help please!
figure out the "inflection point" of the following function
f(x)=5x³ + 2x² − 3x​

Answer:

The answer is 15 minutes after 3:00

Answer:

7.65

Step-by-step explanation:

sqrt((x2-x1)^2+(y2-y1)^2)

sqrt((-4-3.5)^2+(2.5-1)^2)

sqrt(-7.52+1.5^2)

sqrt(56.25+2.25)

sqrt(58.5)

= 7.65

The ideals (x), (y), and (x, y) in q[x, y] are prime. The proof involves showing that the quotient ring q[x, y]/(x), q[x, y]/(y), and q[x, y]/(x, y) are integral domains, which indicates that the ideals are prime.

To prove that the ideals (x), (y), and (x, y) are prime in q[x, y], we consider the quotient rings q[x, y]/(x), q[x, y]/(y), and q[x, y]/(x, y).

For each quotient ring, we need to show that it is an integral domain, meaning it has no zero divisors. This can be done by verifying that any nonzero elements in the quotient rings cannot multiply to give zero.

In the case of q[x, y]/(x), any nonzero element in the form f(x, y) + (x) where f(x, y) is not divisible by x, cannot multiply with another nonzero element to give zero.

Similarly, in q[x, y]/(y) and q[x, y]/(x, y), nonzero elements in the respective forms f(x, y) + (y) and f(x, y) + (x, y) where f(x, y) is not divisible by y or (x, y) respectively, cannot multiply to give zero.

Since all three quotient rings are integral domains, the ideals (x), (y), and (x, y) are prime in q[x, y].

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Answer: When you are simplifying exponential terms raised to another exponent, the way to simplify them is to multiply the exponents together.

Step-by-step explanation:

The distance between two points is given as;

The number beneath the radical symbol is 58.

Answer:

(4,3)

Step-by-step explanation:

f(x) = a(x-h)^2 +k is the vertex form of a parabola

where (h,k) is the vertex

f(x) = (x-4)^2 +3

    yields a  vertex of (4,3)

Answer: The answer is A 4,3

Step-by-step explanation:

Answer:

24d^2 - 62d + 35

Step-by-step explanation:

To expand this expression, you can use the FOIL method, which stands for First, Outer, Inner, Last. It means that you multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add them all up.

So,

(6d - 5)(4d - 7) = 6d x 4d - 6d x 7 - 5 x 4d + 5 x 7

= 24d^2 - 42d - 20d + 35

= 24d^2 - 62d + 35

Therefore, the solution is 24d^2 - 62d + 35

Answer: \(24d^{2} -62d +35\)

Step-by-step explanation:

Expanding it you get \(24d^{2} - 42d - 20d + 35\). Simplifying you get \(24d^{2} -62d +35\).

Answer:

x = 5a + 5G

Step-by-step explanation:

x/5 - g = a

x/5 = a + g

x = 5(a+g)

x = 5a + 5G

The value of the length AG is 9.1 cm

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

The figure

The length AG is calculated as

AG² = Sum of the squares of the dimensions

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

AG² = 5² + 7² + 3²

Evaluate

AG² = 83

So, we have

AG = 9.1

Hence, the length is 9.1 cm

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Answer:

-175

Step-by-step explanation:

bc its farther than -150 from the 0

The surface area of the rectangular pyramid is 72 m^2. Answer: (B) 72 m^2.

The rectangular pyramid has a rectangular base of dimensions 4 meters by 4 meters, so the area of the base is:

A_base = length * width = 4 m * 4 m = 16 m^2

The triangular faces are isosceles triangles with base 4 meters and height 7 meters, so the area of each triangular face is:

A_tri = 0.5 * base * height = 0.5 * 4 m * 7 m = 14 m^2

There are four triangular faces, so the total area of the triangular faces is:

4 * A_tri = 4 * 14 m^2 = 56 m^2

The surface area of the pyramid is the sum of the areas of the base and the triangular faces, so:

SA = A_base + 4 * A_tri = 16 m^2 + 56 m^2 = 72 m^2

Therefore, the surface area of the pyramid is 72 m^2. Answer: (B) 72 m^2.

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Based on the ratio, Anders uses 72.73g of sugar, 145.46g of butter, and 581.84g of flour to make his scones.

Anders makes scones using the ratio 1:2:8 for sugar, butter, and flour respectively. This means that for every 1 gram of sugar, he uses 2 grams of butter and 8 grams of flour.

To find out how much of each ingredient he uses, we can use the following steps:

1. Add the ratios together: 1 + 2 + 8 = 11

2. Divide the total amount of ingredients by the sum of the ratios: 100 + 300 + 400 = 800 / 11 = 72.73

3. Multiply each ratio by the result from step 2 to find the amount of each ingredient:

Sugar: 1 x 72.73 = 72.73g

Butter: 2 x 72.73 = 145.46g

Flour: 8 x 72.73 = 581.84g

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(a)The inverse Laplace transform of F(s) = 21 / ((s + \((\sqrt(2))^4\)) is f(t) = 21\(t^3e^(-\sqrt(2)t\)).

(b) The inverse Laplace transform of F(s) = 6 / (s + 1)\(^3\) is f(t) = 3\(t^2e^-^t\).

(c) The inverse Laplace transform of F(s) = 4 / (\(s^2\) - 2s - 3) is f(t) = 2\(e^t\) - \(e^-^3^t\).

To find the inverse Laplace transform, we can use the property that the Laplace transform of \(t^n\) is n! / \(s^n^+^1\), where n is a non-negative integer. In this case, we have F(s) = 21 / ((s + \((\sqrt(2))^4\)), which is in the form of 1 / (s + a)^n, where a = \(\sqrt2\)and n = 4. Using the property, we can express F(s) in terms of t:

F(s) = 21 / ((s + \((\sqrt(2))^4\))

= 21 / (\(s^4\) + 4\(\sqrt(2)s^3\)+ 8\(s^2\) + 8\(\sqrt(2)s\) + 4)

Comparing this expression to the Laplace transform of t^3, we can determine the inverse Laplace transform:

f(t) = 21\(t^3e^-^\sqrt2t)\)

Using the same property as in the previous case, we can rewrite F(s) as:

F(s) = 6 / \((s + 1)^3\)

= 6 / (\(s^3 + 3s^2\) + 3s + 1)

Comparing this to the Laplace transform of \(t^2\), we find:

f(t) = 3\(t^2e^-^t\)

To find the inverse Laplace transform, we can factor the denominator:

F(s) = 4 / (\(s^2\) - 2s - 3)

= 4 / ((s - 3)(s + 1))

Using partial fraction decomposition, we can write F(s) as:

F(s) = A / (s - 3) + B / (s + 1)

Solving for A and B, we find A = 2 and B = -1. Therefore, the inverse Laplace transform is:

f(t) = 2\(e^3^t\) - \(e^-^t\)

These are the inverse Laplace transforms of the given functions.

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The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

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The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

a) The differential equation expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is suffering from Warfarin  is given a pill containing 2.5 mg of Warfarin then,

dQ/dt = -kQ
here Q(0) = 2.5

b) The differential equation the expressing the quantity Q(t)  of warfarin in the body, at t hours later when a patient who is not suffering from Warfarin  is given a pill containing 0.5 mg/hr then,

dQ/dt = -kQ + r
where Q(0) = 0
Here
k = rate constant
r = rate of administration
The differential equation concerning the given question is Q' = -2.5Q Q(0) = 0 . Therefore the required correct answer for the question is Option A.

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The rate at which Warfarin leaves the body should be proportional to the amount still in the body, not a constant rate of 2.5. So the correct differential equation for part (b) is:

Q' = 0.5 - kQ, where Q(0) = 0

Where k is the proportionality constant for the rate of elimination.

Explanation

(a) Let's denote the rate of elimination as k, where k > 0. Since the elimination rate is proportional to the amount of warfarin, we can write the differential equation as:

Q'(t) = -kQ(t)

Given that the initial condition is a 2.5 mg pill, the initial condition should be:

Q(0) = 2.5

So the differential equation for part (a) is:

Q'(t) = -kQ(t), Q(0) = 2.5

(b) In this case, the patient receives warfarin intravenously at a rate of 0.5 mg/hour. Thus, we should add the rate of administration to our equation:

Q'(t) = 0.5 - kQ(t)

The initial condition is still that the patient has no warfarin in her system:

Q(0) = 0

So the differential equation for part (b) is:

Q'(t) = 0.5 - kQ(t), Q(0) = 0

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For the quadratic equation -2x²+12x-13, the range is option D: All real numbers less than or equal to 5.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The values for x and h(x) are given in the table.

Real numbers can be said to be all continuous values of quantity, which can be negative or positive values.

The range of h, h(x), in the table given are all real numbers.

The quadratic equation from the points in the table can be deduced as -2x²+12x-13.

The maximum of the graph is at (3,5).

For a parabola ax²+bx+c with Vertex (xv,yv) -

If a<0, then the range is f(x) ≤ yv.

If a>0, then the range is f(x) ≥ yv.

Since, a = -2, then f(x)≤ 5.

Therefore, the range values of h is f(x)≤ 5.

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The utility function U on R^n is quasiconcave if and only if the preference relation ⪰ it represents is convex.


To prove that the utility function U is quasiconcave if and only if the preference relation ⪰ is convex, we need to show two implications.
1. If U is quasiconcave, then ⪰ is convex:
  If U is quasiconcave, it means that for any two points x, y in the domain of U and for any λ in the range [0, 1], the following inequality holds: U(λx + (1-λ)y) ≥ min{U(x), U(y)}. This property implies that the preference relation ⪰ is convex, as it satisfies the conditions of convexity.

2. If ⪰ is convex, then U is quasiconcave:
  If ⪰ is convex, it means that for any two points x, y in the domain of U and for any λ in the range [0, 1], if x ⪰ y, then λx + (1-λ)y ⪰ y. This implies that U(λx + (1-λ)y) ≥ U(y), which satisfies the definition of quasiconcavity.
Therefore, the utility function U is quasiconcave if and only if the preference relation ⪰ is convex.

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Answer:

radius = 5

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

(x - 2)² + (y - 6)² = 25 ← is in standard form

with r² = 25 ( take the square root of both sides )

r = \(\sqrt{25}\) = 5

Answer:

i = 1000cm2

ii = 100000cm3

Step-by-step explanation:

for q i

surface area of base = l* b

= 50* 20

1000cm^2

for q 2

volume l*b*h

= 50*20*10

= 100000cm^3

hope it will be helpfull

Answer:

102°

Step-by-step explanation:

Supplementary angles sum to 180° , then

other angle = 180° - 78° = 102°

The XYZ corporation will receive $1500000 for all the shares sold.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given: Cost of 1 share = $15

To find: Money received on selling 100000 shares.

Finding:

By unitary method,

Money received on selling 1 share = $15

Money received on selling 100000 shares = 15(100000) = $1500000

Hence, The XYZ corporation will receive $1500000 for all the shares sold.

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Answer:

8n+2n-6=34

Step-by-step explanation:

2.5(cos 5π/6  + i sin 5π/6) is the polar form  of the complex number

Complex numbers are numbers that are expressed in the form of a+ib, where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1)

Given: the complex number (5√3)/4 - 5/4 i

In polar form:

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

θ  = tan⁻¹( (-5/4) / (5√3 /4) )

θ = -30°

θ = -30+180 = 150°

θ = 5π/6

r = √( (5√3)/4)² +(- 5/4)²) = 2.5

Thus,

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

r(cosθ + isinθ) = 2.5(cos 5π/6  + i sin 5π/6 )

Therefore, the polar form  of the complex number is 2.5(cos 5π/6  + i sin 5π/6)

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The cosine of 45 degrees is √2 / 2.

In a 45-45-90 triangle, the two legs are congruent and the hypotenuse is √2 times the length of each leg. The angles of a 45-45-90 triangle are 45 degrees, 45 degrees, and 90 degrees.

To find the cosine of 45 degrees, we can use the definition of cosine in a right triangle, which is defined as the ratio of the adjacent side to the hypotenuse. In a 45-45-90 triangle, the adjacent side and the hypotenuse are the same length.

Since the side lengths of a 45-45-90 triangle are in the ratio 1:1:√2, let's assume the length of one leg is x. Then, the length of the other leg is also x, and the length of the hypotenuse is √2x.

Now, let's consider the cosine of 45 degrees:

cos(45 degrees) = adjacent side / hypotenuse

= x / √2x

= 1 / √2

To simplify the expression, we can multiply both the numerator and the denominator by √2:

cos(45 degrees) = (1 / √2) * (√2 / √2)

= √2 / 2

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The answer is three

None, one or infinitely many solutions

The transfer function H(s) = (62,893)/(s + 62,893) can be transformed to a digital filter representation H(z) using the bilinear transform.

The bilinear transformation is a common method used for converting analog filters to digital filters. It maps the entire left-half of the s-plane (analog) onto the unit circle in the z-plane (digital). The transformation equation is given by:

s =\((2/T) * ((1 - z^(-1)) / (1 + z^(-1)))\)

where s is the Laplace variable, T is the sampling period, and z is the Z-transform variable.

To convert the given analog LPF transfer function H(s) = (62,893)/(s + 62,893) to a digital filter representation, we substitute s with the bilinear transformation equation and solve for H(z):

H(z) = H(s) |s = \((2/T) * ((1 - z^(-1)) / (1 + z^(-1)))\)

= \((62,893) / (((2/T) * ((1 - z^(-1)) / (1 + z^(-1)))) + 62,893)\)

Simplifying the equation further yields the digital filter transfer function H(z):

H(z) = \((62,893 * (1 - z^(-1))) / (62,893 + (2/T) * (1 + z^(-1)))\)

The resulting H(z) represents the digital filter equivalent of the given 1st order analog LPF. This transformation enables the implementation of the filter in a digital signal processing system.

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Answer:

a). To find the median from a set of numbers, you need to arrange them from ascending order (smallest to biggest), and then you need to find the number in the middle

b). 32

Step-by-step explanation:

b). Smallest to biggest

29, 30, 31, 32, 33, 34, 37

From the set of numbers given, we can clearly see that 32 is in the middle.

An

$52

Step bro

suck it

Answer:

52$

Step-by-step explanation:

Divide for the unit price of 1 book.

You get $52

The required question of the given problem are solved below.

A distance-time graph shows how far an item has gone in a given time. It is a straightforward line diagram that signifies distance versus time discoveries on the chart. Distance is plotted on the Y-pivot. Time is plotted on the X-pivot.

1) he take 20 minutes to get to his friends house.

2) he stayed 60 - 20 = 40 minutes at his first friends house.

3) he take 70 - 60 = 10 minutes to ride his bike from his first friends house to his second friends house.

4) 30 minutes, he stayed his second friend

Then

Difference = 40 - 30 = 10 minutes

So, he stay 10 minutes longer than first friend.

5) In part E, he is riding towards his home.

6) In part A of the graph he is travelling faster.

7) he went 10 kilometer away from his house.

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