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Rama09 [41]
3 years ago
9

What is the decimals in tenth that less than 3.81 but greater than 3.0

Mathematics
1 answer:
polet [3.4K]3 years ago
5 0
3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8
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Convert from rectangular to polar coordinates:Note: Choose r and θ such that r is non-negative and 0 ≤ θ < 2πa. (6,0)b. (9,9/
Anuta_ua [19.1K]

Answer:

The polar coordinates are as follow:

a. (6,2π)

b. (18, π/3)

c. (2√2 , 3π/4)

d. (2, 5π /6)

Step-by-step explanation:

To convert the rectangular coordinates into polar coordinates, we need to calculate r, θ .

To calculate r, we use Pythagorean theorem:

r = \sqrt{ x^{2} +y^{2} } ---- (1)

To calculate the θ, first we will find out the θ '  using the inverse of cosine as it is easy to calculate.

So,    θ '  = cos ⁻¹  (x/r)

If  y  ≥  0  then  θ  =  ∅

If  y  <  0  then  θ  =  2 π  −  ∅

For a. (6,0)

Sol:

Using the formula in equation (1). we get the value of r as:

r = \sqrt{6^{2} + 0^{2}  }

r = 6

And ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (6/6)

∅  =cos ⁻¹   (1) = 2π

As If  y  ≥  0  then  θ  =  ∅

So ∅ = 2π

The polar coordinates are (6,2π)

For a. (9,9/\sqrt{3})

Sol:

r = 9 + 3(3) = 18

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (9/18)

∅ = cos ⁻¹   (1/2) = π/3

As  If  y  ≥  0  then  θ  =  ∅

then θ  = π/3

The polar coordinates are (18, π/3)

For (-2,2)

Sol:

r =√( (-2)²+(2)² )

r = 2 √2

and ∅  = cos ⁻¹  (x/r)

∅ = cos ⁻¹  (-2/ 2 √2)

∅ = 3π/4

As  If  y  ≥  0  then  θ  =  ∅

then   θ  = 3π/4

The polar coordinates are (2√2 , 3π/4)

For (-√3, 1)

Sol:

r = √ ((-√3)² + 1²)

r = 2

and ∅  = cos ⁻¹  (x/r)

∅  = cos ⁻¹ ( -√3/2)

∅  = 5π /6

As  If  y  ≥  0  then  θ  =  ∅

So  θ  = 5π /6

The polar coordinates are (2, 5π /6)

6 0
2 years ago
X<br> 451<br> 412<br> 451<br> Find the value of x.<br> A. 42<br> 2<br> B. 4<br> C. 43<br> D. 43
marysya [2.9K]

Answer:

B. 4

Step-by-step explanation:

cos(45°) = x/4√2

√2/2 = x/4√2

x = 4√2•√2/2

x = 4

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3 years ago
For lunch, Ruby orders the items shown below Ham and cheese sandwich $4.95
nika2105 [10]

Answer: 9.38

Step-by-step explanation:

I added them all up and then found what 11 percent of all of that was. Rounded it up and added it to the total.

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What is the equation of the line that has a slope of 3 and a​ y-intercept of​ 2?
svetoff [14.1K]

The equation of a line is written as t = ax + b where a is the slope and b is the y-intercept.

Using the slope and y intercept given the equation is:

Y = 3x + 2

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2 years ago
Slater begins saving for college tuition. He invests $1000 in an account that pays 2.5% simple interest. How many years before h
Brrunno [24]
The formula is Interest = principle times rate times time in years.
                        I=prt        

p=1000
r= 0.025
t=x

To find the amount of interest that is earned in a specific time frame, subtract the final amount of money by the principal. 1500-1000=500.

500 = 1000(0.025)x
500 = 25x   
x= 20 years
 
6 0
3 years ago
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