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3 years ago

2) Use a graph to find the length of DE if D(4, -3) and E(-5, -7).

Mathematics

1 answer:

noname [10]3 years ago

3 0

Answer:

The answer rounded to the nearest tenth is 9.8.

Step-by-step explanation:

The answer itself is really long so I rounded to the tenths place.

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Determine if the given mapping phi is a homomorphism on the given groups. If so, identify its kernel and whether or not the mapp

shtirl [24]

Answer:

(a) No. (b)Yes. (c)Yes. (d)Yes.

Step-by-step explanation:

(a) If $\phi: G \longrightarrow G$ is an homomorphism, then it must hold

that $b^{-1}a^{-1}=(ab)^{-1}=\phi(ab)=\phi(a)\phi(b)=a^{-1}b^{-1}$ ,

but the last statement is true if and only if G is abelian.

(b) Since G is abelian, it holds that

$\phi(a)\phi(b)=a^nb^n=(ab)^{n}=\phi(ab)$

which tells us that $\phi$ is a homorphism. The kernel of $\phi$

is the set of elements g in G such that $g^{n}=1$ . However,

$\phi$ is not necessarily 1-1 or onto, if $G=\mathbb{Z}_6$ and

n=3, we have

$kern(\phi)=\{0,2,4\} \quad \text{and} \quad\\\\Im(\phi)=\{0,3\}$

(c) If $z_1,z_2 \in \mathbb{C}^{\times}$ remeber that

$|z_1 \cdot z_2|=|z_1|\cdot|z_2|$ , which tells us that $\phi$ is a

homomorphism. In this case

$kern(\phi)=\{\quad z\in\mathbb{C} \quad | \quad |z|=1 \}$ , if we write a

complex number as $z=x+iy$ , then $|z|=x^2+y^2$ , which tells

us that $kern(\phi)$ is the unit circle. Moreover, since

$kern(\phi) \neq \{1\}$ the mapping is not 1-1, also if we take a negative

real number, it is not in the image of $\phi$ , which tells us that

$\phi$ is not surjective.

(d) Remember that $e^{ix}=\cos(x)+i\sin(x)$ , using this, it holds that

$\phi(x+y)=e^{i(x+y)}=e^{ix}e^{iy}=\phi(x)\phi(x)$

which tells us that $\phi$ is a homomorphism. By computing we see

that $kern(\phi)=\{2 \pi n| \quad n \in \mathbb{Z} \}$ and

$Im(\phi)$ is the unit circle, hence $\phi$ is neither injective nor

surjective.

7 0

3 years ago

Find x and round to the nearest tenth:)

Thepotemich [5.8K]

Answer:

x = 31.8°

Step-by-step explanation:

Applying the Law of Sines, we have:

$\frac{sin(x)}{12} = \frac{sin(75)}{22}$

Multiply both sides by 12

$\frac{sin(x)}{12} \times 12 = \frac{sin(75)}{22} \times 12$

$sin(x) = \frac{sin(75) \times 12}{22}$

$sin(x) = 0.5269$

$x = sin^{-1}(0.5269)$

x = 31.8° (nearest tenth)

8 0

3 years ago

» How many quarts are in 2 gallons?

telo118 [61]

Answer:

Step-by-step explanation:

there are 4 quarts in one gallon and if there are 2 there ill be 8

i hope this helped

5 0

2 years ago

Read 2 more answers

PLEASE HELP IM DESPERATE I DID THIS KHAN AT LEAST 7 TIMES IM SO DEPRESSED I JUST WANT TO GET THIS DONE WITH!

crimeas [40]

Answer:

y = (-3/2) x + 3

Step-by-step explanation:

The line passes through (0, 3) and (2, 0)

Slope = (0 - 3)/(2 - 0) = -3/2

Let y = (-3/2) x + b

Use (0, 3) to get b:

3 = (-3/2)*0 + b, so b = 3

Then y = (-3/2) x + 3

4 0

2 years ago

3. What is the area of the triangle below?<br> 6.0 ft^2<br> 8.6 ft^2<br> 15.0 ft^2<br> 17.2 ft^2

Crazy boy [7]

Answer:

6.0 ft^2

Step-by-step explanation:

hope this helps

3 0

2 years ago

2) Use a graph to find the length of DE if D(4, -3) and E(-5, -7).​

2) Use a graph to find the length of DE if D(4, -3) and E(-5, -7).