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3 years ago

7

Carol walks 12km at xkm/h and then a further 6 km at (x-1) km/h the total time taken is 5 hours . Write an equation in terms of

x and show that it simplifies to 5x squared -23x+12=0

1 answer:

Arisa [49]3 years ago

8 0

Step-by-step explanation:

12/x + 6/(x-1) = 5

12(x-1) + 6(x) = 5(x)(x-1)

18x - 12 = 5x² - 5x

5x² - 23x + 12 = 0. (Shown)

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Please help with geomtry

notsponge [240]

Angle ADB is a right angle, which is given.

The measure of ADB is 90 degrees by definition of right angle.

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BDC = ADB because 90 = 90

Overall, the two triangles are congruent by SAS.

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3 years ago

How do you simplify 2i<6u?

tiny-mole [99]

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3 years ago

the volume v of a right circular cylinder of radius r and heigh h is V = pi r^2 h 1. how is dV/dt related to dr/dt if h is const

laiz [17]

In general, the volume

$V=\pi r^2h$

has total derivative

$\dfrac{\mathrm dV}{\mathrm dt}=\pi\left(2rh\dfrac{\mathrm dr}{\mathrm dt}+r^2\dfrac{\mathrm dh}{\mathrm dt}\right)$

If the cylinder's height is kept constant, then $\dfrac{\mathrm dh}{\mathrm dt}=0$ and we have

$\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dt}{\mathrm dt}$

which is to say, $\dfrac{\mathrm dV}{\mathrm dt}$ and $\dfrac{\mathrm dr}{\mathrm dt}$ are directly proportional by a factor equivalent to the lateral surface area of the cylinder ( $2\pi r h$ ).

Meanwhile, if the cylinder's radius is kept fixed, then

$\dfrac{\mathrm dV}{\mathrm dt}=\pi r^2\dfrac{\mathrm dh}{\mathrm dt}$

since $\dfrac{\mathrm dr}{\mathrm dt}=0$ . In other words, $\dfrac{\mathrm dV}{\mathrm dt}$ and $\dfrac{\mathrm dh}{\mathrm dt}$ are directly proportional by a factor of the surface area of the cylinder's circular face ( $\pi r^2$ ).

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3 years ago

Which expression is equivalent to 5 (4x+3)-2

dolphi86 [110]

Answer:

20x + 13

Step-by-step explanation:

5(4x + 3) - 2

5× 4x + 5×3 - 2

20x + 15 - 2

20x + 13

7 0

3 years ago

Read 2 more answers

Finding an Equation of a Tangent Line In Exercise, find an equation of the tangent line to the graph of the function at the give

Inga [223]

Answer:

y = 1/e

y = 0.37

Step-by-step explanation:

y = (ln x)/x; (e, 1/e)

Step 1

Find the point of tangency.

It's given as (e,1/e) or (2.72,0.37)

Step 2

Find the first derivative, and evaluate it at x=e

Using product rule.

d(uv) = udv + vdu

Where u = lnx and v = 1/x

du = 1/x , dv = -1/x^2

f'(x) = -lnx/x^2 +1/x^2

f'(x) = (1-lnx)/x^2

At x = e

f'(e) = (1-lne)/e^2

f'(e) = 0

The slope of the tangent line at this point is m= 0

Step 3

Find the equation of the tangent line at (e,1/e) with a slope of m=0

y−y1 = m(x - x1)

y-(1/e) = 0(x-1)

y = 1/e

y = 0.37

6 0

3 years ago