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2 years ago

What is 3(x+2)+2(x+2) ?

Mathematics

2 answers:

likoan [24]2 years ago

4 0

Answer:

5x +10

Step-by-step explanation:

3(x+2)+2(x+2)

Distribute

3x+6 +2x+4

Combine like terms

5x +10

Maru [420]2 years ago

4 0

Answer:

5x+10

simplified if you want: x+2

Step-by-step explanation:

3x+6+2x+4

5x+10

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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

2 years ago

Create an equation that represents a parabola that opens upward

algol13

For a parabola that opens upward, it must be a quadratic equation whose coefficient of x2 is a positive number.

So, I'll say x2+5x+6.

8 0

2 years ago

In which quadrant is ( 5,4 ) is located<br>this is hw and i wanna get a good grade plz helpp!!!!

Andre45 [30]

(5,4)

On a system of 2 perpendicular axis with O as origine, the pair (5,4) means:

5 is the distance from the origin O and situated on x-axis (on the right of O)
4 is the distance from the origin O and situated on y-axis (above O)

Then the pair (5,4) is situated in the 1st Quadrant

8 0

2 years ago

What number would this be?

kobusy [5.1K]

Answer:

Approximately 775,000.

Step-by-step explanation:

The number is almost in between 750,000 and 800,000. The number in the middle of these two is 775,000.

4 0

3 years ago

Read 2 more answers

Kid got 50 things of ravioli. He puts 30 rats in his ravioli. What is the percentage of ravioli that doesn't have rats in it com