3 years ago

Please help and show working out

Mathematics

1 answer:

never [62]3 years ago

8 0

Hope you understand my working out.

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Pamela is 12 years younger than Jiri. The sum of their ages is 80. What is Jiri's age?<br> years old

vfiekz [6]

80/2= 40
46-34= 12
So Pamela is 34 & Jiri is 46

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3 years ago

What does it mean for a differential equation to be autonomous?

andrew11 [14]

The term "autonomous" refers to an ordinary differential equation that relates the derivatives of the dependent variable as a function *only* of the dependent variable. In other words, the ODE doesn't explicitly depend on the independent variable.

Examples:

$y'=y^2-1$ is autonomous

$y'=y^2-1+x$ is *not* autonomous

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3 years ago

[(4x + 15) / 5x)] = 1/2

Arada [10]

One way in which to approach this problem would be to treat it as an equation of ratios and to cross multiply:

<span>[(4x + 15) / 5x)] = 1/2 could be written as:

4x + 15 1
----------- = ---
5x 2

Then 8x + 30 = 5x

3x = -30, and so x = -10 (answer). Be certain to check this answer through substitution!

</span>

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3 years ago

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given

Fed [463]

See attachment for one such shell. The volume is given by the sum of infinitely many thin shells like this, each with radius $x$ and height determined by the vertical distance between the upper blue curve and the lower orange curve for any given $x$ , i.e. $8e^x-8e^{-x}$ .

The volume is then

$2\pi\displaystyle\int_0^1x\left(8e^x-8e^{-x}\right)\,\mathrm dx=16\pi\int xe^x(e^{2x}-1)\,\mathrm dx=\dfrac{32\pi}9(e^3-4)\approx179.677$

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3 years ago

What is : 96 x 68.43 ?

enot [183]

96 times 68.43 would be 6569.28, or 6579 7/25

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2 years ago