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yaroslaw [1]
3 years ago
12

What does the phrase"between 7.2 and 7.6, inclusive" mean?

Mathematics
1 answer:
nalin [4]3 years ago
3 0
The phrase gives you an interval where the extremes are included.

The intervals may be indicated in several ways. 
 7.2 ≤ x ≤ 7.6
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Lines a and d are
ICE Princess25 [194]

Answer:

perpendicular (90 deg to each other)

Step-by-step explanation:

8 0
3 years ago
The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. A) Use differentials to estimate the max
siniylev [52]

Answer:

A) The maximum error in the calculated surface area: 25cm^2

Relative error: 0.013

B) The maximum error in the calculated volume: 162cm^2

Relative error: 0.019

Step-by-step explanation:

A) The formula for the surface area is:

A=4\pi r^2

The measured value is the circumference which is equal to:

C=2\pi r

then the radius is:

r=\frac{C}{2\pi}

Substituting in the formula of the surface:

A=4\pi(\frac{C}{2\pi})^2\\A=4\pi(\frac{C^2}{4\pi^2})\\A=\frac{C^2}{\pi}

Using the formula to calculate the error:

dy=f'(x)dx

Where x is the variable measured and y is a function of x(y=f(x)).

dA=f'(C)dC\\dA=\frac{2C^{(2-1)}}{\pi}dC\\dA=\frac{2C}{\pi}dC

We have C=80cm and dC=0.5cm

dA=\frac{2C}{\pi}dC\\dA=\frac{2(80)}{\pi}(0.5)\\dA=\frac{160}{\pi}(0.5)\\dA=50.9296(0.5)\\dA=25.4648\approx25cm^2

The relative error is the maximum error divide by the total area. The total area is: A=\frac{C^2}{\pi}=\frac{(80)^2}{\pi}=\frac{6400}{\pi}=2037.1833cm^2

\frac{dA}{A}=\frac{25.4648}{2037.1833} =0.0125\approx0.013

B) The formula for the volume is:

V=\frac{4}{3} \pi r^3

Using r=\frac{C}{2\pi}

V=\frac{4}{3} \pi r^3\\V=\frac{4}{3} \pi (\frac{C}{2\pi})^3\\V=\frac{4}{3} \pi (\frac{C^3}{8\pi^3})\\V=\frac{1}{3}(\frac{C^3}{2\pi^2})\\V=\frac{C^3}{6\pi^2}

The maximum error is:

dV=\frac{3C^{3-1}}{6\pi^2}dC\\dV=\frac{C^{2}}{2\pi^2}dC\\dV=\frac{(80)^{2}}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=(324.2278)(0.5)\\dV=162.1139\approx162cm^2

The calculated volume is:

V=\frac{C^3}{6\pi^2}\\V=\frac{(80)^3}{6\pi^2}\\V=\frac{512000}{6\pi^2}\\V=8646.0743

The relative error is:

\frac{dV}{V}=\frac{162.1139}{8646.0743}=0.0188\approx0.019

3 0
3 years ago
Help I have to turn this is tomorrow and I don’t know how to do it
jenyasd209 [6]

Step-by-step explanation:

The area of the triangular base is: 19

square units

How to calculate the base area

The given parameters are:

Volume = 27.36 cubic units

Height = 2.88 unit

The volume of a triangular prism is:

V = 0.5 * B *h

Where B represents the base area.

So, we have:

27.36 = 0.5 * B * 2.88

27.36 B * 1.44 -

Solve for B

B = 19

Hence, the area of the triangular base is: 19 square units

6 0
2 years ago
Anybody wanna be friends? please?
qaws [65]
Sureeeee brainliest pleasee
5 0
3 years ago
What is the equation that passes through the point (3,-6) and has a slope of 3/4?
Vladimir79 [104]

Answer:

lol

Step-by-step explanation:

Some oone idea about this ??

3 0
2 years ago
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