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Ulleksa [173]
3 years ago
11

The edge of a cube was found to be 15 cm with a possible error in measurement of 0.2 cm. Use differentials to estimate the maxim

um possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (Round your answers to four decimal places.)
Mathematics
1 answer:
Umnica [9.8K]3 years ago
7 0

Answer:

A) Maximum error = 36 cm²

B) Relative Error = 0.0267

C) percentage error = 2.67%

Step-by-step explanation:

Surface area of the cube is;

A(x) = 6x²

Where x is the length of the edge of the cube.

dA/dx = 12x

When x is small like in this case, we can write;

ΔA/Δx ≈ 12x

Thus, ΔA ≈ 12x•Δx

A) Maximum error = 12*15*0.2

Maximum error = 36 cm²

B) Relative Error = Max Error/Surface Area

Surface area = 6 x 15² = 1350

Thus,relative error = 36/1350

Relative Error = 0.0267

C) percentage error = Relative Error x 100%

percentage error = 0.0267 x 100%

percentage error = 2.67%

π

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For function f, you'll use the two points (1,6) and (2,12) since x ranges from x = 1 to x = 2 for function f

The slope through these two points is 
m = (y2-y1)/(x2-x1)
m = (12-6)/(2-1)
m = 6/1
m = 6

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For function g, you'll use (2,4) and (3,20)

The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (20-4)/(3-2)
m = 16/1
m = 16

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For function h, you'll use (0,-6) and (2,-18). The y coordinates can be found by plugging in x = 0 and x = 2 respectively into h(x)

The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (-18-(-6))/(2-0)
m = (-18+6)/(2-0)
m = (-12)/(2)
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The order from left to right is: h, f, g

6 0
3 years ago
I NEED NUMBER 4 PLEEEEEASE
german
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8 0
3 years ago
in the year 2005 a company made $6.6 million in profit for each consecutive year after that their profit increase by 9% how much
posledela

Answer:

$9.3 million

Step-by-step explanation:

Given that the company profit increases by 9% yearly from 2005.

Using the exponential growth formula;

A = P(1+r)^(t) .....1

Where;

A = final amount/value of profit

P = initial amount/value = $6.6 million

r = growth rate yearly = 9% = 0.09

t = time of growth in years = 2009 - 2005 = 4 years

Substituting the values;

A = 6.6(1+0.09)^(4)

A = 6.6(1.09)^(4)

A = 9.3164386 million

A = $9.3 million

The companies profit in the year 2009 to the nearest 10th of $1 million is $9.3 million

5 0
3 years ago
Solve for x.<br> (x - 3)^2 -10 = 15
Brut [27]

Answer:

Step-by-step explanation:

Let's go:

(x - 3)^2 - 10 = 15 \\\ (x - 3)^2 = 15 + 10 \\\ (x - 3)^2 = 25 \\\ x - 3 = \sqrt{25} \\\ x - 3 = \pm 5

Solution #1:

x - 3 = 5

x = 5 + 3

x = 8

Solution #2:

x - 3 = - 5

x = - 5 + 3

x = - 2

I hope I helped you.

3 0
3 years ago
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Answer:

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Step-by-step explanation:

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