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Lady_Fox [76]
3 years ago
15

Latrell is going to put chocolate ice cream in x bowls for his friends. He will put 0.75 cups of ice cream in each bowl. Which e

quation represents this situation where t is the total number of cups of ice cream Latrell will put in the bowls?
Mathematics
1 answer:
krek1111 [17]3 years ago
6 0

Answer:

0.75 cups of ice cream

x bowls

t is the total number of cups of ice cream

.75x = t

example"

If you have 5 bowls.

.75 (cups of ice cream) * 5 (bowls) = 3.75 cups of ice cream needed

Step-by-step explanation:

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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

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(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

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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

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(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.

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Step-by-step explanation:

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