.

h = -2 and k = 1

g(x) = (x - (-2))^2 +1

g(x) = (x + 2)^2 + 1

5 0
2 years ago
Nora and Lila are reading the same novel for book club.
stich3 [128]

Answer:

<u>1. Nora and Lila be on the same page of the book after 6 days and a half.</u>

<u>2. Nora and Lila be on the page 180.</u>

Step-by-step explanation:

1. Let's check the information given to resolve the question:

Current page of the novel that Nora is reading now = 128

Pages per day Nora reads = 8

Current page of the novel that Lila is reading now = 102

Pages per day Lila reads = 12

Days ahead for Nora and Lila will be on the same page = x

2. After how many days of reading will Nora and Lila be on the same page of the book?

128 + 8x = 102 + 12x

8x - 12x = 102 - 128 (Subtracting 12x and 128 at both sides)

-4x = -26

x = 6.5

<u>Nora and Lila be on the same page of the book after 6 days and a half.</u>

<u>3.</u> What page will they be on?

Nora : 128 + 8 (6.5) = 128 + 52 = 180

Lila : 102 + 12 (6.5) = 102 + 78 = 180

<u>Nora and Lila be on the page 180</u>

4 0
3 years ago
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