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Gemiola [76]
3 years ago
15

The diagram shows a tetrahedron.

Mathematics
1 answer:
gavmur [86]3 years ago
5 0
<h3>Answer: Angle BDC = 76.3 degrees</h3>

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

Work Shown:

For now focus on triangle ABC. Since this is a right triangle, we can use the pythagorean theorem to find the hypotenuse BC.

a^2 + b^2 = c^2

(AC)^2 + (AB)^2 = (BC)^2

8^2 + 10^2 = (BC)^2

(BC)^2 = 164

BC = sqrt(164)

BC = 12.806248 approximately

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

Move onto triangle ABD. Find the missing side BD through the pythagorean theorem

a^2 + b^2 = c^2

(AD)^2 + (AB)^2 = (BD)^2

5^2 + 10^2 = (BD)^2

125 = (BD)^2

(BD)^2 = 125

BD = sqrt(125)

BD = 11.1803399 which is approximate

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

Move onto triangle ADC. We'll use the pythagorean theorem again

a^2 + b^2 = c^2

(AC)^2 + (AD)^2 = (CD)^2

8^2 + 5^2 = (CD)^2

89 = (CD)^2

(CD)^2 = 89

CD = sqrt(89)

CD = 9.433981 also approximate

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

Focus on triangle BCD. We have the following side lengths

  • BC = 12.806248
  • BD = 11.1803399
  • CD = 9.433981

Let

  • side d be opposite angle D, so d = BC = 12.806248
  • side b be opposite angle B, so b = CD = 9.433981
  • side c be opposite angle C, so c = BD = 11.1803399

Note the use of uppercase letters for angles and lowercase letters for side lengths.

We can then use the law of cosines to find the angle we're after

d^2 = b^2 + c^2 - 2*b*c*cos(D)

12.806248^2=9.433981^2+11.1803399^2-2*9.433981*11.1803399*cos(D)

163.999987837504=213.999997787893-210.950228380284*cos(D)

-210.950228380284*cos(D) = -50.000009950389

cos(D) = (-50.000009950389)/(-210.950228380284)

cos(D) = 0.237022781792173

cos(D) = arccos(0.237022781792173)

D = 76.2891111084541

D = 76.3

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For this case we have the following equation:
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 Answer:
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3 years ago
Marcus has $40 in his pocket. Joseph has twice as much as Marcus, Jenna has half as much as Marcus, and Sam has one-third as muc
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3 years ago
Read 2 more answers
tennis balls with a diameter of 2.5in are sold in cans of three. the can is a cylender. what is the volume of the area not occup
mina [271]

Answer:

The volume of the area not occupied by the tennis balls is 12.28 cubic inches.

Step-by-step explanation:

It is given that tennis balls with a diameter of 2.5in are sold in cans of three. the can is a cylinder.

Radius of ball = Radius of can = \frac{2.5}{2}=1.25

Height of can = 2.5\times 3=7.5

The volume of sphere is

V=\dfrac{4}{3}\pi r^3

where, r is radius of sphere.

The volume of a tennis balls is

V=\dfrac{4}{3}\pi (1.25)^3

V=8.18123

V\approx 8.18

Volume of three tennis balls is

V_1=3\times 8.18=24.54

The volume of cylinder is

V=\pi r^2h

The volume of can is

V_2=\pi (1.25)^2(7.5)

V_2=36.81553

V_2\approx 36.82

The volume of the area not occupied by the tennis balls is

Volume = Volume of cylinder - Volume of three tennis balls

            = 36.82 - 24.54 = 12.28 inches

Therefore, the volume of the area not occupied by the tennis balls is 12.28 cubic inches.

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3 years ago
Help please ! need asap
Dimas [21]

Answer:

x° = 139

step 1 :

180 - (37 + 38)

= 180 - 75

= 105°

step 2 :

180 - 105

= 75°

step 3 :

180 - 116

= 64°

step 4 : this step to find the value of x

x° = 180° - (64 + 75)°

= 180° - 139°

= 41

x° = 41

<h3>#CMIIW</h3>
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2 years ago
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igomit [66]

Answer:

If I have x cars and sell 12 how many cars do I have left.

Step-by-step explanation:

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