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3 years ago

I WILL GIVE BRAINLIEST

Mathematics

2 answers:

Keith_Richards [23]3 years ago

8 0

"ratio" is the answer to this

Ilia_Sergeevich [38]3 years ago

8 0

Ratio of two integers

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The expression 1.01*1.005(^t) gives the amount of money, in thousands of dollars, in Carter's savings account (t) years after he

dimulka [17.4K]

Answer:

Step-by-step explanation:

Carter's savings account had $1,010 it when he opened it.

4 0

3 years ago

What is the value of x? (Type an integer or a decimal.)

AfilCa [17]

Answer:

2.8

Step-by-step explanation:

10× X = 7× 4

X = 7×4/10 = 2.8

4 0

3 years ago

What is the answer for <br> three fourths x equals nine

Dmitry [639]

Answer:

x=12

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

3 0

3 years ago

Y varies inversely with x. If y = -8 when x = -7, find the y when x=-4.

lora16 [44]

Answer:

y =-14

Step-by-step explanation:

Inverse variation is of the form

xy = k where k is a constant

(-7)(-8) = k

56 = k

The equation is

xy = 56

Let x = -4

(-4)y = 56

y = 56/-4

y =-14

8 0

3 years ago

Find the work done by F= (x^2+y)i + (y^2+x)j +(ze^z)k over the following path from (4,0,0) to (4,0,4)

babunello [35]

$\vec F(x,y,z)=(x^2+y)\,\vec\imath+(y^2+x)\,\vec\jmath+ze^z\,\vec k$

We want to find $f(x,y,z)$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=x^2+y$

$\dfrac{\partial f}{\partial y}=y^2+x$

$\dfrac{\partial f}{\partial z}=ze^z$

Integrating both sides of the latter equation with respect to $z$ tells us

$f(x,y,z)=e^z(z-1)+g(x,y)$

and differentiating with respect to $x$ gives

$x^2+y=\dfrac{\partial g}{\partial x}$

Integrating both sides with respect to $x$ gives

$g(x,y)=\dfrac{x^3}3+xy+h(y)$

Then

$f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+h(y)$

and differentiating both sides with respect to $y$ gives

$y^2+x=x+\dfrac{\mathrm dh}{\mathrm dy}\implies\dfrac{\mathrm dh}{\mathrm dy}=y^2\implies h(y)=\dfrac{y^3}3+C$

So the scalar potential function is

$\boxed{f(x,y,z)=e^z(z-1)+\dfrac{x^3}3+xy+\dfrac{y^3}3+C}$

By the fundamental theorem of calculus, the work done by $\vec F$ along any path depends only on the endpoints of that path. In particular, the work done over the line segment (call it $L$ ) in part (a) is

$\displaystyle\int_L\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(4,0,0)=\boxed{1+3e^4}$

and $\vec F$ does the same amount of work over both of the other paths.

In part (b), I don't know what is meant by "df/dt for F"...

In part (c), you're asked to find the work over the 2 parts (call them $L_1$ and $L_2$ ) of the given path. Using the fundamental theorem makes this trivial:

$\displaystyle\int_{L_1}\vec F\cdot\mathrm d\vec r=f(0,0,0)-f(4,0,0)=-\frac{64}3$

$\displaystyle\int_{L_2}\vec F\cdot\mathrm d\vec r=f(4,0,4)-f(0,0,0)=\frac{67}3+3e^4$

8 0

3 years ago