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seraphim [82]
2 years ago
10

The area of the kite is 60in^2. Find the value of x.

Mathematics
1 answer:
Mashcka [7]2 years ago
6 0

Answer:

8 in

Step-by-step explanation:

Area = (d1 × d2)/2

d1 = 15 in

d2 = x in

60 = ( 15 * x)/2

120 = 15x

x = 120/15

= 8 in

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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
Mark glues together four pieces of wood to make one long strip. The pieces measure 16.75 inches, 9 inches, 24.25 inches, and 12.
strojnjashka [21]

Given that,

Length of 4 pieces of wood are 16.75 inches, 9 inches, 24.25 inches, and 12.5 inches.

To find,

The length of the strip of wood.

Solution,

Mark glues together four pieces of wood to make one long strip.

Long strip = The sum of 16.75 inches, 9 inches, 24.25 inches, and 12.5 inches.

L = 16.75 + 9 + 24.25 + 12.5

= 62.5 inches

Hence, the strip of wood is 62.5 inches long.

6 0
2 years ago
Two angles are supplementary. One angle measures 60 degrees. What is the measure of the other angle?
Sophie [7]
120 degrees because supplementary degree is 180 so 60+ 120 equals 180 degrees
7 0
3 years ago
Castel bought one cantaloupe for $2. How<br> many cantaloupes can Kathryn buy if she<br> has $4?
Pani-rosa [81]

Answer:

She can 2 cantaloupes with $4

Step-by-step explanation:

4÷2=2

5 0
2 years ago
Read 2 more answers
NO LINKS<br><br> p = -44 ÷ 11. <br><br> 444<br><br> -444<br><br> -4<br><br> 4
umka2103 [35]

-44 divided by 11 is -4

8 0
2 years ago
Read 2 more answers
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