If $20,000 is invested at 7% for 15 years, find the future value if the interest is compounded daily(365 days)

The two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16

Let the two variables be x and y

If the product of the numbers is 300, hence

xy = 300

x = 300/y ........ 1

If the sum of the first and four times the second is a minimum, then;

P(x, y) = x + 4y .................. 2

Substitute equation 1 into equation 2:

P(x, y) = x + 4y

P(y) = 300/y + 4y

If this function is at mimimum, hence dP/dy = 0

dP/dy = -300/y² + 4 = 0

-300/y² + 4 = 0

-300 + 4y² = 0

4y² = 300

y² = 300/4

y²=   75

y = 7.66

Since xy = 300

x = 300/7.66

x = 39.16

Hence the two positive numbers whose product is 300 and such that the sum of the first and four times the second is a minimum are 7.66 and 39.16

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The second derivative of the composition between two functions is described by the following expression:

[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]

Mathematically speaking, a composition between two functions is defined by the following operation:

[tex]f\,\circ\,g\,(x) =f(g(x))[/tex] (1)

By Chain Rule we get the first and second derivatives of the composition:

First derivative

[tex]\frac{d}{dx} (f\,\circ\,g\,(x)) = \frac{df}{dg}\cdot \frac{dg}{dx}[/tex] (2)

Second derivative

[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex] (3)

The second derivative of the composition between two functions is described by the following expression:

[tex]\frac{d^{2}}{dx^{2}} (f\,\circ\,g\,(x)) = \frac{d^{2}f}{dg^{2}}\cdot \frac{dg}{dx} + \frac{df}{dg} \cdot \frac{d^{2}g}{dx^{2}}[/tex]

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Answer:

Upendrakishore Roy Chowdhury; 12 May 1863 – 20 December 1915) was a Bengali writer and painter. He was the first person who introduced the colour printing in bangal. He started the first color children's magazine Sandesh in 1913.

Step-by-step explanation:

history ig

Answer:

F

Step-by-step explanation:

If you look at that triangle and do trigonometry with sin, you would have to do opposite/hypotenuse. This would be (square root of 3)/2

Answer:

-15 = -5x

5x = 15

Step-by-step explanation:

Answer:

The answer would be B. You solve it by substituting the x and y values in the expression, and seeing if it makes a true statement.

Step-by-step explanation:

Answer:

Step-by-step explanation: its a

Answer:

75

Step-by-step explanation:

60 divided by 4/5 is 75

Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

The scenario could be modeled as a linear equation to produce the mathematical model written as : y = 10x + 7

Number of cards from previous card = 7

Number of cards per cardstock purchased = 10

Let :

Number of cardstocks purchased = x

Total Number cards made = y

The total number of cards made, y can be expressed thus :

(Number of cards per cardstock purchased × number of cardstocks purchased) + number of previous cards

This means :

y = 10x + 7

Therefore, the required equation is y = 10x + 7

Answer:

Step-by-step explanation:

h = 44sin13 = 9.89784... = 9.90 ft

Answer: 49 : 32

Step-by-step explanation:

12 1/4 = 49/4

12 1/4 : 8 = 49/4 : 8

12 1/4 : 8 = 49/4 : 8/1

12 1/4 : 8 = 49/4 : 32/4

12 1/4 : 8 = 49 : 32

12 1/4 : 8 = 49 : 32

Answer:

  145. YZ = 48 in

  147. XY = 6 ft

  148: XY = 3 in

Step-by-step explanation:

In each case, multiply the given proportion by a value that makes it match the given information about the segments.

XY is 24in, lines XY:YZ = 1:2. What is the length of line YZ?

Multiply the proportion by 24 in:

  XY : YZ = (24 in)(1) : (24 in)(2) = 24 in : 48 in

  YZ = 48 in . . . (C)

__

YZ is 9ft, lines XY:YZ= 2:3. What is the length of line XY?

Multiply the proportion by 3 ft:

  XY : YZ = (3 ft)(2) : (3 ft)(3) = 6 ft : 9 ft

  XY = 6 ft . . . (B)

__

YZ is 1ft, line XY:YZ = 1:4. What is the length of line XY?

Multiply the proportion by 3 in:

  XY : YZ = (3 in)(1) : (3 in)(4) = 3 in : 12 in = 3 in : 1 ft

  XY = 3 in . . . (A)

Answer:

I believe that it is $901.20

Step-by-step explanation:

I make this assumption Because when we withdraw, we take away. If Kayla wrote these for checks, you just simply add them up and you get a total of $901.20.

We aren’t sure how much she had before withdrawing this money

Answer:

3e-3/2f-3/8

Step-by-step explanation:

You multiply everything in the parenthesis with 1/2. 1/2*6e=3e, 3f*1/2=3/2f, 3/4*1/2=3/8. This would be the answer.

Answer:

v=1

Step-by-step explanation:

-2(2v + 11) + 1 =-5(9v – 4) ​

Distribute the -2 and -5.

-4v-22+1=-45v+20

Calculate the sum.

-4v-21=-45v+20

Move the variable to the left-hand side and change the sign.

-4v-21+45v=20

Move the constant to the right-hand side and change the sign.

-4v+45v=20+21

Collect like terms.

41v=20+21

Add the numbers.

41v=41

Divide both sides by 41

v=1

Hope this helps :)

Answer:

v = -1/49

Step-by-step explanation:

distribute

-4v - 22 + 1 = 5(9v-4)

add the numbers -21 + 1 = -21

distribute the other parenthesis

-4v  - 21 = 45v -20

add 21 to both sides to get v by itself

-4v - 21 + 21 = 45v + 20 + 21

-4v = 45v + 1

substract 45 v on both side now

-4v - 45v = 45v + 1 - 45v

simplify

-49v = 1

divide -49 on both side

v = -1 / 49

Answer: 15.6

Step-by-step explanation:

In 15.56, the digit in the tenths place is the second 5. 15.56. So look at the hundredths place (6). If the digit in the hundredths place is smaller than 5, round down. If it's 5 or more, round up. 6 > 5, so we round the tenths place up by one number to get 15.6.

Answer:

Step-by-step explanation:

d = 277/tan12 = 1,303.1825... m = 1.3 km

The nearest tenth of a foot, the distance from the town to the base of the cliff is approximately 1337.3 feet.

The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

The angle of depression is 12 degrees, and the side opposite the angle is the height of the cliff (277 feet), while the side adjacent to the angle is the distance from the town to the base of the cliff (which we want to find).

Let's denote the distance from the town to the base of the cliff as "d."

The tangent of the angle of depression is given by:

tan(12°) = opposite / adjacent

tan(12°) = 277 / d

Now, solve for "d":

d = 277 / tan(12°)

Using a calculator:

d ≈ 1337.25 feet

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Step-by-step explanation:

The domain is set of x-values:

The range is set of y-values:

True, False, False, True, False, False

Answer:

The equation of the line is: x = 0

Answer:

B

Step-by-step explanation:

since the value is -2 1/4, the point must be less than -2, so it cant be C or D. Since A is less than -3, it cant be A so the point is B

Answer:

Is ka answers D ha.........

Answer:

The answer is D.

Step-by-step explanation:

(8 ,33) = ([tex]x_{1} , y_{1} )[/tex]

m = 3

To find the equation, use the formula:

y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])

Put the values in the equation

y - 33 = 3(x - 8)

y - 33 = 3x - 24

Now to get only the y, put the [tex]y_{1}[/tex]

y - 33 = 3x - 24

    33           33

------------------------

   y    =  3x + 9

Answer:

0.002

Step-by-step explanation:

the digit "2" in this equation represents 0.02 or also 2/100

1/10 of 2/100 would be like multiplying 1/10 and 2/100 and that would get us 2/1000

2/1000 is also 0.002

0.002 is the value of the digit 2 in the number 1,947.5286​.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here we have,

the number 1,947.5286​.

the digit "2" in this equation represents 0.02 or also 2/100

1/10 of 2/100 would be like multiplying 1/10 and 2/100

and that would get us 2/1000

i.e.

2/1000 is also 0.002

Hence, 0.002 is the value of the digit 2 in the number 1,947.5286​.

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Answer:

Step-by-step explanation:

-3 (xy+2y)+5y-x

-3xy-6y+5y-x

-3xy-y-x

Answer:

22.5

Step-by-step explanation:

50%of5+20%=22.5

50/100×5=2.5

2.5+20=22.5%

Answer:

3 gallons

Step-by-step explanation:

10=100 percent

10/5 =2

5-2=3

3 gallons

Answer:

x=7°

Step-by-step explanation:

From the picture it tells us that all side are equal

so that means every side is 60°

Let's make an equation

9x-3°=60°

add 3 on both sides

9x=63°

divide both sides by 9

x=7°

Answer:

Step-by-step explanation:

Let,

The req. number be = x

So,

Two - thirds of the number

[tex] = \frac{2}{3} x[/tex]

Then, it is reduced by 13

[tex] = \frac{2}{3} x - 13[/tex]

After that,

The req. result we get is = 7

Therefore,

By the problem,

[tex] = > \frac{2}{3} x - 13 = 7[/tex]

[tex] = > \frac{2}{3} x = 7 + 13[/tex]

[tex] = > \frac{2}{3}x = 20[/tex]

[tex] = > \frac{2}{3} x \times \frac{3}{2} = 20 \times \frac{3}{2} [/tex]

=> x = 30

Hence,

The req. number is 30.

Given that :

To Find :

Solution :

Let's assume the number as x

According to the question :

[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 = 7 }[/tex]

Adding 13 to both sides we get :

[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 + 13 = 7 + 13 }[/tex]

[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x = 20 }[/tex]

Now, Multiplying both sides by [tex] \dfrac{3}{2} [/tex] we get :

[tex]\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x \times \dfrac{3}{2} = 20 \times \dfrac{3}{2} }[/tex]

[tex]\qquad \sf \: { \dashrightarrow \dfrac{ \cancel2}{ \cancel3}x \times \dfrac{{ \cancel3}}{ \cancel{2}} = \cancel{20} \times \dfrac{3}{ \cancel{2}} }[/tex]

[tex]\qquad \sf \: { \dashrightarrow x = 10 \times {3} }[/tex]

[tex]\qquad \bf \: { \dashrightarrow x = 30 }[/tex]

Therefore, The number is 30.