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maksim [4K]
3 years ago
15

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.

8 0
3 years ago
How do you solve: 3In5+4Inx
Dafna11 [192]

Answer:

ln(125xx^{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

6 0
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.

7 0
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
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