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4 years ago

The sum of three consecutive terms x, y and z of an arithmetic progression is 45. If y=1/2(x+z), find the value of y.

Mathematics

1 answer:

Len [333]4 years ago

3 0

Answer:

y = 15

Step-by-step explanation:

x + y + z = 45 → (1)

Given

y = $\frac{1}{2}$ (x + z)

Multiply both sides by 2 to clear the fraction

2y = x + z ← substitute into (1)

2y + y = 45

3y = 45 ( divide both sides by 3 )

y = 15

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If s represents speed write an inequality to represent how fast a person can legally dive a vehicle in a school zone with a spee

ELEN [110]

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3 years ago

Hamburgers sell for 3 pounds for 6 dollars. if samantha buys 10 pounds for hamburgers how much will she pay

tamaranim1 [39]

You would start by 6÷3. This would tell you that for every proud of hamburger you pay $2.

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Therefore, your answer is $20.

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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

3 years ago

I need help ASAP,, pleaseeee

jolli1 [7]

Answer:

1a) (-7,-3)

1b) (7,3)

1c) (3,-7)

3) 2 (180)

4) sorry I can't figure this one out

5) If it says 180° about the origin then it is (-5,10) if it isn't about the origin the say what it is in the comments and I will try to look at it again

Step-by-step explanation:

8 0

4 years ago

Help me with this question please, thank you !

Salsk061 [2.6K]

Answer:

Step-by-step explanation:

[(27divided by (-3)-9] divided by [15-21}

=[-9-9] divided by 3

= 6divided by 3 = 2

<h2><u><em>if answer is correct so mark me as brain lest :-)</em></u></h2>

5 0

2 years ago

The sum of three consecutive terms x, y and z of an arithmetic progression is 45. If y=1/2(x+z), find the value of y.​

The sum of three consecutive terms x, y and z of an arithmetic progression is 45. If y=1/2(x+z), find the value of y.