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Serga [27]
2 years ago
14

Find the value of 373 using the identity (x − y)3 = x3 − 3x2y + 3xy2 − y3. Show all work.

Mathematics
1 answer:
Paladinen [302]2 years ago
7 0

Answer:

37^3 = 50653

Step-by-step explanation:

Given

(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

Required

Find 37^3

Express 37 as 40 - 3

So, we have:

37^3 = (40 - 3)^3

Compare to (x -y)^3

x = 40\ and\ y = 3

Substitute 40 for x and 3 for y in (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

(40 - 3)^3 = 40^3 - 3*40^2*3 + 3*40*3^2 - 3^3

Evaluate all exponents

(40 - 3)^3 = 64000 - 3*1600*3 + 3*40*9 - 27

Evaluate all products

(40 - 3)^3 = 64000 - 14400 + 1080 - 27

(40 - 3)^3 = 50653

Hence:

37^3 = 50653

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What is 140/180 as a decimal
Naddika [18.5K]
I think the answer is 0.8 or 0.78. 
You divide 140/180 which gives you 0.77777778
You can either round up to the nearest hundredth or tenth. 
7 0
3 years ago
In the diagram below, trapezoid ABCD maps to trapezoid A’B’C’D’
snow_tiger [21]

Answer:

C'

Step-by-step explanation:

Given

ABCD to A'B'C'D'

Required

Corresponding angle of C

ABCD to A'B'C'D' means that the following angles are corresponding

A \to A'

B \to B'

C \to C'

D \to D'

Hence, C' corresponds to C

6 0
2 years ago
Read 2 more answers
6.<br> The area of the book cover is 14 in.? and the length is 2} in. What is the width?
aleksley [76]

Answer:

the width is 7 inches

Step-by-step explanation:

A = l * w

14 = 2 * w

what does w equal?

14 / 2 = 7

2 * w / 2 = w

7 = w

4 0
3 years ago
How long would it take for a race car traveling at a speed of 150 km/hr to travel 3000m?
IRINA_888 [86]

Answer:

  1.2 minutes

Step-by-step explanation:

The applicable relationship between speed, distance, and time is ...

  time = distance/speed

  = (3 km)/(150 km/h) = (3/150) h = 1/50 h

  = (60 min)/50 = 1.2 minutes

6 0
3 years ago
8000$ is invested in an account the yields 6% interest per year. After how many years will the account worth 13709.60$ if the in
ozzi

Answer:

After 9 years the account will be worth 13709.60$

Step-by-step explanation:

We are given the following in the question:

We are given the following in the question:

P = $8000

r = 6% = 0.046

n = 12

The compound interest is given by:

A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}

where A is the amount, p is the principal, r is the interest rate, t is the time in years.

Putting the values, we get,

13709.60 = 8000\bigg(1+\dfrac{0.06}{12}\bigg)^{12t}\\\\\dfrac{13709.60}{8000} = \bigg(1+\dfrac{0.06}{12}\bigg)^{12t}\\\\\Rightarrow 1.7137 = (1.005)^{12t}\\\Rightarrow t \approx 9

Thus, after 9 years the account will be worth 13709.60$

5 0
3 years ago
Read 2 more answers
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