Please answer maths problem 100 up for grabs

There is no stationary point at x = 2. The nature of the curve at x = 2 cannot be determined since there is no stationary point.

To verify that the curve has a stationary point at x = 2, we need to find the derivative of the equation and set it equal to zero.

Given the equation:

y = 2x + 1/(x-1)²

Let's find the derivative dy/dx:

dy/dx = d/dx [2x + 1/(x-1)²]

To find the derivative, we can use the power rule and the chain rule. Let's differentiate each term separately:

For the first term, 2x, the derivative is 2.

For the second term, 1/(x-1)², we can rewrite it as (x-1)^(-2) to apply the power rule. The derivative is then:

d/dx [(x-1)^(-2)] = -2(x-1)^(-3) * d/dx (x-1)

Using the chain rule, d/dx (x-1) = 1, so the derivative becomes:

-2(x-1)^(-3) * 1 = -2/(x-1)^3

Now, let's set dy/dx equal to zero and solve for x:

-2/(x-1)^3 = 0

This equation is satisfied when the numerator is equal to zero:

-2 = 0

However, -2 is not equal to zero, which means there is no x value that makes dy/dx equal to zero.

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Step-by-step explanation:

14 out of 20 were full in the experiment   14/20 = 7/10 chance that the next one will be full too.

Answer:

28.2 cm

Step-by-step explanation:

Circumference of circle = 2π r

Value of π = 3.14

Putting the required values,

Circumference = 2 × 3.14 × 4.5

= 6.28 × 4.5

= 28.2

Hence the circumference of the circle is 28.2 cm

Hello !

2(5 - 2 * 3 - 4)​

= 2(5 - 6 - 4)

= 2 * (-5)

= -10

The cosine of the angle θ in the circle s -12/13

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

The unit circle

Where we have

(x, y) = (-12/13, -5/13)

In a unit circle, we have

(cos θ, sin θ) = (x, y)

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

cos θ = -12/13

Hence, the cosine of the angle θ is -12/13

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Answer:

Step-by-step explanation:

You want to identify the graphs that go with each of these functions, along with a particular point on the curve.

The equations are written here in standard form, factored form, and vertex form. (The "factored form" is sometimes called "intercept form.") Each of these forms can be analyzed for characteristics relevant to identifying the corresponding graph.

In general, we can readily identify the opening direction, based on the sign of the leading coefficient. Depending on the form, we can also identify zeros, the vertex, and the y-intercept.

The line of symmetry (x-coordinate of the vertex) of the equation in the form ax² +bx +c is x = -b/(2a). That is, it will be left of the y-axis when the coefficients 'a' and 'b' have the same sign.

The graph of equation A will be graph 4, the only one with its vertex left of the y-axis. The y-intercept is the constant: point S = (0, 9).

Equation B has a positive leading coefficient, so opens upward. The zeros of the factors are -3 and +9, so identify the places where the graph crosses the x-axis. Graph 3 is the only one that opens upward and has x-intercepts. Point R is (9, 0).

The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k); leading coefficient 'a'

Equation C has its vertex at (h, k) = (3, 9) and opens upward (a>0). Graph 1 is the only one matching those characteristics. Point P is the vertex, so point P is (3, 9).

Equation D is the same as equation B, but with a negative leading coefficient. That is, it opens downward and crosses the x-axis in two places, at x = -3 and x = 9. Graph 2 is matches this description. The left zero is point Q, (-3, 0).

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its:

[tex]\pi \times {r}^{2} \times h[/tex]

The ordered pairs on the graph with the given equation will be of the form (x, 2).

Given a linear equation,

-4y = -8

We have to find the ordered pairs on the given graph.

Dividing both sides of the equation by -4,

y = 2

So for any point on the line, the y coordinate will be 2.

So any general point on the graph will be of the form, (x, 2).

Graph is a line parallel to the X axis.

Hence the orderd pairs are of the form (x, 2).

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Answer:

The given function f(x) = alxl is not a valid absolute value function because the absolute value symbol is represented by two vertical bars (|) and not the letter "l". Additionally, the point (3,-4) cannot be on the graph of an absolute value function because the output of an absolute value function is always non-negative.

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Answer:

  x = 1, 12

Step-by-step explanation:

You want the solutions to y = x² -13x +12 when y = 0, using the quadratic formula.

The quadratic formula gives the solutions to ...

  ax² +bx +c = 0

as ...

  [tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Your equation has a = 1, b = -13, c = 12, so the solutions are ...

  [tex]x = \dfrac{-(-13)\pm\sqrt{(-13)^2-4(1)(12)}}{2(1)}=\dfrac{13\pm\sqrt{169-48}}{2}\\\\\\x=\dfrac{13\pm11}{2}\\\\\boxed{x=\{12,1\}}[/tex]

This answer is correct because we used and evaluated the formula correctly. There are several ways to check the answer is correct.

A graph of the equation is attached. It shows the x-intercepts (zeros) to be x = 1 and x = 12.

When the equation is factored, it looks like ...

  y = (x -12)(x -1)

The zeros are the values of x that make the factors zero: 12 and 1.

The equation can be rewritten to simplify evaluating it:

  y = (x -13)x +12

For x = 1, y = (1 -13)(1) +12 = -12 +12 = 0.

For x = 12, y = (12 -13)(12) +12 = -12 +12 = 0.

The values x = 1 and x = 12 are zeros of the function.

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The acceleration of the runner is 0.2 m/s².

We can use the following equation to get the runner's acceleration:

Acceleration (a) = (Final Velocity - Initial Velocity) / Time

In this case, the initial velocity (u) is 0 m/s, the final velocity (v) can be calculated using the formula:

v = s / t

where t is the amount of time spent and s is the distance travelled.

The time taken (t) and the distance travelled (s) are both provided as 500 m.

Calculate the b (v):

v = 500 m / 50 s

v = 10 m/s

Plug into the formula for acceleration:

a = (10 m/s - 0 m/s) / 50 s

a = 10 m/s / 50 s

a = 0.2 m/s²

Therefore, the acceleration of the runner is 0.2 m/s².

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Answer:

36 hours

Step-by-step explanation:

1 person will be larger than 12 hours certainly

therefore 12*3 = 36

Answer:

36 hours

Step-by-step explanation:

P. : h

3. : 12

1. : ?

3÷1=3

12×3=36 times by 3 because if there are less people painting the room it's going to take more time

so it's takes 1 person 36 hours to paint the room

It will cost approximately $16 per person if 95 people rent the bus.

The price per person of renting a bus varies inversely with the number of people renting the bus. This means that as the number of people increases, the price per person decreases, and vice versa.

Given that it costs $20 per person when 76 people rent the bus, we can use this information to find the constant of variation (k) in the inverse variation equation. Let's denote the number of people as "n" and the cost per person as "c":

c = k/n

We can substitute the values into the equation to solve for k:

20 = k/76

Multiplying both sides by 76 gives:

k = 20 × 76 = 1520

Now, we can determine the cost per person when 95 people rent the bus by plugging the values into the equation:

c = 1520/95 ≈ 16.00

Therefore, it will cost approximately $16 per person if 95 people rent the bus.

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To find out what percentage 25 is of 500, you can use the following formula:

percentage = (part / whole) x 100

In this case, 25 is the part and 500 is the whole. So, we can substitute these values into the formula:

percentage = (25 / 500) x 100

Simplifying the equation:

percentage = 0.05 x 100

percentage = 5%

Therefore, 25 is 5% of 500.

I hope it helps!

Answer:

5 % of 500 is 25

Step-by-step explanation:

500 * x% = 25

Divide each side by 500

x% = 25/500

x% = .05

Change to percent

x = 5

5 % of 500 is 25

The cardinal number for the given set. A {20, 22, 24, 26, 34} sees; The given set has a cardinal number of 5.

This is further explained below.

Generally, cardinal numbers are an extension of the natural numbers that are used to assess the cardinality of sets. Cardinals are often referred to by their shorter form, cardinals. A finite set has a cardinality that is equal to a natural number, which is the number of items that are included inside the set.

A set of counting numbers is called its cardinal number. There is speculation that they are cardinals as well. Cardinal numbers are whole, non-fractional numerals, beginning with 1 and continuing in numerical order. Cardinal numbers include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

To conclude it, The provided set A equals {20, 22, 24, 26, 34}

The number of unique components that make up a set is referred to as the cardinal number.

The given set has a cardinal number of 5, which is denoted by the notation n(A).

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Answer: The cardinal number for the given set is 5

Step-by-step explanation:

The cardinal number for a set is the quantity, or how many numbers are in the set. Since Set A has these numbers {20, 22, 24, 26, 34}, you can easily indicate how many numbers are in there. The n(a) quantity in the set would be the number five.

Since there is five numbers in this set, therefore, the cardinal number for the given set would be simply 5.

Answer: 8.5

Step-by-step explanation: 45-45-90 triangle will always have the same length of legs. The hypotenuse will be the leg length times √2

a^2+b^2=c^2

A and B are the same.

6^2+6^2=6√2✅

6√2=8.5✅

Answer:

average=9 hours

Step-by-step explanation:

10hours on Friday

12 hours on Saturday

300 mins to hours= 300÷60=5

5 hours on Sunday

average=10+12+5

average=27

average=27÷3

average=9 hours

Answer:

Step-by-step explanation:

The Axiom of Pairing in mathematics states that for any two sets, there exists a set that contains exactly those two sets as its only elements. In other words, given sets A and B, there exists a set {A, B} whose only elements are A and B.

For example, consider the sets A = {1, 2} and B = {3, 4}. According to the Axiom of Pairing, there exists a set that contains exactly these two sets as its only elements. We can form such a set as {A, B} = {{1, 2}, {3, 4}}, where A and B are the elements of the set. Thus, {A, B} is a set that satisfies the Axiom of Pairing.

The proposition X^2 > 0 for every real number x is true.

We are given that;

The equation x^2 > 0

Now,

The square of any real number is always greater than or equal to zero.

An example of a mathematical proposition is “For all real numbers x, x + 1 = 2.” This is a proposition because it makes a claim about all real numbers x.

Therefore, by the given function X^2 > 0 the answer will be true.

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Step-by-step explanation:

To determine whether a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the three sides of the given triangle as a = 23, b = 30, and c = 19. We can check if these side lengths satisfy the Pythagorean theorem as follows:

c^2 = a^2 + b^2

19^2 = 23^2 + 30^2

361 = 529 + 900

Since 361 is not equal to 529 + 900, we can see that the given triangle is not a right triangle.

Using cosine addition formula, the value of cos(a + b) is -16/25

Using cosine addition formula, the exact value of cos (a + b) is calculated as;

cos(a + b) = cos a × cos b - sin a × sin b

Our given data;

cos a = 4/5,  0 < a < π/2

cos b = 5/13, -π/2 < b < 0

Using Pythagorean identity;

sin a and sin b;

sin² x + cos² x = 1

To solve for a;

sin a = √(1 - cos² a) = √(1 - (4/5)²) = √(1 - 16/25) = √(9/25) = 3/5

Solving for b;

sin b = √(1 - cos² b) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13

Substituting the values into cosine addition formula

cos(a + b) = (4/5) * (5/13) - (3/5) * (12/13)

cos(a + b) = (20/65) - (36/65)

cos(a + b) = -16/65

Therefore, the exact value of cos(a + b) is -16/65.

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so we have a point at -2-i or -2 - 1i, that means that both "x" and "y" are negative, the only occurs in the III Quadrant, so hmmm let's find the modulus and angle θ

[tex]\stackrel{a}{-2}\stackrel{b}{-1i}\hspace{5em} \begin{cases} r=\sqrt{(-2)^2 + (-1)^2}\\ \qquad \sqrt{5}\\ \theta =tan^{-1}\left( \frac{-1}{-2} \right)\\[1em] \qquad \approx 206.57^o \end{cases} \\\\\\ \stackrel{\textit{let's keep in mind that}}{\sqrt[3]{\sqrt{5}}\implies \left( 5^{\frac{1}{2}} \right)^{\frac{1}{3}}}\implies 5^{\frac{1}{6}}\implies \sqrt[6]{5} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\boxed{k=0}\hspace{5em} \sqrt[ 3 ]{\sqrt{5}} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o }{3} \right) +i \sin\left( \cfrac{ 206.57^o }{3} \right)\right] \\\\\\ \sqrt[6]{5}\left[ \cos(68.86^o) +i \sin(68.86^o)\right] ~~ \approx ~~ 0.47~~ + ~~1.22i \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=1}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 566.57^o }{3} \right) +i \sin\left( \cfrac{ 566.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(188.86^o) +i \sin(188.86^o)\right] ~~ \approx ~~ -1.29~~ - ~~0.20i \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=2}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 926.57^o }{3} \right) +i \sin\left( \cfrac{ 926.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(308.86^o) +i \sin(308.86^o)\right] ~~ \approx ~~ 0.82~~ - ~~1.02i[/tex]

just a quick clarification, notice that if we get the inverse tangent of (-1 / -2) the angle we get will be in the range of ±π/2, that's because that is the range inverse tangent is restricted to, however, our terminal point on the complex plane is on the III Quadrant, not the 1st one, so we use the reference angle on the III Quadrant, and that is about 206.57°.

The standard deviation is around 1.06, and there are on average 2 frogs having the feature.

Given that the trait is usually found in 1 out of every 8 frogs, the probability of a frog having the trait is p = 1/8. Therefore, the probability of a frog not having the trait is q = 1 - p = 7/8.

(a) To find the probability of not finding any frogs with the trait, we calculate the probability of a frog not having the trait and raise it to the power of the number of trials:

P(X = 0) = (7/8)¹⁶ ≈ 0.0747

(b) To find the probability of finding at least 1 frog with the trait, we subtract the probability of finding none from 1:

P(X ≥ 1) = 1 - P(X = 0) ≈ 1 - 0.0747 ≈ 0.9253

(c) The mean (μ) and standard deviation (σ) of the number of frogs with the trait can be calculated using the formulas:

μ = np

σ = √(npq)

For this case, n = 16, p = 1/8, and q = 7/8:

μ = 16 * (1/8) = 2

σ = √(16 * (1/8) * (7/8)) ≈ 1.06

Therefore, the mean number of frogs with the trait is 2, and the standard deviation is approximately 1.06.

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The meaning of the number 30,500 is given as follows:

The maximum altitude of the airplane.

The coordinates of the vertex are (h,k), meaning that:

Considering a leading coefficient a, the quadratic function is given as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

The function for this problem is given as follows:

y = -16(t - 12)² + 30500.

The coordinates of the vertex are given as follows:

(12, 30500).

The leading coefficient is negative, hence the meaning of the vertex is given as follows:

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Answer:

Step-by-step explanation:

sin 325=sin (360-35)=-sin 35=-t

cos 325=cos (360-35)=cos  35=√(1-sin²35)=√(1-t²)

tan 215=tan (180+35)=tan 35

[tex]=\frac{sin~35}{cos~35} \\=\frac{-t}{\sqrt{1-t^2} }[/tex]

Answer:

Shorter leg is 6

Step-by-step explanation:

In a 30°-60°-90° triangle, the hypotenuse is twice the length of the shorter leg. Therefore, if the hypotenuse is 12, then the shorter leg is 6.

Answer:

12% more than 72 is

80.64

Step-by-step explanation: