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3 years ago

you invest 1000 in an account that pays simple interest of 6% for 30 years what. How much money will you have in 30 years

Mathematics

2 answers:

Genrish500 [490]3 years ago

6 0

A = P(1+rt)
A = 1000(1+.06x30) = 2800

Scorpion4ik [409]3 years ago

3 0

I=PRT
Interest=Principal times Rate times Time

principal=amount invested
r=rate in decimal
t=time in years

so
P=1000
r=6$=0.06
t=30yr

I=(1000)(0.06)(30)
I=1800 interest

you will have 1000+1800 or $2800 in 30 years

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A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

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3 years ago

Use complete sentences to describe how measurements of position in two directions (vertical and horizontal) are sufficient enoug

Diano4ka-milaya [45]

By using a coordinate system I believe you can find the position of any objects on a flat surface.

If you have an eraser on your table and would like to know its position, you could make your own x and y axis and see in which quadrant your object is in.
your eraser could be 2 units in the x direction (horizontal) and 5 units in the y direction (vertical).

Now you can use this 'x and y' axis that you have drawn to locate any object.
If you want to be accurate, you should draw your axes with a meter ruler and choose your point of origin.

Hope I answered your question.

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DanielleElmas [232]

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amm1812

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3 years ago

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KATRIN_1 [288]

Answer: $x^{\frac{2}{3} }$

Step-by-step explanation:

We have several properties of exponents in use here. The two that are used are:

$(x^{a})(x^{b}) = x^{a + b}$ (Exponents with the same base that are being multiplied together can have the exponents added)

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