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]
3 years ago
14

90 POINTS MATH

Mathematics
2 answers:
satela [25.4K]3 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]3 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
A number K increased by 10 is the same as 24 what’s the equation
polet [3.4K]
The equation is K + 10 = 24.
3 0
3 years ago
Factor the trinomial below.
Shtirlitz [24]
Option C is your answer. 
8 0
3 years ago
Read 2 more answers
A train traveled the first 200 miles of its trip at a speed of 50 mph and the next 130 miles at a speed of 65 mph. What was the
12345 [234]
55 miles per hour, to answer questions like these you need to calculate the time (T=D/R) for each individual portion of the trip, add the time together to get total time, and then divide the total distance by the total time in order to get the average velocity in mph.
4 0
3 years ago
Hevesh wants to make 2 lines of dominoes that are both 21 inches long. Each line has dominoes spaced 1 and 1/2 inches apart. How
aliya0001 [1]

Answer: 30 dominoes in total.

Step-by-step explanation:

Each line is 21 inches long.

the space between dominoes is 1 + 1/2 inches.

(assuming that the distance includes the domino itself) Now, we need at least two dominoes to see this distance,

The we have N + 1 dominoes per line, and the distance is:

N*(1 + 1/2)inches = 21 inches

If we find N, we can find the number of domineoes in each line:

N = 21/(1 + 1/2) = 14

This means that we have 14  + 1 = 15 dominoes in each line, and we have two lines, so we have 30 dominoes in total.

3 0
3 years ago
Find the volume of the prism. Round to the nearest tenth if necessary.
spayn [35]

Answer:

27.2

Step-by-step explanation:

V = (1/2)(2.6)(5.1)(4.1), which is 27.2 to the nearest tenth

8 0
2 years ago
Other questions:
  • What is the solution of the system
    14·2 answers
  • a stock that was selling for $48 a share split 2-for-1. Before the split, the company had 3.4 million shares of stock outstandin
    13·2 answers
  • Which multiplication expression is equal to
    6·2 answers
  • Please help I’ll mark brainliest, it looks like it’s not the whole thing but it is.
    13·2 answers
  • use benchmarks to estimate the sum 11/15 +1/8 A.about 1/2 B.about 3/4 C.about 1 D.about 1 1/2
    9·2 answers
  • NO LINKS/FLIES PLEASE .
    10·1 answer
  • Is root -2 a irrational number? plz explain
    10·2 answers
  • GUYS CAN YOU PLEASE HELP ME? Write an equation for each word problem.
    12·2 answers
  • BRAINLIEST <br> Solve for X. Round to the nearest tenth.
    13·2 answers
  • 3 qt = ___ gal (it will be a decimal)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!