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
AlekseyPX
3 years ago
13

A triangle has side lengths of 10, 11, and 15. What type of triangle is it? Procedure: 102 ?? 112 + 152 100 ?? 121 + 225 100 &lt

; 346 Conclusion: This triangle is an acute triangle.
Mathematics
1 answer:
stepladder [879]3 years ago
3 0
<span> The triangle seems to be a scalene triangle because all three of its sides are different. </span>
You might be interested in
Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is
strojnjashka [21]

Answer:

Step-by-step explanation:

The original equation is 121y''+110y'-24y=0. We propose that the solution of this equations is of the form y = Ae^{rt}. Then, by replacing the derivatives we get the following

121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

121r^2+110r-24=0

Recall that the roots of a polynomial of the form ax^2+bx+c are given by the formula

x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

r_1 = -\frac{12}{11}

r_2 = \frac{2}{11}

So, in this case, the general solution is y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

c_1 + c_2 = 1

c_1\frac{-12}{11} + c_2\frac{2}{11} = 0(or equivalently c_2 = 6c_1

By replacing the second equation in the first one, we get 7c_1 = 1 which implies that c_1 = \frac{1}{7}, c_2 = \frac{6}{7}.

So y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}

b) By using y(0) =0 and y'(0)=1 we get the equations

c_1+c_2 =0

c_1\frac{-12}{11} + c_2\frac{2}{11} = 1(or equivalently -12c_1+2c_2 = 11

By solving this system, the solution is c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}

Then y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}

c)

The Wronskian of the solutions is calculated as the determinant of the following matrix

\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2

By plugging the values of y_1 and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

e^{\int -p(x) dx}

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}

Note that this function is always positive, and thus, never zero. So y_1, y_2 is a fundamental set of solutions.

8 0
3 years ago
The following box plot represents the average heights of the students in Mrs. Hill's sixth grade math class.
Svetllana [295]

Answer:

Step-by-step explanation:

Half of the students in Mrs. Hill's class are between 147 centimeters and 154 centimeters tall. (correct)

The median height of the students in Mrs. Hill's class is 152 centimeters. (correct)

The interquartile range of this data set is 15 centimeters.  (incorrect, 154-147=17 cm)

The mean height of the students in Mrs. Hill's class is 152.5 centimeters.  (we don't get to know the mean height from the graph).

6 0
3 years ago
Read 2 more answers
Each side of the pentagon is the same length. Is the shape a regular pentagon?
Ad libitum [116K]
If the sides of the pentagon are the same length, it is probably a regular pentagon. If the angles are all the same within the shape, it is definitely a regular pentagon.
6 0
3 years ago
Read 2 more answers
Please help meeeee!!
Xelga [282]

Answer:

-27

Step-by-step explanation:

order of operations 2÷2 = 1 +53 =54

3x1 = 3 -5 = -2

54÷-2 = -27

5 0
2 years ago
The exact average of a set of six test scores is 92. Five of these scores are 90, 98, 96, 94, and 85. What is the other test sco
nordsb [41]

Answer:

89

Step-by-step explanation:

92 = (90 + 98 + 96+ 94 + 85 + x )/6

92*6 = 90 + 98 + 96+ 94 + 85 + x

552 - (90 + 98 + 96+ 94 + 85) = x

x = 89

8 0
3 years ago
Other questions:
  • 700,000 divided by 70,000
    7·2 answers
  • a tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 2 grams of salt per liter is then p
    10·1 answer
  • Convert the following equation into simultaneous equation and solve
    8·1 answer
  • 4 Sam was asked to place the numbers shown below in order from least to greatest.
    9·1 answer
  • Como podria la logica contribuir con la convivencia social
    5·1 answer
  • A particular model rocket kit uses the scale 1:144. The actual rocket is 168 ft tall. How tall will the model rocket be when com
    11·1 answer
  • 286 divided by 8 equals
    13·2 answers
  • Please help me with this!!!
    5·1 answer
  • Directions: Find the odds and the probability of the event(s) occuring.
    12·1 answer
  • PLSS HELP Identify the five important values from this box and whisker plot. Explain how you got your answers
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!