A point P lies on the line with equation y= 4-3X. The point P is a distance √34 from the origin. Find the two possible positions Of point P

Step-by-step explanation:

1: change 'sin²A' and 'cos²B' into (1-cos²A)and (1-sin²A) respectively.

2:open the brackets and put signs accordingly.

3: cancel (-1) and (+1).

4: remaining is your answer.

To form an equation from a word problem, we can recognize variables and operations from keywords.

Let the number of weeks be a.

We're given:

Because $200 is the minimum account required, we know that the amount earned must be greater than or equal to 200.

[tex]200\leq[/tex]

Our current savings and money can be calculated by adding 15a and 32:

[tex]200\leq15a+32[/tex]

[tex]200\leq15a+32[/tex]

Answer:

Read explanation

Step-by-step explanation:

I answered another one of your questions just like this in detail so I'll keep this one shorter.

Domain: (-∞, 0]

Range: (-3,∞)

x-intercept: Approximately -3.75

y=intercept: -3

Answer:

probability result of sample space would result in 12/144

Step-by-step explanation:

as result there is 12 numbers on each dice, blth have exact same numbers, resulting in 144 combinations ti be thrown as sample space event outcome wluld be;

1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12

2/1 2/2 2/3 2/4 2/5 2/6 2/7 2/8 2/9 2/10 2/11 2/12

3/1 3/2 3/3 3/4 3/5 3/6 3/7 3/8 3/9 3/10 3/11 3/12

4/1 4/2 4/3 4/4 4/5 4/6 4/7 4/8 3/9 4/10 4/11 4/12

5/1 5/2 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/10 5/11 5/12

6/1 6/2 6/3 6/4 6/5 6/6 6/7 6/8 6/9 6/10 6/11 6/12

7/1 7/2 7/3 7/4 7/5 7/6 7/7 7/8 7/9 7/10 7/11 7/12

8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8 8/9 8/10 8/11 8/12

9/1 9/2 9/3 9/4 9/5 9/6 9/7 9/8 9/9 9/10 9/11 9/12

10/1 10/2 10/3 10/4 10/5 10/6 10/7 10/8 10/9 10/10 10/11 10/12

11/1 11/2 11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12

12/1 12/2 12/3 12/4 12/5 12/6 12/7 12/8 12/9 12/10 12/11 12/12

giving 12 matching numbers in a 144 possible rolled outcome

mathematic formula would be P(A) = n(A)/n(S)

As P(A)= probabolity of event A

n(A)= number of favouravle outcome

n(S)= total number of outcome in sample space

giving

12=2/144=0,0138888889

The given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.

To prove, we go by the right-hand side of the equation:

cot x - d/dx x.cot x.

We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.

cot x - {x. d/dx(cot x) + cot x. d/dx(x)}

= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}

= cot x + x. cosec²x - cot x

= x. cosec²x

= The left-hand side of the equation.

Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.

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The minimum number of books required to be equally distributed among the students are 1,440 books.

To find the minimum required books so that they can be equally distributed:

The number of students in three sections of class 6th are 32, 36, and 40.

Now, find the LCM od 32, 36, and 40.

The LCM od 32, 36, and 40 will be 1,440.

Therefore, the minimum number of books required to be equally distributed among the students are 1,440 books.

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Answer:

  1.314 MJ

Step-by-step explanation:

As water is removed from the tank, decreasing amounts are raised increasing distances. The total work done is the integral of the work done to raise an incremental volume to the required height.

There are a couple of ways this can be figured. The "easy way" involves prior knowledge of the location of the center of mass of a cone. Effectively, the work required is that necessary to raise the mass from the height of its center to the height of the discharge pipe.

The "hard way" is to write an expression for the work done to raise an incremental volume, then integrate that over the entire volume. Perhaps this is the method expected in a Calculus class.

The mass of the water being raised is the product of the volume of the cone and the density of water.

The cone volume is ...

  V = 1/3πr²h . . . . . . for radius 2 m and height 8 m

  V = 1/3π(2 m)²(8 m) = 32π/3 m³

The mass of water in the cone is then ...

  M = density × volume

  M = (1000 kg/m³)(32π/3 m³) ≈ 3.3510×10^4 kg

The center of mass of a cone is 1/4 of the distance from the base to the point. In this cone, it is (1/4)(8 m) = 2 m from the base.

The discharge pipe is 2 m above the base of the cone, so is 4 m above the center of mass. The work required to lift the mass from its center to a height of 4 m above its center is ...

  W = Fd = (9.8 m/s²)(3.3510×10^4 kg)(4 m) = 1.3136×10^6 J

As the water level in the conical tank decreases, the remaining volume occupies a space that is similar to the entire cone. The scale factor is the ratio of water depth to the height of the tank: (y/8). The remaining volume is the total volume multiplied by the cube of the scale factor.

  V(y) = (32π/3)(y/8)³

The differential volume at height y is the derivative of this:

  dV = π/16y²

The work done to raise this volume of water to a height of 10 m is ...

  (9.8 m/s²)(1000 kg/m³)(dV)((10 -y) m) = 612.5π(y²)(10 -y) J

The total work done is the integral over all heights:

  [tex]\displaystyle W=612.5\pi\int_0^8{(10y^2-y^3)}\,dy=\left.612.5\pi y^3\left(\dfrac{10}{3}-\dfrac{y}{4}\right)\right|_0^8\\\\W=612.5\pi\dfrac{2048}{3}\approx\boxed{1.3136\times10^6\quad\text{joules}}[/tex]

It takes about 1.31 MJ of work to empty the tank.

The 8 cm circle radius and the location of the circle X gives the following values;

(a) tan(<XAB) = -(r - 8)/(2•r + 4) = (8 - r)/8

Which gives;

(b) <XAB is approximately 0.644 radians

(c) The area of the shaded region is approximately 3.107 cm²

8 × (8 - r) = 0.5 × 16 × (8 + r) × sin(A)

(8 - r) = (8 + r) × sin(A)

sin(A) = (8 - r)÷(8 + r)

(8 - r)² = 8² + (8 + r)² - 2×8×(8 + r)×cos(A)

16×(8 + r)×cos(A) = (8² + (8 + r)²) - (8 - r)²

Which gives;

cos(A) = ((8² + (8 + r)²) - (8 - r)²) ÷ (16×(8 + r))

cos(A) = (2•r + 4)/(r + 8)

tan(A) = ((8 - r)÷(8 + r))/( (2•r + 4)/(r + 8))

tan(A) = -(r - 8)/(2•r + 4) = (8 - r)/8

(8 - r)/(2•r + 4) = (8 - r)/8

8 = 2•r + 4

2•r + 4 = 8

Therefore;

(b) sin(A) = (8 - r)÷(8 + r)

sin(A) = (8 - 2)÷(8 + 2) = 0.6

Therefore;

<XAB = <A = arcsin(0.6) ≈ 0.644 rad

<XAB in degrees ≈ 36.87°

Angle at sector PXQ = 180° - 2 × (36.87°) ≈ 106.26°

Area of sector PXQ ≈ (106.26°/(360°)) × π × 2²

(106.26°/(360°)) × π × 2² ≈ 3.71

Area of sector APO ≈ (36.87°/(360°)) × π × 8² ≈ 20.59

Area of triangle AXB = 8 × (8-2) = 48

The shaded area is therefore;

48 - (2×20.59 + 3.71) ≈ 3.107

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a) The radius of the small circle is 2 centimeters.

b) The measure of the angle XAB is approximately equal to 51.340°.

c) The area of the shaded region is approximately equal to 2.423 square centimeters.

In this question we must analyze a geometrical system formed by three semicircles and a circle. The small circle touches the two side semicircles tangentially at points P and Q and the uppermost section of it also tangent to the central semicircle (point R).

(a) Therefore, we have to solve the following system of equations:

8² + h² = (8 + r)²      (1)

h + r = 8      (2)

By (2) in (1):

8² + (8 - r)² = (8 + r)²

32 · r = 64

r = 2

The radius of the small circle is 2 centimeters.

(b) The measure of the angle XAB is found by trigonometric functions:

tan m ∠ XAB = OX / AO

tan m ∠ XAB = 10 / 8

m ∠ XAB ≈ 51.340°

The measure of the angle XAB is approximately equal to 51.340°.

(c) The area of the shaded region if the area of the triangle AXB minus the areas of the three circular sections, that is:

A = 0.5 · (16 cm) · (10 cm) · sin 51.340° - (51.340° / 180°) · π · (8 cm)² - 0.5 · (77.320° / 180°) · π · (2 cm)²

A ≈ 2.423 cm²

The area of the shaded region is approximately equal to 2.423 square centimeters.

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Answer:

1/15 of the dishes on the menu are vegetarian pasta.

Step-by-step explanation:

1/10 of 2/3 of all dishes are vegetarian pasta.

1/10 of 2/3 of all = 1/10 * 2/3 * 1 = 2/30 = 1/15

Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.

Given that;

Hence 6 gems are gotten every  120sec and 30 seconds

Hence 6 gems are gotten every  150seconds

Next we convert 1 hour to seconds

1 hour = ( 60 × 60 × 1 )sec = 3600sec

Now,

6 gems can be gotten every  150seconds

x gems can be gotten every 3600 seconds

x = ( 6 × 3600 ) / 150

x = 21600 / 150

x = 144 gems

Given that one can get 6 gems every 2 minutes and 30 seconds, one will have 144 gems after one hours.

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The value of given trigonometric value cos(22. 5°) is 0.387.

According to the statement

we have given that the trigonometric value and we have to find the exact value of that given value with the help of the half angle formula.

So, For this purpose, we know that the

The half angle formulas are used to find the exact values of the trigonometric ratios of the angles like 22.5°.

So,

The given value is :

cos(22. 5°)

Then the value of cos half angle formula is

[tex]cos (theta/2) = +- sqrt((1-cos theta) / 2)[/tex]

then

The value of θ/2 is 22.5 degree.

And θ is 22.5*2

θ = 45 degree

and cos 45 degree is 1/squareroot 2

And by this the value of given value become is

[tex]cos 22.5 = +\sqrt{((\sqrt{2} -1)/(2 \sqrt{2} )) } = + 0.3827[/tex]

So, The value of given trigonometric value cos(22. 5°) is 0.387.

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The magnitude of the larger earthquake is about 1.3 greater than the magnitude of the smaller earthquake.

In physics, significance is defined actually as “distance or quantity.” It depicts the absolute or relative course or size wherein an object moves within the sense of motion. it's miles used to express the scale or scope of something. In physics, importance normally refers to distance or quantity.

Magnitude is described as big in size or very vital. An example of value is the depth of the Grand Canyon. An instance of importance is the dimensions of the trouble of world hunger. (geology) A measure of the amount of energy launched by using an earthquake, as indicated on the Richter scale.

The magnitude is more than a few that characterizes the relative size of an earthquake. value is primarily based on the measurement of the maximum movement recorded with the aid of a seismograph.

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The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

I’m going to assume that your values are in the form of:

(r,θ,z)=(4,6π,2π/3)

where

(r,θ)are the polar coordinates of the point’s projection in the xy-plane

z is the usual z-coordinate in the Cartesian coordinate system

Now solving for Cartesian coordinates:

x=rcosθ=4cos(6π)=4(0.86)=3.44

y=rsinθ=4sin(6π)=2

Now for spherical transformation, note that:

(ρ,θ,ϕ)

ρ is the distance between P and the origin

θ is the same angle used to describe the location in cylindrical coordinates

ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π

OK, now that we have that out of the way, let’s compute:

ρ=r2+z2 = 5

θ=θ=6π

ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

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Answer:

Step-by-step explanation:

A chord is a straight line that connects two points on a curve. An arrangement of three or more notes that blend harmoniously when played together.

A section of a circle has both endpoints on the circle. Chords are the sections of a circle.

Therefore, the final answer is "chords".

I hope this helps, let me know if you have any questions.

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Answer:

  i) 441π cm² ≈ 1385.4 cm²

  ii) 196π cm² ≈ 615.8 cm²

Step-by-step explanation:

The areas of circles with radius 21 cm or diameter 28 cm can be found using the appropriate area formula.

The formula for the area of a circle based on its radius is ...

  A = πr²

When the radius is 21 cm, the area is ...

  A = π(21 cm)² = 441π cm² ≈ 1385.4 cm²

The formula for the area of a circle based on its diameter is ...

  A = (π/4)d²

When the diameter is 28 cm, the area is ...

  A = (π/4)(28 cm)² = 196π cm² ≈ 615.8 cm²

Answer:

Before multiplying by pi. 441π cm²

After multiplying by pi. 1384.74 cm²

Step-by-step explanation:

The formula for area of a circle is πr².

r=radius

Square the radius.

21²=441

If they want the answer in this form: 441π cm². If not, then use 3.14 for π.

441*3.14=1384.74

The answer is 1384.74 cm².

Hope this helps!

Mya would have both lessons on the same day again on the 12th day.

In order to determine when they would have the both lessons on the same day, the common multiple of 6 and 4 has to be determined. A multiple of a number is the product of an integer and that number. A common multiple is the multiple that is common to two or more numbers.

Multiple of 6 = 6, 12, 28, 24, 30, 36,

Multiple of 4 = 4, 8, 12, 16, 20, 24, 28

Common multiple = 12

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The points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).

Given:

f(x) = -0.5x+2

g(x) = x³ - 5x² + 3

The point of intersection exists the point where f(x) = g(x)

x³ - 5x² + 3 = - 0.5x + 2

x³ - 5x² + 3 + 0.5x - 2 = 0

x³ - 5x² + 0.5x + 1 = 0

Factorize and estimate the value of x

Let x = 0.53 and 4.85

substitute the value of x = 0.53

f(0.53) = -0.5(0.53) + 2

f(0.53) = -0.265 + 2

f(0.53) = 1.375

If x = 4.85

f(4.85) = -0.5(4.85) + 2

f(4.85) = -2.425 + 2

f(4.85) = -0.245

Therefore, the points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).

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Answer:

Step-by-step explanation:

Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.

AB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon

∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon

ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence

FB ≅ BD ≅ DF . . . . CPCTC

ΔBDF is equilateral . . . . definition of equilateral triangle

Jane lost 5 points in the game.

Given that, Jane gained 25 points in the first round of a game. In the second round, she lost 40 points and in the third round, she gained 10 points.

We need to write and evaluate an expression to find how many points Jane gained or lost.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Now, for the given situation we can write an expression as follows:

25 – 40 + 10

=25 + 10 + ( -40 )

=35 -40= -5

Therefore, Jane lost 5 points in the game.

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There are 8855 ways in which a 4-member committee be formed from 23 members

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The number of ways that a 4-member committee be formed from 23 members is:

Number of ways = 23! / [(23 - 4)!4!] = 8855 ways

There are 8855 ways in which a 4-member committee be formed from 23 members

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Answer:

The answer is 212,520.

Step-by-step explanation:

This is a permutation, not a combination. So, we need to follow the formula

[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]

Plug in the numbers and solve:

[tex]nP_{r}= \frac{23!}{(23-4)!}[/tex]

[tex]nP_{r}= \frac{23!}{19!}\\[/tex]

[tex]nP_{r}= \frac{25,852,016,738,884,976,640,000}{121,645,100,408,832,000}[/tex]

[tex]nP_{r}= 212,520[/tex]

Because 212,520 is an answer choice, this is the correct answer.

Let's try solving the problem using the order of operations method, otherwise known as PEMDAS.

[tex]\begin{tabular}{c | l}Order of Operation & Required Operation \\\cline{1-2}1 & Parentheses () \\2 & Exponents e^{x} \\3 & Multiplication \times \\4 & Division \div \\5 & Addition + \\6 & Subtraction -\end{tabular}[/tex]

We are given this question :

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 7 \times .8}[/tex]

Since there are no parentheses or exponents, let's multiply.

[tex]\mathrm {\frac{7}{4} - 9 \div .08 + \frac{4}{5} - 5.6}[/tex]

The next step is to divide.

[tex]\mathrm {\frac{7}{4} - 112.5 + \frac{4}{5} - 5.6}[/tex]

After that, add.

[tex]\mathrm {\frac{7}{4} - 112.5 + 0.8 - 5.6}[/tex]

[tex]\mathrm {\frac{7}{4} - 111.7 - 5.6}[/tex]

Finally, subtract the remaining terms.

[tex]\mathrm {1.75 - 111.7 - 5.6}[/tex]

[tex]\mathrm {-109.95 - 5.6}[/tex]

[tex]\mathrm {-115.55}[/tex]

The final answer is -115.55.

I hope this helped solve the problem.

Good luck on your studies!

Answer:

-115.55

Step-by-step explanation:

7/4 -9÷ .08 + 4/5 -7 * .8

I would change fractions to decimals

1.75 - 9 ÷ .08  +.8 -7 * .8

Now using pemdas, multiply and divide from left to right

1.75 -112.5 +.8 -7 * .8

1.75 -112.5 +.8 -5.6

Now add and subtract from left to right

-110.75+.8 -5.6

-109.95-5.6

-115.55

Answer: 3.2

Step-by-step explanation: 3.2 is the answer because the number 7 is higher than 5. so the number 1 goes up by one, which that equals 3.2

Answer:

x^2-3/3x

Step-by-step explanation:

=x*x-1*3/3*x

=x^2-3/3x

Based on the given tast content; the ratio of green cars to white cars is 1 : 2 and it can be said that there are twice as many white cars as green cars.

Ratio of green cars to white cars = 24 : 48

= 24 / 48

= 1 / 2

Ratio of green cars to white cars = 1 : 2

Therefore, the ratio of green cars to white cars is 1 : 2 and it can be said that there are twice as many white cars as green cars

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The integer value of the given integers is 20.

According to the statement

we have given that the some integers values like a = 3, b = 2, c = 10 and we have to find the intresult = c *b it means integer result = c *b

So, For this purpose we know that the

An integer is a whole number (not a fractional number) that can be positive, negative, or zero.

And here integer a = 3 and b = 2 and c = 10 and we have to find the value of c *b then

intresult = c *b

Substitute the values in it then

intresult = 10 *2

intresult = 20.

So, the intresults is 20 from the given numbers.

Hence, The integer value of the given integers is 20.

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The line that is not another name for Q is RL

For a line to represent the point Q, the following must be true:

Using the above highlights,

Hence, the line that is not another name for Q is RL

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From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

By critically observing the table (see attachment), we can logically deduce that relationship between the amount of ink and the size of the sign is modeled by this function:

f(x) = x²

From the table, the domain are all real numbers and they can be substituted for x to return a valid f(x) value:

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Steps for Factoring:

1) Find CM (common factor) for the expression: 3

   Factor out 3 =>

   [tex]3(6x^{2}+13x-5)[/tex]

2)Factor the above expression by grouping:

  The expression needs to be written as [tex]6x^{2} + ax+ bx -5[/tex]

 a and b should add up to 13 and multiply up to -30 (6 × -5)

By Guess & Check we find that the pair is a = -2 and b = 15 (-2+15; -2 × 15)

3) Now we can rewrite [tex](6x^{2}+13x-5)[/tex] as [tex](6x^{2} -2x)+(15x-5)\\[/tex]

Factor out 2x in the first group and 5 in the second group:

[tex]2x(3x-1)+5(3x-1)\\[/tex]

As 3x-1 is on both sides, now we can do the operation: 2x+5 (distributive property)

(3x-1) (2x+5)

The answer is 3(3x-1) (2x+5)

Hope it helps!

The area of the grass that will be watered is given by  800/9 pi ft^2.

What is the area of a circle?

The area of a circle of radius r is given by:

A = πr²

In this problem, a rotating sprinkler head sprays water as far as 20 feet, hence the radius is of r = 20 ft.

It covers a central angle of 80º, while an entire circle has 360º, hence the area of grass that will be watered corresponds to 80/360 = 2/9 of the area of the circle.

Hence the watered area in ft² is given by-

A = 2/9 π × (20)²

   = 800π/ 9

Therefore, the area of the grass that will be watered is given by  800/9 pi ft^2.

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