The height of a falling pinecone can be represented by y = -16° +64 where t is the time in seconds
and y is the height of the pinecone in feet. Write and solve an equation to find the number of seconds it
will take for the pinecone to reach the ground.
A. 4 seconds
B. 6 seconds
C. 2 seconds
D. 1.5 seconds

The graph of the models the piecewise function for the given situation is attached below.

What is piecewise function?

A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a certain interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a means to express the function.

Given that for the first 5 hours, 2 inches of snow fell every hour.

The height of the snow can represent by y = 2x, 0 ≤ x ≤ 5

Where x represents the time and y is the height of the snow.

The height of the snow is (5 × 2) = 10 inches after 5 hours.

After 5 hour, there is no snowfall.

The level of snow is y = 10 when 5 ≤ x ≤ 10.

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The curvature at the point (2,8,-1) X = 2t, Y = 8[tex]t^{3/2}[/tex], Z = -t² is √2/152 when the formula is k = | r'(t)×r''(t) |/||r''(t)||³.

Given that,

We have to find the curvature at the point (2,8,-1) X = 2t, Y = 8[tex]t^{3/2}[/tex], Z = -t².

We know that,

The curve is  x = 2t, y = 8[tex]t^{3/2}[/tex], z = -t².

Putting 2t=2

t=1

So,

t=1 at the point (2,8,-1)

Also r(t) = <2t, 8[tex]t^{3/2}[/tex], -t²>

r'(t) = <2, 8(3/2)√t, -2t>

r''(t) = <0,6/√t,-2>

||r''(t)|| = √(2²+(12√t)²+(-2t)

||r''(t)|| = √(4+144t+4t²)

Cross product = r'(t) × r''(t) = [tex]\left[\begin{array}{ccc}i&j&k\\2&12\sqrt{t} &-2t\\0&6/\sqrt{t} &-2\end{array}\right][/tex]

=i(-24√t+12√t)-j(-4-0)+k(12/√t-0)

=-12√ti+4j+12/√tk

| r'(t)×r''(t) |= √(-12√t)²+4²+(12/√t)² = √(144t+16+144/t)

The curvature at the point t=1 is k = | r'(t)×r''(t) |/||r''(t)||³

k = √(144t+16+144/t) /√(4+144t+4t²)³

k = √(144(1)+16+144/(1)) /√(4+144(1)+4(1)²)³

k = √304/ (152)³

k = √2/152

Therefore, the curvature at the point (2,8,-1) X = 2t, Y = 8[tex]t^{3/2}[/tex], Z = -t² is √2/152 when the formula is k = | r'(t)×r''(t) |/||r''(t)||³.

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1) Given information

2) [tex]\overline{RT} \cong \overline{RT}[/tex] (reflexive property)

3) [tex]\triangle RST \cong \triangle RQT[/tex] (SSS)

4) [tex]\angle STP \cong \angle QTP[/tex] (CPCTC)

5) [tex]\overline{PT} \cong \overline{PT}[/tex] (reflexive property)

6) [tex]\triangle SPT \cong \triangle QPT[/tex] (SAS)

7) [tex]\angle SPT \cong \angle QPT[/tex] (CPCTC)

The slope of the function represents the change in height per day. In the given function, h = 3d, the slope is 3. This means that for every 1 unit increase in the number of days, the height of the corn plant increases by 3 units (in this case, centimeters).

Therefore, the correct answer is (C) The change in height per day.

Slope of Function represents the change in height per day.(Option C)

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is

[tex]m=\frac{dy}{dx}[/tex] = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be shown as

tan θ = Δy/Δx

So, the slope of a line is tanΘ.

So as slope represents change in y per change in x, in the given question as y is height and x is days, slope is change in height per day.

Slope of Function represents the change in height per day.(Option C)

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To find the value of k in a function, you need to know the equation of the function and the input values for which you want to find the output, and then substitute these values into the equation and solve for k.

A function is a relationship between each element of a non-empty set A and at least one element of another non-empty set B. Functions are the central idea of calculus in mathematics. The functions are special types of relations. A function is a rule that generates a unique outcome for each input x in mathematics.

The collection of all input values that you can use in a function without running into problems or producing undefined results is generally referred to as the domain of the function. When dealing with functions, it is crucial to keep in mind the function's domain because utilizing input values outside of the domain might provide erroneous or undefinable outputs.

To find the value of k in a function, you need to know the equation of the function and the input values for which you want to find the output.

For example, if the function is defined as f(x) = kx + b, and you want to find the value of k for a particular value of x, you can substitute the value of x into the equation and solve for k.

For example, if the function is f(x) = kx + b and you want to find the value of k when x = 2, you can substitute 2 for x in the equation to get:

f(2) = k(2) + b

Solving this equation for k gives:

k = (f(2) - b)/2

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The solution to the equation for x is that the equation −20x + 40 = −20x + 20 has no solution

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

[tex]−20x+40=−20x+20[/tex]

Rewrite the above equation properly

So, we have the following representation

−20x + 40 = −20x + 20

Collect the like terms in the above equation

This gives

20x - 20x = 20 - 40

Evaluate the like terms in the above equation

So, we have the following representation

0 = -20

The above equation is false

Hence, the equation has no solution

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The difference between ASA and AAS congruence rule is While AAS refers to the two corresponding angles and the non-included side, ASA refers to any two angles and the included side.

Two postulates that assist us in determining whether two triangles are congruent are ASA and AAS. ASA means "Angle, Side, Point", while AAS signifies "Angle, Angle, Side". If two figures are the same size and shape, they are congruent. To put it another way, the same person appears in two distinct locations in two congruent figures. According to the ASA congruence rule, two triangles are congruent when the angles and included sides of one side are equal to those of another side. However, if two angles and one side of one triangle are equal to two angles and one side of another triangle, then they are congruent, as stated by AAS. Both ASA and AAS are the same as though two points of one triangle are equivalent to two points of another triangle then clearly the third points will likewise be the same.

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Slack and strict are the two types of linear inequalities we deal with our daily examples in mathematics.

Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities. Equivalent inequality refers to linear inequalities with the same solution. Both equality and inequality are subject to laws.

An inequality is comparable if both sides are multiplied by a positive value. An inequality's direction can be changed by multiplying both sides by a negative amount.

There are two types of linear inequalities

Slack: inequalities containing sign ≤ or ≥  between LHS and RHS.

Strict: inequalities containing < or > between LHS and RHS.

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Answer:

n = 4

Step-by-step explanation:

You have ____ when you divide both sides of equation 3n = 12 by 3:

3n = 12

3n/3 = 12/3

n = 4

Answer:

Step-by-step explanation:

slope equals rise over run

count over from one dot to the other ,  starting on the left

down 3 ,  over 6

down means negative, so

- 3/6

or  -1/2

Sunil need to score 93% on the 6th test to be able to get 90% as the average in her Chemistry class.

In Mathematics, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. In statistics, the mean is the average of the given sample or data set. It is equal to the total of observations divided by the number of observations. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

In this case, let x be the missing value.

Now, we have:

Average = 90%

Total all values = 74% + 92% + 83% + 98% + 100% + x = 447% + x

Number of values = 6

Average = Total all values / Number of values

90% = (447% + x) / 6

447% + x = 540%

x = 540% – 447%

x = 93%

Hence, the missing value is 93%, which means Sunil need to score 93% on the 6th test to be able to get 90% as the average in her Chemistry class.

Although part of your question is missing, you might be referring to this full question: Sunil wants to earn a 90% in her Chemistry class. On the first 5 test, she received a 74%, 92%, 83%, 98%, 100%. What must she score on the 6th test to get the 90% she wants?

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Answer:

  A)  -9

Step-by-step explanation:

You want a graphical solution to the system of equations ...

The graph is attached. It shows the solution is (-9, 1).

The x-coordinate of the solution is -9.

Limit base x to a f(x) is equal to infinity if we can say f(x) arbitrarily large for all x sufficiently x=a, from both sides, without actually letting x=a.

Given that,

We have to find how do we know if the limit is positive infinity or a negative infinity.

We know that,

On a number line, numbers move closer to positive infinity as they advance to the left and negative infinity as they move to the right. Positive infinity is always larger than any number, while negative infinity is always smaller.

Now,

We say

Limit base x to a f(x) is equal to infinity if we can say f(x) arbitrarily large for all x sufficiently close to x=a, from both sides, without actually letting x=a.

And

Limit base x to a f(x) is equal to negative infinity if we can say f(x) arbitrarily large and negative for all x sufficiently close to x=a, from both sides, without actually letting x=a.

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Answer:

y = [tex]\frac{40}{11}[/tex] x + 50

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 50 ) and (x₂, y₂ ) = (11, 90 )

m = [tex]\frac{90-50}{11-0}[/tex] = [tex]\frac{40}{11}[/tex]

the line crosses the y- axis at (0, 50 ) ⇒ c = 50

y = [tex]\frac{40}{11}[/tex] x + 50 ← equation of line

Answer:

There is no answer.

Step-by-step explanation:

4(2x+3) = 3+8x-11

Group together common terms on the right & use the distributive property on the left.

4(2x) + 4(3) = (3-11) +8x

8x + 12 = 8x -8

Combine like terms. Subtract 8x from both sides.

12 = -8

Answer: 64 = 8^2.

Step-by-step explanation:

The logarithmic equation log8 64 = 2 can be rewritten in exponential form as follows:

log8 64 = 2

64 = 8^2

Therefore, the exponential form of the given logarithmic equation is 64 = 8^2.

A) An unbounded problem is one for which the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible.

B) If a model has alternative optimal solutions the objective is maximized (or minimized) by more than one combination of decision variables, all of which have the same objective function value.

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

C) The shadow price indicates how much the value of the objective function will change as the right-hand side of a constraint is increased by 1.

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Answer:

(0, 6 )

Step-by-step explanation:

(x, y ) → (x - 4, y + 2 )

mans subtract 4 from the original x- coordinate and add 2 to the original y- coordinate, that is

(4, 4 ) → (4 - 4, 4 + 2 ) → (0, 6 )

The radius of X² y² 16 is 4.

X² y² 16 is a circle equation. To solve for the radius, we need to divide both sides by 4, then take the square root of both sides. So, 16/4 = 4 and √16 = 4. Therefore, the radius of X² y² 16 is 4. As a reminder, the equation for the radius of a circle is r = √(x² + y²). Therefore, when solving for the radius of a circle, the first step should be to divide both sides of the equation by 4 and then take the square root of both sides.

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Answer: 2

Step-by-step explanation:

If you have four sticks of butter that equal a pound, and each stick is 1/2 a cup, then a pound of butter is equal to 2 cups. This is because 1/2 x 4 = 2. Each stick of butter is 1/2 a cup, and since there are four sticks in a pound, the total amount of butter in cups is 2 cups.

The SSS (side-side-side), SAS (side-angle-side) and AAS (angle-angle-side) are basic congruence criteria to prove the congruency of two triangles.

Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal.

The basic terms of the agreement are as follows.

Now, let's talk about SSS, SAS, and AAS basic Congruence Criteria.

SSS Congruence Criteria:

SSS Criterion stands for Side-Side-Side Criterion. According to this criterion, two triangles are congruent if three sides of one triangle are equal to the corresponding sides of the other triangle.

SAS Congruence Criteria :

SAS Criterion stands for Side-Angle-Side Criterion. By this criterion, two triangles are congruent if his two sides and included angles of one triangle are equal to the corresponding sides and included angles of the other triangle.

AAS Congruence Criteria:

AAS Criterion stands for Angle-Angle-Side Criterion. According to the AAS criterion, two triangles are congruent if any two angles and excluded sides of one triangle are equal to the corresponding angles and excluded sides of the other triangle.

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Direct Ratios and/or Variations

Indirect proportions, inverse proportions, or variations

Thus, Inverse proportion is defined as y = k/x, k is the proportionality constant .

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The natural numbers are “closed” under addition and multiplication.

A set is closed (under an operation) if and only if the operation on any two elements of the set produces another element of the same set. The set of whole numbers is “closed” under addition and multiplication.

A set of number with a defined operation (e.g. addition, multiplication etc.), such that the outcome of the operation between any two numbers is also a member ot the set.

A Closed Set Math has a way of explaining a lot of things, and one of those explanations is called a closed set.This closed set includes the limit or boundary of 3.

When a set has closure, it means that when you perform an operation on the set, then you'll always get an answer from within the set. This doesn't mean that the set is closed though. Open sets can have closure. Mathematical examples of closed sets include closed intervals, closed paths, and closed balls.

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The first factor of the expression has a degree of 2.

The second factor has a degree of 3.

The third factor has a degree of 2.

The product has a degree of 7.

[tex](a^{2} ) (2a^{3} )(a^{2}-8a+9)[/tex]

The given expression of this problem is:

The degree of an expression is deduct by the exponent of each power.

So, the first factor of the expression has a degree of 2, because that's the exponent.

The second factor has a degree of 3.

The third factor has a degree of 2.

Now, to know the degree of the product, we have to solve the expression, and see what is the degree of the resulting polynomial expression:

[tex](a^{2})(2a^{3})(a^{2} -8a+9)[/tex]

[tex]2a^{5} (a^{2} -8a+9)[/tex][tex]\\2a^{7} -16a^{6}+18a^{5}[/tex]

so, as you can see, the product has a degree of 7.

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The power output of student is P = 1241.34W

Let the mass of the student be m, length of the rope be l and the time taken by the student to climb the rope be t seconds.

Therefore, it is given that

m = 95kg

l = 4m

t = 3 seconds

Now we know that the formula of work done against the gravity (W) is given by

W = m x g x h

where m is the mass of the object,

g is the gravitational constant with g = 9.8 [tex]m/s^{2}[/tex]

and h is the height of the object from refernce, which in this case is l = 4m

Now, putting these values in work done formula we get,

W = 95 x 9.8 x 4

W = 3724 J

Now to find the power output, we know that

Power = (Work done)/(time taken)

Power = 3724/3

Therefore, power output of the student is equal to 1241.34W

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Answer:

-10 =x

Step-by-step explanation:

100 + 2x = 140 + 6x

Solve for x

Subtract 2x from each side

100 + 2x-2x = 140 + 6x-2x

100 = 140 +4x

Subtract 140 from each side

100-140 = 140+4x-140

-40 = 4x

Divide each side by 4

-40/4 = 4x/4

-10 =x

The solution set for the given systems of equations : 5x + 2y = 7 and y = x + 1 is x = 5/7 and y = 12/7

Solving the equations :

5x + 2y = 7                                         (1)

y = x + 1                                              (2)

Subtracting x on both sides of equation (2)

y - x = 1

Multiplying the equation by 5 on both sides

5y - 5x = 5                                          (3)

Adding equation (1) and (3) we get

5x + 2y + 5y - 5x = 7 + 5

7y = 12

y = 12/7

Solving for x by substituting y = 12/7 in (2)

12/7 = x + 1

x = 12/7 - 7/7

x = 5/7

--The question is incomplete, answering to the question below--

"What is the solution set of the given systems? 5x + 2y = 7 and y = x + 1"

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Answer:

Slope: 3/2

Y-intercept: (0,-4)

X-intercept: (8/3 , 0)
Step-by-step explanation:

To find the y-intercept, I just put in 0 for x.

3(0) - 2y = 8

-2y = 8

y = -4

So, the y-intercept is at (0,-4)

To find the x-intercept, I just put in 0 for y.

3x - 2(0) = 8

3x = 8

x = 8/3

So, the x-intercept is at (8/3, 0)

The slope is 3/2

I don't see the picture. Can you send it in the message.

y = -[tex]\frac{5}{3}[/tex]x+5  equation has an X intercept of 3 and a y intercept of 5 .

  The point on a line where it crosses an axis is referred to as the "intercept." The slope of the line passes through a point called an intercept on the y-axis.

The equation for a line, which is written as y = mx+c, which stands for slope and y-intercept, respectively, reflects this.

The two main intercepts are X-intercept and Y-intercept. Where the line crosses the x and y axes, respectively, is where the line's x-intercept and y-intercept are situated.

In this case, you are given both intercepts.

Plot a line from the third x-axis point.

On the y-axis, place the coordinates y = 5.

The necessary line is a straight line that passes through these two places is

y = -[tex]\frac{5}{3}[/tex]x+5

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