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Kitty [74]
3 years ago
13

Samantha opened a savings account and deposited $200.00. The account earns 10% interest, compounded monthly. If she wants to use

the money to buy a new bicycle in 3 years, how much will she be able to spend on the bike?
Mathematics
1 answer:
noname [10]3 years ago
6 0

Answer:

200(1.10^1)

Step-by-step explanation:

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Megan has 40$ in her wallet. She wants to buy a dress. The regular price of the dress is 45$. The dress is sold at a discount of
devlian [24]

Answer:

yes

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require
Aleksandr-060686 [28]

Answer:

r\approx 1.084\ feet

h\approx 1.084\ feet

\displaystyle A=11.07\ ft^2

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

  •  Produce a function which depends on only one variable
  •  Compute the first derivative and set it equal to 0
  •  Find the values for the variable, called critical points
  •  Compute the second derivative
  •  Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 ft^3. The volume of a cylinder is given by

\displaystyle V=\pi r^2h

Equating it to 4

\displaystyle \pi r^2h=4

Let's solve for h

\displaystyle h=\frac{4}{\pi r^2}

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

\displaystyle A=\pi r^2+2\pi rh

Replacing the formula of h

\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )

Simplifying

\displaystyle A=\pi r^2+\frac{8}{r}

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

\displaystyle A'=2\pi r-\frac{8}{r^2}=0

Rearranging

\displaystyle 2\pi r=\frac{8}{r^2}

Solving for r

\displaystyle r^3=\frac{4}{\pi }

\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet

Computing h

\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

\displaystyle A''=2\pi+\frac{16}{r^3}

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}

\boxed{ A=11.07\ ft^2}

8 0
3 years ago
Work out (5x10^3) x (5x10^7) standard form
dmitriy555 [2]
5*10^3 * 5*10^7= 5*5 *10^3*10^7=25*10^10

Generally u are allowed to leave it as it is but if no

25*10^10=25 * 10000000000 = 250000000000

Here u are!
3 0
3 years ago
Find the measure of each numbered angle for each figure
cricket20 [7]

Answer:

Angle 1 is 58. Angle 2 is 32.

Step-by-step explanation:

The measure of Angle ACB is 90 because C is on the circle and A and B connect to form a diameter of the circle. So, Angle 1 and Angle 2 add up to 90 (total degrees in triangle - 90). Now you can add the expressions the question gave for Angle 1 and Angle 2, and you get 7x + 6. So you have the equation 7x + 6 = 90. Solve the equation and you get x = 12. Now you can plug in that value for x into the expressions for Angles 1 and 2 to find their measures.

6 0
3 years ago
The distance between Capeton and Jonesville is 80 miles. The scale on the map is 0.75 in. : 10 miles. How far apart are the citi
Mnenie [13.5K]
The answer to this question is 6 in. Hope this helps.
7 0
3 years ago
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