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
dedylja [7]
2 years ago
15

A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the rectangle is the intersection

point of the legs of the triangle and the opposite vertex lies on the hypotenuse. Find the largest area (in cm 2 ) of the rectangle and its dimensions (in cm) given that the two equal legs of the triangle have length 4.
Mathematics
1 answer:
svet-max [94.6K]2 years ago
5 0

Answer:

x  =  2  cm

y  = 2  cm

A(max) =  4 cm²

Step-by-step explanation: See Annex

The right isosceles triangle has two 45° angles and the right angle.

tan 45°  =  1  =  x / 4 - y        or     x  =  4  -  y     y  =  4  -  x

A(r)  =  x* y

Area of the rectangle as a function of x

A(x)  =  x  *  (  4  -  x )       A(x)  =  4*x  -  x²

Tacking derivatives on both sides of the equation:

A´(x)  =  4 - 2*x             A´(x)  =  0            4   -  2*x  =  0

2*x  =  4

x  =  2  cm

And  y  =  4  - 2  =  2  cm

The rectangle of maximum area result to be a square of side 2 cm

A(max)  = 2*2  =  4 cm²

To find out if A(x) has a maximum in the point  x  =  2

We get the second derivative

A´´(x)  =  -2           A´´(x)  <  0   then A(x) has a maximum at  x = 2

You might be interested in
I need help plz. Thank you
chubhunter [2.5K]
B. i think...you should take a pic of the WHOLE paper
7 0
3 years ago
Read 2 more answers
HELP I WILL MARK U BRAINLIEST!!
Nostrana [21]
Y-7 is your answer. You welcome
3 0
3 years ago
Read 2 more answers
How do you shade 1/4 of a rectangle with 12 equal parts
Alexxandr [17]
Find 1/4 of 12. 

12 x 1/4 = 3

Shade 3/12
5 0
3 years ago
Read 2 more answers
Find the value of x 3x+6 41 6x-5 4x+7 62 7x-11
padilas [110]

Answer:

13

Step-by-step explanation:

Simplifying

3x + 6 + 7x + -11 + 41 + 62 + 6x + -5 + 4x + 7 = 360

Reorder the terms:

6 + -11 + 41 + 62 + -5 + 7 + 3x + 7x + 6x + 4x = 360

Combine like terms: 6 + -11 = -5

-5 + 41 + 62 + -5 + 7 + 3x + 7x + 6x + 4x = 360

Combine like terms: -5 + 41 = 36

36 + 62 + -5 + 7 + 3x + 7x + 6x + 4x = 360

Combine like terms: 36 + 62 = 98

98 + -5 + 7 + 3x + 7x + 6x + 4x = 360

Combine like terms: 98 + -5 = 93

93 + 7 + 3x + 7x + 6x + 4x = 360

Combine like terms: 93 + 7 = 100

100 + 3x + 7x + 6x + 4x = 360

Combine like terms: 3x + 7x = 10x

100 + 10x + 6x + 4x = 360

Combine like terms: 10x + 6x = 16x

100 + 16x + 4x = 360

Combine like terms: 16x + 4x = 20x

100 + 20x = 360

Solving

100 + 20x = 360

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-100' to each side of the equation.

100 + -100 + 20x = 360 + -100

Combine like terms: 100 + -100 = 0

0 + 20x = 360 + -100

20x = 360 + -100

Combine like terms: 360 + -100 = 260

20x = 260

Divide each side by '20'.

x = 13

Simplifying

x = 13

4 0
3 years ago
Si 2/3 de los 84 pasajeros de un bus de Transmilenio son hombres, ¿cuántas
Rina8888 [55]

Answer:

A

Step-by-step explanation:

Aquí, tenemos 2/3 como hombres.

La fracción de mujeres es, por lo tanto, 1-2 /3 = 1/3

Entonces 1/3 de 84 son mujeres Por lo tanto, el número de mujeres es 1/3 * 84 = 28

7 0
3 years ago
Other questions:
  • Quotient of 24 and 3 plus x
    5·2 answers
  • Serious answers only please. The question is in the photo.
    5·1 answer
  • 1. The beginning steps for determining the center and radius of a circle using the completing the square method are shown below:
    15·1 answer
  • Explain the difference in meaning between I-3I and -3.
    6·2 answers
  • How can you write a fraction equivalent to 60/80 and with a denominator that is less than 80?
    5·1 answer
  • The function N(t)=300/(1+299e^-0.36t) describes the spread of a rumor among a group of people who have heard the rumor, and (t)
    7·1 answer
  • 2.Which set of ordered pairs does ***NOT*** represent a function?
    9·2 answers
  • Question 4
    5·2 answers
  • Pls help taking im taking
    8·1 answer
  • Modern Electronics offers a one-year monthly installment plan for a big screen TV. The payment for the first month is 882, and t
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!