$8,200 is invested in an account earning 5% interest (APR), compounded quarterly.
Write a function showing the value of the account after t years, where the annual
growth rate can be found from a constant in the function. Round all coefficients in
the function to four decimal places. Also, determine the percentage of growth per
year (APY), to the nearest hundredth of a percent.

This question is missing some parts. Here is the complete question.

Consider the oriented path which is a straight line segment L running from (0,0) to (16,16).

(a) Calculate the line inetrgal of the vector field F = (3x-y)i + xj along line L using the parameterization B(t) = (2t,2t), 0 ≤ t ≤ 8.

Enter an exact answer.

[tex]\int\limits_L {F} .\, dr =[/tex]

(b) Consider the line integral of the vector field F = (3x-y)i + xj along L using the parameterization C(t) = [tex](\frac{t^{2}-256}{48} ,\frac{t^{2}-256}{48} )[/tex], 16 ≤ t ≤ 32.

The line integral calculated in (a) is ____________ the line integral of the parameterization given in (b).

Answer: (a) [tex]\int\limits_L {F} .\, dr =[/tex] 384

              (b) the same as

Step-by-step explanation: Line Integral is the integral of a function along a curve. It has many applications in Engineering and Physics.

It is calculated as the following:

[tex]\int\limits_C {F}. \, dr = \int\limits^a_b {F(r(t)) . r'(t)} \, dt[/tex]

in which (.) is the dot product and r(t) is the given line.

In this question:

(a) F = (3x-y)i + xj

r(t) = B(t) = (2t,2t)

interval [0,8] are the limits of the integral

To calculate the line integral, first substitute the values of x and y for 2t and 2t, respectively or

F(B(t)) = 3(2t)-2ti + 2tj

F(B(t)) = 4ti + 2tj

Second, first derivative of B(t):

B'(t) = (2,2)

Then, dot product between F(B(t)) and B'(t):

F(B(t))·B'(t) = 4t(2) + 8t(2)

F(B(t))·B'(t) = 12t

Now, line integral will be:

[tex]\int\limits_C {F}. \, dr = \int\limits^8_0 {12t} \, dt[/tex]

[tex]\int\limits_L {F}. \, dr = 6t^{2}[/tex]

[tex]\int\limits_L {F.} \, dr = 6(8)^{2} - 0[/tex]

[tex]\int\limits_L {F}. \, dr = 384[/tex]

Line integral for the conditions in (a) is 384

(b) same function but parameterization is C(t) = [tex](\frac{t^{2}-256}{48}, \frac{t^{2}-256}{48} )[/tex]:

F(C(t)) = [tex]\frac{t^{2}-256}{16}-\frac{t^{2}-256}{48}i+ \frac{t^{2}-256}{48}j[/tex]

F(C(t)) = [tex]\frac{2t^{2}-512}{48}i+ \frac{t^{2}-256}{48} j[/tex]

C'(t) = [tex](\frac{t}{24}, \frac{t}{24} )[/tex]

[tex]\int\limits_L {F}. \, dr = \int\limits {(\frac{t}{24})(\frac{2t^{2}-512}{48})+ (\frac{t}{24} )(\frac{t^{2}-256}{48}) } \, dt[/tex]

[tex]\int\limits_L {F} .\, dr = \int\limits^a_b {\frac{t^{3}}{384}- \frac{768t}{1152} } \, dt[/tex]

[tex]\int\limits_L {F}. \, dr = \frac{t^{4}}{1536} - \frac{768t^{2}}{2304}[/tex]

Limits are 16 and 32, so line integral will be:

[tex]\int\limits_L {F} \, dr = 384[/tex]

With the same function but different parameterization, line integral is the same.

Answer:

C

Step-by-step explanation:

She spent $80

Answer:

19

Step-by-step explanation:

1. y= -5x + 12

  y= -5x – 7

2. -5x + 12

   -(-5x – 7)

3. -5x + 12

    5x + 7

    0   +19

4. 19

Answer: a) 76 : 24

              b) 24 : 76

Step-by-step explanation: Odds describe the possibility an event will occur, i.e., is the ratio of an event being successful with the chance of an event failing. It can be in favor or against:

a) Odds in favor

[tex]favor=\frac{76/100}{24/100}[/tex]

[tex]favor=\frac{76}{24}[/tex]

or

favor = 76 : 24

Odds in favor of a man agreeing owning a house is an important part of adult life is 76 : 24.

b) Odds against

[tex]against=\frac{24/100}{76/100}[/tex]

[tex]against=\frac{24}{76}[/tex]

or

against = 24 : 76

Odds against of a man agrreing that owning a house is an important part of adult life is 24 : 76

Answer:

The slope is -3

Step-by-step explanation:

Step-by-step explanation:

if the line equation is in the form

y = ...

the slope is always the factor of x.

x + y = 4

y = -x + 4

so, the slope is -1.

a parallel line has the same slope.

when having a surviving point we can use the point-slope form as equation :

y - y1 = m(x - x1)

with m being the slope, and (x1, y1) being a point on the line.

so,

y - 3 = -1(x - 2)

simplified we get

y - 3 = -x + 2

y = -x + 5

that would be the slope-intercept form (+5 being the interception point on the y-axis).

Answer: -90

Step-by-step explanation:

Answer:

8 w

Step-by-step explanation:

yes

Answer:

4 w

Step-by-step explanation:

So first, let's check,

Substitute 4(w=4) for each expression and then evaluate

3(4)=12

4+8=12

4(4)=16

16-4=12

16 is not equal to 12, so the answer is 4 w

Answer:

15

Step-by-step explanation:

The range of a group of numbers is the highest number in the sequence minus the lowest number.

Which in this case was 51 - 36 = 15.

Hope this Helps!

:D

Answer:

b

Step-by-step explanation:

Answer: you need to add them together then add BAND D to the same expersion

the answer is step by step CFE

Answer:

90

Step-by-step explanation:

Answer: -2

Step-by-step explanation: from the equation, -4m +6 = 14, you subtract 6 from both sides and get -4m=8, and the last step is to divide both sides by -4 and you get m=-2.

Answer:

X=58/3=19 1/3

Step-by-step explanation:

32-x=0.4(2x-7)

32-x=0.8x-2.8

32-x-0.8=-2.8

32-.18x=-2.8

-1.8x=-2.8

-1.8x=-34.8

x=58/3

Answer:

center of mass

X = [tex]\frac{my}{m} = \frac{28}{19}[/tex]

Y = [tex]\frac{mx}{m} = \frac{872}{95}[/tex]

Step-by-step explanation:

y = x and x = 0

parabola ; y = 20 - x^2

attached below is the detailed solution

M = [tex]\frac{152}{3}[/tex]б

Mx =  [tex]\frac{6976}{15}[/tex]б

My = [tex]\frac{224}{3}[/tex]б

X = [tex]\frac{my}{m} = \frac{28}{19}[/tex]

Y = [tex]\frac{mx}{m} = \frac{872}{95}[/tex]

Answer:

12x +4y + 3z=36

Step-by-step explanation:

The equation of plane is given by

z-zo = a(x-xo) + b(y-yo)

pass through (1,3,4)

Z -4 = a(x -1) +b(y-3)

The question is asking us to optimize a and b. To minimize the volume V both a and b should be negative as the normal vector should be towards the negative x and y direction so that a finite tetrahedron can be formed in the first octant.

we need x , y and z intercepts o define volume

x intercept( y, z =0) = [tex]\frac{a+3b-4}{a}[/tex]

y intercept (x, z =0) = [tex]\frac{a+3b-4}{b}[/tex]

z intercept ( x, y =0) = -(a+3b-4)

Base = [tex]\frac{(a+3b-4)^2}{2ab}[/tex]

Volume = [tex]\frac{1}{3}*base*height[/tex]

Volume(a, b) = [tex]\frac{-(a+3b-4)^3}{6ab}[/tex]

now we differentiate partially in terms to a and b the volume to minimize and get a and b.

ΔV(a, b) = [tex]\frac{-1}{6}(\frac{3(a+3b-4)^2ab-b(a+3b-4)^3}{a^2b^2}[/tex] ,[tex]\frac{-1}{6}(\frac{9(a+3b-4)^2ab-a(a+3b-4)^3}{a^2b^2}[/tex]  = 0

Taking the first part of differential it will give

b(a+3b-4) [3a -(a+3b -4)] =0

(a+3b-4) [tex]\neq 0[/tex] because the volume will become zero if this becomes true

2a -3b = -4  ..................(1)

similarly the second part of the differential will give

a-6b=4 ................(2)

on solving 1 and 2 we get

a = -4 and b = -4/3

so the equation will be

Z -4 = -4(x -1) - 4/3*(y-3)

final equation

12x +4y + 3z=36

Answer:

So now D would be at (-4 , 2)

Step-by-step explanation:

From D, you can calculate every other letter’s location. Yeah.

Answer:

Please mark me as brainliest!

Step-by-step explanation:

The coordinates:

D: ( 2,6 )

A: ( 2, 1 )

B: ( 5, 1 )

C: ( 5, 6 )

You want to translate this down 4 units and left 6 units.

So what you would do is this:

Formula = ( x - 6 , y - 4 )

D: ( -4, 2 )

A: ( -4, -3 )

B: ( -1, -3 )

C: ( -1, 2 )

Answer:

/_FCB

Step-by-step explanation:

As, supplementry means they add up to 180°

So a straight angle = /_DCB = 180°

So /_DCF + /_x = /_DCB

So, /_x = /_FCB

So answer = /_FCB

Answer:

5x

Step-by-step explanation:

mutuply and remeber a letter by it self has a one infront

Answer:

12:13, 12 to 13

Step-by-step explanation:

Answer:

a) linear pair angles: 1&2, 2&3, 3&4, 1&4... etc (any angles that are adjacent, or right next, to each other that add up to be 180 degrees)

b) All linear pair angles are adjacent angles but not all adjacent angles are linear pairs. So pick any linear pair angle you got because they will always be adjacent. (1&2, 2&3, 3&4, 1&4... etc)

c) vertically opposite angles: 1&3, 2&4, 5&7, 6&8, 9&11, 10&12

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

The base of the model merry-go-round is 450in², and the actual merry-go-round's base is 400 times larger.

Therefore the base of the actual merry-go-round is 180,000in². However, the question asks for the answer in square feet.

180,000in² in squared feet is:

1,250ft² (your final answer)

Answer:

Step-by-step explanation:

u = 2v

(2v)² = v² + 3

4v² - v² = 3

3v² = 3 ⇒ v = 1 and u = 2

Answer:

3x=60

4x=80

Step-by-step explanation:

I think you've typed it wrong it must be 140 packets. All you need to do is assume 3:4 as 3x and 4x and add it

so 7x=140

x=20

3x=60

4x=80

Answer:is there a picture I can refer to?

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

If the students are asked to plant 1/4 of the packet, and they planted six seeds, you would have to multiply 4 x 6 to get a product of 24.

Answer:

Step-by-step explanation:

3/8=0.375

11/16=0.6875

0.375+0.6875=1.0625