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Mathematics

1 answer:

diamong [38]3 years ago

5 0

V= x*(10-2x)(8-2x)

for greatest volume, differentiate v w.r.t x and equate to 0,

dv/dx= (10-2x)(8-2x) + x(-2)(8-2x)+ x(10-2x)(-2)=0

you get x from solving the quadratic equation. volume will be max at that x

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Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (0, 11, −8) and

NNADVOKAT [17]

Answer:

The vector equation of the line is $\overrightarrow {r}=(11j-8k)+t(4i-4j+6k)$ and parametric equations for the line are $x=4t$ , $y=11-4t$ , $z=-8+6t$ .

Step-by-step explanation:

It is given that the line passes through the point (0,11,-8) and parallel to the line

$x=-1+4t$

$y=6-4t$

$z=3+6t$

The parametric equation are defined as

$x=x_1+at,y=y_1+bt,z=z_1+ct$

Where, (x₁,y₁,z₁) is point from which line passes through and <a,b,c> is cosine of parallel vector.

From the given parametric equation it is clear that the line passes through the point (-1,6,3) and parallel vector is <4,-4,6>.

The required line is passes through the point (0,11,-8) and parallel vector is <4,-4,6>. So, the parametric equations for the line are

$x=4t$

$y=11-4t$

$z=-8+6t$

Vector equation of a line is

$\overrightarrow {r}=\overrightarrow {r_0}+t\overrightarrow {v}$

where, $\overrightarrow {r_0}$ is a position vector and $\overrightarrow {v}$ is cosine of parallel vector.

$\overrightarrow {r}=(11j-8k)+t(4i-4j+6k)$

Therefore the vector equation of the line is $\overrightarrow {r}=(11j-8k)+t(4i-4j+6k)$ and parametric equations for the line are $x=4t$ , $y=11-4t$ , $z=-8+6t$ .

3 0

3 years ago

80% of what number is 20

Olin [163]

the answer is 16 because .80 times 20 is 16

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4 years ago

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VMariaS [17]

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Step-by-step explanation: