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prohojiy [21]
2 years ago
9

celia made 3 1/2 cups of rice. A serving of rice is 2/3 cups. how many servings of rice did celia make?

Mathematics
1 answer:
Nonamiya [84]2 years ago
5 0

Answer:

E. 5 1/4

Step-by-step explanation:

Divide the total cups of rice(3 1/2) by a serving of rice (2/3)

This is my first answer!

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Share 96 sheep in the ratio 7:1:4
Artemon [7]

Answer:

56:8:48

Step-by-step explanation:

1] add th eratio numbers together

7+1+4=12

2} write the ratio as fractions

7/12  1/12  4/12

3] use the formula (ration number/total number * number of sheeps)

a] 7/12 * 96 = 56

b] 1/12 * 96 = 8

c] 4/12 * 96 = 48

3] write your answer as a ration

7 : 1 : 4 = 56 : 8 : 48

6 0
3 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

#SPJ1

7 0
1 year ago
Maria had $22 to spend on five pencils. After buying them she had $12.
Ganezh [65]

Answer:

$2

Step-by-step explanation:

did it in my head........

5 0
3 years ago
Question: 1
Sedbober [7]
The answer is 29

29 is the answer because:
Following PEMDAS
5*6=30
3+30=33
33-4=29
3 0
3 years ago
The parent function f(x) = x^2 is vertically stretched by a scale factor of 2, translated 14 units right, and 6 units up. Which
Elena-2011 [213]

Answer:

(1)\; G(x)=2(x-14)^2+6

Step-by-step explanation:

Assuming, right and up are positive directions.

The given parent function, f(x)=x^2

Let f_1(x) be the function when the parent function is stretched by a scale factor of 2.

So, f_1(x)=2f(x)

\Rightarrow f_1(x)=2x^2

Let f_2(x) be the function when f_1(x) is translated 14 units right.

So, f_2(x)=f_1(x-14)

\Rightarrow f_2(x)=2(x-14)^2

Again, let f_3(x) be the function when f_2(x) is translated 4 units up.

So, f_3(x)=f_2(x)+6

\Rightarrow f_3(x)=2(x-14)^2+6

So, the resulting function, f_3(x)=G(x)=2(x-14)^2+6.

Hence, option (1) is correct.

4 0
3 years ago
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