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2 years ago

(English to algebra) twice the difference of w less than five

Mathematics

2 answers:

denpristay [2]2 years ago

5 0

i believe its 2(5-w)

Free_Kalibri [48]2 years ago

5 0

I think it's: 2 ( w - 5 ) . The grammar makes it hard.

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Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graph

diamong [38]

Answer:

a) 8π

b) 8/3 π

c) 32/5 π

d) 176/15 π

Step-by-step explanation:

Given lines : y = √x, y = 2, x = 0.

a) The x-axis

using the shell method

y = √x = , x = y^2

h = y^2 , p = y

vol = ( 2π ) $\int\limits^2_0 {ph} \, dy$

= $( 2\pi ) \int\limits^2_0 {y.y^2} \, dy$

∴ Vol = 8π

b) The line y = 2 ( using the shell method )

p = 2 - y

h = y^2

vol = ( 2π ) $\int\limits^2_0 {ph} \, dy$

= $( 2\pi ) \int\limits^2_0 {(2-y).y^2} \, dy$

= ( 2π ) * [ 2/3 * y^3 - y^4 / 4 ] ²₀

∴ Vol = 8/3 π

c) The y-axis ( using shell method )

h = 2-y = h = 2 - √x

p = x

vol = $(2\pi ) \int\limits^4_0 {ph} \, dx$

= $(2\pi ) \int\limits^4_0 {x(2-\sqrt{x} ) } \, dx$

= ( 2π ) [x^2 - 2/5*x^5/2 ]⁴₀

vol = ( 2π ) ( 16/5 ) = 32/5 π

d) The line x = -1 (using shell method )

p = 1 + x

h = 2√x

vol = $(2\pi ) \int\limits^4_0 {ph} \, dx$

Hence vol = 176/15 π

attached below is the graphical representation of P and h

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2 years ago

Solve the following quadratic by completing the square. y = x2 - 6x + 7

kobusy [5.1K]

Answer:

x = 5 or x = 1

Step-by-step explanation:

x² - 6x + 7 = 0

x² - 6x = -7

x² - 6x + 9 = -7 + 9 1/2 of the x term than square it and add it the both sides.

(x - 3)(x - 3) = 2

( x -3)² = 2

$\sqrt{(x - 3)^2$ = $\sqrt{2}$

(x - 3) = ± 2

x - 3 = 2 or x - 3 = -2

x = 5 or x = 1

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