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3 years ago

How do I find this answer and what is the answer?

Mathematics

2 answers:

Ilia_Sergeevich [38]3 years ago

8 0

QR = PR - PQ

QR = 13y + 25 - (8y + 5)
QR = 13y + 25 - 8y - 5
QR = 5y + 20 <==

kramer3 years ago

6 0

The length of QR is the length of PR minus the length of PQ. So write out the formula:
(13y + 25) - (8y + 5)

Expand
13y + 25 -8y - 5

Combine
5y + 20

So the length of QR is 5y + 20

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1 year ago

Surface integrals using an explicit description. Evaluate the surface integral \iint_{S}^{}f(x,y,z)dS using an explicit represen

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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

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

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2 years ago

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2 years ago

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A 4-kilogram bag of birdseed costs $12.69. What is the unit price, rounded to the

igomit [66]

Answer:

$3.17

Step-by-step explanation:

Take the $12.69 and divide it by the 4 kilograms and you get 3.17. (This is rounded)

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3 years ago

An isosceles triangle has a base 9.2 units long. If the congruent side lengths have measures to the first decimal place, what is

Nadusha1986 [10]

Question:

An isosceles triangle has a base of 9.6 units long. If the congruent side lengths have measures to the first decimal place, what is the possible length of the sides? 9.7, 4.9, or 4.7

Answer:

4.9 is the shortest possible length of the sides.

Step-by-step explanation:

Given:

The base of the triangle base = 9.2 units

To Find:

The shortest possible length of the sides = ?

Solution:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

So According to the theorem

$x+x > 9.6$