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Vaselesa [24]
3 years ago
14

Teresa’s age is 5 years more than twice Ben’s age.

Mathematics
1 answer:
Oliga [24]3 years ago
6 0
If Ben is 7 years old your going to do 7×2+5 to get Teresa's age then you add her age to his age. so your going to multiply 7×2 and add the answer of 7×2 to 5.
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What is the prime factorization of 74
mash [69]
74 is a composite number. 74=1*74 or 2*37. Factors of 74: 1,2,37,74. Prime factorization: 74=2*37.
3 0
3 years ago
X^2-5x=14 solve for x
elixir [45]

Answer:

x=7, -2.

Step-by-step explanation:

x^2-5x=14

x^2-5x-14=0

factor out the trinomial,

(x-7)(x+2)=0

zero property,

x-7=0, x+2=0,

x=0+7=7,

x=0-2=-2

8 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
What do the differences between the equation of a
EastWind [94]

Answer:

it tells u what color

Step-by-step explanation:

8 0
2 years ago
For the function F defined by F(x) = x2 – 2x + 4, find F(b+3).
Ivanshal [37]

Answer:

\displaystyle F(b + 3) = b^2 + 4b + 7

Step-by-step explanation:

We are given the function:

\displaystlye F(x) = x^2 - 2x + 4

And we want to find F(<em>b</em> + 3).

We can substitute:

\displaystyle F(b + 3) = (b + 3)^2 - 2(b+3) + 4

Expand:

\displaystyle = (b^2 + 6b + 9) + (-2b -6) + 4

Rearrange:

\displaystyle = (b^2) + (6b-2b) + (9 - 6 + 4)

Combine like terms. Hence:

\displaystyle = b^2 +4b + 7

In conclusion:

\displaystyle F(b + 3) = b^2 + 4b + 7

6 0
3 years ago
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