Matematicas III- Geometria analitica 1- Calcula el perimetro y área de las triángulos Cuyos vertices son a) A(2,2) B(7,-1) ((3,-8) ​

The length of the third side, which is opposite the angle of 84°, is approximately 30.1 units.

Given is a triangle with angles 64° and 32°, and side 21.1 and 30, we need to find the third side,

So, according to the angle sum property of triangle,

Third angle = 180° - (64° + 32°)

Third angle = 84°

To find the length of the third side, which is opposite the angle of 84°, we can use the Law of Sines.

The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides of a triangle.

Let's label the triangle with angles A, B, and C, and sides a, b, and c, respectively.

In this case, angle A is 84°, angle B is 64°, and angle C is 32°. Side a is the side opposite angle A, side b is the side opposite angle B, and side c is the side opposite angle C.

Using the Law of Sines, we have the following equation:

sin(A) / a = sin(B) / b = sin(C) / c

We want to find the length of side a, so we can rearrange the equation as follows:

sin(A) / a = sin(B) / b

Now we can substitute the given values:

sin(84°) / a = sin(64°) / 30

To find side a, we can solve for it algebraically:

a = (sin(84°) × 30) / sin(64°)

Calculating this expression, we get:

a ≈ 30.1

Therefore, the length of the third side, which is opposite the angle of 84°, is approximately 30.1 units.

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Answer:

  2

Step-by-step explanation:

You want to know the mode of a dot plot that could be represented as ...

  1 | x x

  2 | x x x x x

  3 | x x x

  4 | x x x x

  5 | x x

The mode is the data element that appears most often in the data set.

The 5 xs above the 2 is the largest number of xs that appear anywhere, so 2 is the mode.

<95141404393>

Pam will use 27/50 cups of apple juice.

An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.

To get how many cups of apple juice Pam will use, we must calculate 3/5 of 9/10 cups.

The 3/5 of 9/10 is:

= (3/5) * (9/10)

= (3 * 9) / (5 * 10)

= 27/50

Therefore, Pam will use 27/50 cups of apple juice.

Translated question:

A recipe calls for 9/10 cups of apple juice. Pam is preparing 3/5 of the recipe. How many cups of apple juice will Pam use?​

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The dimensionless product relating the torque, rotation rate, volume, and air density is:

Pi = (torque) * (rotation rate)² * (volume)^(1/3)

To find a dimensionless product relating the torque (ML²T⁻²) produced by an automobile engine, the engine's rotation rate (T⁻¹), the volume V of air displaced by the engine, and the air density p, we can make use of the Buckingham Pi theorem.

The Buckingham Pi theorem states that in a physical problem involving n variables with k fundamental dimensions, there will be n - k dimensionless quantities that can be formed as products of powers of the original variables.

In this case, we have 4 variables with 3 fundamental dimensions: torque (M L² T⁻²), rotation rate (T⁻¹), volume (L³), and air density (M L⁻³). Therefore, we expect to have 4 - 3 = 1 dimensionless product.

Let's define the dimensionless product (Pi) as:

Pi = (torque)ᵃ * (rotation rate)ᵇ * (volume)ᶜ * (air density)ᵈ

To determine the powers (a, b, c, d), we equate the dimensions on both sides of the equation:

M L² T⁻² = (M)ᵃ * (T⁻¹)ᵇ * (L³)ᶜ * (M L⁻³)ᵈ

Equating the dimensions of mass (M):

1 = a + d

Equating the dimensions of length (L):

2 = 3c - 3d

Equating the dimensions of time (T):

-2 = -b

Solving these equations, we find:

a = 1

b = 2

c = 1/3

d = 0

This dimensionless product captures the relationship between these variables, independent of their specific units and scaling factors.

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Answer:

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

What percent of $8400 is $672?

Answer:

8%

Step-by-step explanation:

To find the percentage that was donated to hospitals, we can set up the following equation:

[tex]\sf \dfrac{total\: donation}{ total \:sales} * 100 = percentage \:donated[/tex]

In this case, the total donation was $672 and the total sales were $8,400.

Substituting these values into the equation, we get:

[tex]\sf \dfrac{672}{8400} * 100 = percentage \:donated[/tex]

Simplifying this expression:

(0.08) * 100 = percentage donated

8% = percentage donated

Therefore, the home decor store donated 8% of $8,400 to hospitals.

The values of r for which y = e^(rx) satisfies the differential equation y″ - 64y = 0 are r = 8 and r = -8.

First, differentiate y twice:

y' = [tex]re^{rx}[/tex]

y'' = r²[tex]e^{rx}[/tex]

y'' - 64y = r²[tex]e^{rx}[/tex] - 64[tex]e^{rx}[/tex] = 0

[tex]e^{rx}[/tex] * ([tex]r^{2}[/tex] - 64) = 0

[tex]r^{2}[/tex] - 64 = 0:

Solving this quadratic equation gives:

[tex]r^{2}[/tex] = 64

r = ±8

Therefore, the values of r that satisfy the differential equation are r = 8 and r = -8.

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Let y″−64y=0.

Find all values of r such that y=kerx satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list.

The area of sector in the given circle is 275π/6 square meters.

We have to find the area of sector which measures 165 degrees and radius of circle is 10m.

Area = (θ/360)πr²

where θ is the angle in degrees, π is the mathematical constant pi (approximately 3.14159), and r is the radius of the circle.

In this case, the angle is 165 degrees and the radius is 10 meters. Plugging these values into the formula, we get:

Area = (165/360)π(10)²

Area = (11/24) × π × 100

Area =1100/24π

=275π/6 square meters.

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Answer:

h = 4 units

Step-by-step explanation:

Given equation:

[tex]\text{A}_{\text{trapezoid} } = \dfrac{1}{2}(h)(b_{1} + b_2)[/tex]

Given numerical values:

Plug in all values into the equation and simplify it to find the height:

[tex]\implies \text{28} = \dfrac{1}{2}(h)(6 + 8)[/tex]

[tex]\implies\text{28} = (h)(3 + 4) = 7h[/tex]

[tex]\implies h = \dfrac{28}{7} = 4[/tex]

Therefore, the measure of the height is 4 units.

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5m is the height of a cone with a diameter of 12 m whose volume is 188 m³.

To find the height of a cone, we can use the formula for the volume of a cone and solve for the height.

The formula for the volume of a cone is:

V = (1/3)× π × r² × h

Given that the diameter of the cone is 12 m, the radius (r) is half of the diameter, which is 6 m.

We are also given that the volume of the cone is 188 m³.

Using the formula, we can rearrange it to solve for the height (h):

h = (3V) / (πr²)

Plugging in the values:

h = (3 × 188) / (3.14 × 6²)

h = 564 / (3.14 × 36)

h = 564 / 113.04

h =4.9916

h=5

Therefore, the height of a cone with a diameter of 12 m whose volume is 188 m³ is 5 m.

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The volume of a pyramid with a square base is 3172.608 cubic meter.

Given that, the side length of the base is 14.4 m and the height of the pyramid is 15.3 m.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, volume = 14.4²×15.3

= 3172.608 cubic meter

Therefore, the volume of a pyramid with a square base is 3172.608 cubic meter.

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The information which would be enough to prove the triangles to be congruent are either DE = RP or ∠F = ∠Q.

Given two triangles,

ΔDEF and ΔRPQ.

If ΔDEF is congruent to ΔRPQ, then the corresponding vertices of D, E and F are R, P and Q respectively.

Already we have from the figure,

∠D = ∠R

DF = RQ

Now, it is enough to prove either DE = RP or ∠F = ∠Q.

When DE = RP, by SAS congruence theorem, corresponding two sides and the included angle of each triangle are equal and thus triangles are congruent.

When ∠F = ∠Q, by ASA congruence theorem, corresponding two angles and the included side of each triangle are equal and thus triangles are congruent.

Hence the information required are either DE = RP or ∠F = ∠Q.

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hello

the answer to the question is:

volume of sphere = ⁴⁄₃πr³

4.5π = ⁴⁄₃πr³ ----> r³ = 3.375 ----> r = 1.5 cm

Answer:

hello

the answer to (a) is:

y = kx ----> y = (1/8)x

and the answer to (b) is:

if x = 7

y = (1/8) × 7 = 7/8 or 0.875

The circumference of the circle is 88 units given the radius 14 units

Circumference of a circle is the measurement of the boundary of the circle or the path or the boundary that surrounds the shape. It is also called Perimeter of a circle.

Howto determine this

Given the radius of the circle = 14

Circumference of a circle = 2πr

Where π = 22/7

Circumference of circle = 2 * 22/7 * 14

Circumference of circle = 44/7 * 14

Circumference of circle = 616/14

Circumference of circle = 88 units

Therefore, the Circumference of circle is 88 units

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DC and DE are tangents to the circle at C and E respectively A is the centre of the circle B lies on the circle and BAE is a straight line L N

7.2.1: AABC is parallel to ADEC (AABC|||ADEC).

7.2.2: This completes the proof of both statements:

AABC|||ADEC and AE · EC = BC · DE.

To prove that AABC is parallel to ADEC, we can make use of the properties of tangents and alternate angles.

Proof:

AABC|||ADEC

DC and DE are tangents to the circle at C and E, respectively.

BAE is a straight line.

To prove AABC|||ADEC, we need to show that the alternate interior angles are congruent.

First, let's consider angle AED and angle ABC.

These angles are alternate interior angles formed by transversal AE intersecting the lines DE and BC.

Since DE is a tangent to the circle at E, angle AED is a right angle (90 degrees).

We know that a tangent to a circle is perpendicular to the radius at the point of tangency.

angle AED = 90 degrees.

Let's consider angle ABC. Since DC is a tangent to the circle at C, angle ABC is also a right angle (90 degrees).

Again, this follows from the property that a tangent is perpendicular to the radius at the point of tangency.

Since both angle AED and angle ABC are right angles, they are congruent:

angle AED = angle ABC.

By the alternate interior angle if two lines are intersected by transversal and the alternate interior angles are congruent, then the lines are parallel.

AABC is parallel to ADEC (AABC|||ADEC).

7.2.2 Showing that AE · EC = BC · DE

To prove that AE · EC = BC · DE, we can use the fact that AABC is parallel to ADEC.

Since AABC is parallel to ADEC, we can apply the intercept theorem or the proportionality theorem.

According to the intercept two parallel lines intersect a set of parallel lines, then the segments formed on one transversal are proportional to the corresponding segments formed on any other transversal.

Using the intercept theorem, we can write the following proportion:

AE/BC = DE/EC

To find AE · EC, we can cross-multiply the proportion:

AE · EC = BC · DE

We have shown that AE · EC is equal to BC · DE.

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The surface area of the larger solid is approximately 172 mm sq. approx

Given

The volume of the smaller solid = 540 mm cube

The volume of the larger solid = 857.5 mm cube

The surface area of the smaller solid = 108 mm sq.

Required to find the surface area of the larger solid =?

Let the surface area of the larger solid be x.

(surface area of smaller solid) / (volume of smaller solid) = (surface area of larger solid) / (volume of larger solid)

Putting the values in the above formula we get the value of x.

108 mm^2 / 540 mm^3 = x / 857.5 mm^3

x = 171.5 mm sq

Thus, the surface area of the larger solid is approximately 172 mm sq

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Answer:

[tex]\\[/tex]

Step-by-step explanation:

We know that the total number of kids is 150. We can find the number of kids with green, brown, and gray eyes using the given percentages:

[tex]\sf\dashrightarrow Green\: eyes = 6\: kids[/tex]

[tex]\sf\dashrightarrow Brown\: eyes = 0.52 \times 150 = 78\: kids[/tex]

[tex]\sf\dashrightarrow Gray\: eyes = 0.16 \times 150 = 24\: kids[/tex]

[tex]\\[/tex]

To find the number of kids with blue eyes, we can subtract the number of kids with green, brown, and gray eyes from the total number of kids:

[tex]\sf\dashrightarrow Blue\: eyes = 150 - 6 - 78 - 24[/tex]

[tex]\sf\dashrightarrow Blue\: eyes = 42\: kids[/tex]

[tex]\\[/tex]

Finally, we can calculate the percentage of kids with blue eyes by dividing the number of kids with blue eyes by the total number of kids and multiplying by 100:

[tex]\sf\implies Percentage = \dfrac{42}{150} \times 100[/tex]

[tex]\sf\implies Percentage = \dfrac{4,200}{150}[/tex]

[tex]\sf\implies Percentage = \green{28\%}[/tex]

[tex]\\[/tex]

[tex]\\[/tex]

Therefore, 28% of the kids have blue eyes.

The value of x that is measure of angle R from the given triangle PQR is 60°.

In the given triangle PQR, angle P is right angle and measure 90°, angle Q measures 30° and angle R measures x.

We know that, sum of the interior angles of triangle is 180°.

Here, ∠P+∠Q+∠R=180°

90°+30°+∠R=180°

120°+∠R=180°

∠R=180°-120°

∠R=60°

Therefore, the value of x that is measure of angle R from the given triangle PQR is 60°.

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Answer: 48

Step-by-step explanation: median of list of consecutive integers is the mean of the endpoints. (31+65)/2

This distribution of snowfall amounts is skewed to the right

Data is said to be skewed to the right or positively skewed, when the tail of the distribution extends more towards the right side of the data. This means that there are a few larger values or outliers that pull the mean or median towards the higher end of the scale, resulting in a longer tail on the right side of the distribution.

In a positively skewed distribution majority of the data is concentrated towards the lower values.

Considering the stemplot the majority of the data is in the lower values

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Answer:

to the second part

18.7 inches

Answer:

V = lwh

Step-by-step explanation:

The volume of a rectangular prism or a rectangle stretched is the basic rectangle area formula ( wh ) multiplied by the new factor, the length ( l ). This makes the formula V = lwh
Hope this helped

The container is indeed big enough to store 560 sugar cubes.

To determine if the container is big enough to store 560 sugar cubes, we need to calculate the volume of the container and compare it to the total volume occupied by the sugar cubes.

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

In this case, the dimensions of the container are:

Length (l) = 6 inches

Width (w) = 4 inches

Height (h) = 3 inches

Using the formula, the volume of the container is calculated as follows:

V = 6 inches * 4 inches * 3 inches

V = 72 cubic inches

Now, let's calculate the volume occupied by a single sugar cube:

The side length of a sugar cube is 0.5 inches, so the volume of a single sugar cube is:

V_cube = 0.5 inches * 0.5 inches * 0.5 inches

V_cube = 0.125 cubic inches

To determine the number of sugar cubes that can fit in the container, we divide the volume of the container by the volume of a single sugar cube:

Number of sugar cubes = V_container / V_cube

Number of sugar cubes = 72 cubic inches / 0.125 cubic inches

Number of sugar cubes = 576

Since the number of sugar cubes that can fit in the container is 576, which is greater than the required 560 sugar cubes, we can conclude that the container is indeed big enough to store 560 sugar cubes.

Therefore, the container can comfortably accommodate the desired quantity of sugar cubes while providing a tight seal to keep ants away.

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The actual area of logo 2 would be = 45ft²

The area of logo 2 would be = 2.5in²

To determine the actual area of logo 2, the given dimensions are first converted to ft and the formula for the area of square is used. That is

Actual area of logo 2 = a²

a = 1/2 in (convert to ft)

But 1 in = 6 ft

1/2in = 3ft

Then divide the logo 2 in various squares to get 5 equal squares.

Area = 5(a²)

= 5×3×3

= 45ft²

The area of the logo 2 model = 5(0.5) = 2.5in²

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Answer:

Set your calculator to degree mode.

[tex]x = {cos}^{ - 1} \frac{3.9}{8.5} = 62.7 \: degrees[/tex]

Angle x measures about 62.7°.

UIF at 1% of the basic salary is R234.

The actual dimension of the kitchen on the floor is 0.036 meters.

2.2.1. UIF stands for Unemployment Insurance Fund.

2.2.2. To calculate UIF at 1% of the basic salary, we multiply the basic salary by 1%:

UIF = 1% of Basic Salary

= 1/100 x Basic Salary

Given that the Basic Salary is R23,400, we can calculate UIF:

UIF = 1/100 x 23,400

= 234

Therefore, UIF at 1% of the basic salary is R234.

2.2.3. One benefit of contributing UIF by the employee is that it provides financial protection against unemployment. If an employee becomes unemployed, they may be eligible to receive UIF benefits, which can provide temporary financial support during the period of unemployment.

2.2.4. Unfortunately, the values of B and C are not provided in the given information. If you provide the values, I can assist you with determining them.

3.1.1. The scale used is 1:100.

3.1.2. If the dimension (length) of the kitchen on the plan is 3.6 cm, to determine the actual dimension in meters, we need to scale it up by the scale factor:

Scale factor = 1/100 (since it's a 1:100 scale)

Actual dimension = Dimension on the plan x Scale factor

= 3.6 cm x (1/100)

= 0.036 meters

Therefore, the actual dimension of the kitchen on the floor is 0.036 meters.

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Answer:

y = [tex]\frac{2}{3}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m = [tex]\frac{4-0}{0-(-6)}[/tex] = [tex]\frac{4}{0+6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = [tex]\frac{2}{3}[/tex] x + 4 ← equation of line

The true comparisons are:

B. 3.114 > 3.112: In this case, the number 3.114 is greater than 3.112, as the digit in the thousandth place (4) is greater than the corresponding digit in 3.112 (1).

D. 0.541 > 0.145: Here, the number 0.541 is greater than 0.145 because the digit in the hundredth place (4) is greater than the corresponding digit in 0.145 (1).

E. 0.141 < 0.19: In this example, the number 0.141 is indeed less than 0.19, as the digit in the hundredth place (1) is less than the corresponding digit in 0.19 (9).

Option A is not a true comparison because 32.03 is actually less than 32.3. The digit in the hundredth place is 0 in both numbers, and the digit in the thousandth place is 3 in 32.03, while it is 0 in 32.3.

Option C is also not a true comparison since 4.003 is greater than 3.996. The digit in the thousandth place (4) is greater than the corresponding digit in 3.996 (3).

Answer: -D) 0.541 > 0.145

-B) 3.114 > 3.112

-E) 0.141 < 0.19

explanation: The number 3.114 is greater than 3.112, as the digit in the thousandth place (4) is greater than the corresponding digit in 3.112 (1). Here, the number 0.541 is greater than 0.145 because the digit in the hundredth place (4) is greater than the corresponding digit in 0.145 (1). In this example, the number 0.141 is indeed less than 0.19, as the digit in the hundredth place (1) is less than the corresponding digit in 0.19 (9).

The resultant vector of the operation 13u - 2w is given as follows:

13u - 2w = <45, 115>.

The vectors in the context of this problem are defined as follows:

When we multiply a vector by a constant, each component of the vector is multiplied by the constant, hence:

Then when the two vectors are subtracted, the equivalent components of each vector are subtracted, hence:

13u - 2w = <39, 117> - <-6, 2>

13u - 2w = <45, 115>.

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Answer:

[tex]\displaystyle \frac{2}{15}(2-x^3)^{\frac{5}{2}}-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+C[/tex]

Step-by-step explanation:

[tex]\displaystyle \int x^5\sqrt{2-x^3}\,dx\\\\=\int x^5(2-x^3)^{\frac{1}{2}}\,dx\\\\=\int x^3x^2(2-x^3)^{\frac{1}{2}}\,dx[/tex] <-- Breaking up [tex]x^5[/tex] into [tex]x^3x^2[/tex] helps us later

Let [tex]u=2-x^3[/tex] and [tex]du=-3x^2\,dx[/tex] so that [tex]2-u=x^3[/tex] and [tex]\displaystyle -\frac{1}{3}du=x^2dx[/tex]:

[tex]\displaystyle -\frac{1}{3} \int (2-u)u^{\frac{1}{2}}\,du\\\\=-\frac{1}{3} \int 2u^{\frac{1}{2}}-u^{\frac{3}{2}}\,du\\\\=-\frac{1}{3}\biggr(\frac{4}{3}u^{\frac{3}{2}}-\frac{2}{5}u^{\frac{5}{2}}\biggr)+C\\\\=-\frac{1}{3}\biggr(\frac{4}{3}(2-x^3)^{\frac{3}{2}}-\frac{2}{5}(2-x^3)^{\frac{5}{2}}\biggr)+C\\\\=-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+\frac{2}{15}(2-x^3)^{\frac{5}{2}}+C\\\\=\frac{2}{15}(2-x^3)^{\frac{5}{2}}-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+C[/tex]