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3 years ago

A rectangle has a height of x+9 and a width of x^2+2x.

Mathematics

1 answer:

Irina-Kira [14]3 years ago

4 0

Answer:

The area of the entire rectangle is given by: x^3 + 11x^2 + 18x

Step-by-step explanation:

The calculation of its area is straightforward, we only need to multiply its height times its width:

A = (x + 9)(x^2 + 2x)= x^3 + 2x^2 + 9x^2 +18x = x^3 + 11x^2 + 18x

Therefore the are are of the entire rectangle is given by: x^3 + 11x^2 + 18x

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You are the treasurer for a local charity. At the beginning of the month the balance was $820.64. The charity received donations

djverab [1.8K]

Beginning Balance: 820.64
Add:
donations: 500 + 55 + 25 580.00
Deduct:
electric bill: 40.64
postage bill: 12.75
rental : 445.00 <u> (498.39)</u>
Ending Balance 902.25

The balance at the end of the month is $902.25

6 0

3 years ago

Simplify:(y²+z²) -2yz

VMariaS [17]

Answer:

$(y-z)^{2}$

Step-by-step explanation:

$(y^{2}+z^{2} ) -2yz\\\\y^{2} +z^{2} - 2yz\\\\y^{2} +2yz + z^{2}\\\\(y-z)^2\\$

5 0

3 years ago

Steven is taking out a loan in the amount of $5,000. His choices are a 3-year loan at 5% simple interest and a 5 -year loan at 4

Andre45 [30]

I do believe it’s 250$

**The first choice:**
Principal: 5,000$
Rate(%): 5
Time(year): 3 years
A: 5,750$

**Second choice**
Principal: 5,000$
Rate(%): 4%
Time(year): 5 years
A: 6,000$

6,000-5,750=250$

Hope this helps!

8 0

3 years ago

For each vector field f⃗ (x,y,z), compute the curl of f⃗ and, if possible, find a function f(x,y,z) so that f⃗ =∇f. if no such f

butalik [34]

$\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k$

Let

$\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k$

The curl is

$\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)$

where $\partial_\xi$ denotes the partial derivative operator with respect to $\xi$ . Recall that

$\vec\imath\times\vec\jmath=\vec k$

$\vec\jmath\times\vec k=\vec i$

$\vec k\times\vec\imath=\vec\jmath$

and that for any two vectors $\vec a$ and $\vec b$ , $\vec a\times\vec b=-\vec b\times\vec a$ , and $\vec a\times\vec a=\vec0$ .

The cross product reduces to

$\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k$

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

$\nabla\times\vec f=\vec0$

which means $\vec f$ is indeed conservative and we can find $f$ .

Integrate both sides of

$\dfrac{\partial f}{\partial y}=2xze^{2xyz}$

with respect to $y$ and

$\implies f(x,y,z)=e^{2xyz}+g(x,z)$

Differentiate both sides with respect to $x$ and

$\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}$

$2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}$

$4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}$

$\implies g(x,z)=4\sin(xz^2)+h(z)$

Now

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)$

and differentiating with respect to $z$ gives

$\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}$

$2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}$

$\dfrac{\mathrm dh}{\mathrm dz}=0$

$\implies h(z)=C$

for some constant $C$ . So

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C$

3 0

3 years ago

A jet plane can carry up to 200,000 liters of fuel. It used to 130,000 liters of fuel during a flights. What percentage of the f

LekaFEV [45]

65%
Step-by-step explanation:
Given: Full capacity= 200000 litres
Amount of fuel used during flight= 130000 litres
Now, finding percentage of fuel used on the flight.
∴ Percentage of fuel used=
Solving it, we will get
∴ 65% of fuel capacity been used in this flight.

7 0

3 years ago