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V125BC [204]
3 years ago
15

What is the surface area of a triangular based pyramid with a slant height of 8 and a base length of 5? Rounded to the nearest h

undredth.
Mathematics
1 answer:
torisob [31]3 years ago
3 0
(<span>used with a singular verb</span><span>) the systematic treatment of magnitude,relationships between figures and forms, and relations betweenquantities expressed <span>symbolically</span></span>
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What is the measure of angle TRV? 20° 50° 60° 130°
Svetllana [295]

Answer: 130

Step-by-step explanation:

8 0
3 years ago
Surface integrals using an explicit description. Evaluate the surface integral \iint_{S}^{}f(x,y,z)dS using an explicit represen
Jobisdone [24]

Parameterize S by the vector function

\vec r(x,y)=x\,\vec\imath+y\,\vec\jmath+f(x,y)\,\vec k

so that the normal vector to S is given by

\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=\left(\vec\imath+\dfrac{\partial f}{\partial x}\,\vec k\right)\times\left(\vec\jmath+\dfrac{\partial f}{\partial y}\,\vec k\right)=-\dfrac{\partial f}{\partial x}\vec\imath-\dfrac{\partial f}{\partial y}\vec\jmath+\vec k

with magnitude

\left\|\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}\right\|=\sqrt{\left(\dfrac{\partial f}{\partial x}\right)^2+\left(\dfrac{\partial f}{\partial y}\right)^2+1}

In this case, the normal vector is

\dfrac{\partial\vec r}{\partial x}\times\dfrac{\partial\vec r}{\partial y}=-\dfrac{\partial(8-x-2y)}{\partial x}\,\vec\imath-\dfrac{\partial(8-x-2y)}{\partial y}\,\vec\jmath+\vec k=\vec\imath+2\,\vec\jmath+\vec k

with magnitude \sqrt{1^2+2^2+1^2}=\sqrt6. The integral of f(x,y,z)=e^z over S is then

\displaystyle\iint_Se^z\,\mathrm d\Sigma=\sqrt6\iint_Te^{8-x-2y}\,\mathrm dy\,\mathrm dx

where T is the region in the x,y plane over which S is defined. In this case, it's the triangle in the plane z=0 which we can capture with 0\le x\le8 and 0\le y\le\frac{8-x}2, so that we have

\displaystyle\sqrt6\iint_Te^{8-x-2y}\,\mathrm dx\,\mathrm dy=\sqrt6\int_0^8\int_0^{(8-x)/2}e^{8-x-2y}\,\mathrm dy\,\mathrm dx=\boxed{\sqrt{\frac32}(e^8-9)}

5 0
2 years ago
Graph the line with slope 1 passing through the point (5,1).
vfiekz [6]

Answer:

y= x-4

Step-by-step explanation:

Since we have a point, and the slope, we can use the point slope formula

y-y_{1}=m(x-x_{1}  )

m is the slope, y1 is the y coordinate of the point and x1 is the x coordinate of the point.

We know that m is 1, y1 is 1, and x1 is 5, so we can substitute them in

y-1=1(x-5)

Solve for y by isolating it

Distribute the 1

y-1=1*x+ 1*-5

y-1=x-5

Add 1 to both sides

y=x-4

7 0
3 years ago
Read 2 more answers
What is 43.586 rounded to the nearest hundredth
USPshnik [31]
The answer is 43.590.
5 0
3 years ago
Read 2 more answers
The dimensions of a rectangular building
galina1969 [7]
Area of a rectangle is length x width.

So the area is 15000 because 150 x 100 = 15000
6 0
2 years ago
Read 2 more answers
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