Answer:
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
Answer:
y = x - 8
Step-by-step explanation:
The equation of the straight line which is perpendicular to the straight line y = -x -3, will be y = x + c' ....... (1), where c' is a constant.
{This is because the product of the slopes of two mutually perpendicular straight line is -1}
Now, (3,-5) point satisfies equation (1).
Hence, -5 = 3 +c', ⇒c' = -8.
Therefore, the equation of the required straight line in slope-intercept form is y = x - 8 (Answer)
{Note: The slope-intercept form of a straight line is y = mx + c, where m is the slope of the line i.e. tanФ, and c is the length of y-axis intercept.}
Hmm well, here an example y=3 ,
<span> y=3 ,</span> rather than the <span><span> x−</span><span> x−</span></span> axis.) Your integrand looks fine and reduces to
<span><span> (9−18sinx+9<span>sin2</span>x) − (9−18cosx+9<span>cos2</span>x)</span><span> (9−18sinx+9<span>sin2</span>x) − (9−18cosx+9<span>cos2</span>x)</span></span>
<span><span>= 18 (cosx−sinx) + 9 (<span>sin2</span>x−<span>cos2</span>x) = 18 (cosx−sinx) − 9 cos2x .</span><span>= 18 (cosx−sinx) + 9 (<span>sin2</span>x−<span>cos2</span>x) = 18 (cosx−sinx) − 9 cos2x .</span></span>
The evaluation of the volume is then
<span><span>π <span><span>[<span> 18 (sinx+cosx) − <span>92</span>sin2x </span>]</span><span>π/4</span>0</span></span><span>π <span><span>[<span> 18 (sinx+cosx) − <span>92</span>sin2x </span>]</span>0<span>π/4</span></span></span></span>
<span><span>= π <span>(<span> [ 18 ( <span><span>2–√</span>2</span>+<span><span>2–√</span>2</span>) − <span>92</span>⋅1 ] − [ 18 (0+1) − <span>92</span>⋅0 ] </span>)</span> </span><span>= π <span>(<span> [ 18 ( <span>22</span>+<span>22</span>) − <span>92</span>⋅1 ] − [ 18 (0+1) − <span>92</span>⋅0 ] </span>)</span> </span></span>
<span><span>= π ( 18<span>2–√</span> − <span>92</span> − 18 ) = π ( 18<span>2–√</span> − <span>452</span> ) or <span><span>9π</span>2</span> ( 4<span>2–√</span> − 5 ) ,</span></span>