1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Soloha48 [4]
2 years ago
14

90 POINTS MATH

Mathematics
2 answers:
satela [25.4K]2 years ago
6 0
<h3>Answer:</h3>

1.25 < y < 8.32124...

<h3>Step-by-step explanation:</h3>

The least y can be is the value that makes the angle in the smaller triangle be zero. (This condition will exist when the difference of side lengths is 4.)

... 4y -5 = 0

... y = 5/4 . . . . . add 5, divide by 4.

_____

The greatest y can be is the value obtained when the triangle is isosceles. For the larger triangle, that makes the side lengths (s) be ...

... 3/s = sin(43°/2)

... s = 3/sin(21.5°)

Then for the smaller triangle, that makes the angle be ...

... 4y -5 = arcsin(2/s) = arcsin(2/3·sin(21.5°))

... y = 1.25 + arcsin(2/3·sin(21.5°))/4

... y ≈ 8.32124

Amanda [17]2 years ago
3 0

Answer:

1.25 < y <= 8.32124

Step-by-step explanation:

We use the law of cosines for two triangles:

c^2 = a^2 + b^2 - 2 a b \cos(\gamma) \\ d^2 = a^2 + b^2 - 2 a b \cos(\delta)

This answer shows how to use the Reduce and Exists functions of Mathematica to solve either this problem, or the general problem of a pair of triangles with two sides of one triangle equal to two sides of the other triangle.  That answer (with c,\, d,\, \gamma,\, \text{and}\ \delta as independent variables which must be given ranges) has 11 cases, and would be a terrible waste of time to find by hand.

The law of cosines is used twice, with the same values for <em>a</em> and <em>b</em>, but different values for <em>c</em> and <em>γ</em> . Here I use the constants c = 6\,\ \gamma = 43°\, \ d = 4. The following equations and inequalities are supplied to Reduce, with an Extential quantifier specifying that Reduce should discover the range of values for \cos(\gamma).

\text{problem}=\exists _{\{a,b\}}\left(\begin{array}{ccc}36=a^2+b^2-2 a b \cos (43 {}^{\circ})\ \ \land\\16=a^2+b^2-2 a b \cos (\delta )\,\,\land\\ 0

This proves (since we used Reduce, not Solve, which is less reliable) that

  • a triangle exists that has angle 43°, two adjacent sides of length a and b and opposite side of length 6, and that
  • a second triangle exists with unknown angle, adjacent sides a and b equal to the corresponding sides of the first triangle, and opposite side length 4.
  • There is only one range of angles which satisfy the requirements.

\text{mincos}=\text{First}[\text{red}]\ \ \text{gives}\ \ \frac{1}{9} (4 \cos (43 {}^{\circ})+5)\\\text{maxcos}=\text{Last}[\text{red}]\ \ \text{gives}\ \ 1\\\\\text{Solve}[4 y-5=\delta,y ]\ \ \ \text{gives}\ \ \ \left\{\left\{y\to \frac{\delta }{4}+\frac{5}{4}\right\}\right\}\\ \\\\\ \frac{5}{4}

You might be interested in
10. You used 8 cups of sugar while baking three dozen cookies and one cake. If you used 1.25 cups of sugar for the cake and the
DanielleElmas [232]

Answer:

I got 5.65

Step-by-step explanation:

36/8= 4.5,  4.5 +1.25= 5.65

8 0
3 years ago
Mr. Gengel wants to make a shelf with boards that are 1 1/3 feet long. If he has an 18-foot board, how many pieces can he cut fr
irina1246 [14]

Answer:

13

Step-by-step explanation:

1 1/3 = 4/3

18 ÷ 4/3

= 13

3 0
3 years ago
What is EG? Round to the nearest tenth if necessary.
slava [35]

Answer:

26.

Step-by-step explanation:

As the vertex angles are equal:

24/54 = x / x+10

54x = 24x + 240

30x = 240

x = 8

So EG = x + x + 10

=  8 + 8 + 10

= 26..

7 0
3 years ago
The perimeter of one face of a cube is 16cm. Calculate the volume of the cube.
erastova [34]

Answer:

4

Step-by-step explanation:

Perimeter equation: Length + Width * 2

so divide 2 by 16

which gives you 8 and minus that by its half so you get 4

4 0
2 years ago
NEED HELP
Reptile [31]

Answer:

B I'm pretty sure

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • James is buying a table.He finds the same table for sale in two different shops.
    10·1 answer
  • Can someone help Me ? I suck at Riemann sums in general
    11·1 answer
  • One angle of a right triangle measures 15°. What is the measure of the other acute angle?
    8·1 answer
  • If f(x)=x+2 and g(x)=3x^2+7x find (f x g)(x)
    6·1 answer
  • 1/8 quarters is how many gallons
    11·1 answer
  • What is lighter, 1 kg of feather or 1 kg of iron?
    7·2 answers
  • Alex bought a skateboard online. The price of the skateboard was $105. The state sales tax of 7% was added, and then a $25 charg
    5·1 answer
  • |2| + |-13| =<br><br> BRAINLIST AND EXTRA POINTS
    12·2 answers
  • Help me please I beg of you
    5·1 answer
  • Pls help thank you :)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!