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Mathematics

2 answers:

AnnZ [28]3 years ago

6 0

Answer:

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

To calculate m use the slope formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (3, 6) and (x₂, y₂ ) = (8, 4)

m = $\frac{4-6}{8-3}$ = - $\frac{2}{5}$ , hence

y = - $\frac{2}{5}$ x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (8, 4), then

4 = - $\frac{16}{5}$ + c ⇒ c = 4 + $\frac{16}{5}$ = $\frac{36}{5}$

y = - $\frac{2}{5}$ x + $\frac{36}{5}$ ← equation of line

Diano4ka-milaya [45]3 years ago

5 0

D, love y= -2/5x+ 36/5

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Arlecino [84]

I've attached a plot of one such cross-section (orange) over the region in the x-y plane (blue), including the bounding curves (red). (I've set $y=1.25$ for this example.)

The length of each cross section (the side lying in the base) has length determined by the horizontal distance $x$ between the y-axis $x=0$ and the curve $y=\sqrt x$ . In terms of $y$ , this distance is $x=y^2$ . The height of each cross section is twice the value of $y$ , so the area of each rectangular cross section should be $2y^3$ .

This means the volume would be given by the integral

$\displaystyle\int_0^22y^3\,\mathrm dy$