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2 years ago

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debt A sum of $80000 cam Rs 31000 due in 3 years and a debt of Rs 2000 due in 4 years is to be Paid by single payments 4 years h

ence, Let the current rate of interest be 5% per annum and be compounded annually What should be the single payment due?

1 answer:

Gennadij [26K]2 years ago

5 0

Answer:

551.25

im sorry if its wrong

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Y=0.5x+3.5 on graphs

tresset_1 [31]

You should go up 3.5 on the Y-Axis and then go up .5 and over 1.

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3 years ago

How many sticks would be in pattern n

S_A_V [24]

Answer:

Depending on the equation it will change

n=1 (not in an equation)

Step-by-step explanation:

Pls mark BRAINLIEST

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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.

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3 years ago

Which of the given values are in the interval (-3,1]?

Vladimir [108]

The values coming in the interval (-3,1] are -2, -1, 0, and 1.

<h3>What is defined as the term interval notations?</h3>

An interval is represented on a number line using interval notation. In all other sayings, it is a method of writing real number line subsets.
An interval is made up of numbers that fall between two specific data set.
Intervals can be categorized according to the numbers in the set.

Interval Open: The endpoints of a inequality are not included in this type of interval.
Interval Closure; The endpoints of a inequality are included in this type of interval.
Interval with Half-Open Doors: This interval contains only one of inequality's endpoints.

The given interval notation is;

(-3,1], it is the case of half open half close.

-3 comes with the open interval, it means its value will not be included in the interval.

1 is with the closed interval, it means its value will be included in the interval.

Thus, the values lying between the interval (-3, 1] are -2, -1, 0, and 1.

To know more about the interval notations, here

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1 year ago

The cost of a student ticket to the school play is $7. Write an equation that correctly relates the total cost, c, for a particu

Mazyrski [523]

C = $7s
independent variable ie the changing variable is s
dependent variable ie the non changing variable is c

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2 years ago

Read 2 more answers