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Volgvan
3 years ago
11

What does 30 ≤ x + 10 ≤ 80 simplify to

Mathematics
1 answer:
MakcuM [25]3 years ago
4 0

Answer:

20 ≤ x ≤  70

Step-by-step explanation:

Given that:

30 ≤ x + 10 ≤ 80

By solving the left half inequality first:

30 ≤ x + 10

Subtracting 10 from both sides:

30 - 10  ≤ x + 10 -10

20  ≤ x

Now solving inequality of right half:

x + 10 ≤ 80

Subtracting 10 from both sides:

x + 10 -10 ≤ 80 - 10

x ≤  70

So after simplification we get:

20 ≤ x ≤  70

I hope it will help you!

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Which function is equivalent to y = 3(x + 2)2 + 7?
Tems11 [23]

Answer:

The answer is D

Step-by-step explanation:

I wish i can explan but i got to go, piece

7 0
2 years ago
For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f
Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

1.

\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0

We want to find f such that \nabla f=\vec F. This means

\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)

\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C

\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}

so \vec F is conservative.

2.

\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)

\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)

\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C

\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}

so \vec F is conservative.

3.

\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0

so \vec F is not conservative.

4.

\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0

Then

\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)

\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)

\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C

\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}

so \vec F is conservative.

4 0
3 years ago
Help plz :((<br> I'll give brainliest
tamaranim1 [39]

For A. the muddy water will slowly begin to decrease because it's been left out in the sun, some of the water will begin to evaporate.

(I don't know about B, or C, but I tried my best on A.)

Make sure to put in your own words. :)

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3 years ago
Simplify (6g4h5)2<br> What is the answer
SVETLANKA909090 [29]

Answer:

12g8h10

Multiply each variable quantity by 2 and combine.

6 0
2 years ago
Xkslgmvkdkskfnfjndngkckgkdks
NeX [460]
X-3=66
x=69

69+41+(y-9)=180
110+y-9=180
101+y=180
y=79
7 0
3 years ago
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