The wind broke a 24 metres high tree. The top of this tree touches the ground. At what height did the tree break if the broken part makes an angle of 30° with the ground?​

The given surface is [tex]\cos(xy) = e^z-2[/tex]. The unit vector normal to this surface at the point (1, π, 0) is[tex]\vec{n}=\langle 0, 0, 1\rangle[/tex].

A vector with a magnitude of one is termed a unit vector. To determine a unit normal vector for the given surface, start by describing the surface as a function of form F(x, y, z). Next, calculate this function's gradient and then normalize the outcomes.

Consider the normal vector [tex]\vec{n}=\langle a, b, c\rangle[/tex]  to the plane ax + by + cz = d. Given [tex]\cos(xy) = e^z-2[/tex] then, z = ln(2+cos(xy)).

At point (x₀,y₀,z₀), the equation for the tangent plane to z = f(x,y) is written as, [tex]z-z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)[/tex]. The value of [tex]f_x[/tex] and [tex]f_y[/tex] are

[tex]f_x = \frac{-y \sin(xy)}{(2+\cos(xy))}[/tex] and [tex]f_y =\frac{ -x \sin(xy) }{ (2+\cos(xy))}[/tex].

At *x, y) = (1, π), the value of [tex]f_x[/tex] and [tex]f_y[/tex] is zero. Then, the equation of the tangent plane is given as z-0=0+0 ⇒ z=0.

Then, the resulting unit normal vector is [tex]\vec{n}=\langle 0, 0, 1\rangle[/tex].

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On solving the the provided question we can say that -  in the equation we have 12a - 3b = 84 - 30 = 54

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here, we have

a = 7 and b = 10

so, 12a - 3b

84 - 30 = 54

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Answer:

P is equal to or greater than 27  

(c)

Step-by-step explanation:

The orthocenter for an obtuse triangle is always outside the circumcircle in which the obtuse triangle is drawn.

In geometry, each triangle has a few highly significant points that go along with it. One such point is the triangle's orthocenter, which is identified as the location where the triangle's altitudes cross.

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The orthocenter for an obtuse triangle is always outside the circumcircle in which the obtuse triangle is drawn.

In geometry, each triangle has a few highly significant points that go along with it. One such point is the triangle's orthocenter, which is identified as the location where the triangle's altitudes cross.

An altitude of a triangle is a line segment that extends perpendicularly from one of its vertices to the side opposite that vertex. A triangle with an angle larger than 90° is said to have an obtuse angle. The heights of the vertices of the acute angles of an obtuse triangle reside outside of the triangle due to the way the triangle is constructed.

The orthocenter, or the location where the three elevations intersect, must therefore be outside of the circumcircle in which the triangle is inscribed.

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The complete question is as follows:

Is the orthocenter for an obtuse triangle always outside the circumcircle which the obtuse triangle is drawn in?

x/12 > 10 is the inequality that describes the problem. This inequality represents the fact that Turner made more than 10 fluid ounces of apple cider, and that he divided that amount evenly among 12 mugs.

Algebra is a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations. The idea that there is such a separate branch of mathematics, as well as the term algebra to identify it, came about gradually through time. This article traces the development of the equation notion, number systems, symbols for representing and modifying mathematical claims, and the contemporary abstract structural perspective of algebra.

The order in which you perform operations in arithmetic and algebra is governed by a number of laws. The Commutative, Associative, and Distributive Laws are the three that receive the most attention.

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In this case, the proportion (79%) only applies to the sample of 481 consumers and thus it is a statistic because it represents the sample.

The distinction between a parameter and a statistic is that a parameter refers to a sample property, but a statistic is referred to as a population distribution characteristic.

For instance, a population mean is a parameter, but a sample mean is a statistic.

Although we can use it to draw conclusions about the population, in this case, the proportion (79%) only applies to the sample of 481 consumers and is thus only a statistic.

Therefore, This percentage is a statistic because it represents the sample.

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The number of points in a large outer ring and a smaller bull's-eye are 18 points and 84 points respectively.

In order to write a system of equations that model this situation, we would assign variables to the large outer ring and the smaller bull's-eye respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into algebraic equation as follows for both Megan and Paula:

3x + 4y = 390

4x + 5y = 492

In this scenario, we would use an online graphing calculator to plot and solve the above system of equations graphically, with a point of intersection at (18, 84) as shown in the image attached below.

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Answer:

a.x²+4x+4

=x²+2x+2x+4

=X(X+2)+2(X+2)

=(X+2)(X+2)

=(X+2)²

b.x²-12x+27

=x²-9x-3x+27

=X(x-9)-3(x-9)

=(x-9)(x-3)

c.x²-x-42

=x²-7x+6x-42

=X(x-7)+6(x-7)

=(X+6)(x-7)

d.x²+8x-9

=x²+9x-x-9

=X(X+9)-1(X+9)

=(x-1)(X+9)

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T3(x) = x - x^2/2 + x^3/6.

The Taylor polynomial of degree 3 for the function f(x) = x + e^-x centered at a = 0 is given by:

T3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3

= 1 + (-1 + 1)x + (e^-0 - (-1)(-1)e^-0)x^2/2! + (0 + (-1)(-1)(-1)e^-0)x^3/3!

= x - x^2/2 + x^3/6

So T3(x) = x - x^2/2 + x^3/6.

An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics.

The nth Taylor polynomial of the function is a polynomial of degree n that is created by the partial sum of the first n + 1 terms of a Taylor series. Approximations of a function made by Taylor polynomials get generally better as n rises. Quantitative estimates of the mistake brought about by the use of such approximations are provided by Taylor's theorem. If a function's Taylor series is converging, its total is the upper bound of the Taylor polynomials' infinite sequence. A function's Taylor series sum may not match.

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Answer:

In isosceles triangle two sides are equal,

So,

3x-1=2x+2

x=3

Perimeter=sum of all sides

=3x-1+2x+2+2x

=7x+1

Substituting value of x

Perimeter=7(3)+1

=21+1

=22

Thus x=3

:. Perimeter of a triangle=22 square units

The absolute value graph shifted to the right 5 units is

Transformation is a term used in mathematics to refer to the movements made by objects.

Translation refers to a type of transformation that involve a linear movement.

Translation has to do with the following movements

The up and down movements are on the vertical direction controlled by the y coordinate.

While the left and right movements are on the horizontal direction controlled by the x coordinate.

The movement represented by the absolute value equation  |x - 5| is is translation 5 units right

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|

The missing lengths of the sides  a = 3 inches  , b =  3√3 inches  .

90 -60 -30 triangle .

We have given 90 -60 -30 triangle with hypotenuses = 6 in.

By the 90 -60 -30 triangle rule  :  The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle and the length of the longer leg is 3√ times the length of the shorter leg.

Then Shorter leg = a longer leg = b.

Hypotenuse = 2 * Shorter leg .

Plug the values.

6 =  2 *  Shorter leg .

On dividing both sides by 2

Shorter leg (a)  = 3 inches .

Then by the rule :  longer leg is 3√ times the length of the shorter leg.

Longer leg =  3√Shorter .

Longer leg (b)  =  3√3 inches  .

Therefore, a = 3 inches  , b =  3√3 inches  .

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The probability of getting exactly 8 girls out of 11 births is 21.9%.

The binomial probability formula is used to calculate the probability of getting a certain number of successes (in this case, girls) out of a fixed number of trials (in this case, 11 births).

The first part of the formula (11 choose 8) is the number of ways to choose 8 girls out of 11 births, which is 330.

i.e;    (11 choose 8) * (0.5)^8 * (0.5)^3 = 330

The second part of the formula (0.5)^8 represents the probability of getting 8 girls out of 11 births assuming each birth has a probability of 0.5 of being a girl.

The third part of the formula (0.5)^3 represents the probability of getting 3 boys out of 11 births assuming each birth has a probability of 0.5 of being a boy.

i.e; (11 choose 8) * (0.5)^8 * (0.5)^3 = 330 * 0.00390625 * 0.125 = 0.21875

When we multiply all of these values together we get the final probability of getting exactly 8 girls out of 11 births, which is approximately 0.21875 or about 21.9%.

Therefore, the probability of getting exactly 8 girls out of 11 births is given by the binomial probability formula: (11 choose 8) * (0.5)^8 * (0.5)^3 = 330 * 0.00390625 * 0.125 = 0.21875 or about 21.9%.

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Answer:

Eight workers can pave a 1-mile stretch of road in 6 hours.

Step-by-step explanation:

Answer:

yes to all 3

Step-by-step explanation:

A

3z = 21 ( isolate z by dividing both sides by 3 )

z = 7

B

n + 14 = 36 ( subtract 14 from both sides )

n = 22

C

[tex]\frac{3}{4}[/tex] v = 12 ( multiply both sides by 4 to clear the fraction )

3v = 48 ( divide both sides by 3 )

v = 16

The number of distinct prime factors are 17

The term prime factors in math is defined as a method to find the prime factors of a given number and it can be said a composite number.

As per the definition of prime factor here we have know that a and b have 7 prime factors in common.

Then it can be written as a*b has 28 prime factors

And here we also know that the number of prime factors of a or b that are not common to both is 21

Here we have also know that a has less prime factors than b so at most 10 of these 21 extra prime factors belong to a

Then the  the most prime factors that  a  can have is calculated as

=> 7 + 10 = 17

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Answer:

Step-by-step explanation:

Let, f(x) = y

y = 5 + √(5x - 3)

((y - 5)² = 5x + 3

y² - 10y + 25 - 3 = 5x

x = (y² - 10y +22)/5

so, [tex]f^{-1} (y)[/tex] = (y² - 10y +22)/5

[tex]f^{-1} x[/tex] = (x² - 10x + 22)/5

Compared to a 95% confidence interval, a 99% confidence interval will be wider.

A confidence interval is a range of values that is likely to contain the true population mean, with a certain level of confidence.

The level of confidence is usually represented as a percentage, such as 95% or 99%. The higher the level of confidence, the wider the confidence interval will be. This is because a higher level of confidence means that the researcher wants to be more certain that the true population mean falls within the interval, so they will make the interval wider to increase the chances of this happening.

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Question 5

The remaining interior angle is [tex]135^{\circ}[/tex].

[tex]\frac{x}{\sin 19^{\circ}}=\frac{32}{\sin 135^{\circ}}\\ \\ x=\frac{32 \sin 19^{\circ}}{\sin 135^{\circ}} \\ \\ x \approx 14.7[/tex]

Question 6

The remaining interior angle is [tex]27^{\circ}[/tex].

[tex]\frac{x}{\sin 27^{\circ}}=\frac{28}{\sin 75^{\circ}}\\\\x=\frac{28\sin 27^{\circ}}{\sin 75^{\circ}}\\\\x \approx 13.2[/tex]

Question 7

The remaining interior angle is [tex]59^{\circ}[/tex].

[tex]\frac{x}{\sin 59^{\circ}}=\frac{9}{\sin 70^{\circ}}\\\\x=\frac{9\sin 59^{\circ}}{\sin 70^{\circ}}\\\\x \approx 8.2[/tex]

Question 8

The remaining interior angle is [tex]95^{\circ}[/tex].

[tex]\frac{x}{\sin 33^{\circ}}=\frac{16}{\sin 95^{\circ}}\\\\x=\frac{16 \sin 33^{\circ}}{\sin 95^{\circ}}\\\\x \approx 8.7[/tex]

Answer:

5. False.

Look at the graph.

Every one day, the cost jumps $30 instead of $60.

Therefore, it is false.

6. True.

Like I said, Every one day, the cost jumps $30.

So when x increases by 1, y increases by 30.

So, y = 30x is correct.

7. False.

Use the equation in the 6th question.

y = 30x.

Put x = 7.

You get y = 210, not 200.

So. it is false.

8. True

Again, same thing.

Use the equation in the 6th question.

y = 30x.

Put x = 9.

You get y = 270.

So the statement is correct.

Pls mark as brainliest for no apparent reason. Cheers

There are two solutions for equation [tex]3x^2-6x+2=0[/tex] are [tex]1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex].

and solutions are irrational solutions.

Every nth degree equation has a total of 'n' real or hypothetical roots. The polynomial [tex]f (x)[/tex] is exactly divisible by ([tex]x -a[/tex] ), which means that ([tex]x -b[/tex] ) is the factor of the provided polynomial [tex]f(x)[/tex].

The theory of equations in algebra refers to the study of algebraic equations, which are equations defined by polynomials. Any expression with one or more terms is considered to be a polynomial. Knowing when an algebraic problem has an algebraic solution was a major challenge in the theory of equations.

Here solution of equation:

[tex]3x^2-6x+2=0\\3x^2-6x+2+1-1=0\\3x^2-6x+3=1\\3(x^2-2x+1)=1\\3(x-1)^2=1\\x=1+\frac{1}{\sqrt{3}} , 1-\frac{1}{\sqrt{3}}[/tex]

So here two solutions are presented for given equation.

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Step-by-step explanation:

Suppose that his age is x.

then the opposite of his age is -x.

from the question above, the equation can be written as

[tex] - x + 43 = 27[/tex]

[tex]then \: \\ x = 16[/tex]

Answer:

(2x-7)(9x+2)

Step-by-step explanation:

Find The Least Common Multiplier of 9x+2, 2x-7

Answer:

30, 75, 105

Step-by-step explanation:

The median and the quartiles of the data-set are given as follows:

The median of a data-set is the middle value of the data-set, that is, the value of which 50% of the data-set is less than and 50% of the data-set is greater than.

The data-set is composed by 16 elements, which is an even cardinality, hence the median is the mean of the 8th and of the 9th elements, as follows:

Median = (20 + 24)/2

Median = 22.

Then the first quartile is the median of the first seven elements of the data-set, which is the fourth element, hence it is of 13.

The third quartile is the median of the last seven elements of the data-set, hence it assumes a value of 29.

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Answer: first quartile is 14 , the median is 22 , and the third quartile is 28

Step-by-step explanation:because I answered that on my homework and it worked.Take words from people who have tried it before!!!

Answer:

Step-by-step explanation:

Step-by-step explanation:

first

for washing 10 houses we get (14*10) dollars which is 140

now for washing cars ur frirnd gets (28*5) which is also 140

so u both earn the same amount

hence the answer is neither.

Answer: The function that models the relationship between the number of games played (n) and the number of credits remaining on the card (C(n)) is C(n) = 5n.

Step-by-step explanation: This function can be derived by realizing that each game costs 5 credits to play, so as the number of games played (n) increases, the number of credits remaining on the card (C(n)) decreases by 5 for each game played.

For example, if Shivani played 16 games before her card ran out of credits, we can substitute n = 16 into the function to find that C(16) = 5(16) = 80 credits. This means that her card had 80 credits on it before she started playing games.

To plot points on the graph, we can select a few different values of n and substitute them into the function to find the corresponding values of C(n). Here are a few examples:

When n = 0, C(n) = 5(0) = 0. This represents the case when Shivani has not played any games yet and has no remaining credits on her card.

When n = 8, C(n) = 5(8) = 40. This represents the case when Shivani has played 8 games and has 40 credits remaining on her card.

When n = 16, C(n) = 5(16) = 80. This represents the case when Shivani has played 16 games and her card has no remaining credits.

We can plot these points on the graph and label them (0,0), (8,40), (16,0) respectively.

Note that the y-intercept is (0,0) and the x-intercept is (16,0)

Graph:

n C(n)

0 0

8 40

16 0

The graph is a straight line starting from (0,0) and going down till (16,0) with a slope of -5.

Answer:

[tex]67^{\circ}[/tex]

Step-by-step explanation:

Angles that form a linear pair add to [tex]180^{\circ}[/tex].

Answer:

Step-by-step explanation:

Since angles x and 113° all lie on a straight line,

x + 113° = 180°   (angles on a straight line add up to 180°)

therefore,  x = 180°-113°

x = 67°