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Tiger Woods drives a golf ball a horizontal distance of 285 yards. If the ball 4 points
reached a maximum height of 40 yards, what is the parabolic equation
that models the path of the golf ball? Show the work (at least 3 steps) you
would take to find an equation that models the situation. Show the
equation at the end.

Answer:

x = 7

Step-by-step explanation:

→ Find perimeter of rectangle

x + x + 4 + x + x + 4 = 4x + 8

→ Find perimeter of triangle

2x - 3 + 3x - 4 + x + 1 = 6x -6

→ Equate 2 expressions together

4x + 8 = 6x - 6

→ Minus 8 from both sides

4x = 6x - 14

→ Minus 6x from both sides

-2x = -14

→ Divide both sides by 2

x = 7

Answer:

∠ 1 = 58°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

117° is an exterior angle of the triangle, then

∠ 1 + 59° = 117° ( subtract 59° from both sides )

∠ 1 = 58°

The product of \(-2x^{3}\) + x - 5 and \(x^{3}\) - 3x - 4 is \(-2x^{6}\) + \(7x^{4}\) + \(3x^{3}\) + \(12x^{2}\) - 4x + 20. The order of the polynomials does not affect the result; they yield the same product.

a) To find the product of \(-2x^{3}\) + x - 5 and \(x^{3}\) - 3x - 4, we multiply each term in the first expression by each term in the second expression and combine like terms.

\(-2x^{3}\) * \(x^{3}\) = -2\(x^{6}\)

\(-2x^{3}\) * (-3x) = 6\(x^{4}\)

\(-2x^{3}\) * (-4) = 8\(x^{3}\)

x * \(x^{3}\) = \(x^{4}\)

x * (-3x) = -3\(x^{2}\)

x * (-4) = -4x

-5 * \(x^{3}\) = -5\(x^{3}\)

-5 * (-3x) = 15\(x^{2}\)

-5 * (-4) = 20

Combining all the terms, we have:

-2\(x^{6}\) + 6\(x^{4}\) + 8\(x^{3}\) + \(x^{4}\) - 3\(x^{2}\) - 4x - 5\(x^{3}\) + 15\(x^{2}\) + 20

Simplifying further:

-2\(x^{6}\)+ 7\(x^{4}\) + 3\(x^{3}\) + 12\(x^{2}\) - 4x + 20

Therefore, the product of -2\(x^{3}\) + x - 5 and \(x^{3}\) - 3x - 4 is -2\(x^{6}\) + 7\(x^{4}\) + 3\(x^{3}\) + 12\(x^{2}\) - 4x + 20.

(b) The product of two polynomials is commutative, which means that changing the order of the polynomials being multiplied does not affect the result. In other words, the product of \(x^{3}\) - 3x - 4 and -2\(x^{3}\) + x - 5 will be the same as the product obtained in part (a).

Therefore, the product of -2\(x^{3}\) + x - 5 and \(x^{3}\) - 3x - 4 is equal to the product of \(x^{3}\) - 3x - 4 and -2\(x^{3}\) + x - 5. The order of the polynomials being multiplied does not impact the final result, so both expressions yield the same product.

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Answer:

the answer is B.FALSE

Step-by-step explanation:

hope it helps

There are 12 sheets of cardboard in the stack based on the model and the expression.

Part A: To determine the number of sheets of cardboard in a stack, we can use the model of a ruler.

Part B: Using the ruler model, we can compare the height of the stack (2 1/4 inches) to the thickness of each sheet (3/16 inches). We divide the height of the stack by the thickness of each sheet to find the number of sheets in the stack.

Part C: The expression that can be used to determine the number of sheets of cardboard in a stack is:

Number of sheets = Height of the stack / Thickness of each sheet

Part D: The expression relates to the model by dividing the height of the stack (measured in inches) by the thickness of each sheet (also measured in inches). This division represents the number of times the thickness of each sheet fits into the height of the stack, giving us the total number of sheets.

For example, if the height of the stack is 2 1/4 inches and the thickness of each sheet is 3/16 inches, we can calculate:

Number of sheets = (2 1/4) / (3/16) = (9/4) / (3/16) = (9/4) * (16/3) = 12.

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When we look for the constant rate of change, we subtract the first two y-values in the first place:

Answer:

.25 dollars or 25 cents

Step-by-step explanation:

128/2=64                         32/2=16

64/2=32                          16/2=8                        

32/2=16                           8/2=4

16/2=8                             4/2=2

8/2=4                               2/2=1

4/2=2                               1/2=(1/2)

2/2=1                                (1/2)/2=(1/4)

1/4 of 1 dollar is 25 cents

Answer:

10xy

Step-by-step explanation:

-5(-2)=10

Answer:

10xy

Step-by-step explanation:

Negative 5 times negative 2 equlas 10

Our answer is 10xy.

I hope it helps!:)

Answer:

32

Step-by-step explanation:

The answer would be 32:);)

Answer: C

Step-by-step explanation:

According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

At one classroom for economics and another for other topics, they dumped 122 stamped envelopes with addresses and $20 bills inside each.

Let the money returned = R

economics classes = E

other classes = O

a). The following gives the probability statement for the overall percentage of the money returned: 100.P (R)

b). The probability statement that the percentage of money recovered from economics classes is 100.P(R|E)

c). The probability statement that displays the percentage of money returned from the other classes is 100.P(R|O).

d). No, because P(R) is not equal to P(R|E), the money returned is not independent of the classes.

e).  According to the study, economists are not more self-centered than persons in other classes because 51% of the envelopes returned from economics classes and 36% from other classes.

The complete question is:

Three professors at George Washington University did an experiment to determine if economists are more selfish than other people. They dropped 122 stamped, addressed envelopes with $20 cash in two different classrooms (one economics, one not) on the George Washington campus. Of these, 42% were returned overall. From the economics class 51% of the envelopes were returned. From the other class 36% were returned.

From

the business, psychology, and history classes 31% were returned.

Let: R = money returned; E = economics classes; O = other classes

a. Write a probability statement for the overall percent of money returned.

b. Write a probability statement for the percent of money returned out of the economics classes.

c. Write a probability statement for the percent of money returned out of the other classes.

d. Is money being returned independent of the class? Justify your answer numerically and explain it.

e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Include numbers to justify your answer.

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Answer:

6AJNSDJN

Step-by-step explanation:

Answer:

8/50

5/50

10/50

38/50

45/50

Step-by-step explanation:

The required area is approximately 39.36 square units.

The given polar curves are r = 18cos(θ) and r = 9cos(θ). We are interested in finding the area of the region that is bounded by these curves and the rays θ = 0 and θ = π/4.

First, we need to find the points of intersection between these two curves.

Setting 18cos(θ) = 9cos(θ), we get cos(θ) = 1/2. Solving for θ, we get θ = π/3 and θ = 5π/3.

The curve r = 18cos(θ) is the outer curve, and r = 9cos(θ) is the inner curve. Therefore, the area of the region bounded by the curves and the rays can be expressed as:

A = (1/2)∫(π/4)^0 [18cos(θ)]^2 dθ - (1/2)∫(π/4)^0 [9cos(θ)]^2 dθ

Simplifying this expression, we get:

A = (1/2)∫(π/4)^0 81cos^2(θ) dθ

Using the trigonometric identity cos^2(θ) = (1/2)(1 + cos(2θ)), we can rewrite this as:

A = (1/2)∫(π/4)^0 [81/2(1 + cos(2θ))] dθ

Evaluating this integral, we get:

A = (81/4) θ + (1/2)sin(2θ)^0

Plugging in the limits of integration and simplifying, we get:

A = (81/4) [(π/4) + (1/2)sin(π/2) - 0]

Therefore, the area of the region bounded by the curves and the rays is:

A = (81/4) [(π/4) + 1]

A = 81π/16 + 81/4

A = 81(π + 4)/16

A ≈ 39.36 square units.

Hence, the required area is approximately 39.36 square units.

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Answer:

D) y =   -2

The equation of the perpendicular line to the given line is  y = -2

Step-by-step explanation:

Explanation:-

Given point (-3,-2)

In graph the equation of line  x = 8 ( parallel to y- axis )

                              1 x + o y - 8 =0

The equation of the perpendicular line to the given line  

                        b x - a y + k =0

                       o x - 1 y + k =0 ...(i)

The equation (i) is Paases through the point ( -3,-2)

                        0 ( -3) -1(-2) + k =0

                               2 + k =0

                                     k = -2

∴The equation of the perpendicular line to the given line  is

     put k = -2 in equation (i)    

                        o x - 1 y + k =0

                      - y +(-2) =0

                       - y = 2

                         y = -2

Final answer:-

∴The equation of the perpendicular line to the given line is  y =-2

Answer:

h/2

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

8•4=32 it's not that bad

The unit vector with positive x-component that is orthogonal to both p(0) and p′(0) is \(v_u_n_i_t\) = v / ||v|| = ⟨-1,0,0⟩.

First, we need to find the vector that represents the position of the curve at t=0, which is p(0) = ⟨-1,0,0⟩.

Then we need to find the vector that represents the velocity of the curve at t=0, which is p'(t) = ⟨2t,2,4t⟩, so p'(0) = ⟨0,2,0⟩.

To find a unit vector that is orthogonal to both p(0) and p'(0), we can use the cross product:

v = p(0) x p'(0)

where "x" denotes the cross product. This will give us a vector that is perpendicular to both p(0) and p'(0), but it may not be a unit vector. To make it a unit vector, we need to divide by its magnitude:

\(v_u_n_i_t\) = v / ||v||

where "||v||" denotes the magnitude of v.

So let's calculate v:

v = p(0) x p'(0) = ⟨0,0,2⟩ x ⟨0,2,0⟩ = ⟨-4,0,0⟩

And the magnitude of v is:

||v|| = sqrt((-4)^2 + 0^2 + 0^2) = 4

So the unit vector that is orthogonal to both p(0) and p'(0) and has a positive x-component is:

\(v_u_n_i_t\) = v / ||v|| = ⟨-1,0,0⟩

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The volume of the given solid is equal to the triple integral of 1 over the region bounded by the coordinate planes and the plane 6x + 7y + z = 42. This can be written as:

\($\iiint 1\, dV = \iiint 1\, dx\, dy\, dz$\)

The region of integration is bounded by the coordinate planes x = 0, y = 0, and z = 0, and the plane 6x + 7y + z = 42. This is a right triangular prism with vertices (0,0,0), (6,0,0), and (0,6,42). To calculate the volume, we will use the triple integral in cylindrical coordinates, which can be written as:

\($\iiint 1\, dV = \int0^{2\pi}\int0^6\int_0^{42/7} r\, dz\, dr\, d\theta$\)

The volume of the given solid is given by:

\($\frac{504\pi}{7}$\)

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Answer:

D. Rational Number

Step-by-step explanation:

The amount of sugar in the entire shipment is 97(1)/(2) tons.

We are given that a shipment of sugar fills 2(1)/(5) containers. If each container holds 3(3)/(4) tons of sugar, we need to find the amount of sugar in the entire shipment.

Step-by-step explanation:

One container of sugar holds 3(3)/(4) tons of sugar. There are 2(1)/(5) containers of sugar in the shipment.

Amount of sugar in one container = 3(3)/(4) tons

Amount of sugar in 2(1)/(5) containers

= 2(1)/(5) × 3(3)/(4) tons

= 13/5 × 15/4 = 195/20

= 97(1)/(2) tons

Therefore, the amount of sugar in the entire shipment is 97(1)/(2) tons.

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The first-order system representing the given second-order differential equation is du/dt = v and dv/dt = 5v - 6.5u - 7sin(3t), with the initial condition [u(1), v(1)] = [7.5, 9].

To rewrite the second-order differential equation u" - 5u' + 6.5u = 7sin(3t) as a set of first-order equations, we introduce a new variable v to represent the u'. Therefore, we have u' = v. Differentiating this equation with respect to t, we obtain u" = v'.

Substituting these expressions back into the original equation, we have v' - 5v + 6.5u = 7sin(3t).

Now, we can express the system of first-order equations in matrix form as [du/dt, dv/dt] = [v, 5v - 6.5u - 7sin(3t)].

The initial value of the vector-valued solution for this system is given as [u(1), v(1)] = [7.5, 9].

In summary, the first-order system representing the given second-order differential equation is du/dt = v and dv/dt = 5v - 6.5u - 7sin(3t), with the initial condition [u(1), v(1)] = [7.5, 9].

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Answer:

4x-5y=3

-3=4x-5y

Step-by-step explanation:

4x-5y = 3

4x-5y = -3

both statements have different answers but has the same problem making the statement x=x and 0=0 making it have no solution

Answer:

The solution to the system of equation is;

Explanation:

Given the system of equations;

Let us solve by elimination, multiply equation 2 by 2 and add to equation 1 to eliminate y;

adding to equation 1;

we can now use the value of r to solve for y;

Therefore, the solution to the system of equation is;

Answer:

Honestly YOU have to write what you think a hero means. I know most of yall on here are lazy and just want people to answer questions for you.. but cmon. What do YOU think a hero means?

Saddle points are critical point that the function didn't in local maximum points nor in a local minimum position. Saddle pointly mostly happen in the multivariable functions. In simple, saddle point is everything on the function accept the local maxima and minimum maxima. The proof what is the saddle shown in the picture. As you can see, the curve besides local maxima and minimum maxima is create an area like a saddle, thats why its called saddle point.

Saddle point availability can be calculate by this logic: lets say we have r = f(q, w), then the point (q, w, r) is told to be a saddle point if each derivatives fq(q, w) and fw(q, w) subside,and f  is not in any local maximum or local minima value at (x, y).

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Answer:

Amir 20 Rita 45

Step-by-step explanation:

20/4=5

5*9=45

so this satisfices the ration 4:9

Answer:

Amir : 20 sweets and Rita : 45 sweets

Step-by-step explanation:

Rita has 25 more in all answers. to get the answer, this is to see which one : 4:9 ; 20:45.

we multiply 4 and 45 and 9 and 20. if we multiply them, both answers are 180. this means it is equal and that is the answer.

The graph that has a slope of 4/5 is the one represented by the equation y = (4/5)x. In this graph, the slope represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In this case, for every 5 units of horizontal change (run), there is a vertical change (rise) of 4 units.

The graph can be visualized as a line that goes up 4 units for every 5 units it moves to the right. This means that as x increases by 5 units, y increases by 4 units. Similarly, as x decreases by 5 units, y decreases by 4 units.

By plotting points on the graph, we can see that the line will have a positive slope, moving upward from left to right. The steepness of the line corresponds to the ratio 4/5, indicating that it is relatively steep but not as steep as a line with a slope of 1.

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