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3 years ago

22. A rectangular container, whose base is a square

Mathematics

1 answer:

Pie3 years ago

7 0

Answer:

the will be volume is 6cm

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The curves r1(t) = 2t, t2, t4 and r2(t) = sin t, sin 5t, 2t intersect at the origin. Find their angle of intersection, θ, correc

masya89 [10]

Answer:

Therefore the angle of intersection is $\theta =79.48^\circ$

Step-by-step explanation:

Angle at the intersection point of two carve is the angle of the tangents at that point.

Given,

$r_1(t)=(2t,t^2,t^4)$

and $r_2(t)=(sin t , sin5t, 2t)$

To find the tangent of a carve , we have to differentiate the carve.

$r'_1(t)=(2,2t,4t^3)$

The tangent at (0,0,0) is [ since the intersection point is (0,0,0)]

$r'_1(0)=(2,0,0)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{2^2+0^2+0^2} =2$

Again,

$r'_2(t)=(cos t ,5 cos5t, 2)$

The tangent at (0,0,0) is

$r'_2(0)=(1 ,5, 2)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{1^2+5^2+2^2} =\sqrt{30}$

If θ is angle between tangent, then

$cos \theta =\frac{r'_1(0).r'_2(0)}{|r'_1(0)|.|r'_2(0)|}$

$\Rightarrow cos \theta =\frac{(2,0,0).(1,5,2)}{2.\sqrt{30} }$

$\Rightarrow cos \theta =\frac{2}{2\sqrt{30} }$

$\Rightarrow cos \theta =\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =cos^{-1}\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =79.48^\circ$

Therefore the angle of intersection is $\theta =79.48^\circ$ .

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3 years ago

How do you solve: 3In5+4Inx

Dafna11 [192]

Answer:

ln(125x $x^{4}$ )

Step-by-step explanation:

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3 years ago

Find the radius of the circle whose equation is (x + 5)2 + (y + 8)2 = 16

Oxana [17]

The radius is 4.

Find the radius of the circle whose equation is (x + 5)2 + (y + 8)2 = 16

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3 years ago

Factors can be defined as ________ which divide the dividend without leaving any reminder

Svetradugi [14.3K]

Answer:

Factors can be defined as a number or algebraic expression which divide the dividend without leaving any reminder.

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3 years ago

How to get x by it's self 12 - 12x = -6x + 48

anastassius [24]

Answer:

Step-by-step explanation:

12 - 12x = -6x + 48

Add 12x to both sides. That eliminates the x term on the left side.

12 = 6x + 48

Subtract 48 from both sides. That eliminates the constant term on the right side.

-36 = 6x

x = -6

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3 years ago