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3 years ago

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:

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

You might be interested in

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

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