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3 years ago

What is the smallest prime factor of 1821?

2 answers:

8 0

Prime factor is a number that can be divided by itself and 1 to get the quotient 0. so according to 1821 this can be divided by 1 and 3 to get a 0 quotient so because 1(unique number ) is not considered as a prime factor 3 is the answer for this question.

GarryVolchara [31]3 years ago

3 0

Answer: 3×607

Step-by-step explanation:

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Find the solutions of each equation on the interval [0, 2π). si (3pi/2+x)+ sin (3pi/2+x)=-2

ANEK [815]

Answer:

The solutions are 0° and 3π

Step-by-step explanation:

On solving the equation given;

$sin(\frac{3\pi}{2}+x )+ sin(\frac{3\pi}{2}+x ) = -2\\2sin(\frac{3\pi}{2}+x ) = -2\\sin(\frac{3\pi}{2}+x ) = -1\\\frac{3\pi}{2}+x = sin^{-1}-1\\ \frac{3\pi}{2}+x = -\frac{\pi}{2} \\x = -\frac{\pi}{2} -\frac{3\pi}{2} \\x = \frac{-4\pi}{2} \\x = -2\pi\\$

<u>Since sin is negative in the 3rd and 4th quadrant, </u>

In the 3rd quadrant;

x =180°+2π

x = π + 2π

x = 3π

In the 4th quadrant;

x = 360°-2π

x = 2π-2π

x = 0°

6 0

3 years ago

A lender offers a $4,000 loan for 3 months at 6% interest

Harrizon [31]

The question isnt clear

4 0

3 years ago

Write equation of the line containing (4,2) and (3,5)<br> in slope-intercept form.

11Alexandr11 [23.1K]

Answer:

The equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:

y=-3x+14

Step-by-step explanation:

Given the points

(4, 2)

(3, 5)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(4,\:2\right),\:\left(x_2,\:y_2\right)=\left(3,\:5\right)$

$m=\frac{5-2}{3-4}$

$m=-3$

We know that the slope-intercept form of the line equation is

$y=mx+b$

where m is the slope and b is the y-intercept

substituting m=-3 and the point (4, 2) to get the y-intercept i.e. b

$y=mx+b$

2=(-3)4 + b

2 = -12 + b

b = 2+12

b = 14

Now, substituting b=14 and m=-3 in the slope-intercept form to determine the equation of a line in the slope-intercept.

$y=mx+b$

y=(-3)x+(14)

y=-3x+14

Thus, the equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:

y=-3x+14

6 0

3 years ago

Cristina made a one-time yearly payment of $18 to access a streaming music service. She purchased 15 songs each month at $1.20 p

mafiozo [28]

The total amount of money Christina spent on streaming music service in a year is $36

<h3>How to find the total cost</h3>

One time payment = $18
Cost of each song = $1.20
Number of songs = 15

Total yearly cost = One time payment + Cost of each song(Number of songs)

= 18 + 1.20(15)

= 18 + 18

= $36

Therefore, the total amount of money Christina spent on streaming music service in a year is $36

Learn more about total cost:

brainly.com/question/2021001

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7 0

3 years ago

Given the following relations on the set of all integers where (x,y)∈R if and only if the following is satisfied. (Check ALL cor

Wewaii [24]

Answer:

a) symmetric

b) symmetric, reflexive, transitive

c) antisymmetric

d) symmetric

Step-by-step explanation:

(a) x+y = 0

- this relation is not reflexive, because the only element that relates with itself is 0. x+x = 2x, x+x = 0 only if 2x = 0, hence x = 0. Since 0 relates with itself, then the relation isnt irreflexive either.

Note that for x,y such that x R y, we have that x+y = 0, therefore, y = -x.

-If x,y,z are such that x R y, y R z, then y = -x, z = -y = -(-x) = x. In general x does not relate with z because z=x and the relation isnt reflexive, thus the relation is not transitive. For example, if x = z = 2, y = -2, we have that xRy, yRz, but x does not relate with z.

- This realtion is symmetric due to the commutativity of the sum. If xRy, then x+y = 0, and y+x = x+y = 0, hence yRx. Therefore, the relation cant be antisymmetric, because every element different from 0 relates to its opposite. For example 2R-2, -2R2 but 2 ≠ -2.

b) x-y is an integer

Since we are taking the substraction of two integers, the result will always be integer. Hence, every pair of elements relate within each other. As a result, the relation is symmetric, reflexive and transitive. However, it is not irreflexive nor antisymmetric, because for example 4R4, and 4R8, 8R4, but 4 is not 8.

c) x = 2y

Note that x = 2x only if x = 0, so the relation is neither reflexive nor irreflexive.

The relation is not symmetric, for example, 4R2 because 4 = 2*2, but 2 does not relate with 4, because 4*2 = 8. However, the relation is antisymmetric, because if xRy, yR2, we have

x = 2y

y = 2x = 2(2y) = 4y

since y = 4y, y should be 0, and x = 2*0 = 0. Therefore x=y = 0. The relation is antisymmetric.

The relation isnt transitive: 2R4, 4R8, but 2 does not relate with 8 because 8*2 = 16.

d) xy>1

since 0² = 0, 0 does not relate with itself, hence the relation is not reflexive. It is not irreflexive either, because, for example, 2*2 = 4 > 2, thus 2 relates with itself.

The relation is not transitive: 1 relates with every integer greater than itself, but it does not relate with itself, for example 1R7 and 7R1 because 1*7=7*1 = 7 > 1, but 1*1 = 1, it is not greater than 1, hence 1 doesnt relate with itself. This also shows that the relation is not antisymmetric either, because 1R7, 7R1 but 1≠7. The relation, however, is symmetric due to the commutativity of the product. If xy > 1, then yx = xy >1 as well.

I hope that works for you!

8 0

4 years ago