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Dvinal [7]
3 years ago
15

Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,.to find the following:

Mathematics
1 answer:
Rasek [7]3 years ago
6 0
a)\\\\
a_{n+1}-a_n=d\\
for\ n=1\\
a_2-a_1=d\\
d=3-1=2\ - difference\ between\ two\ consecutive\ terms\\\\
b)\\
a_n=a_1+(n-1)d\\
n=101\\
a_{101}=1+(101-1)*2\\
a_{101}=1+100*2=200+1=201\\\\
c)\\
Sn=\frac{a_1+a_n}{2}*n\\
n=20\\
a_n=a_{20}=1+(20-1)*2=1+38=39\\
Sn=\frac{1+39}{2}*20=400\ \ Sum\ of\ the\ first\ 20 \ numbers.
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John saved $50,000. and wants to put the money into an Index Annuity that pays an average of 8.4% per year, compounded semi-annu
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2 years ago
A truncated cone has horizontal bases with radii 18 and 2. A sphere is tangent to the top, bottom, and lateral surface of the tr
MariettaO [177]
<h3>Answer:  6 units</h3>

===================================================

Explanation:

A truncated cone is where we start with a regular 3D cone and chop off the top. The portion up top is a smaller cone, which we'll ignore. The bottom part is the truncated cone portion.

In the real world, a lampshade is one example of a truncated cone.

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

Let x be the radius of the sphere.

We'll be focusing on a vertical cross section of the truncated cone. Refer to figure 1 in the diagram below.

We have the following points

  • A = center of the sphere
  • B = center of the circular base of the truncated cone
  • C = point 18 units to the right of point B
  • E = point directly above point A, and its the center of the circular top of the truncated cone
  • D = point 2 units to the right of point E
  • F = the location where the circle touches the slanted curved side of the truncated cone
  • G = point directly below point D, and located on segment BC

We'll connect a few of those points forming the dashed lines in figure 1.

To start off, draw a segment from D to G. This forms rectangle BGDE with sides of EB = 2x and BG = 2. The side BC is 18 units, so that must mean GC = BC - BG = 18 - 2 = 16.

Since EB = 2x, this means DG is also 2x.

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

Now focus on triangles ABC and AFC. They are congruent right triangles. We can prove this using the HL (hypotenuse leg) theorem. Recall that the radius of a circle is perpendicular to the tangent line, which is why angle AFC is 90 degrees. Angle ABC is a similar story.

Because they are congruent right triangles, this indicates side BC is the same length as side FC. Therefore, FC = 18

Through similar logic, triangles ADE and ADF are congruent as well which leads to ED = FD = 2.

Combine sides FD and FC to get the length of DC

DC = FD+FC = 2+18 = 20

This is the hypotenuse of the right triangle GCD

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

After all that, we have the right triangle GCD with the legs of 2x and 16. The hypotenuse is 20. Refer to figure 2 shown below.

As you can probably guess, we'll use the pythagorean theorem to find the value of x.

a^2 + b^2 = c^2

(DG)^2 + (GC)^2 = (CD)^2

(2x)^2 + (16)^2 = (20)^2

4x^2 + 256 = 400

4x^2 = 400-256

4x^2 = 144

x^2 = 144/4

x^2 = 36

x = sqrt(36)

x = 6 is the radius of the sphere.

7 0
2 years ago
Can someone please help me with this:) ​
madam [21]

Answer:  c

Step-by-step explanation:

3 0
3 years ago
What transformation of Figure 1 results in Figure 2?
Hatshy [7]

Answer

A

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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