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3 years ago

If possible find the area of the triangle defined by the following: a=32, b=24, y=75°

1 answer:

4 0

If y=75 degrees is the angle between sides a and b, then yes, it is possible to calculate the area of the triangle.

To answer further, we use the sine function to do the calculation.
The area is given by
Area = absin(y)/2 = 32*24*sin(75)/2 = 370.92 to two decimal places.

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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) = 14t4 i + t6 j,

Lisa [10]

$\vec r(t)=14t^4\,\vec\imath+t^6\,\vec\jmath$

$\mathrm d\vec r=(56t^3\,\vec\imath+6t^5\,\vec\jmath)\,\mathrm dt$

$\vec f(x,y)=xy\,\vec\imath+6y^2\,\vec\jmath\implies\vec f(x(t),y(t))=14t^{10}\,\vec\imath+6t^{12}\,\vec\jmath$

Then the line integral is

$\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^1(14t^{10}\,\vec\imath+6t^{12}\,\vec\jmath)\cdot(56t^3\,\vec\imath+6t^5\,\vec\jmath)\,\mathrm dt$

$=\displaystyle\int_0^1(36t^{17}+784t^{13})\,\mathrm dt=\boxed{58}$

7 0

4 years ago

The surface area of a triangular pyramid is 1836 ft2.

mojhsa [17]

1836 ÷ 4 = 459 ft^2 B

8 0

3 years ago

There are 90 chickens on the farm if 60% of the animals on the farm are chickens ,how many animals are on the farm?

LekaFEV [45]

150 is the right answer

7 0

3 years ago

Read 2 more answers

1. Joshua has a ladder that is 12 ft long. He will lean the ladder against a vertical wall. For safety reasons, he wants the ang

marishachu [46]

Let h=height where top of ladder touches wall and x be distance from wall to bottom of ladder...

tana=h/x

a=arctan(h/x) and a≤75

arctan(h/x)≤75 now taking tan of both sides :P

h/x≤tan75 now we have an ugly x value that we need to get rid of:

Using the pythagorean theorem we know:

144=x^2+h^2, x^2=144-h^2, x=√(144-h^2) now we can use this in our inequality for x

h/√(144-h^2)≤tan75

h^2/(144-h^2)≤(tan75)^2

h^2≤144(tan75)^2-h^2(tan75)^2

h^2+h^2(tan75)^2≤144(tan75)^2

h^2(1+(tan75)^2)≤144(tan75)^2

h^2≤[144(tan75)^2]/(1+(tan75)^2)

h^2≤134.353829

h≤11.5911

So he cannot have the top of the ladder 11.8 ft above the ground and not exceed a 75° angle with the ground.

I worked it the hard way just to go through the process. However we could have used a simple trig function to see that maximum height of the top of the ladder....

sin75=h/12

h=12sin75

h≈11.59 ft. That would be the maximum height given that we did not want to exceed 75° with the ground.

7 0

3 years ago

Catherine paid $159.00 for an MP3 player. If the price paid includes a 6% sales tax, which of the following equations can be use

Colt1911 [192]

<u>ANSWER: </u>

The equation is y = 1.06x, so option D is correct.

<u>EXPLANATION:</u>

Given:

Amount Catherine is paid for an MP3 player=$159.00

The price paid includes a sales tax= 6%

To find:

Equations that can be used to determine the price of the MP3 player before tax?

Solution:

Now, we know that, total cost = selling price of item + sales tax on item

y = x + 6% of x

y = x + $\frac{6}{100}x$

y = x + 0.06x

y = 1.06x

Hence, the equation is y = 1.06x, so option D is correct.

7 0

3 years ago