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3 years ago

Solve the equation for θ, where 0 ≤ θ ≤ 2π.

Mathematics

1 answer:

leonid [27]3 years ago

8 0

Answer:

Theta=1.57rad, 4.71rad, 0rad, 2π rad, π rad and –π rad

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What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?

grin007 [14]

A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.

1. $Z_{11}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{4};$
$5\cdot 4=20=\overline{9};$
$5\cdot 5=25=\overline{3};$
$5\cdot 6=30=\overline{8};$
$5\cdot 7=35=\overline{2};$
$5\cdot 8=40=\overline{7};$
$5\cdot 9=45=\overline{1};$
$5\cdot 10=50=\overline{6}.$

The multiplicative inverse of 5 in $Z_{11}$ is 9.

2. $Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{3};$
$5\cdot 4=20=\overline{8};$
$5\cdot 5=25=\overline{1};$
$5\cdot 6=30=\overline{6};$
$5\cdot 7=35=\overline{11};$
$5\cdot 8=40=\overline{4};$
$5\cdot 9=45=\overline{9};$
$5\cdot 10=50=\overline{2};$
$5\cdot 11=55=\overline{7}.$

The multiplicative inverse of 5 in $Z_{12}$ is 5.

3. $Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{2};$
$5\cdot 4=20=\overline{7};$
$5\cdot 5=25=\overline{12};$
$5\cdot 6=30=\overline{4};$
$5\cdot 7=35=\overline{9};$
$5\cdot 8=40=\overline{1};$
$5\cdot 9=45=\overline{6};$
$5\cdot 10=50=\overline{11};$
$5\cdot 11=55=\overline{3};$
$5\cdot 12=60=\overline{8}.$

The multiplicative inverse of 5 in $Z_{13}$ is 8.

8 0

3 years ago

1.A house worth $250,000 has an coinsurance clause of 90 percent. The owners insure the property for $191,250. They then have a

Arisa [49]

1. Multiply the value of the house by the percent:

250,000 x 0.9 = 225,000

Divide the amount the owner insured by the clause amount:

191,250/225,000 = 0.85

Multiply that by the amount of damage:

0.85 x 80,000 = 68,000

They will receive $68,000

2. Follow the same steps as above:

180,000 x 0.75 = 135,000

101,250 / 135,000 = 0.75

0.75 x 50,000 = 37,500

They will receive $37,500

8 0

3 years ago

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i need help solving my homework it says : A rectangular prism has a length of 4 cm and a width of 5 cm. The volume of the prism

sashaice [31]

The volume is length * width * height. Length * width is 4 * 5 or 20, so we have that 20 * height = 200. Divide by 20 to get height = 10.

4 0

3 years ago

Y=4(-1)+3<br> Linear Equations

rewona [7]

Your equation states y = 4(-1) + 3

Since the parentheses touch the number 4 which means you multiply, we will start with that first.

4 × -1 or 4(-1) (it means the same thing) would be -4

Now let us combine the equation.

y = -4 + 3

The addition property is included now,

-4 + 3 = -1

Therefore, your answer would be y = -1

Hope this helped! :D

7 0

2 years ago

Elena has 14 pieces of bannana bread. She gives an equal amount of bannana bread to 4 friends. How many peices of bannana bread

Mashutka [201]

You have to divide the 14 pieces amongst 4 friends: 14/4. This can be simplified into a fraction. Since both the numerator and denominator can be divided by 2, you can simplify the fraction to 7/2 and make it into a mixed number 3 1/2, or decimal form 3.5. Each friend got three and a half pieces of banana bread.

6 0

2 years ago

Read 2 more answers