a) 8801
+2031
_______​

sorry i was going to show work but my water spill on the paper. so answer is 556.05cm^2

a) The area formula for the rectangle is equal to A = r² · sin 2θ.

b) By derivative tests, the maximum possible area of the rectangle is 16 square centimeters.

c) The dimensions of the rectangle are: Width: 5.66 cm, Height: 2.83 cm

In this problem we must determine the maximum possible area of a rectangle inscribed in a semicircle by means of first and second derivative tests. First, derive the area formula of the rectangle:

A = w · h

A = (2 · r · cos θ) · (r · sin θ)

A = 2 · r² · sin θ · cos θ

A = r² · sin 2θ

Where:

Second, perform first derivative test: (r - Constant)

A = 2 · r² · cos 2θ

2 · r² · cos 2θ = 0

cos 2θ = 0

θ = 45°

Third, perform second derivative test: (θ = 45°)

A'' = - 4 · r² · sin 2θ

A'' = - 4 · r² (MAXIMUM)

Fourth, determine the maximum possible area of the rectangle:

A = 4² · sin 90°

A = 16 cm²

Fifth, determine the width and the height of the rectangle: (r = 4, θ = 45°)

w = 2 · r · cos θ

w = 2 · 4 · cos 45°

w = 8 · √2 / 2

w = 4√2 cm

w = 5.66 cm

h = r · sin θ

h = 4 · sin 45°

h = 4 · √2 / 2

h = 2√2 cm

h = 2.83 cm

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Answer:

SRTZ is not a parallelogram.

Slope of SZ:

[tex]m = \frac{ - 2 - 1}{1 - ( - 2)} = - 1[/tex]

Slope of RT:

[tex]m = \frac{0 - 3}{2 - 1} = - 3[/tex]

Since the slopes of SZ and RT are not equal, SRTZ is not a parallelogram.

The conditional value probability is solved and P ( F | E ) = 6/17

Given data ,

P ( E ) = 0.85

P ( F ) = 0.4

P ( E ∩ F ) = 0.3

Now , the formula for conditional probability to calculate P(F|E):

P(F|E) = P(E ∩ F) / P(E)

We are given that P(E) = 0.85 and P(E ∩ F) = 0.3, so we can substitute those values in:

P(F|E) = 0.3 / 0.85

Simplifying this fraction, we get:

P(F|E) = 6/17

Hence , the probability of F given that E has occurred is 6/17 or approximately 0.35.

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The volume of the stump is 7451.9 cubic inches.

The volume of a cylinder can be calculated using formula below:

V = πr²h

where r is the radius and h is the height of the cylinder

We have circumference (C) = 61 in.

Let's find the radius (r) using the formula:

C = 2πr

61 = 2 * 22/7 * r

r = 9.70 in

h = 2.1 ft  = 2.1 * 12 = 25.2 in

Substituting into V = πr²h:

V = 22/7 * 9.70² * 25.2

V = 7451.9 cubic inches

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Entonces n is 0,00779 moles,

Los casi 5 sextillones (5 con 21 ceros) de moléculas de HNO3 provocaron la quemadura en la piel del analista.

Para responder a esta pregunta, necesitamos saber la masa molar de HNO3, que es 63,01 g/mol. Usando esta información, podemos calcular el número de moles de HNO3 en los 0,49 g de gotas usando la fórmula: n = m/M, donde n es el número de moles, m es la masa y M es la masa molar.

Como un mol contiene el número de moléculas de Avogadro (6,022 x 10^23), podemos calcular el número de moléculas de HNO3 en las gotas que causaron la quemadura: 0,00779 moles x 6,022 x 10^23 moléculas/mol = 4,69 x 10^21 moléculas .

Es importante recordar que los ácidos concentrados como el HNO3 pueden ser extremadamente peligrosos y pueden causar quemaduras graves, por lo que siempre se deben tomar las precauciones de seguridad adecuadas en un entorno de laboratorio.

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Answer:

1)  A = 32.6°, C = 111.4°, b = 12.0

2) A = 53.6°, B = 85.7°, C = 40.7°

Step-by-step explanation:

Given values of triangle ABC:

First, find the measure of side b using the Law of Cosines for finding sides.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

As the given angle is B, change C for B in the formula and swap b and c:

[tex]b^2=a^2+c^2-2ac\cos(B)[/tex]

Substitute the given values and solve for b:

[tex]\implies b^2=11^2+19^2-2(11)(19)\cos(36^{\circ})[/tex]

[tex]\implies b^2=482-418\cos(36^{\circ})[/tex]

[tex]\implies b=\sqrt{482-418\cos(36^{\circ})}[/tex]

[tex]\implies b=11.9929519...[/tex]

Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles A and C.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{19^2+(11.9929519...)^2-11^2}{2(19)(11.9929519...)}[/tex]

[tex]\implies \cos(A)=0.842229094...[/tex]

[tex]\implies A=\cos^{-1}(0.842229094...)[/tex]

[tex]\implies A=32.6237394...^{\circ}[/tex]

To find the measure of angle C, substitute the values of a, b and c into the formula:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{11^2+(11.9929519...)^2-19^2}{2(11)(11.9929519...)}[/tex]

[tex]\implies \cos(C)=-0.364490987...[/tex]

[tex]\implies C=\cos^{-1}(-0.364490987...)[/tex]

[tex]\implies C=111.376260...^{\circ}[/tex]

Therefore, the remaining side and angles for triangle ABC are:

[tex]\hrulefill[/tex]

To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

Given sides of triangle ABC:

Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{21^2+26^2-17^2}{2(21)(26)}[/tex]

[tex]\implies \cos(C)=\dfrac{828}{1092}[/tex]

[tex]\implies C=\cos^{-1}\left(\dfrac{828}{1092}\right)[/tex]

[tex]\implies C=40.690560...^{\circ}[/tex]

To find the measure of angle B, swap b and c in the formula, and change C for B:

[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\implies \cos(B)=\dfrac{21^2+17^2-26^2}{2(21)(17)}[/tex]

[tex]\implies \cos(B)=\dfrac{54}{714}[/tex]

[tex]\implies B=\cos^{-1}\left(\dfrac{54}{714}\right)[/tex]

[tex]\implies B=85.6625640...^{\circ}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{17^2+26^2-21^2}{2(17)(26)}[/tex]

[tex]\implies \cos(A)=\dfrac{524}{884}[/tex]

[tex]\implies A=\cos^{-1}\left(\dfrac{524}{884}\right)[/tex]

[tex]\implies A=53.6468753...^{\circ}[/tex]

Therefore, the measures of the angles of triangle ABC with sides a = 21, b = 26 and c = 17 are:

The number that is one-third of 343 is 49.

1/3 of 343 can be found by multiplying 343 by 1/3:

1/3 x 343 = (1/3) x (343) = 343/3

To simplify the result, we can divide both the numerator and denominator by the greatest common factor (GCF) of 343 and 3, which is 7:

343/3 = (343 ÷ 7) / (3 ÷ 7) = 49/1

Therefore, 1/3 of 343 is 49.

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Answer:

∆TSU ~ ∆PJM by SAS since 10/14 = 5/7 and 15/21 = 5/7, and angle S is congruent to angle J.

The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.

We can use the conservation of momentum equation:

(mboat + mperson) * vboat = mperson * vperson

(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)

230 kg * vboat = 56 kg * (0.80 m/s + vperson)

vboat = (56/230) * (0.80 m/s + vperson)

vperson = 0.80 m/s + vboat

vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)

(174/115) * vperson = (504/115) * m/s

Dividing both sides by (174/115), we get:

vperson = 2.896 m/s

vboat = (56/230) * (0.80 m/s + vperson)

Substituting the value of vperson, we get:

vboat = 1.337 m/s

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On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.

Using the cosine ratio, the value of the marked side in the image given below is approximately: y = 167.7.

The cosine ratio is defined as the ratio of the length of the hypotenuse of the right triangle over the length of the side that is adjacent to the reference angle. It is given as:

cos ∅ = length of hypotenuse/length of adjacent side.

From the image attached below, we have the following:

Reference angle (∅) = 37°

length of hypotenuse = 210

length of adjacent side = y

Plug in the values:

cos 37 = y/210

210 * cos 37 = y

y = 167.7

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Answer:

12 cm

Step-by-step explanation:

By hypotenuse theorem,

x² + 35² = 37²

x² + 35*35 = 37*37

x² + 1225 = 1369

x² = 1369 - 1225

x² = 144

x² = 12*12

x² = 12²

x = 12 cm

The Interquartile range for the given data set is 51.

The interquartile range for a given data set, the values of the first quartile (Q1) and the third quartile (Q3). The interquartile range is the difference between Q3 and Q1.

First, let's arrange the data set in ascending order:

4, 5, 6, 27, 27, 41, 48, 54, 64, 71, 78, 79

To find Q1, which represents the lower quartile, we need to locate the median of the lower half of the data set. Since the data set has 12 values, the lower half consists of the first 6 values:

4, 5, 6, 27, 27, 41

The median of this lower half is the average of the middle two values, which are 6 and 27:

Q1 = (6 + 27) / 2 = 33 / 2 = 16.5

To find Q3, the upper quartile, we need to locate the median of the upper half of the data set. Again, since the data set has 12 values, the upper half consists of the last 6 values:

48, 54, 64, 71, 78, 79

The median of this upper half is the average of the middle two values, which are 64 and 71:

Q3 = (64 + 71) / 2 = 135 / 2 = 67.5

Finally, we can calculate the interquartile range by subtracting Q1 from Q3:

Interquartile range = Q3 - Q1 = 67.5 - 16.5 = 51

Therefore, the interquartile range for the given data set is 51.

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The center and radius for each equation are as follows:

40. Center: (3, 2), Radius: 8

41. Center: (-8, 4), Radius: 6

42. Center: (-4, 12), Radius: 2

43. Center: (4, -15), Radius: 3

The standard equations of a circle is given as (x - h)² + (y - k)² = r²

Where the center are (h, k) and the radius of the circle is r.

40. (x - 3)² + (y - 2)² = 64

  Center: (3, 2)

  Radius: √64 = 8

41. (x + 8)² + (y - 4)² = 36

  Center: (-8, 4)

  Radius: √36 = 6

42. (x + 4)² + (y - 12)² = 4

  Center: (-4, 12)

  Radius: √4 = 2

43. (x - 4)² + (y + 15)² = 9

  Center: (4, -15)

  Radius: √9 = 3

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Answer:

--------------------

If Gauri spends 0.75 of her salary every month, that means she saves 0.25 of her salary:

Divide the total 39000 by her monthly savings:

So it will take Gauri 13 months to save rupees 39000.

The missing sides of the triangle are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 30º, we have that:

Hence the hypotenuse RS is obtained as follows:

sin(30º) = 6/RS

1/2 = 6/RS

RS = 6 x 2

RS = 12.

Applying the cosine, we have that:

cos(30º) = 6/SX

[tex]\frac{\sqrt{3}}{2} = \frac{6}{SX}[/tex]

[tex]SX = \frac{12}{\sqrt{3}}[/tex]

[tex]SX = 4\sqrt{3}[/tex]

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Answer: Point P

Step-by-step explanation: over 2 up 1 (2,1)

Answer: M

Step-by-step explanation:

When x = 3, y = 2, and z = 4, the value of the expression 5x - 2y + 4z is 27.

The correct answer is (c) 27.

To evaluate the expression 5x - 2y + 4z when x = 3, y = 2, and z = 4, we substitute the given values into the expression and perform the   arithmetic calculations. Here's the step-by-step process:

Step 1: Replace x with 3, y with 2, and z with 4 in the expression:

5(3) - 2(2) + 4(4)Step 2:

Perform the multiplications first:

15 - 4 + 16

Step 3: Perform the additions and subtractions from left to right:

15 - 4 + 16 = 11 + 16 = 27.

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We can see here that the given side lengths cannot  be used to form a unique triangle because the shorter sides do not add up to the longer side.

The fundamental geometric shape of a triangle has three sides and three angles. It is a triangular polygon with three edges.

We can see here that in order to determine if the given side lengths:

3.4 cm, 3.1 cm, 6.6 cm

can form a unique triangle, many different triangles, or no triangle, we need to check if they satisfy the triangle inequality theorem.

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Let's check the conditions:

3.4 cm + 3.1 cm = 6.5 cm

6.5 cm > 6.6 cm (Not satisfied)

3.4 cm + 6.6 cm = 10 cm

10 cm > 3.1 cm (Satisfied)

3.1 cm + 6.6 cm = 9.7 cm

9.7 cm > 3.4 cm (Satisfied)

he specified side lengths cannot be used to create a triangle because the total of the two shorter sides' lengths (3.4 cm and 3.1 cm) is not larger than the length of the longest side (6.6 cm).

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Answer:

The Value of Y is -8

Step-by-step explanation:

I believe it is -8 because giving the function, y = 8 - 2x, given that x = 8, we can replace the value into a function. y = 8 - 2(8) = 8 - 16 = -8.

So therefore, the value of y is -8. Hopes this helps :p

Answer:

0.75 can be written as :-

[tex] \frac{75}{100} [/tex]

and in simplest form it is:-

[tex] \frac{3}{4} [/tex]

so the answer is 3/4

The expression (yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp) is simplified to obtain

2/y

The given expression is

(yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp)

The expression is simplified individually, using different each equation in the expression

yx + y + px + p

= y(x + 1) + p(x + 1)

= (y + p)(x + 1)

5x² + 10x +5

= 5(x² + 2x + 1)

= 5(x² + 1)

(10x + 10)

= 10(x + 1)

(y² + yp)

= y(y + p)

bringing the equations together and simplifying further

(y + p)(x + 1) / 5(x² + 1) * 10(x + 1) / y(y + p)

= 10(x + 1)(x + 1) / 5y(x² + 1)

= 10(x² + 1) / 5y(x² + 1)

= 2/y

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Answer:

  1460 square inches

Step-by-step explanation:

You want the area of a semicircle with diameter 61 inches.

The area of a circle is given by ...

  A = (π/4)d²

The area of a semicircle is half that, so is ...

  A = (π/8)d²

  A = (3.14/8)(61 in)² ≈ 1460 in²

The area of the semicircular window is about 1460 square inches.

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The graph of the logarithmic function is attached below with a vertical asymptote at x = -8 and two integer coordinates at (2, -7) and (1, -10).

The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log).

To plot the graph of the given function, we simply need to use a graphing calculator.

The given function is;

f(x) = -3log₃(x + 8) - 4

To find the asymptotes of the graph;

x + 8 > 0

x > -8

The vertical asymptotes is at x = -8

The two points with integer coordinates are (2, -7) and (1, -10)

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The volume of the pyramid is 18069333.33 units³ and the surface area is 391600 units ²

A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces.

Surface area of a pyramid is expressed as;

area of 4 lateral face + area of base

area of base = 440²

= 193600 units²

area of a lateral = 1/2 bh

= 1/2 × 440 × 356

= 78320

For four surfaces = 4 × 78320 = 313280

Total surface area = 313280+78320

= 391600 units ²

Volume of a pyramid is expressed as;

V = 1/3base area × height

V = 1/3 × 440² × 280

V = 18069333.33 units³

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You can write 27% as a fraction like this: [tex]\frac{27}{100}[/tex] . (27/100).

Or as a decimal 0.27.

Luis traveled approximately 31,736.8 inches on his bicycle.

We have,

To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.

Given:

Radius of the tires (r) = 20p (2.54) inches

Number of complete turns (n) = 50

The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Substituting the given radius into the formula, we have:

Circumference = 2π * (20p) inches

Now we can calculate the distance traveled (d):

Distance = Circumference x Number of complete turns

Distance = 2π x (20p) x 50 inches

To simplify the calculation, we can approximate π as 3.14:

Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches

Calculating this expression, we find:

Distance ≈ 31736.8 inches

Therefore,

Luis traveled approximately 31,736.8 inches on his bicycle.

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The complete question.

What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns

Answer: To solve the inequality x^2 + 3x - 4 > 0, we can use the method of factoring.

First, we can factor the quadratic expression:

x^2 + 3x - 4 = (x + 4)(x - 1)

Now we can find the values of x that make the expression greater than zero by looking at the sign of the expression for each factor and applying the sign rules of multiplication:

Using this method, we can create a sign chart:

x x + 4 x - 1 x^2 + 3x - 4

-4 0 -5 +6

-1 + - -

1 + + +

0 + - -

2 + + +

From the sign chart, we can see that the expression is greater than zero for x < -4 or x > 1. Therefore, the solutions to the inequality are all real numbers x such that x < -4 or x > 1. We can write this as:

x < -4 or x > 1