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The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, th

sveta [45]

Answer:

Step-by-step explanation:

The average value of all the pennies, nickels, dimes, and quarters in Paula's purse is 20 cents. If she had one more quarter, the average value would be 21 cents. How many dimes does she have in her purse

7 0

1 year ago

The Cartesian coordinates of a point are given. (a) (−5, 5) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0

Alex73 [517]

Answer:

a)

(i) The coordinates of the point in polar form is (5√2 , 7π/4)

(ii) The coordinates of the point in polar form is (-5√2 , 3π/4)

b)

(i) The coordinates of the point in polar form is (6 , π/3)

(ii) The coordinates of the point in polar form is (-6 , 4π/3)

Step-by-step explanation:

* Lets study the meaning of polar form

- To convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ):

1. r = √( x2 + y2 )

2. θ = tan^-1 (y/x)

- In Cartesian coordinates there is exactly one set of coordinates for any

given point

- In polar coordinates there is literally an infinite number of coordinates

for a given point

- Example:

- The following four points are all coordinates for the same point.

# (5 , π/3) ⇒ 1st quadrant

# (5 , −5π/3) ⇒ 4th quadrant

# (−5 , 4π/3) ⇒ 3rd quadrant

# (−5 , −2π/3) ⇒ 2nd quadrant

- So we can find the points in polar form by using these rules:

[r , θ + 2πn] , [−r , θ + (2n + 1) π] , where n is any integer

(more than 1 turn)

* Lets solve the problem

(a)

∵ The point in the Cartesian plane is (-5 , 5)

∵ r = √x² + y²

∴ r = √[(5)² + (-5)²] = √[25 + 25] = √50 = ±5√2

∵ Ф = tan^-1 (y/x)

∴ Ф = tan^-1 (5/-5) = tan^-1 (-1)

- Tan is negative in the second and fourth quadrant

∵ 0 ≤ Ф < 2π

∴ Ф = 2π - tan^-1(1) ⇒ in fourth quadrant r > 0

∴ Ф = 2π - π/4 = 7π/4

OR

∴ Ф = π - tan^-1(1) ⇒ in second quadrant r < 0

∴ Ф = π - π/4 = 3π/4

(i) ∵ r > 0

∴ r = 5√2

∴ Ф = 7π/4 ⇒ 4th quadrant

∴ The coordinates of the point in polar form is (5√2 , 7π/4)

(ii) r < 0

∴ r = -5√2

∵ Ф = 3π/4 ⇒ 2nd quadrant

∴ The coordinates of the point in polar form is (-5√2 , 3π/4)

(b)

∵ The point in the Cartesian plane is (3 , 3√3)

∵ r = √x² + y²

∴ r = √[(3)² + (3√3)²] = √[9 + 27] = √36 = ±6

∵ Ф = tan^-1 (y/x)

∴ Ф = tan^-1 (3√3/3) = tan^-1 (√3)

- Tan is positive in the first and third quadrant

∵ 0 ≤ Ф < 2π

∴ Ф = tan^-1 (√3) ⇒ in first quadrant r > 0

∴ Ф = π/3

OR

∴ Ф = π + tan^-1 (√3) ⇒ in third quadrant r < 0

∴ Ф = π + π/3 = 4π/3

(i) ∵ r > 0

∴ r = 6

∴ Ф = π/3 ⇒ 1st quadrant

∴ The coordinates of the point in polar form is (6 , π/3)

(ii) r < 0

∴ r = -6

∵ Ф = 4π/3 ⇒ 3rd quadrant

∴ The coordinates of the point in polar form is (-6 , 4π/3)

6 0

3 years ago

Please help i will give brainliest!!

Romashka-Z-Leto [24]

5.78x10^7
If you need an explanation on how then let me know :)

4 0

3 years ago

the base of this right prism is an equilateral triangle. the approximate height of the base is 15.6 cm. what is the approximate

Andrew [12]

Hello!

To find the surface area you can divide the prism into the 2D shapes it is made of

First list out all the shapes

2 triangles with bases of 18 and heights of 15.6
3 rectangles with side lengths of 20 and 18

First find the area of the triangles

The equation to find the area of a triangle is

$A = \frac{hb}{2}$

A is area
h is height
b is base

Put in the values you know

$A = \frac{18 * 15.6}{2}$

Solve

A = 140.4

The triangles have an area of 140.4 units

Next we find the area of a the rectangles

To do this we multiply the sides

18 * 20 = 360

The rectangles have areas of 360 units

Now we add all the areas

There are 2 triangles and 3 rectangles

140.4 + 140.4 + 360 + 360 + 360 = 1360.8

The answer is B) 1360.8cm squared

Hope this helps!

6 0

3 years ago

Lily wants a square beach blanket that will cover at least 36 square feet of space. if s represents the length of one side of th

lbvjy [14]

Area of square = atleast 36 = length *width, where l = w (since it's a square)

If A=36, l = w = 6
If A = 37, l = w = 6.08
if A =38, l = w = 6.16

So the solution set is s => 6 (s is bigger than or equal to 6)

5 0

3 years ago