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ivann1987 [24]
3 years ago
13

The diagram shows a square divided into strips of equal width. Three strips are black and two are grey. What fraction of the per

imeter of the square is grey?
Mathematics
1 answer:
astra-53 [7]3 years ago
8 0
2/5 at the top nd bottom, but 0/5 on the sides. So 2/5 + 0/5= 1/5
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Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x3 and y = x. (10 points)
USPshnik [31]
See the graph attached.

The midpoint rule states that you can calculate the area under a curve by using the formula:
M_{n} = \frac{b - a}{2} [ f(\frac{x_{0} + x_{1} }{2}) +  f(\frac{x_{1} + x_{2} }{2}) + ... +  f(\frac{x_{n-1} + x_{n} }{2})]

In your case:
a = 0
b = 1
n = 4
x₀ = 0
x₁ = 1/4
x₂ = 1/2
x₃ = 3/4
x₄ = 1

Therefore, you'll have:
M_{4} = \frac{1 - 0}{4} [ f(\frac{0 +  \frac{1}{4} }{2}) +  f(\frac{ \frac{1}{4} + \frac{1}{2} }{2}) +  f(\frac{\frac{1}{2} + \frac{3}{4} }{2}) + f(\frac{\frac{3}{4} + 1} {2})]
M_{4} = \frac{1}{4} [ f(\frac{1}{8}) +  f(\frac{3}{8}) +  f(\frac{5}{8}) + f(\frac{7}{8})]

Now, to evaluate your f(x), you need to look at the graph and notice that:
f(x) = x - x³

Therefore:
M_{4} = \frac{1}{4} [(\frac{1}{8} - (\frac{1}{8})^{3}) + (\frac{3}{8} - (\frac{3}{8})^{3}) + (\frac{5}{8} - (\frac{5}{8})^{3}) + (\frac{7}{8} - (\frac{7}{8})^{3})]

M_{4} = \frac{1}{4} [(\frac{1}{8} - \frac{1}{512}) + (\frac{3}{8} - \frac{27}{512}) + (\frac{5}{8} - \frac{125}{512}) + (\frac{7}{8} - \frac{343}{512})]

M₄ = 1/4 · (2 - 478/512)
     = 0.2666

Hence, the <span>area of the region bounded by y = x³ and y = x</span> is approximately 0.267 square units.

6 0
3 years ago
Evaluate the expression, below, when a = 2 and b = 5. <br><br> (3 + a)² • (4 – b) + √36
stellarik [79]

Answer:

-19

Step-by-step explanation:

1) substitute a with 2 and b with 5

(3 + 2)^2 * (4-5) + √36

2) solve the brackets and the square root

(5^2) * (-1) + 6

3) solve the power

25 *(-1) + 6

4) solve the multiplication

-25 + 6

5) solve the sum

- 19

6 0
2 years ago
What is the value of d in 3/4(8x-6)-2=1/2-x
Salsk061 [2.6K]

Answer: 32/35

Step-by-step explanation:

got it correct

7 0
3 years ago
A car traveling south is 200 kilometers from its starting point after 2 hours. What is the average velocity of the car?
Eddi Din [679]
D. 100 kilometers/hour
8 0
3 years ago
Someone, please help me with this asap! And no links or weird answers, please!
kupik [55]

Answer:

b = 4

Step-by-step explanation:

subtract by 5 on both sides. ur left with

{b}^{2}  = 16

square root b and 16. the square root cancels out b squared. find the square root of 16. the square root of 16 is 4

3 0
2 years ago
Read 2 more answers
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