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Agata [3.3K]
3 years ago
5

3 over 7 = − 1 over 7 q

Mathematics
1 answer:
Finger [1]3 years ago
6 0
Q= - 1/3 is the answer-move the negative sign to the left multiply both sides by 7q then cancel 7 then finally divide both sides by 3. Hope this helps
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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
U<br> Question 8<br> Find the value of the variable in the parallelogram.<br> (6a + 10)<br> 130°
Alexus [3.1K]

Answer:

20

Step-by-step explanation:

(6a + 10) = 130

(6 x 20) + 10 = 130

120 - 10 = 130

130 = 130

5 0
3 years ago
I beg for someone. I need a maximum, minimum, domain, and range of polynomial:
elena-s [515]

Answer:

  • domain: all real numbers, (-∞, ∞)
  • range: all real numbers, (-∞, ∞)
  • maximum: +∞
  • minimum: -∞

Step-by-step explanation:

The function is an odd-degree polynomial. The domain and range of any odd-degree polynomial is (-∞, +∞). It has no finite maximum or minimum.

There are 3 local maxima, and 3 local minima. The ones that are non-zero are irrational. Those are about -150.018, -580.455, and 578.545. If you're seriously expected to solve for these values, no doubt you have been given a method for doing so. Use that method.

These local extreme values are reported by the Desmos on-line graphing calculator.

3 0
3 years ago
Find the area please don’t lie to me
astra-53 [7]

Answer:

<h2>108 yd²</h2>

Step-by-step explanation:

The formula of an area of a trapezoid:

A=\dfrac{b_1+b_2}{2}\cdot h

<em>b₁, b₂</em><em> - bases</em>

<em>h</em><em> - height</em>

From the picture we have

b_1=19yd,\ b_2=5yd,\ h=9yd

Substitute:

A=\dfrac{19+5}{2}\cdot9=\dfrac{24}{2}\cdot9=12\cdot9=108\ yd^2

3 0
3 years ago
Chord JK intersects chord ST at point L. Find the length of St. If necessary, round to the tenths place.
raketka [301]

Answer:

(C)19

Step-by-step explanation:

The diagram is drawn and attached.

Using the intersecting chord theorem

SL X LT = JL X LK

x X 12 = 14(x-1)

12x=14x-14

12x-14x=-14

-2x=-14

x=7

Therefore:

ST= SL + LT

=x+12

=7+12

ST=19

The correct option is C

5 0
3 years ago
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