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tensa zangetsu [6.8K]
3 years ago
6

HELP ASAP PLEASE!

Mathematics
1 answer:
Genrish500 [490]3 years ago
4 0

Step-by-step explanation:

lets take a look....

In order to find the perimeter of a triangle you have to get the sum of all sides. In other words,

Blue triangle:

p = (4x +2) + (7x + 7) + (5x  - 4) \\ p = 4x + 2 + 7x + 7 + 5x - 4 \\ p = 16x + 5

Red triangle:

p = (x + 3) + (2x - 5) + (x + 7) \\ p = x + 3 + 2x - 5 + x + 7 \\ p = 4x + 5

Difference:

d = (16x + 5) - (4x + 5) \\ d = 16x + 5 - 4x - 5 = 12x \\ d = 12x

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Which statement best describes the area of Triangle ABC shown below?
sergeinik [125]

Answer:

  It is one-half the area of a rectangle with sides 4 units × 3 units

Step-by-step explanation:

One side of the triangle is on the line y = 2 between points x=2 and x=6. So, that side has length 6-2 = 4.

The opposite vertex has y-value 5, so is 3 units away from the line y = 2.

The area of the triangle can be considered to have a base of 4 and a height of 3. In the formula ...

  A = (1/2)bh

we find the area to be ...

  A = (1/2)×(4 units)×(3 units) . . . . triangle area

__

A rectangle's area is the product of its length and width. So, a rectangle that is 4 units by 3 units will have an area of ...

  A = (4 units)×(3 units) . . . . rectangle area

Comparing the two area formulas, we see that the triangle area is 1/2 the area of the rectangle with sides 4 units × 3 units.

5 0
3 years ago
your family went out to dinner to celebrate your grandmas 100th birthday. The total for the dinner was $208.60, so your parents
Allushta [10]

Answer:

\%Tip = 13.04\%

Step-by-step explanation:

Given

Tip= \$31.29

Bill = \$208.60

Required

Determine the percentage of the tip

First, we calculate the amount paid

Amount = Tip + Bill

Amount = \$31.29 + \$208.60

Amount = \$239.89

The percentage of the tip is then calculated using:

\%Tip = \frac{Tip}{Amount} * 100\%

\%Tip = \frac{31.29}{239.89} * 100\%

\%Tip = \frac{31.29* 100}{239.89} \%

\%Tip = \frac{3129}{239.89} \%

\%Tip = 13.04\%

8 0
2 years ago
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
tresset_1 [31]

Because I've gone ahead with trying to parameterize S directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over S straight away, let's close off the hemisphere with the disk D of radius 9 centered at the origin and coincident with the plane y=0. Then by the divergence theorem, since the region S\cup D is closed, we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV

where R is the interior of S\cup D. \vec F has divergence

\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z

so the flux over the closed region is

\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0

\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\iint_D\vec F\cdot\mathrm d\vec S}

Parameterize D by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec k

with 0\le u\le9 and 0\le v\le2\pi. Take the normal vector to D to be

\vec s_u\times\vec s_v=-u\,\vec\jmath

Then the flux of \vec F across S is

\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0

\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}

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deff fn [24]
<span>Its speed is 18.05 m/s</span>
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Lady bird [3.3K]
44
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120
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3 years ago
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