Number 5. Need to write an equation

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

svet-max [94.6K]

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

5 0

2 years ago

Please Identify the congruent triangles in the figure.

Tpy6a [65]

The missing steps are each right angles and $\angle R \cong \angle O$ .

Solution:

Step 1: Given data:

$\overline {P Q} \cong \overline{M N}$

$\overline{Q R} \cong \overline{N O}$

$\overline{P R} \cong \overline{M O}$

Step 2: In the two polygons,

$\angle Q =90^\circ$ and $\angle N =90^\circ$

$\angle Q \cong \angle N$ (Each right angle)

Step 3: Given

$\angle P \cong \angle M$

Step 4: By third angle theorem,

If two angles in one triangle are congruent to the two angles in the other triangle, then the third angles in the triangles also congruent.

$\angle R \cong \angle O$

Step 5: By the definition of congruent polygons,

If two same shape polygons have all the angles are congruent and all the corresponding sides are congruent then the polygons are congruent.

Hence $\Delta P Q R \cong \Delta M N O$ .

Therefore the missing steps are each right angles and $\angle R \cong \angle O$ .

5 0

3 years ago

The Jensen family took a trip in September. Sally is calculating the gas mileage in miles per gallon for her dads SUV. When he f

Fynjy0 [20]

U don't have enough information to answer the question because u need to know how much the gas is per gallon

3 0

3 years ago

Marissa has 10 grapes. Roger has 3 times as many grapes as Marissa. How many grapes do Marissa and Roger have in all?

postnew [5]

Answer:

The answer is 40

Step-by-step explanation:

First, since roger has 3 times as many grapes as Marissa. do 10 times 3. The answer is 30. Roger has 30 grapes. The question is asking how much they have all together. Add 30 plus 10 and the answer that you will get is 40. The answer is 40

7 0

3 years ago

Q4.

goblinko [34]

The coding of the statistic is used to make it easier to work with the large sunshine data set

The mean of the sunshine is 3.05 $\overline 6$

The standard deviation is approximately 18.184

Reason:

The given parameters are;

The sample size, n = 3.

∑x = 947

Sample corrected sum of squares, Sₓₓ = 33,065.37

The mean and standard deviation = Required

Solution:

$Mean, \ \overline x = \dfrac{\sum x_i}{n}$

The mean of the daily total sunshine is therefore;

$Mean, \ \overline x = \dfrac{947}{30} \approx 31.5 \overline 6$

$s = \dfrac{x}{10 } - \dfrac{1}{10}$

$E(s) = \dfrac{Ex}{10 } - \dfrac{1}{10}$

$E(s) = \dfrac{31.5 \overline 6}{10 } - \dfrac{1}{10} = 3.05 \overline 6$

The mean ≈ 3.05 $\overline 6$

Alternatively

, $The \ mean \ of \ the \ daily \ total \ sunshine, \, s = \dfrac{31.5 \overline 6 - 1}{10 } = 3.05\overline 6$

The mean of the daily total sunshine, $\overline s$ ≈3.05 $\overline 6$

$Var(s) = Var \left(\dfrac{x}{10 } - \dfrac{1}{10} \right)$

$Var(s) = \left(\dfrac{1}{10}\right)^2 \times Var \left(x \right)$

Therefore;

$Var(s) = \left(\dfrac{1}{10}\right)^2 \times 33,065.37 = 330,6537$

Therefore;

$s = \sqrt{330.6537} \approx 18.184$

The standard deviation, $s_s$ ≈ 18.184

Learn more about coding of statistic data here:

brainly.com/question/14837870

3 0

2 years ago