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Ksenya-84 [330]
3 years ago
10

The side length of a square ice cube is claimed to be 1.0 inches, correct to within 0.001 inch. Use linear approximation to esti

mate the resulting error, measured in squared inches, in the surface area of the ice cube.
Mathematics
1 answer:
Olenka [21]3 years ago
3 0

Answer:

0.012

Step-by-step explanation:

Linear approximation says that,

f(x) \approx f(x_o)+f'(x_o)(x-x_o)

For a cube the surface area is 6x^2.

So the side is 1.0 inch in, the surface area is =6\times1^2 = 6 square inches.  

In Linear approximation means you ignore the term x_o^2 , if x_o is a small number, because then x_o^2 will be a very smalle number and that does not contribute much to the error.  

So the surface area is approximately,

6x^2=6x_o^2+12x_o(x-x_o)

So here, x=1.001, x_o=0.001

The error in the area is approximately,

12 \times 0.001=0.012

So the error is 0.012.


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murzikaleks [220]

Answer: m=\frac{-30}{79},\ y=5.40

Step-by-step explanation:

Given

Points are \left(6\frac{1}{3},3\right),\ \left(19\frac{1}{2},-2\right)

Convert mixed numeral to fraction

\left(6\frac{1}{3},3\right)\Rightarrow \left(\dfrac{19}{3},3\right)\\\\\left(19\frac{1}{2},-2\right)\Rightarrow \left(\dfrac{39}{2},-2\right)

Slope of the line is

\Rightarrow m=\dfrac{3-(-2)}{\dfrac{19}{3}-\dfrac{39}{2}}\\\\\Rightarrow m=\dfrac{5}{\dfrac{38-117}{6}}\\\\\Rightarrow m=\dfrac{-30}{79}

Equation of line

\Rightarrow \dfrac{y-3}{x-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\text{for y-intercept, put x=0}\\\\\Rightarrow \dfrac{y-3}{0-\dfrac{19}{3}}=\dfrac{-30}{79}\\\\\Rightarrow y-3=\dfrac{190}{79}\\\\\Rightarrow y=3+2.40\\\Rightarrow y=5.40

3 0
3 years ago
Find the perimeter of a square equal in area to two squares whose sides are 12 m and 5 m respectively
KatRina [158]
Formula for perimeter a+b+a+b

12+5+12+5= 17+17= 34 .34=P
5 0
3 years ago
The slope of a line passing through H (-2, 5) is -3/4. Which ordered pair represents a point on this line?
oksano4ka [1.4K]
Answer:
(6,-1)

Explanation:
The slope of the line can be calculated using the following formula:
slope = \frac{y2-y1}{x2-x1}

We are given that:
slope = -0.75
point (x1,y1) is (-2,5)

We will use each of the given points to calculate the corresponding slope, then compare the calculated slope with the given one.

For point (6,-1):
slope = \frac{-1-5}{6--2} = -0.75 ........> accepted choice

For point (2,8):
slope = \frac{8-5}{2--2} = 0.75 ........> rejected choice

For point (-5,1):
slope = \frac{1-5}{-5--2} = 4/3 ........> rejected choice

For point (1,1):
slope = \frac{1-5}{1--2} = -4/3 ........> rejected choice

Therefore, the first option is the only correct one.

Hope this helps :)
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Smart Dot, multiply the cost per hour by number of hours (t) and add to the monthly fee:

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3 years ago
-4 plus what number is 04
o-na [289]

Answer:

Set up an equation

-4+x=4 Add 4 to each side

x=8

So

-4 plus eight is 4

5 0
3 years ago
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