MATHEMATICS HIGH SCHOOL

Solve the equation sin^2x= 3 cos^2x. The value of x that satisfies the equation if x lies in the second quadrant is what degrees?

The value of x that satisfies the equation if x lies in the third quadrant is what degrees?

Answers

Answer 1

Answer:

Step-by-step explanation:

sin^2(x)= 3 cos^2(x)

Subtract sin^2(x) on both sides

0=3cos^2(x)-sin^2(x)

By Pythagorean Identity sin^2(x)+cos^2(x)=1, we can replace cos^2(x) with 1-sin^2(x)

0=3(1-sin^2(x))-sin^2(x)

Distribute

0=3-3sin^2(x)-sin^2(x)

Combine like terms

0=3-4sin^2(x)

Add 4sin^2(x) on both sides

4sin^2(x)=3

Divide both sides by 4

sin^2(x)=3/4

Take the square root of both sides

sin(x)=+ or - sqrt(3/4)

sin(x)=+ or - sqrt(3)/sqrt(4)

sin(x)=+ or - sqrt(3)/2

This happens on the unit circle at

60 degrees

120 degrees

240 degrees

300 degrees

If we go around and around again forwards or backwards, we get the infinitely many other solutions including the one's already stated in the following solution sets

(60 +360n) degrees

(120 +360n)degrees

(240 +360n)degrees

(300 +360n)degrees

where n is an integer

x is 120 degrees or (120+360n) degrees in the second quadrant. I didn't know if you were just looking for solutions in the first nonnegative cycle of the unit circle or not.

240 degree one or the (240+360n) degrees terminates in the third.

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A vendor has 30 umbrellas to sell. He sells them for $20 each. The function m(u) = 20u models the total amount of money the vendor makes from selling u umbrellas. What are the practical domain and range of the function?

Answers

Answer:

Step-by-step explanation:

Domain={0,30},Range={0,600

Total number of umbrellas=3

Price for each umbrella is =$20

m(u)=20u

as we know

u = umber of umbrellas

m(u) total amount vendor makes by selling u number of umbrellas

So Practically,The extreme cases are

when the vendor sells 0 umbrellas/ no umbrellas

when he sells all the umbrellas

So Domain is {0,total number of umbrellas}={0,30}

Putting this extreme value of domains as u in function m(u),

we get the range of m(u)={0$20,30$20}

⇒ Range={0,$600}

Answer:

domain 0,30 range 0,600

Step-by-step explanation:

Given the values in the probability distribution table, determine the standard deviation. A. 3.2
B. 13.9
C. 3.9
D. 2.0

Answers

Answer:

D. 2.0 is the right answer

Step-by-step explanation:

Note: All decimals were converted to fractions.

The standard deviation of the given distribution is:

σ=1.965

Answer:

1.96

Step-by-step explanation:

Solution:-

- We will use the table given to determine the standard deviation of random variable x. From descriptive statistics we have the following formula for standard deviation (s.d) :

s.d (x) = sqrt ( Var(x) )

- The formula for Variance ( Var (x) ) is also taken from descriptive statistics as follows:

$Var(X) = E ( X^2) + [ E(X) ] ^2$

- Where,

$E ( X^2) = 0^2*0.15 + 1^2*0.07 + 2^2*0.19 + 3^2*0.09 + 4^2*0.16 + 5^2*0.23 +6^2*0.11 \n\nE ( X^2) = 13.91 \n\n$

$E(X) = 0*0.15\:+\:1*0.07\:+\:2*0.19\:+\:3\cdot \:0.09\:+\:4\cdot \:0.16\:+\:5\cdot \:0.23\:+6\cdot \:0.11\n\nE(X) = 3.17\n\n(E(X))^2 = 10.0489$

- So the variance is:

Var ( X ) = 13.91 - 10.0489 = 3.8611

s.d (x) = √3.8611 = 1.96

Which value of n makes the following equation true? 4 1/2 x 2 2/3=(4 1/2 x n) + (4 1/2 x 2/3)

Answers

N equals zero is a possible answer

Answer:78

Step-by-step explanation:

Help on logarithmic equation

Answers

$\log _( 2 ){ \left( 3-x \right) } +\log _( 2 ){ 5 } =2\log _( 3 ){ 5 } \n \n \log _( 2 ){ \left( 5\left( 3-x \right) \right) } =\log _( 3 ){ \left( { 5 }^( 2 ) \right) } \n \n { 2 }^{ \log _( 3 ){ 25 } }=5\left( 3-x \right) \n \n { 2 }^{ \log _( 3 ){ 25 } }=15-5x\n \n 5x=15-{ 2 }^{ \log _( 3 ){ 25 } }\n \n x=\frac { 15 }{ 5 } -\frac { { 2 }^{ \log _( 3 ){ 25 } } }{ 5 } \n \n x=3-\frac { { 2 }^{ \log _( 3 ){ 25 } } }{ 5 }$

What is z?
Z/100= 6/4

Answers

Answer:

z = 150

Step-by-step explanation:

Answer:

Step-by-step explanation:

6-4=2

200/100=2

i think

at a lunch stand, each hamburger has 50 more calories than each order of fries. if 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?

Answers

The correct answer is 370. A system of equations can be used, where h represents the number of calories in a hamburger and f represents the number of calories in an order of fries. The equation 2 h plus 3 f equals 1,700 represents the fact that 2 hamburgers and 3 orders of fries contain a total of 1700 calories, and the equation h equals f plus 50 represents the fact that one hamburger contains 50 more calories than an order of fries. Substituting f plus 50 for h in 2 h plus 3 f equals 1,700 gives 2, parenthesis, f plus 50, close parenthesis, plus 3 f, equals 1,700. This equation can be solved as follows:

2 f plus 100 plus 3 f equals 1,700

5 f plus 100 equals 1,700

5 f equals 1,600

f equals 320

The number of calories in an order of fries is 320, so the number of calories in a hamburger is 50 more than 320, or 370.

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