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2 years ago

Evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y) = xy i + 6y2 j r(t) = 16t6 i + t4 j,

0 ≤ t ≤ 1

Mathematics

1 answer:

netineya [11]2 years ago

7 0

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=\int_{t=0}^{t=1}\mathbf f(\mathbf r(t))\cdot\mathrm d(16t^6\,\mathbf i+t^4\,\mathbf j)$
$=\displaystyle\int_0^1\bigg(16t^{10}\,\mathbf i+6t^8\bigg)\cdot\bigg(96t^5\,\mathbf i+4t^3\,\mathbf j\bigg)\,\mathrm dt$
$=\displaystyle\int_0^1(1536t^{15}+24t^{11})\,\mathrm dt=98$

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8_murik_8 [283]

Let, the height of the building be x ft.

Given the building casts 35ft shadow.

The height of the flagpole given which is 22ft and casts a shadow of 10ft.

Now to find the height of the building we have to equate the ratio of height and shadow of the building and the flagpole.

So we can write,

x/35 = 22/10

To find x, we have to get rid of 35 from the left side and have to move it to right side. As 35 is divided there, we will multiply 35 to both sides.

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2 years ago

What is the perimeter P of △DEF to the nearest whole number?

schepotkina [342]

Answer:

perimeter of ΔDEF ≈ 32

Step-by-step explanation:

To find the perimeter of the triangle, we will follow the steps below:

First, we will find the length of the side of the triangle DE and FF

To find the length DE, we will use the sine rule

angle E = 49 degrees

e= DF = 10

angle F = 42 degrees

f= DE =?

we can now insert the values into the formula

cross-multiply

f sin 49° = 10 sin 42°

Divide both-side by sin 49°

f = 10 sin 42° / sin 49°

f≈8.866

which implies DE ≈8.866

We will now proceed to find side EF

To do that we need to find angle D

angle D + angle E + angle F = 180° (sum of interior angle)

angle D + 49° + 42° = 180°

angle D + 91° = 180°

angle D= 180° - 91°

angle D = 89°

Using the sine rule to find the side EF

angle E = 49 degrees

e= DF = 10

ange D = 89 degrees

d= EF = ?

we can now proceed to insert the values into the formula

cross-multiply

d sin 49° = 10 sin 89°

divide both-side of the equation by sin 49°

d= 10 sin 89°/sin 49°

d≈13.248

This implies that length EF = 13.248

perimeter of ΔDEF = length DE + length EF + length DF

=13.248 + 8.866 + 10

=32.144

≈ 32 to the nearest whole number

perimeter of ΔDEF ≈ 32

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Answer:

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We are given the following information in the question:

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We have to write a relationship with the help of an inequality for the ages of citizens who are not allowed to vote.

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So x should be less than 18.

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