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Crank
3 years ago
14

Given: 3x + 1 = -14; Prove: x = -5 Statements

Mathematics
1 answer:
WINSTONCH [101]3 years ago
4 0

Step-by-step explanation:

3x + 1 = -14

3x = -14 - 1

3x = -15

x= -15÷3

x= -5

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(x+1)^1/2
Step2247 [10]

Answer:

Step-by-step explanation:

L.C.M. of 2 and 3=6

Raise to the power 6

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
3 years ago
8(3a+5)???? please help!!!!!! ASAP!!!!
r-ruslan [8.4K]

I'm assuming your teacher wants you to distribute. If so, then you multiply the outer term 8 by each term inside (3a and 5). After that you add.

8 times 3a = 24a

8 times 5 = 40

So 8(3a+5) becomes 24a+40

We do not combine 24a and 40 as they are not like terms. So we leave 24a+40 as it is.

3 0
3 years ago
Read 2 more answers
Write a function rule for the table.
pashok25 [27]

Answer:

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7 0
2 years ago
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The formula for velocity of an object is the equals d over t where he is a velocity of the object t is the distance traveled and
butalik [34]

Answer:

(a)\ t =\frac{d}{v}

(b)\ d = vt

Step-by-step explanation:

<em>The question is mixed up with details of another question. See comment for original question</em>

<em />

<u>Given</u>

v = \frac{d}{t}

v \to velocity

d \to distance

t \to time

Solving (a): Solve for time

We have:

v = \frac{d}{t}

Cross multiply

t * v = d

Make t the subject

t =\frac{d}{v}

Solving (b): Solve for distance

We have:

v = \frac{d}{t}

Cross multiply

d = v * t

d = vt

7 0
3 years ago
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