The quadratic function d = -2x^2+ 10 models a skateboarders distance,
in feet, from the bottom of a hill, x seconds after the skateboarder starts moving down the hill.
After how many seconds, is the skateboarder 1 ft from the bottom of the hill?

Answer:

113

Step-by-step explanation:

the formula is: π(d/2)^2

so:

π(12/2)^2=113.09...

Rounded that equals 113.0

Hope that helped! Let me know if you have any other questions.

Answer:

113.0 ft²

Step-by-step explanation:

Solution Given:

diameter(d) :12 ft

radius(r) = d/2= 12/2=6 ft

now

we have

area of the circle= πr²=22/7*6²= 113. 14 ft² =113 ft²

You are right

The solution for the given initial-value is 6ty + t² - 9t + 4y² - y = 12

An initial value problem is a differential equation that is accompanied by an initial condition that specifies the value of one or more variables at a particular time or at a particular point in space. The initial value problem is to find the solution of the differential equation that satisfies the given initial condition. The solution of the initial value problem describes the behavior of the system over time or as a function of space based on the given initial conditions.

The given initial value problem is a non-linear ordinary differential equation and can be solved using numerical methods such as Runge-Kutta methods or numerical integration.

The solution to the initial value problem gives the function y(t) that satisfies the differential equation and the initial condition y(-1) = 2.

Given that

(6y + 2t − 9)dt = (8y 6t − 1)dy = 0

and y = -2

As both = 0 then (6y + 2t − 9)dt = (8y + 6t − 1)dy

that is

(6(-2) + 2t − 9)dt = (8(-2) + 6t − 1)d(-2)

−21dt + 2dt² = 34d−12dt

2dt² − 9dt - 34d

d(2t² −9t−34)

Integration both sides

6ty + t² - 9t + 4y² - y = c

Using y(-1) = 2

-12 + 1 + 9 + 16 - 2 = c

c = 12

Thus, the solution for the given initial-value is 6ty + t² - 9t + 4y² - y -12 = 0

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The coefficient of q in the sum of these two expression is 1/2.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expressions are (2/3q −3/4) and (−1/6 q − 2).

We have to add these two expressions.

First arrange in such a way that like terms are together.

(2/3q −3/4) + (−1/6 q − 2) = (2/3q - 1/6q) + (-3/4 - 2)

                                        = (4/6q - 1/6q) + (-3/4 - 8/4)

                                        = 3/6q - 11/4

                                        = 1/2 q - 11/4

Hence the sum of the given expressions is 1/2 q - 11/4. And the coefficient of q is 1/2.

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The remaining ratios for the angle are:

sin θ = 2/√7

cos θ = √3 /√7

tan θ = 2/√3

sec θ = √7 /√3

cot θ = √3 /2

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Trigonometry is used to determine the lengths of the sides of a triangle when one or more angles and/or the lengths of one or more sides are known.

The remaining ratios are as follows

csc θ = √7 /2

Since sin θ = 1/cscθ

sin θ = 2/√7

Remember: sin θ= opposite/hypotenuse  = 2/(√7)

adjacent =  √((√7)² - 2²) = √3

cos θ = √3 /√7   (adjacent/hypotenuse)

tan θ = 2/√3  (opposite/adjacent)

sec θ = 1/cos θ

sec θ = √7 /√3

cot θ = 1/tan θ

cot θ = √3 /2

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The algebraic expression is 2 + y.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Sum of 2 and y

This can be written as,

2 + y

Thus,

The expression is 2 + y.

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The angle in the sector formed in radian is 5/4 π

The length of an arc is defined as the part of the circumference of a circle which is bounded by two radii.

The length of an arc = tetha / 360 × 2πr

where( tetha) is the angle

r is the radius

360° = 2π

therefore :

15π/2 = tetha/2π × 2× 6 × π

15π/2 = 6 tetha

tetha = 15π/2 ÷ 6

tetha = 15/12 π

tetha = 5/4 π

therefore the value of the angle in radian Is 5/4 π

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By applying inverse function concept, it can be concluded that the table that could be used to verify that the function modeling Fahrenheit temperature, F(C), based on a given Celsius temperature, C, is the inverse of C(F) is option A:

C           -20      -15      -5

F(C)        -5         4       23

An inverse function can be defined as a type of function that is obtained by inverting (undoing) the operation of the given function f(x).

In Mathematics, if f(x) is a given function, its inverse function has the following property f⁻¹(f(x)) = x.

We already have this table:

F       -4        5       23

C(F)   20    -15      -5

By applying the concept of inverse function, we can form a new table to represent the inversion function of the above table:

C           20      -15      -5

F(C)        -4        5       23

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Full question attached.

The x-intercept of the function is given by x=±9

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The function y=x²-81

To find x-intercepts of the functions we set y=0

Thus y=x²-81

x²-81=0

x=√81

x=±9

Hence, The x-intercept of the function is given by x=±9

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The probability of randomly drawing a vowel is 2/7, option C is correct.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given a set of cards spell P, E, R, C, E, N, T, S

total cards = 8

so total outcome = 8

to find  the probability of randomly drawing a vowel,

set contains 2 vowels,

a favorable outcome for vowel = 2

probability =  favorable outcome/total outcome

P(vowel) = 2/7

Hence option C is correct.

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Using Scalar multiplication, If all the conditions are satisfied, then the set is a subspace of R³

The result of multiplying a real number by a matrix is known as a scalar multiplication. Each entry of the matrix is multiplied by the specified scalar in scalar multiplication.

The following requirements must be met in order to establish whether a set is a subspace of R3 under addition and scalar multiplication:

Closure under addition: If elements u and v are present, then u plus v must also be present.

If u is a member of the set and k is any scalar, then ku must likewise be a member of the set. Closure under scalar multiplication.

The zero vector is contained in: The set must contain the zero vector (0, 0, 0).

includes all negative vectors; if u is in the set, then -u must also be.

These conditions must be checked for each set, and your response must be supported.

The set is a subspace of R³ if all the conditions are met.

The set is not a subspace of R³ if any of the requirements are not met.

Consequently, the set is a subspace of R³ if all of the conditions are met.

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Complete question -

There are 187.425 pounds in 85 kilograms. The solution has been obtained by using the unit conversion.

What is unit conversion?

The same feature is expressed in a different unit of measurement using a unit conversion. For instance, you may represent time in minutes rather than hours or distance in feet rather than miles. It happens frequently when measurements are given in one set of units, like feet, but are demanded in another set, like chains.

We are given 85 kilograms which are to be converted into pounds.

We know that 1 kilogram = 2.205 pounds(approx)

So,

⇒85 kilograms = 85 * 2.205

⇒85 kilograms = 187.425 pounds

Hence, there are 187.425 pounds in 85 kilograms.

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The truth value of a is False and after seeing the result of 1st statement b is true.

A mathematical statement like "3 is bigger than 4," "an infinite set exists," or "7 is prime" is referred to as a proposition.

A statement that is presumptively true is known as an axiom. Although there are several exceptions, mathematical logic can typically classify a claim as true or false given enough information (e.g., "This statement is false").

let p(x):x^2<=4

the domain for x is all positive integers (1, 2, 3, . . .).

(a) p(5)

p(5):25 not equal or less than 4

hence the truth value of a is False

(b)  negation for x;p(x)

after seeing the result of 1st statement b is true.

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The critical points are y = 0 and y = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.

The critical points of the differential equation dy/dx = y^2 - 4y are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:

y² - 4y = 0

y(y - 4) = 0

So the critical points are y = 0 and y = 4.

For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.

At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.

At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.

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The critical points are y = 0 and y = 4.

A differential equation is a mathematical equation that relates an unknown function to its derivatives. It expresses the relationship between an dependent variable (the unknown function) and one or more independent variables. Differential equations are used to model physical, biological, and economical systems, among others.

The critical points of the differential equation [tex]\frac{dy}{dx} = y^{2} - 4y[/tex] are the points where the slope of the solution is equal to zero. We can find these critical points by setting dy/dx = 0 and solving for y:

[tex]y^{2} - 4y[/tex]= 0

[tex]y(y-4)[/tex] = 0

So the critical points are y = 0 and y = 4.

For y < 0, dy/dx is positive, so the solution is increasing. For 0 < y < 4, dy/dx is negative, so the solution is decreasing. For y > 4, dy/dx is positive, so the solution is increasing.

At y = 0, the solution is at a critical point and is semi-stable, meaning that it is stable in one direction but not in the other. For y near 0 and less than 0, the solution is increasing, so it approaches y = 0 as x increases. For y near 0 and greater than 0, the solution is decreasing, so it moves away from y = 0 as x increases.

At y = 4, the solution is at a critical point and is unstable, meaning that it moves away from y = 4 in both directions as x increases.

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The matrix A of T with transformation T: R²→R² and is reflection of the line y = -x is [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

T: IR²→IR² is reflection of the line y = -x.

It is known that e1 = (1,0) and e2 = (0,1) is the standard basis of IR².

So, the transformation is T(e1) = e1' and T(e2) = e2'.

T(e1) = e1' = (0,1)

= 0(1,0) + (-1)(0,1)

= 0 · e1 + (-1) · e2

T(e2) = e2' = (-1,0)

= (-1)(1,0) + 0(0,1)

= (-1) · e1 + 0 · e2

So, now the matrix A becomes [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

Therefore, the new matrix is [tex]\left[\begin{array}{ccc}0&-1\\-1&0\\\end{array}\right][/tex].

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Find the matrix A of T for the following transformation. T: R²→R² is a reflection in the line y = -x.

The area of a triangle is 43.8178 square centimeters

Let the triangle's third side measure "x" cm.

circumference = x+8+11 = 32;

or x = 32-19 = 13 cm.

If we are aware of all three sides of a triangle, we can use "Heron's Formula" to determine its area.

Triangle's surface area equals the square root of s(s-a) (s-b) (s-c);

where s is the triangle's semi-perimeter; a, b, and c are its three sides.

As a result, s = 32/2 = 16 cm; a= 8 cm; b= 11 cm; and c= 13 cm.

Therefore, the triangle's area is equal to the square root of 16 X (16-8) X (16--11) X (16—13).

= Square root of (1920) = (16 X 8 X 5 X 3).

=43.8178 square centimeters

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The question seems incorrect;

What is the area of a triangle, two sides of which are 8cm and 11cm and the perimeter is 32cm?

Just put your name on the check's back to complete a blank endorsement. The teller at the bank will ask if you want to cash it or deposit it after you arrive.

The three types of endorsements available for checks are blank, special, and restriction. When the payee signs their name on the check's top back, it becomes a blank endorsement.

To accomplish this, you just sign the check on the back and inform the bank teller whether you want to deposit it into a certain account or cash it. When depositing a check using mobile deposit or an ATM, a blank endorsement is also acceptable.

To be accepted for deposit, a check needs to have an endorsement on the back. Therefore, always add your signature to the document right before bringing it to the bank in the place provided next to the X.

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Corn's market value  in 5 days will  be 64273.95.

What is exponential decay function?

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

The form of the general exponential decay is:

f(x) = A*(r)ˣ

r is rate

A=initial value

Exponential decay:

y=a(1-r)ᵗ

a= initial value, r in decimal = 0.07, t = 5 days

y= 92389 (1-0.07)⁵

y=  92389(0.93)⁵

y= 64273.95

Corn's market value  in 5 days will  be 64273.95

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Answer:

The expression 2a^2b^2 + 2b^2c^2 + 2a^2c^2 - a^4 - b^4 - c^4 can be factored as:

(2ab^2 + 2bc^2 + 2ac^2)(a^2 - c^2) - (a^2 - b^2)(a^2 - c^2)

= (a^2 + b^2 + c^2)(2ab^2 + 2bc^2 + 2ac^2) - (a^2 - b^2)(a^2 - c^2)

The solution to the equation are k = 2 or k = -3.5

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

2k^2 - 14 = -3k

Express properly

So, we have the following representation

2k^2 + 3k - 14 = 0

Expand the equation

2k^2 + 7k - 4k - 14 = 0

So, we have

k(2k + 7) - 2(2k + 7) = 0

This gives

k - 2 = 0 or 2k + 7 = 0

Evaluate

k = 2 or k = -3.5

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Using conditional probability, it is found that there is a 0.7921 = 79.21% probability that the body is attempting to reject the kidney.

Conditional Probability:

P(A|B)=P(A∩B)/P(A)

where:

P(B|A) is the probability of event B happening, given that A happened.

P(A∩B) is the probability of both A and B happening

P(A) is the probability of A happening.

Event A: Positive test.

Event B: Body attempting to reject the kidney.

The percentages associated with a positive test are:

80% of 30%(experience kidney rejection).

9% of 70%(do not experience kidney rejection).

Hence:

P(A)=0.8*0.3+0.09+0.7

P(A)=0.303

The probability of both a positive test and the body attempting to reject the kidney is:

P(A∩B)=0.8*0.3=0.24

Hence, the conditional probability is:

P(B|A)=0.24/0.303

P(B|A)=0.7921.

0.7921 = 79.21% probability that the body is attempting to reject the kidney.

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Answer:

A

Step-by-step explanation:

As x gets larger, the y-values became more and more negative. This means that as x approach infinity, y approaches negative infinity.

On the other side, as x gets smaller, the y-value also gets more and more negative. This means as x approaches negative infinity, y also approaches negative infinity.

This is shown in answer option A.

The products that result in a difference of squares or a perfect square trinomial are Quadratic Equations, Perfect Square Binomials, and Difference of Squares. Difference of Cubes is incorrect.

Those apply:

All three of these products can be used to solve a variety of problems involving algebraic equations.

The task:

Which products result in a difference of squares or a perfect square trinomial?

Check all that apply:

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Answer:

neither

Step-by-step explanation:

line T: m = -2/3

If line U was parallel to T it would have the same slope (-2/3)

If line U was perpendicular to T it would have a slope that is the negative reciprocal of the slope of line T  (3/2)

The length of side x obtained using trigonometric ratios is 5 units

Trigonometric ratios are expressions that indicate the relationship between the lengths of two of the sides of a right triangle and the interior angles of the right triangle.

The specified triangle is a right triangle, therefore, if the interior angles, and the length of one of the sides is known, the lengths of the other sides can be found.

The right triangle is a 30°-60°-90° right triangle

The length of the hypotenuse side = 10

The length of the leg with measurement x, can therefore, be found using trigonometric ratios follows;

sin(θ) = Opposite/Hypotenuse

sin(30°) = x/10

Therefore; x = 10 × sin(30°)

x = 10 × 0.5 = 5

The length of the side x in the right triangle is 5 units

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The volume of the triangular region with vertices (0,0), (1,0), and (0, 1). Cross-sections perpendicular to the y-axis are isosceles triangles with height 3 is V = 3/4.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

From the given vertices we can write the equation of the base of the triangular region as:

x = 1 - y

The area of the triangular region is given as:

A = 1/2 (b)(h)

A = 1/2 (1-y)(3)

The volume of the region is calculated by taking the integration of the area:

[tex]V = \int\limits^1_0 {\frac{3}{2} [1 - y] } \, dx\\\\V = \frac{3}{2} [y - \frac{y^2}{2} ]_0^1[/tex]

Substituting the values of the limit we have:

V = 3/2 [ 1 - 1/2]

V = 3/2 [1/2]

V = 3/4

Hence, the volume of the triangular region with vertices (0,0), (1,0), and (0, 1). Cross-sections perpendicular to the y-axis are isosceles triangles with height 3 is V = 3/4.

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Answer: The FOIL method (First, Outer, Inner, Last) is a mnemonic used to help solve and simplify multiplication problems by using the distributive property. To use FOIL, you simply multiply the first term of the first factor with the first term of the second factor, the outer terms of the two factors, the inner terms of the two factors, and the last terms of the two factors. Then, you add the results together to obtain the final answer.

For example, in the first problem, (a + b)(2a - 3b^2), we FOIL by first multiplying "a" and "2a": 2a^2. Next, we multiply "a" and "-3b^2": -3ab^2. Then, we multiply "b" and "2a": 2ab. Finally, we multiply "b" and "-3b^2": -3b^3. Now, we add the four results together to get the final answer: 2a^2 + (-3b^2 + 2b)a - 3b^3.

a. (a + b)(2a - 3b^2) = 2a^2 - 3ab^2 + 2ab - 3b^3 = 2a^2 + (-3b^2 + 2b)a - 3b^3.

b. (k - 8)(4k + b) = 4k^2 + bk - 32k - 8b = 4k^2 + (b - 32)k - 8b.

c. (7x^15)(2x + 2) = 14x^16 + 14x^15 = 14x^15 (x + 1).

d. (3ab - 1)(2ab + 6) = 6a^2 b^2 + 2ab - 3ab + 6 - 2ab = 6a^2 b^2 + 4ab +

Step-by-step explanation:

As t increases without bound. N(t) approaches:

N(t) is limited by the number of people who started the rumor.

The correct answer is option (A).

The given exponential model is defined as follows:

[tex]N(t)=5501+49e^{-0.7t}[/tex]

For t = 0

Substitute the value of t = 0 in the above equation,

[tex]N(t)=5501+49e^{-0.7\times0}[/tex]

N(t) = 5501 + 49 × 1

N(t) = 5501 + 49

N(t) = 5550

Thus, 5550 people started the rumor.

Since [tex]49e^{-0.7t}[/tex] is greater than zero for all real t.

Then, [tex]5501+49e^{-0.7t} > 5501\\[/tex]

So, as t increases without bound.

N(t) approaches:

N(t) is limited by the number of people who started the rumor.

Therefore, the correct answer is option (A).

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The complete question is as follows:

The equation [tex]N(t)=5501+49e^{-0.7t}[/tex] models the number of people in a town who have heard a rumor after t days. As t increases without bound, what value does N(t) approach? Interpret your answer.

How many people started the rumor?

N(t) approaches:

A. N(t) is limited by the number of people who started the rumor.

B. N(t) is limited by the carrying capacity of the town.

C. N(t) is limited by the number of days it takes for the entire population to hear the rumor.

D. N(t) is limited by the rate at which the rumor spreads.

E. N(t) is not limited by any value and increases without bounds.

Answer:

-1, 6

0, -3

1, -3.9

2, -3.99

f(x) = 5^2x+1

Step-by-step explanation:

for the first question, after plugging in the values of x, we get our answer to be the 2nd table

-1, 6

0, -3

1, -3.9

2, -3.99

for the second question

f(x) = 5^2x+1

after graphing, we can see it never passes x = 2