La siguiente figura 1, ilustra el salto de una rana sobrepuesto en un plano cartesiano. La longitud del salto es de 9 ft y la altura máxima con respecto al suelo es 3 ft. Encuentra la ecuación estándar a fin de calcular la trayectoria de la rana.

3. La salinidad de los océanos se refiere a la cantidad de material disuelto que se encuentra en una muestra de agua marina. La salinidad S se puede calcular a partir de la cantidad C de cloro en agua de mar con la ecuación S = 0.03 + 1.805 C, donde S y C se miden por peso en partes por millar. Calcula la C si S es 0.35.
4. El arco de un puente es semielíptico, con eje mayor horizontal. La base del arco mide 50 ft de un lado al otro y la parte más alta del arco mide 15 ft arriba de la calzada horizontal. Encuentre la altura del arco a 12 ft del centro de la base.

Investiga la hipérbola con centro en el origen y fuera del origen. Eje focal en x y en y.

2. De las expresiones que se indican a continuación, Identifica si es una recta o ecuación lineal,
una ecuación cuadrática o de segundo grado, una ecuación de tercer grado, una
circunferencia, una hipérbola, justifica tu respuesta y elabora su respectiva gráfica.
3x – 2y + 4= 0
4x + y2 -7 = 0
x2 + y2 = 16
y = x3 - 3x +1
x2 + 4y2 = 4

3. A partir de tu investigación resuelve los siguientes ejercicios:
a) Traza la gráfica
9x2 – 4 y2 = 36
Encuentra los focos y ecuaciones de las asíntotas.
b) Traza la gráfica
4y2 – 2 x2 = 1
Encuentra los focos y ecuaciones de las asíntotas.

c) Dadas las siguientes ecuaciones, decir qué cónica representan:
9 x2 - 4 y2 - 54 x - 16 y + 29 = 0
4 x2 + 2 y2 - 7 x + y - 5 = 0
x2 - 6 x + 5 y - 11 = 0

Answers

Answer 1

Debido a restricciones de longitud invitamos cordialmente a leer la explicación de esta pregunta para aprender sobre las cuestiones de las ecuaciones cónicas.

¿Cómo analizar y aplicar las ecuaciones cónicas?

Según la geometría analítica, existen cinco tipos de secciones cónicas: recta, circunferencia, elipse, parábola e hipérbola. Aquí se presentan problemas que emplean este tipo de ecuaciones.

1) La trayectoria de la rana describe la forma de una parábola. Asumimos que el punto máximo de la trayectoria de la rana es de la forma (h, k) = (0, k), entonces tenemos que la ecuación de la parábola es:

y - k = C · x² (1)

Donde C es la constante del vértice.

Si sabemos que (h, k) = (0, 3) y (x, y) = (9, 0), entonces la ecuación de la parábola es:

C = (0 - 3) / 9²

C = - 1 / 27

La ecuación de la parábola es y - 3 = (- 1 / 27) · x².

2) Se determina el tipo de categoría de cada ecuación:

a) 3 · x - 2 · y + 4 = 0: Recta (a · x + b · y + c = 0)

b) 4 · x + y² - 7 = 0: Parábola ((y² - k) = 4 · p · (x - h))

c) x² + y² = 16: Circunferencia ((x - h)² + (y - k)² = r²)

d) y = x³ - 3 · x + 1: Ecuación cúbica

e) x² + 4 · y² = 4: Elipse (b² · (x - h)² + a² · (y - k)² = a² · b²)

3) Se debe hallar el valor C de la función lineal tal que S = 0.35 por medios algebraicos:

0.35 = 0.03 + 1.805 · C

0.32 = 1.805 · C

C = 0.32 / 1.805

C = 0.177

4) El arco semielíptico tiene una longitud de semieje mayor de 25 pies (paralelo al eje x) y una longitud de semieje menor de 15 pies (paralelo al eje y). Si consideramos que el centro de la elipse está en el origen, entonces tenemos que la ecuación es:

x² / 25² + y² / 15² = 1

y = 15 · √(1 - x² / 25²)

y = 15 · √(1 - 12² / 25²)

y = 13.159 pies

5) a) y b) Ahora graficamos la hipérbola y presentamos las ubicaciones de los focos y las asíntotas correspondientes. a) Las ecuaciones de las asíntotas son y = ± (3 / 2) · x, b) Las ecuaciones de las asíntotas son y = ± (√ 2 / 2) · x.

c) Se puede determinar la naturaleza de cada ecuación por métodos algebraicos:

9 · x² - 4 · y² - 54 · x - 16 · y + 29 = 0

[9 · x² - 2 · 9 · (3 · x) + 81] - [4 · y² - 2 · 8 · (2 · y) + 64] = 116

(3 · x - 9)² - (2 · y - 8)² = 116

9 · (x - 9)² - 4 · (y - 4)² = 116

(x - 9)² /12.889 - (y - 4)² / 29 = 1 - Hipérbola

4 · x² + 2 · y² - 7 · x + y - 5 = 0

[4 · x² - 2 · (7 / 4) · (2 · x) + 49 / 16] + [2 · y² + 2 · (√2 / 2) · (√2 · y) + 1 / 2] = 5

(2 · x - 7 / 4)² + (√2 · y + √2 / 2)² = 5

4 · (x - 7 / 8)² + 2 · (y + 1 / 2)² = 5

(x - 7 / 8)² / 1.25 + (y + 1 / 2)² / 2.5 = 1 - Elipse

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La Siguiente Figura 1, Ilustra El Salto De Una Rana Sobrepuesto En Un Plano Cartesiano. La Longitud Del

Related Questions

please help me with this!

4 glue sticks cost $7.76.
which equation would help determine the cost of 13 glue sticks
choose 1 answer
A x/13 = 4/$7.76
B 13/x = $7.76/4
C 4/$7.76 = 13/x
D 13/4 = $7.76/x
E None of the above

Answers

Answer:

13 glue sticks cost $25.22.

Step-by-step explanation:

4 blue sticks cost $7.76, this means that one glue stick costs

$7.76/4 = $1.94.

Let be the cost of the glue sticks, and be the number of glue sticks; then

We can use this equation to find the cost of 13 glue sticks; we just put into our equation and it gives:

So 13 glue sticks cost $25.22.

Help pleaseeeee guys

Answers

On performing , the "row-operation" 2R₁ + R₂ → R₂ on the matrix "M", the resulting new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex] .

The matrix "M" is given as : [tex]\left[\begin{array}{ccc}5&1&-5\\0&-2&2\end{array}\right][/tex],

We have to apply the Row-Operation : 2R₁ + R₂ → R₂, on the matrix "M",

Performing the row-operation "2R₁ + R₂ → R₂" on a matrix "M" means multiplying the first-row of "M" by 2, and then adding the resulting values to the second-row of "M" to produce a new value for each element in the second row.

This operation does not affect the first row of "M" and changes the values in the second row of "M".

⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\2\times5+0&2\times 1-2&2\times(-5)+2\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10+0&2-2&-10+2\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].

Therefore, the new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].

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Shirley Garcia is a restaurant supplies salesperson and receives 8% of her total sales as commission. Her sales totalled $15,000 during a given week. Find her commission.

Answers

Answer:

8% of $15,000 = .08 × $15,000 = $1,200

can u give an answer

Answers

Answer: 0

Step-by-step explanation:

Put 0 in the front box.

this is because you cant divide 11 apples equally into 6 people; 11 isn't a multiple of 6

What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}

Answers

The domain of function f(x) is given as follows:

{x | 1 ≤ x < 5}.

How to define the domain and range of a function?

The domain of a function is defined as the set containing all possible input values of the function, that is, all the values assumed by the independent variable x in the context of the function.The range of a function is defined as the set containing all possible output values of the function, that is, all the values assumed by the dependent variable y in the context of the function.

The values of x of the function given at the end of the answer are as follows:

Starts at x = 1(closed interval).Ends at x = 5 (open interval).

Hence the domain is given as follows:

{x | 1 ≤ x < 5}.

Missing Information

The function is given by the image presented at the end of the answer.

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Answer:

A - {x | 1 < x < 5}

Step-by-step explanation:

took the Quiz

Find the distance from point X to line p.

Answers

Answer:

[tex]\sf 2\sqrt{17}[/tex]

Step-by-step explanation:

To find the distance of a line using distance formula:

The line from point X intersect the line p at (0 , -3).

( -2 , 5) ⇒ x₁ = -2 & y₁ = 5

(0 , -3) ⇒ x₂ = 0 & y₂ = -3

[tex]\boxed{\bf Distance = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}}[/tex]

[tex]\sf = \sqrt{-2-0)^2+(5-[-3])^2}\\\\=\sqrt{(-2-0)^2 + (5+3)^2}\\\\=\sqrt{(-2)^2+(8)^2}\\\\=\sqrt{4+64}\\\\=\sqrt{68}\\\\=\sqrt{2*2*17}\\\\=2\sqrt{17}[/tex]

if you walked 3 blocks north and then 8 blocks west and then 10 blocks south how far are you from your starting point it each block is 2/10 of a mile?

Answers

You are approximately 3.4 miles from your starting point.

We have,

To solve this problem, we need to use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.

8 | \

| \

|___\

We can see that the three blocks north and 10 blocks south cancel each other out, so we only need to consider the 8 blocks west.

Using the distance formula, we can find that the distance traveled west is:

8 blocks × 2/10 mile per block = 1.6 miles

Now we can use the Pythagorean theorem to find the distance from the starting point:

distance = √(3² + 1.6²)

distance ≈ 3.4 miles

Therefore,

You are approximately 3.4 miles from your starting point.

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Use the figure to answer the following.
a. What is the surface area of the cylinder? Leave your answer in terms of x.
b. Suppose the diameter and the height of the cylinder are cut in half. How does this affect the surface area of the cylinder? Explain
The diameter of the cylinder is 8 and the height is 11

Answers

a. The surface area of the cylinder is 120π square units.

b. Assuming the diameter and the height of the cylinder are cut in half, the surface area of the cylinder would be reduced by a scale factor of 1/4.

How to calculate surface area of a cylinder?

In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):

SA = 2πrh + 2πr²

Where:

h represents the height.r represents the radius.

Note: Radius = diameter/2 = 8/2 = 4 m.

By substituting the side lengths into the formula for the surface area (SA) of a cylinder, we have the following;

Surface area = 2πrh + 2πr²

Surface area = 2(π)(4)(11) + 2(π)(4²)

Surface area = 120π square units.

Part b.

Assuming the diameter and the height of the cylinder are cut in half, we have:

Surface area = 2(π)(4/2)(11/2) + 2(π)((4/2)²)

Surface area = 2(π)(2)(5.5) + 2(π)(2²)

Surface area = (π)(2)(11) + 2(π)(4)

Surface area = 22π + 8π

Surface area = 30π square units.

Scale factor = 30π/120π

Scale factor = 1/4.

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Note: "The diameter of the cylinder is 8 and the height is 11"

I NEED YOUR HELP WITH STATISTICS

Answers

For a probability distribution to be represented, it is needed that P(X = 0) + P(X = 1) = 0.44. Hence one possible example is:

P(X = 0) = 0.40.

P(X = 1) = 0.04.

Discrete random variable to represent a probability distribution =

The sum of all the probabilities must be of 1, hence:

P(X = 0) + P(X = 1) + P(X = 3) + P(X = 4) + P(X = 5) = 1.

Then, considering the table:

P(X = 0) + P(X = 1) + 0.15 + 0.17 + 0.24 = 1

P(X = 0) + P(X = 1) + 0.56 = 1

P(X = 0) + P(X = 1) = 0.44.

Hence one possible value is:

P(X = 0) = 0.40.

P(X = 1) = 0.04.

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Part A: Jan INCORRECTLY finds the surface area of the cone using the following work. Explain Jan's error and find the
correct volume AND surface area of the cone.

Answers

Therefore, Jan has taken the wrong slant height, he has taken height, h is a place of slant height, l. That's why he has got the wrong answer.

How to solve

Given:,

r= d/2

22/2= 11m

Using the Pythagorean theorem, we can find the length:

l =[tex]11\sqrt{5}\\ = 24.6m[/tex]

Therefore, to find the surface area:

SA= 3.14(270.56 + 121)

=[tex]1229.5m^2[/tex]

Therefore, to find the volume:

V= [tex]1/3 \pi.r^2h[/tex]

V= [tex]2786.23m^3[/tex]

Answers

The number of 1/3 inch cubes required to fill the box is 62.

Volume of box

Volume = length × width × height

Height = 7/3

Length = 10/3

width = 8/3

Hence ,

Volume = 7/3 × 10/3 × 8/3 = 560/27

Size of cube = 1/3

Number of cubes required = Volume of box / size of cube

Number of cubes = 560/27 × 3/1

Number of cubes = 1680/27 = 62.22

Therefore, it will take 62 1/3 cubes to fill the box

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Maxine's credit card has an APR of 27.99%. If her current monthly balance, before interest, is $1,834.50, what will her monthly interest charge be? (4 points) $42.78 $42.79 $51.67 $65.54

Answers

Answer:

(b) $42.79

Step-by-step explanation:

You want the monthly interest charge on a balance of $1834.50 when the annual rate is 27.99%.

Monthly rate

The monthly interest rate is the annual rate divided by 12. This means the interest charge is ...

I = Prt . . . . . interest on P at annual rate r for t years

I = $1834.50 × 0.2799 × 1/12 ≈ $42.79

Her monthly interest charge will be $42.79.

18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89

Answers

The requried, Multiplies(with switching factors.) area given below,

693 x 83 = 57489

83 x 693 = 57489

The answer is 57489.

910 x 45 = 40950

45 x 910 = 40950

The answer is 40950.

38 x 84 = 3192

84 x 38 = 3192

The answer is 3192.

409 x 89 = 36401

89 x 409 = 36401

The answer is 36401.

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100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!

Answers

Answer:

[tex]3 {cos}^{2} x - {sin}^{2} x = 0[/tex]

[tex]3 - 3 {sin}^{2} x - {sin}^{2} x = 0[/tex]

[tex]3 - 4 {sin}^{2} x = 0[/tex]

[tex]4 {sin}^{2} x = 3[/tex]

[tex] {sin}^{2} x = \frac{3}{4} [/tex]

sin(x) = +(1/2)√3

x = π/3 + 2kπ or x = 2π/3 + 2kπ

x = -π/3 + 2kπ or x = -2π/3 + 2kπ

(k is an integer)

D
(x+2)(x+6)=0
In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:
O zero product property
O division property
O transitive property
O multiplication property
H
OI

Answers

The property used to calculate x in (x + 2)(x + 6) = 0 is (a) the zero product property

How to determine the property used to calculate x

From the question, we have the following parameters that can be used in our computation:

(x + 2)(x + 6) = 0

The equation when expanded becomes

x + 2 = 0 or x + 6 = 0

In algebra, the zero product property states that

if ab = 0, then a = 0 or b = 0

using the above as a guide, we have the following:

The property used to calculate x is (a) the zero product property

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Please help with that question

Answers

The value of function f (α + β) is determined as (3√3 + 1)/3, (2√2 - 3)/3.

What is the value of function f (α + β)?

The value of f (α + β) is calculated by applying the following formula as follows;

The given functions;

for α: x² + y² = 4

y is given as -1, the value of x is calculated as;

x² + (-1)² = 4

x² + 1 = 4

x² = 3

x = √3

α = (√3, - 1)

for β: x² + y² = 1

x is given as ¹/₃, the value of y is calculated as;

(¹/₃)² + y² = 1

¹/₉ + y² = 1

y² = 1 - ¹/₉

y² = ⁸/₉

y = √ (8/9)

y = 2√2/3

β = (¹/₃, 2√2/3)

The value of function f (α + β) is calculated as;

f(α + β) = (√3, - 1) + (¹/₃, 2√2/3)

f(α + β) = (3√3 + 1)/3, (2√2 - 3)/3

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Show that the points (2, 5), (5 , 2) and (6,6) are composites of a triangle

Answers

The slopes of the lines connecting all the points are distinct. Hence, they form a triangle.

Proof that 3 points form a triangle

To show that the points (2, 5), (5, 2), and (6, 6) form a triangle, we can calculate the slopes of the lines connecting these points. If the slopes are all distinct, then the points form a triangle.

Let's calculate the slopes:

The slope between (2, 5) and (5, 2):

m₁ = (y₂ - y₁) / (x₂ - x₁)

= (2 - 5) / (5 - 2)

= -3/3

= -1

The slope between (2, 5) and (6, 6):

m₂ = (y₂ - y₁) / (x₂ - x₁)

= (6 - 5) / (6 - 2)

= 1/4

The slope between (5, 2) and (6, 6):

m₃ = (y₂ - y₁) / (x₂ - x₁)

= (6 - 2) / (6 - 5)

= 4/1

= 4

Since the slopes of the lines connecting these points are all distinct (-1, 1/4, and 4), the points (2, 5), (5, 2), and (6, 6) form a triangle.

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evaluate xy-y when x = 2 and y = 5

Answers

Answer:

Step-by-step explanation:

Just do as the problem says:

xy-y = (2)(5)-(5) = 10-5 = 5

Answer: 5

Step-by-step explanation: All you have to do is substitute x & y for their respective numbers. In this case, change x for 2 & y for 5, So xy-y becomes 2(5)-5, which equals 10-5, which is 5.

What is the length of Arc LM? Use 3.14 as pi and round your answer to the nearest tenth. please show work, will mark brainliest.

Answers

To find the length of arc LM, we need to use the formula for the circumference of a circle:

C = 2πr

In this case, the arc LM is a portion of the circumference of the circle. To find the length of the arc, we need to determine the angle at the center of the circle that corresponds to the arc.

Looking at the image you provided, we can see that angle LOM is a right angle (90 degrees). The angle at the center of the circle, LOCM, is half of the right angle, which is 45 degrees.

To calculate the length of arc LM, we need to find the fraction of the total circumference represented by the central angle LOCM. The fraction is given by:

Fraction of circumference = Angle at center / 360 degrees

Fraction of circumference = 45 degrees / 360 degrees

Fraction of circumference = 1/8

Now, we can calculate the length of arc LM:

Length of arc LM = Fraction of circumference * Circumference

Length of arc LM = (1/8) * (2πr)

Since the radius (r) is not given in the image, we cannot calculate the exact length of arc LM. However, we can provide the formula for the length of arc LM in terms of the radius:

Length of arc LM = (1/8) * (2πr) = πr/4

So, the length of arc LM is πr/4, where r is the radius of the circle.

If you have the value of the radius, you can substitute it into the formula to find the specific length of arc LM.

50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

Answer:

Step-by-step explanation:

i do this all the time math is my thing

When Grace opens and lays a shipping box out flat, she sees that the top and the bottom of the box
both measure 10 inches by 14 Inches, the sides of the box both measure 14 inches by 8 inches, and
the front and back of the box both measure 8 inches by 10 inches. What is the surface area of Grace's
strooing box?

Answers

The surface area of Grace's shipping box is 664 square inches.

We have,

The box can be divided into six rectangles, each of which represents the face of the box.

To find the surface area of the box, we need to find the area of each face and then add them all up.

The top and bottom of the box are both 10 inches by 14 inches, so the area of each of these faces is:

= 10 x 14

= 140 square inches

The sides of the box are both 14 inches by 8 inches, so the area of each of these faces is:

= 14 x 8

= 112 square inches

The front and back of the box are both 8 inches by 10 inches, so the area of each of these faces is:

8 x 10

= 80 square inches

To find the surface area of the whole box, we add up the areas of all six faces:

= 2(140) + 2(112) + 2(80)

= 280 + 224 + 160

= 664 square inches

Therefore,

The surface area of Grace's shipping box is 664 square inches.

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NO LINKS!!! URGENT HELP PLEASE!!!

The distance between Miami, Florida and Bermuda is about 1042 miles. The distance from Bermuda to San Juan. Puerto Rico is about 965 miles, and the distance from San Juan to Miami is about 1038 miles. Find the area of the triangle formed by the three locations.

Answers

Answer:

444523.45 square miles

Step-by-step explanation:

By using Heron's formula, we can easily find the area of the triangle formed by Miami, Bermuda, and San Juan, we need to use the lengths of the three sides of the triangle.

Let,

Side a: Distance from Miami to Bermuda = 1042 miles

Side b: Distance from Bermuda to San Juan = 965 miles

Side c: Distance from San Juan to Miami = 1038 miles

Now we can use Heron's formula to find the area of the triangle:

s =[tex]\frac{a+b+c}{2}[/tex]

s = [tex]\frac{1042 + 965 + 1038}{2}=1522.5[/tex] miles

A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

A = [tex]\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}=444523.45[/tex]

Therefore, the area of the triangle formed by Miami, Bermuda, and San Juan is approximately 444523.45 square miles.

Answer:

444,523.45 square miles (2 d.p.)

Step-by-step explanation:

To find the area of a triangle formed by the locations of Miami, Bermuda, and San Juan, use Heron's formula.

[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]

Label the three sides of the triangle as 'a', 'b', and 'c', where 'a' is the distance from Miami to Bermuda (1042 miles), 'b' is the distance from Bermuda to San Juan (965 miles), and 'c' is the distance from San Juan to Miami (1038 miles):

a = 1042 milesb = 965 milesc = 1038 miles

To find the half perimeter, s, half the sum of the three side lengths:

[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{1042+965+1038}{2}=1522.5[/tex]

Substitute the values of a, b, c and s into Heron's formula and solve for area, A:

[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}\\&=\sqrt{1522.5(480.5)(557.5)(484.5)}\\&=444523.4468348...\\&=444523.45\; \sf miles^2\;(2\;d.p.)\end{aligned}[/tex]

Therefore, the area of the triangle formed by the three locations is 444,523.45 square miles, to two decimal places.

Si 10 obreros construyen un consultorio médico en 12 dias.¿Con cuántos obreros se hará la misma obra en 15 dias?

Answers

A total of 8 workers are required for a building time of 15 days.

How many workers are needed to complete a building?

In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:

n ∝ 1 / t

n = k / t

Where k is the proportionality ratio, which can be eliminated by building the following formula:

n₁ · t₁ = n₂ · t₂

If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:

n₂ = n₁ · (t₁ / t₂)

n₂ = 10 · (12 / 15)

n₂ = 10 · (4 / 5)

n₂ = 8

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What do they mean and why please

Answers

It means having two variables with the same denominator is just bad luck

What is the surface area of a cone with radius 8 in. and slant height 9 in.?

Answers

The total surface area of the cone is 427.04 square inches.

What is the surface area of the cone?

For a cone of radius R and slant height L, the total surface area is given by the formula:

S = π*R*L + π*R²

Where π = 3.14

In this case, we know that the radius of the cone is 8 inches, and the slant height of the cone is 9 inches.

Then the total surface area of the cone is:

S = 3.14*8in*9in + 3.14*(8in)²

S = 427.04 in²

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A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be 99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.

Answers

The sample size needed to be 99% confident that the sample proportion will not differ from the true proportion by more than 4% is given as follows:

n = 1037.

What is a confidence interval of proportions?

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.

The margin of error is given as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

[tex]\pi = 0.5[/tex]

Then the sample size for M = 0.04 is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]

n = 1037.

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Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

possible answers -
By the cross product property, AB2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by AD.
By the cross product property, AB2 = BC multiplied by AD.

Answers

The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]

Cross-multiplying, we get:

[tex]$AB^2 = BC \cdot AD$[/tex]

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]

Cross-multiplying, we have:

[tex]$AC^2 = BC \cdot AD$[/tex]

Now, we can substitute the derived expressions into the original equation:

[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]

It was made possible by cross-product property.

Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

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We mixed 5l of 45% alcohol, 4l of 82% and 1l of 92% alcohol. How many percent alcohol does the resulting mixture contain? I got 58.6% and im wondering IF that's correct.

Answers

The resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.

To solve this problem

We can calculate the weighted average of the alcohol percentages based on the volumes of each component.

Let's figure out how much alcohol there is overall in the mixture:

Total alcohol is calculated as follows: (Volume of 45% alcohol) * (Property of 45% alcohol) + (Volume of 82% alcohol) * (Property of 82% alcohol) + (Volume of 92% alcohol) * (Property of 92% alcohol).

Total alcohol = (5 liters) * (45%) + (4 liters) * (82%) + (1 liter) * (92%)

Total alcohol = 2.25 liters + 3.28 liters + 0.92 liters

Total alcohol = 6.45 liters

Let's now determine the amount of alcohol included in the final mixture:

Alcohol content is calculated as (total alcohol / total mixture volume) * 100.

The mixture's total volume is = 5 liters + 4 liters + 1 liter = 10 liters

Alcohol content: (6.45 liters / 10 liters) x 100 = 64.5%

Therefore, the resulting mixture contains approximately 64.5% alcohol, not 58.6% as you mentioned.

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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each sine or cosine value to its equivalent measure

Answers

The equivalent sine and cosine values are as follows:

cos(74°) = sin(16°)cos(57°) = sin(33°)sin(32°) = cos(58°)sin(43°) = cos(47°)

What is the relationship between sine and cosine angles?

The relationship between sine and cosine angles is:

sinθ = cos(90 - θ)

This equation is known as the complementary angle identity for sine and cosine. It states that the sine of an angle is equal to the cosine of its complementary angle (90 degrees minus the original angle).

For example, if we have an angle theta = 30 degrees, its complementary angle would be 90 - 30 = 60 degrees.

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Groups 1 and 3 In a class of 42 students, 12 boys and 15 girls know how to read three-letter words in English. 19 boys and 17 girls know how to identify all letters of the alphabet. None of the students in the class can write a sentence of five words if dictated to them. There are 22 boys and 20 girls in the class.
•Using a Venn diagram, show how many boys and girls cannot read a letter or a three-letter word.
•If all students should know how to write a sentence of five words by the end of the academic year, how many groups will you need to form to focus on remedial/tutor support (to teach at the right level)?
• If by the end of the academic year, all students are able to identify all letters, read three-letter words, and write a five-word sentence, what would this Venn diagram look like?

Answers

There are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.

How to solve

The Venn diagram is drawn as shown in the attached image, and it shows that the number of boys and girls who cannot read a letter or a three-letter word is marked as (c+d) which represents 13 boys and 8 girls.

Given:

The class has 42 students.

12 boys and 15 girls are said to know how to read three-letter words in English.

19 boys and 17 girls are said to know how to identify all letters of the alphabet.

None of the students in the class is able to write a sentence of five words if dictated to them.

There are in total 22 boys and 20 girls in the class.

Read three-letter words |

|____________|______________|

| | |

| Boys (12) | Girls (15) | Can read three-letter words

|____________|______________|

| | |

| Boys (10) | Girls (13) | Cannot read three-letter words

_______|____________|______________|

| | |

| Boys (9) | Girls (13) | Can identify all letters

|____________|______________|

| | |

| Boys (13) | Girls (7) | Cannot identify all letters

|____________|______________|

To find the number of boys and girls who cannot read a letter or a three-letter word, we need to add up the numbers in the two bottom circles:

Boys who cannot read a letter or a three-letter word: 10 + 13 = 23

Girls who cannot read a letter or a three-letter word: 13 + 7 = 20

Therefore, there are 23 boys and 20 girls in the class who cannot read a letter or a three-letter word.