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2 years ago

A car travels at an average speed of 48 miles per hour. How long does it take to travel 180 miles?

Mathematics

1 answer:

Sonja [21]2 years ago

4 0

Answer:

3 hours and 45 minutes

Step-by-step explanation:

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The figure is made up of a square and a rectangle. Find the area of the shaded region.

inn [45]

Answer:

$10 \: { \: m}^{2}$

Step-by-step explanation:

area of the shaded region = Area of triangle formed in rectangle with base (10 - 6 = 4) 4m and height 2 m + Area of triangle formed in square with base 2 m and height 6 m

$= \frac{1}{2} \times 4 \times 2 +\frac{1}{2} \times 2\times 6 \\ \\ = 4+6 \\ \\ = 10 \: { \: m}^{2}$

8 0

2 years ago

Read 2 more answers

A watercolor painting is 24 inches long by 11 inches wide. Ramon makes a border around the watercolor painting by making a mat t

sergeinik [125]

Given: It is given that the length of the painting is 24 inches and the width is 11 inches.

To find: Area of the mat

Solution:

The watercolor painting is 24 inches long by 11 inches wide.

So, the area of the painting is:

$\text{Area of painting}=l\times b$

$\text{Area of painting}=24\times 11$

$\text{Area of painting}=264 \text{ in}^2$

The length of painting with mat is = 24 in + 3 in + 3 in = 30 in

The width of painting with mat = 11 in + 3 in + 3 in = 17 in

$\text{Area of painting with mat}=30\times 17$

$\text{Area of painting with mat}=510 \text{ in}^2$

Now to calculate the area of mat subtracts the area of painting from the area of the mat.

$\text{Area of mat}=\text{Area of painting with mat}-\text{Area of painting}\\$

$\text{Area of mat}=510-264$

$\text{Area of mat}=246 \text{ in}^2$

Hence, the area of the mat is 246 in².

6 0

2 years ago

What is (2-2i√3)4 equivalent to?

maxonik [38]

a. (2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

b. (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

To answer the question, we need to know what complex numbers are

<h3>What are complex numbers?</h3>

Complex numbers are numbers of the form z = x + iy

<h3>a. Complex numbers in polar form</h3>

Complex numbers in polar form z = r(cosθ + isinθ) where

r = √(x² + y²) and
θ = tan⁻¹(y/x)

Given that z = (2 - 2i√3)⁴ =

So,

x = 2 and
y = -2√3

So, converting to polar form

r = √(x² + y²)

= √[2² + (-2√3)²]

= √[4 + 4(3)]

= √[4 + 12]

= √16

= 4

θ = tan⁻¹(y/x)

θ = tan⁻¹(-2√3/2)

θ = tan⁻¹(-√3)

θ = -π/3

So, z = r(cosθ + isinθ)

= 4(cos(-π/3) + isin(-π/3))

<h3>Powers of complex numbers</h3>

A complex number z raised to power n is zⁿ = rⁿ(cosnθ + isin(nθ)]

z⁴ = (2 - 2i√3)⁴

= r⁴(cos4θ + isin4θ)

= 4⁴(cos(4 × -π/3) + isin(4 × -π/3))

= 256(cos(-4π/3) + isin(-4π/3))

= 256cis(-4π/3)

(2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

<h3>b. Complex numbers in rectangular form</h3>

The complex number z = r(cosθ + isinθ) in rectangular form is z = x + iy where

x = rcosθ and
y = rsinθ

Given that z⁴ = 256(cos(-4π/3) + isin(-4π/3)) in rectangular form,

x = rcosθ

= 256(cos(-4π/3)

= 256cos(-4 × 60°)

= 256cos(-240)

= 256cos(240)

= 256 × -1/2

= -128

y = rsinθ

= 256sin(-4π/3)

= 256sin(-4 × 60°)

= 256sin(-240)

= -256sin240

= -256 × -√3/2

= 128√3

So, z⁴ = x + iy

= -128 + 128√3

So, (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

Learn more about complex numbers in polar form here:

brainly.com/question/9678010

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7 0

1 year ago

Urgent pls :

Luden [163]

13/52 + 13/52

26/52

1/2

0.5

50%

7 0

2 years ago

Read 2 more answers

Pls helpppp and show work!!

antoniya [11.8K]

Answer:

Step-by-step explanation:

slope m = (y₂ - y₁)/(x₂ - x₁)

= 6-6 / 8 - (-5) = 0/ 8+5 = o

Slope = o. ie the line is parallel to the x-axis.

3 0

2 years ago