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2 years ago

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Michael started a savings account with $300. After 4 weeks, he had $350 dollars. And after 8 weeks, he had $400. What is the rat

e of change of money in his savings account per week?

2 answers:

Keith_Richards [23]2 years ago

4 0

Answer:

$12.50

Step-by-step explanation:

I might be wrong but you can try this answer

riadik2000 [5.3K]2 years ago

4 0

Answer:

The rate is not constant be cause 1 is equal to 12.5 and the other is equal to 11.111

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(GEOMETRY only answer if u know) Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the o

ololo11 [35]

Answer:

option: b is correct.

( b.Yes, because both figures are rectangles and all rectangles are similar )

Step-by-step explanation:

Yes, the rectangle EFGH is a result of dilation of rectangle ABCD with a center of dilation at the origin.

Also The scale factor of the dilation is greater than one as the image is bigger than the pre-image i.e. there is a stretch.

The scale factor could be calculated by the ratuio of the sides of the image to the pre-image rectangle.

Rectangle ABCD: Its vertices have coordinates A(-3,3), B(3,3), C(3,0) and D(-3,0).

Now consider rectangle EFGH: Its vertices have coordinates E(-4,4), F(4,4), G(4,0) and H(-4,0).

Hence the scale factor is:

$\dfrac{EF}{AB}=\dfrac{EH}{AD}=\dfrac{FG}{BC}=\dfrac{HG}{DC}=\dfrac{4}{3}$

Hence the scale factor is: 4/3.

Also

∠A=∠B=∠C=∠D=∠E=∠F=∠G=∠H=90°

( When a shape is dilated the two shapes are similar.And similar shapes have equal interior angles , corresponding sides are proportional ).

Hence option: b is correct.

( b.Yes, because both figures are rectangles and all rectangles are similar )

3 0

2 years ago

Read 2 more answers

Claudia invested $12,000 at an interest rate of 4.5% compounded monthly. In the formula A=p(1+r/n)^nt, A is the worth of an acco

aleksandrvk [35]

Answer: $16,433.42

Step-by-step explanation:

Hi, to answer this question we have to apply the formula given:

A=p (1+r/n)^nt,

r must be in decimal form (percentage divided by 100)

n is equal to 12 ( it compounds 12 times per year)

Replacing with the values given:

A = 12,000 (1+ 0.045/12) ^12(7)

Solving:

A = 12,000 (1+ 0.045/12) ^12(7)

A= 12,000 (1.00375) ^84

A = $16,433.42

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2 years ago

Find three mutually orthogonal unit vectors in R^3 besides plusminus i, plusminus j, and plusminus k. There are multiple ways to

viktelen [127]

Answer:

u=(1,1,2), v=(-3,1,2), w=(1,-2,1/2)

Step-by-step explanation:

Since the vectors must be orthogonal, then they must satisfy that the dot product between them is 0.

Then

$1(x)+1(-1)+2(2)=0\\x=-3$

and $-3(1)-1y+2z=0 \text{ and }\\1+1y+2z=0\\$ .

Solving for y, y=-2z-1 and substituting in the first equation, -3+2z+1+2z=0, then

z=1/2, and y=-2(1/2)-1=-2

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2 years ago

Please help: Tom says he is comparing banks to see what interest rates they offer on savings accounts. Explain how Tom should us

Ksju [112]

Tom would more than likely want to put his money in a bank where it can earn interests.

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2 years ago

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Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further downstream. The in and out flow

Gala2k [10]

Answer:

a) dx / dt = - x / 800

b) x = 500*e^(-0.00125*t)

c) dy/dt = x / 800 - y / 200

d) y(t) = 0.625*e^(-0.00125*t)*( 1 - e^(-4*t) )

Step-by-step explanation:

Given:

- Out-flow water after crash from Lake Alpha = 500 liters/h

- Inflow water after crash into lake beta = 500 liters/h

- Initial amount of Kool-Aid in lake Alpha is = 500 kg

- Initial amount of water in Lake Alpha is = 400,000 L

- Initial amount of water in Lake Beta is = 100,000 L

Find:

a) let x be the amount of Kool-Aid, in kilograms, in Lake Alpha t hours after the crash. find a formula for the rate of change in the amount of Kool-Aid, dx/dt, in terms of the amount of Kool-Aid in the lake x:

b) find a formula for the amount of Kook-Aid in kilograms, in Lake Alpha t hours after the crash

c) Let y be the amount of Kool-Aid, in kilograms, in Lake Beta t hours after the crash. Find a formula for the rate of change in the amount of Kool-Aid, dy/dt, in terms of the amounts x,y.

d) Find a formula for the amount of Kool-Aid in Lake Beta t hours after the crash.

Solution:

- We will investigate Lake Alpha first. The rate of flow in after crash in lake alpha is zero. The flow out can be determined:

dx / dt = concentration*flow

dx / dt = - ( x / 400,000)*( 500 L / hr )

dx / dt = - x / 800

- Now we will solve the differential Eq formed:

Separate variables:

dx / x = -dt / 800

Integrate:

Ln | x | = - t / 800 + C

- We know that at t = 0, truck crashed hence, x(0) = 500.

Ln | 500 | = - 0 / 800 + C

C = Ln | 500 |

- The solution to the differential equation is:

Ln | x | = -t/800 + Ln | 500 |

x = 500*e^(-0.00125*t)

- Now for Lake Beta. We will consider the rate of flow in which is equivalent to rate of flow out of Lake Alpha. We can set up the ODE as:

conc. Flow in = x / 800

conc. Flow out = (y / 100,000)*( 500 L / hr ) = y / 200

dy/dt = con.Flow_in - conc.Flow_out

dy/dt = x / 800 - y / 200

- Now replace x with the solution of ODE for Lake Alpha:

dy/dt = 500*e^(-0.00125*t)/ 800 - y / 200

dy/dt = 0.625*e^(-0.00125*t)- y / 200

- Express the form:

y' + P(t)*y = Q(t)

y' + 0.005*y = 0.625*e^(-0.00125*t)

- Find the integrating factor:

u(t) = e^(P(t)) = e^(0.005*t)

- Use the form:

( u(t) . y(t) )' = u(t) . Q(t)

- Plug in the terms:

e^(0.005*t) * y(t) = 0.625*e^(0.00375*t) + C

y(t) = 0.625*e^(-0.00125*t) + C*e^(-0.005*t)

- Initial conditions are: t = 0, y = 0:

0 = 0.625 + C

C = - 0.625

Hence,

y(t) = 0.625*( e^(-0.00125*t) - e^(-0.005*t) )

y(t) = 0.625*e^(-0.00125*t)*( 1 - e^(-4*t) )

6 0

2 years ago