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kondaur [170]
3 years ago
9

Which of the following is the inverse of y = 12 Superscript x? y = log Subscript one-twelfth Baseline x y = log Subscript 12 Bas

eline StartFraction 1 Over x EndFraction y = log Subscript x Baseline 12 y = log Subscript 12 Baseline
Mathematics
1 answer:
wariber [46]3 years ago
3 0

Answer:

y = lnx/ln12

Step-by-step explanation:

Given the function y = 12^x, to find the inverse of the function, we news to write x as a function of y as shown:

Given y = 12^x

Taking ln of both sides

ln y = ln 12^x

ln y = xln12

Divide both sides by ln12

lny/ln12 = xln12/ln12

x = lny/ln12

x = ln(y-12)

Replacing y with x and x with y

The inverse of the function will be:

y = lnx/ln12

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Answer:

a - (-b), a - (-5)

Step-by-step explanation:

A double negative negative is a positive, so a - (-b) = a + b, and a - (-5) is a + 5. However, a double negative is still a difference, so this answer works.

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Work out the surface area of a cylinder when the height = 18cm and the volume = 1715cm cubed
lara [203]

Answer:

813.4 cm² (nearest tenth)

Step-by-step explanation:

<u>Volume of a cylinder</u>

\sf V=\pi r^2 h \quad\textsf{(where r is the radius and h is the height)}

Given:

  • h = 18cm
  • V = 1715 cm³

Use the Volume of a Cylinder formula and the given values to find the <u>radius of the cylinder</u>:

\implies \sf 1715=\pi r^2 (18)

\implies \sf r^2=\dfrac{1715}{18 \pi}

\implies \sf r=\sqrt{\dfrac{1715}{18 \pi}

<u>Surface Area of a Cylinder</u>

\sf SA=2 \pi r^2 + 2 \pi r h \quad\textsf{(where r is the radius and h is the height)}

Substitute the given value of h and the found value of r into the formula and solve for SA:

\implies \sf SA=2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)^2 + 2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)(18)

\implies \sf SA=2 \pi \left(\dfrac{1715}{18 \pi} \right) + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)

\implies \sf SA=\dfrac{1715}{9} + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)

\implies \sf SA=813.3908956...

Therefore, the surface area of the cylinder is 813.4 cm² (nearest tenth)

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aleksandrvk [35]

Answer:

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