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Bogdan [553]
3 years ago
14

Martin is cleaning the tires of his bicycle. He notices that his bicycle tire has a radius of 8 inches. How much bigger is the a

rea of the tire, than the circumference
Mathematics
1 answer:
algol [13]3 years ago
8 0

Strange question, as normally we would not calculate the "area of the tire." A tire has a cross-sectional area, true, but we don't know the outside radius of the tire when it's mounted on the wheel.

We could certainly calculate the area of a circle with radius 8 inches; it's

A = πr^2, or (here) A = π (8 in)^2 = 64π in^2.

The circumference of the wheel (of radius 8 in) is C = 2π*r, or 16π in.

The numerical difference between 64π and 16π is 48π; this makes no sense because we cannot compare area (in^2) to length (in).

If possible, discuss this situatio with your teacher.



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Deffense [45]
Independent
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7 0
3 years ago
Read 2 more answers
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
In Rhombus ABCD if BD is 24 ft and AD is 15 ft, then what is the length of AC?
Evgen [1.6K]

Answer:

AC = 24ft

Step by Step Explanation.

Given.

Rhombus.

BD = 24ft

AD = 15ft

Required

Length of AC

A rhombus has 4 equal sides; hence, the given shape will be regarded as a parallelogram and not rhombus (see attachment for diagram)

The opposite sides of a parallelogram are always of equal length

From the attached diagram (not drawn to scale), side AC opposites side BD

Given that BD = 24ft, then

AC = BD = 24ft.

Hence, AC = 24ft

4 0
3 years ago
−2x=x^2−6
Iteru [2.4K]

Step-by-step explanation:

Example 1

Solve the equation x3 − 3x2 – 2x + 4 = 0

We put the numbers that are factors of 4 into the equation to see if any of them are correct.

f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a solution

f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2

f(2) = 23 − 3×22 – 2×2 + 4 = −4

f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12

f(4) = 43 − 3×42 – 2×4 + 4 = 12

f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100

The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.

Now we can factorise our expression as follows:

x3 − 3x2 – 2x + 4 = (x − 1)(x2 − 2x − 4) = 0

It now remains for us to solve the quadratic equation.

x2 − 2x − 4 = 0

We use the formula for quadratics with a = 1, b = −2 and c = −4.

We have now found all three solutions of the equation x3 − 3x2 – 2x + 4 = 0. They are: eftirfarandi:

x = 1

x = 1 + Ö5

x = 1 − Ö5

Example 2

We can easily use the same method to solve a fourth degree equation or equations of a still higher degree. Solve the equation f(x) = x4 − x3 − 5x2 + 3x + 2 = 0.

First we find the integer factors of the constant term, 2. The integer factors of 2 are ±1 and ±2.

f(1) = 14 − 13 − 5×12 + 3×1 + 2 = 0 1 is a solution

f(−1) = (−1)4 − (−1)3 − 5×(−1)2 + 3×(−1) + 2 = −4

f(2) = 24 − 23 − 5×22 + 3×2 + 2 = −4

f(−2) = (−2)4 − (−2)3 − 5×(−2)2 + 3×(−2) + 2 = 0 we have found a second solution.

The two solutions we have found 1 and −2 mean that we can divide by x − 1 and x + 2 and there will be no remainder. We’ll do this in two steps.

First divide by x + 2

Now divide the resulting cubic factor by x − 1.

We have now factorised

f(x) = x4 − x3 − 5x2 + 3x + 2 into

f(x) = (x + 2)(x − 1)(x2 − 2x − 1) and it only remains to solve the quadratic equation

x2 − 2x − 1 = 0. We use the formula with a = 1, b = −2 and c = −1.

Now we have found a total of four solutions. They are:

x = 1

x = −2

x = 1 +

x = 1 −

Sometimes we can solve a third degree equation by bracketing the terms two by two and finding a factor that they have in common.

6 0
3 years ago
Read 2 more answers
each day alyssa jogs for 25 minutes on a treadmill she jogs 135 meters a minute at the speed at which alyssa is jogging how many
Fittoniya [83]

Answer: she is jogging 2.25 i think

Step-by-step explanation:

im sorry im not sure i just divided 135 by 60 but i dont think its right:(

5 0
3 years ago
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