a) The Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.
b) The total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.
Nash Equilibrium & Total Payoffa. Nash Equilibrium: A Nash Equilibrium is a set of strategies such that each player's strategy is a best response to the strategies of the other players.
In this game, each person i chooses their effort level x i to maximize their own payoff, which is the worth of the project divided by 2. Their individual payoff is given by:
pi = (2x1x2) / 2 = x1x2
By taking the derivative of pi with respect to xi and setting it to zero, we get the following first-order condition:
dpi/dx i = x2 - xi = 0
Since xi is in the range [0,1], we have xi = x2.
Thus, the Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.
b. Total Payoff: The total payoff of the project is given by:
pt = x1x2 + x1x2 = 2x1x2
By factoring the total payoff function, we get:
pt = 2x1x2 = 2x1x1 = 2x12
So, the total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.
Since the Nash Equilibrium is when both players put in the same effort level, there is no effort level that yields a higher total payoff than the Nash Equilibrium.
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Please I need help , thanks
Answer:
y = -3/4 x + 3
Step-by-step explanation:
y = mx + b You need the m value (slope) and the b (y-intercept value) to the write the equations.
Slope:
Look that the two intercepts of x (4,0) and the y intercept of (0,3). If you start and (4,0) and go up 3 and left 4, you will land back on the line at the point (0,3). Slope is the rise over the run. The rise is up and positive 3. The run is left and negative -4
3/-4 is the same as -3/4
-3/4 is the slope.
y-intercept:
The y intercept is at the point (0,b) In this case, the point is (0,3).
3 is the y-intercept.
y = mx + b Substitute -3/4 for m and 3 for b
y = -3/4 x + 3
at Smalltown University, is reading applications submitted by prospective students. The president of Smalltown University is weary about admitting too many domestic students and not enough international students. However, the applications are blinded so Jenny cannot see if an applicant is a domestic student or international student. Jenny is instructed by the president to admit exactly 14 applicants to the Department of Mathematics in a given year. Suppose that 55 domestic students and 45 international students applied to the Department of Mathematics at Smalltown University this year, and suppose that there is no difference in the qualifications of domestic and international students applying to Smalltown University. Let X represent the number of domestic applicants that Jenny selects this year. Calculate the mean, M. and standard deviation, o, of X. Please give the exact value for the mean and round your standard deviation to the nearest three decimal places. (X) = o(X) =
The mean of X can be calculated using the expected value formula, E(X) = sum of all possible values of X * probability of each value.
Since Jenny has to admit exactly 14 applicants, the possible values of X can be 0 to 14.
The probability of each value can be calculated using the binomial distribution formula, P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where n = 14 (number of applicants Jenny has to admit), k = number of domestic applicants, and p = probability of a domestic applicant (55/100).
So, the expected value of X can be calculated as:
E(X) = sum of P(X=k) * k, for k = 0 to 14
= (0 choose 0) * (55/100)^0 * (45/100)^(14-0) * 0 + (14 choose 1) * (55/100)^1 * (45/100)^(14-1) * 1 + ... + (14 choose 14) * (55/100)^14 * (45/100)^(14-14) * 14
= 7
So, the mean of X, M = E(X) = 7
The standard deviation of X can be calculated using the formula, o(X) = sqrt(E((X-M)^2))
= sqrt(E(X^2) - M^2)
= sqrt((sum of P(X=k) * k^2) - M^2)
= sqrt((0 choose 0) * (55/100)^0 * (45/100)^(14-0) * 0^2 + (14 choose 1) * (55/100)^1 * (45/100)^(14-1) * 1^2 + ... + (14 choose 14) * (55/100)^14 * (45/100)^(14-14) * 14^2 - M^2)
= sqrt(3.65)
So, the standard deviation of X, o(X) = 1.91 (rounded to nearest three decimal places).
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How do I combine 4x and 1/2x in the problem 4x-3+1/2x ?
Not getting how 4x and 1/2x turns to 9/2x
Answer:
Step-by-step explanation:
[tex]4x+\frac{1}{2}x = (4+\frac{1}{2} )x[/tex]
[tex]=(\frac{8}{2} +\frac{1}{2} )x[/tex]
[tex]=\frac{9}{2}x[/tex]
A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 8 inches and a base of 6 inches. The area of the hexagonal base is 93.5 square inches. What is the surface area of the pyramid? Enter your answer in the box. in²
The surface area of the pyramid is A = 265.23 inches²
What is the surface area of the pyramid?The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid
Surface Area of Pyramid = B + ( 1/2 ) ( P x h )
Given data ,
Let the surface area of hexagonal pyramid be represented as A
Surface area of hexagonal pyramid = Area of base + area of lateral surface
Area of the base = 93.5 inches²
Now , the Area of the lateral surface = 3a √ ( h² + ( 3a²/4 ) )
where a = 6 inches
h = 8 inches
Substituting the values in the equation , we get
Area of the lateral surface = ( 3 x 6 ) √ ( 64 + ( 3 x 36 / 4 ) )
On simplifying the equation , we get
Area of the lateral surface = 171.7 inches²
So , Surface area of hexagonal pyramid = Area of base + area of lateral surface
Surface area of hexagonal pyramid A = 93.5 inches² + 171.7 inches²
Surface area of hexagonal pyramid A = 265.23 inches²
Hence , the surface area of hexagonal pyramid is 265.23 inches²
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The first 4 terms in a sequence are 8,5,2,-1 What is the recursive equation?
Answer: The recursive equation for this sequence is t(n+1)=t(n) - 3.
Step-by-step explanation:
The recursive equation for the given sequence is t(n+1) = t(n) - 3. This means that to find the next term in the sequence, we take the previous term and subtract 3 from it.
For example:
t(1) = 8 (first term in the sequence)
t(2) = t(1) - 3 = 8 - 3 = 5 (second term in the sequence)
t(3) = t(2) - 3 = 5 - 3 = 2 (third term in the sequence)
t(4) = t(3) - 3 = 2 - 3 = -1 (fourth term in the sequence)
In general, the recursive equation t(n+1) = t(n) - 3 will give the nth term of the sequence.
It should be noted that the initial condition provided in the question t(0)=-3, t(n+1)=t(n) +11 is incorrect and will not give the same sequence.
Please help if you can, this is due in two days.
Answer:
8.8
Step-by-step explanation:
Property of similar triangles
In a year when the maximum income for Social Security was $118,500, Bart worked at two jobs. In one job he earned $99,112. In his second job, he earned $56,222.
Both of his employers took out Social Security tax. As a result, Bart had paid excess Social Security tax, and the government must return some of it to him. How
much does the government owe him for excess Social Security paid?
Answer:
The government owes Bart the excess Social Security tax that he paid, which is the amount of tax he paid on his income above the maximum income for Social Security. In this case, that would be $118,500 (the maximum income for Social Security) minus $99,112 (what he earned at his first job) minus $56,222 (what he earned at his second job) = $13,166. So the government owes Bart $13,166 for the excess Social Security tax he paid.
Answer:
Step-by-step explanation:
He earned a total of 155,334.
99112 plus 56222.
subtract the max income from the income total
155,334 - 118500 = 36834
He is owed the social security tax he paid on 36834.
The problem does not give the social security rate.
An report describes a survey of 251 adult Americans. Participants in the survey were asked how often they change the sheets on their bed and were asked to respond with one of the following categories: more than once a week, once a week, every other week, every three weeks, or less often than every three weeks. For this group, 11% responded more than once a week, 51% responded once a week, 26% responded every other week, 5% responded every three weeks, and 7% responded less often than every three weeks.
(a) Use the given information to make a relative frequency distribution for the responses to the question. How Often? Relative frequency
More than once a week Once a week Every other week Every three weeks Less often than
every three weeks
More than once a week: 0.11
Once a week: 0.51
Every other week: 0.26
Every three weeks: 0.05
Less often than every three weeks: 0.07
Relative Frequency Survey ResultsTo make a relative frequency distribution, follow these steps:
Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.
Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.
And that's it! These are the relative frequencies for each category in the data.
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indicate which of the following sentences are statements. (select all that apply.) A. 1,024 is the smallest four-digit number that is a perfect square. B.he is a mathematics major. C.128=26 D.X=26
D. X=26 is a mathematical statements, since it can be either correct or incorrect.
To comprehend any mathematical statement, we must first understand what mathematics is all about. When we answer a math problem, the solution is either correct or incorrect. There is no midway to the problems! Any mathematical statement is in the same scenario. A mathematical statement is either correct or incorrect.
In this scenario, the statement, 'A. 1,024 is the smallest four-digit number that is a perfect square.', and 'B. He is a mathematics major.' are correct statements. And 'C. 128=26' is a incorrect statement. Therefore, these options are not the mathematical statements because A and B is correct statement and C is a false statement. Meanwhile, D. X=26 is a mathematical statement because it is either correct or incorrect, depending on the given problem. Therefore D. X=26 is the correct answer for a mathematical statement.
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A and B are points on a polygon. A’ and B are the points under a translation. Find B’
By translation the point B' on the polygon is (0, -8).
What is translation?If the point (x, y) is translated h unit to the right and k unit to the up, its image is (x + h, y + k) and the translation is (h, k)If the point (x, y) is translated h unit to the left and k unit to the right, its image is (x - h, y + k) and the translation is (-h, k)If the point (x, y) is translated h unit to the right and k unit to the bottom, its image is (x + h, y - k) and the translation is (h, -k)If the point (x, y) is translated h unit to the left and k unit to the right, its image is (x - h, y - k), and the translation is (-h, -k)Let us try to answer the question.
The coordinates of point A are as follows: (4, 5)
x = 4 and y
The coordinates of point A' are as follows: (9, -1)
x' = 9 and y' = -1
That is, in the third case above, x increased and y decreased.
The point A has been moved to the right and down.
Using the third rule above (x + h, y - k),
x + h = 9
x = 4
Multiply x by 4.
4 + h = 9
Subtraction of 4 from both sides
4 - 4 + h
= 9 - 4
h = 5
y - k = -1
y = 5
Substitute 5 for y
5 - k = -1
Subtraction of 5 from both sides
5 - 5 - k = -1 - 5
-k = -6
Divide each side by -1.
k = 6
In the third case, the translation is (h, -k).
h = 5 and k = 6
The literal translation is (5, -6)
To find B' the image of the point B
B = (-5, -2)
B' = (x + h, y - k)
B' = (-5 + 5, -2 - 6)
B' = (0, -8)
The complete question is :
" A and B are points on a polygon. A' B' are points of the polygon under a translation. Find B'.
A(4,5) A' (9,-1)
B (-5,-2) B' (0,-8)."
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Can someone solve this please? Ty
The number of months during which the company is not making a profit 18.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
C(x) = 17 - 8x - 2x²
R(x) = 5 - 3x
If there is no profit it means,
R(x) - C(x) = 0
Now,
5 - 3x - ( 17 - 8x - 2x²) = 0
5 - 3x - 17 + 8x + 2x² = 0
2x² + 5x - 12 = 0
Solve for x.
2x² + 5x - 12 = 0
2x² + (8 - 3)x - 12 = 0
2x² + 8x - 3x - 12 = 0
2x(x + 4) - 3(x + 4) = 0
(x + 4)(2x - 3) = 0
x = -4 (rejected) and x = 3/2
Now,
x = 3/2 = 1.5
This means,
1.5 years = 18 months
Thus,
The number of months is 18.
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Based on the graph above, estimate to one decimal place the average rate of change from
The average rate of change from x=1 to x=5 is -1.325.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
at x=1 the value of y is 8.5
x=5 the value of y is 3.2
slope=3.2-8.5/5-1
=-5.3/4
m=-1.325
Hence, the average rate of change from x=1 to x=5 is -1.325.
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Write an exponential function for the graph. Write the function in the form y = a(b)*. W AYA O X please l need help
The exponential function for the graph at the end of the answer is defined as follows:
y = -1.5(2)^x.
How to model the exponential function?The definition of an exponential function is given as follows:
y = ab^x
In which the parameters are defined as follows:
a is the value of y when x = 0.b is the rate of change, that is, by how much y is multiplied when x is increased by one.When x = 0, y = -1.5, hence the parameter a is given as follows:
a = -1.5.
When x = 2, y = -6, hence the parameter b is obtained as follows:
-1.5b² = -6
b² = 4.
b = 2.
Then the function is defined as follows:
y = -1.5(2)^x.
Missing InformationThe function is given by the image presented at the end of the answer.
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The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
W
Answer:
Where is the graph
Step-by-step explanation:
I need it
A farmer wants to make a rectangular field with a total area of 2500 square meters. it is surrounded by a fence. it is divided into 3 equal areas by fences as shown. Express the total length L of all the fence required in terms of the length x of one of the fences which divide the field.
The fence's shortest overall length is 808 meters.
Describe the rectangle.
A quadrilateral having all four interior angles at 90 degrees is a rectangle.
Given that the square field has an area of 800 m2.
Let the rectangle's length and breadth be x and y.
The rectangle's area is then:
A= xy
Or, xy = 800
x = 800/y (1) (1)
The triangle's perimeter is:
2x +2y
The total length of the fence is equal to the perimeter of the triangle plus twice the length or width of the triangle since the fence divides the triangle into three equal portions.
Consequently, the fence's overall length is:
L = 2x + 2y + 2x
L = 4x +2y
the equation above with x = 800/y as a replacement:
L = 4(800/y) + 2y
L = 3200/y +2y (2)
Differentiate the equation with respect to y:
L' = -3200/y² +2
Substitute L'= 0 into the above equation:
0 = -3200/y² + 2
y² = 3200/2
y² = 1600
y = 400
Substitute y = 400 into equation (2):
L = 3200/400 + 2(400)
L = 8 + 800
L = 808
Hence, The fence's shortest overall length is 808 meters
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The weight of a sphere is proportional to its radius cubed. If a sphere of diameter 1 cm has a mass of 10 grams, what diameter sphere has a mass of 640grams?
Answer:
if 1cm-10grams
what Abt 640 grams=64cm
HELPP PLSS What is the measurement of ∠Z
Answer:
Z = 155
Step-by-step explanation:
You know all the angles inside the triangle.
180 - 65 - 90 = X
X = 25
Thus using the supplementary rule (All straight lines have degree of 180), then you can get Z
180 - X = Z
180 -25 = Z
Z = 155
Trisha has a job walking 13 dogs for her neighbors. She can walk one, two, or three dogs on each trip to the park. What is the fewest number of trips Trisha takes to walk all 13 dogs?
The fewest number of trips Trisha takes to walk all 13 dogs is of
Five trips.
How to obtain the fewest number of trips?The fewest number of trips is obtained applying the proportions in the context of this problem.
To minimize the number of trips, we must maximize the number of trips with three dogs, hence:
13/3 = 4 with a remainder of 1.
Hence she needs five trips, divided as follows:
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7j+5−8kb; when j = 0.5 and k = 0.25
The given expression becomes 5.35-2b.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 7j+5-8kb.
Here, j = 0.5 and k = 0.25
Now, substitute j = 0.5 and k = 0.25 in the given expression, we get
7×0.5+5-8×0.25×b
= 0.35+5-2b
= 5.35-2b
Therefore, the expression is 5.35-2b.
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Answer:
6.5
Step-by-step explanation:
Find the 59th term of the
arithmetic sequence 29, 37, 45, ...
Answer:
383
Step-by-step explanation:
37 - 29 = 6
59 x 6 = 353
353 + 29
NO LINKS!!
Shown in the figure is a cross-section of a design for a two-story home. The center height h of the second story has not yet been determined. Find h such that the second story will have the same cross-sectional area as the first story.
h = __________ ft
Answer:
h = 13 ft
Step-by-step explanation:
The cross-sectional area of the first story is the area of a rectangle with width 30 ft and height 8 ft. The area of a rectangle is the product of its width and height.
[tex]\begin{aligned}\implies \textsf{Cross-sectional area of first story}&=30 \times 8\\&=240\; \sf ft^2\end{aligned}[/tex]
The cross-sectional area of the second story is made up of a rectangle with width 30 ft and height 3 ft, and a triangle with base 30 ft and height (h - 3). The area of a triangle is half the product of its base and height.
[tex]\begin{aligned}\implies \textsf{Cross-sectional area of second story}&=(30 \times 3)+\dfrac{1}{2} \times 30 \times (h-3)\\&=90+15(h-3)\\&=90+15h-45\\&=(15h+45)\; \sf ft^2\end{aligned}[/tex]
If the second story has the same cross-sectional area as the first story, then:
[tex]\implies 15h+45=240[/tex]
To find h, solve the equation:
[tex]\begin{aligned}\implies 15h+45&=240\\15h&=195\\h&=13\; \sf ft\end{aligned}[/tex]
Therefore, the value of h such that the second story will have the same cross-sectional area as the first story is 13 ft.
The coordinates of the endpoints of AB are A(–4,8) and B(8,2). Its midpoint is C.
What are the coordinates of C?
The required coordinate of the midpoint C is given as (2, 5), as per the given conditions.
What is the midpoint?Midpoint is that point on the line whose distance from both ends of the line is equal.
Here,
The coordinates of the endpoints of AB are A(–4,8) and B(8,2).
Let the coordinate of point C be (x, y)
Now,
x = x₁ + x₂ / 2 ; y = y₁ + y₂/2
Substitute value in the above expression,
x = -4 + 8 / 2 ; y = 8 + 2 / 2
x = 2 , y = 5
Thus, the required coordinate of the midpoint C is given as (2, 5), as per the given conditions.
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solve each of the given inequalities for z. Which of the inequalities has 5 as a solution
The inequality 4(2.8z + 1.75) > -26.6 has 5 as a solution and its solution is, z > - 3.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequalities are,
⇒ 4(2.8z + 1.75) > -26.6
⇒ 2(1.9z + 1.5) ≤ 18.2
Now, We can solve the inequalities as;
1) ⇒ 4(2.8z + 1.75) > -26.6
Divide by 4;
⇒ 2.8z + 1.75 > - 6.65
Subtract 1.75 both side,
⇒ 2.8z > - 6.65 - 1.75
⇒ 2.8z > - 8.4
Divide by 2.8;
⇒ z > - 8.4/2.8
⇒ z > - 3
Clearly, z = 5 is the solution of the above inequality.
2) 2(1.9z + 1.5) ≤ 18.2
Divide by 2;
⇒ 1.9z + 1.5 ≤ 9.1
Subtract 1.5 both side,
⇒ 1.9z ≤ 9.1 - 1.5
⇒ 1.9z ≤ 7.6
Divide by 1.9;
⇒ z ≤ 7.6/1.9
⇒ z ≤ 4
Clearly, z = 5 is not the solution of the above inequality.
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The complete question is this,
Solve each of the given inequalities for z. Which of the inequalities has 5 as a solution?
Inequality 1 Inequality 2
4(2.8z + 1.75) > -26.6 2(1.9z + 1.5) ≤ 18.2
Please help me out, thanks
Answer:
d
Step-by-step explanation: using logic of dimension analysis , since y represent distance and x represent hours of traveling in train means time then 60 must be speed for equality i.e distance traveled by train per hour , for correcting dimensionaly
d (x) = -(x+7)^(2) +9
domain =
function =
The domain of d(x) = -(x+7)^2 + 9 are the set of all real numbers and the function is d(x) = -(x+7)^2 + 9
How to determine the domain and the function?from the question, we have the following parameters that can be used in our computation:
d(x) = -(x+7)^2 + 9
This means that the function is d(x) = -(x+7)^2 + 9
There is no restriction on the input values, x
So, the domain of d(x) = -(x+7)^2 + 9 is all real numbers, since there is no restriction on the input (x).
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3(x+4).
susushsjsssjsjsjsjskskkddjd
Answer:
3x+12 because of the bracket it makes the 3 multiply the x and
i don’t understand and cant find the formulas to find these things
Answer:
7.30%; $1452.024.45%; 15.56 yearsStep-by-step explanation:
You want the interest rate and account balance after 10 years if the investment of $700 doubles in 9 1/2 years with interest compounded continuously. And, you want the interest rate and doubling time if a $900 investment has a value of $1405 after 10 years with continuous compounding.
Compound interestThese problems are solved by making use of the compound interest formula for continuously compounded interest. In each case, you fill in the values you know, and solve for the one you don't know.
A = Pe^(rt)
$700The investment doubles after 9.5 years, so we have ...
2·700 = 700e^(9.5r)
Dividing by 700 and taking natural logs, we find the rate to be ...
ln(2) = 9.5r
r = ln(2)/9.5 ≈ 0.072963 ≈ 7.30%
Using the exact value in the computation of the balance, we get ...
A = 700e^(10·(ln(2)/9.5)) = 700·2^(10/9.5) = 700·2^(20/19)
A = 1452.02
The annual rate is 7.30%; the balance in 10 years is $1452.02.
$900The balance after 10 years is ...
1405 = 900e^(r·10)
ln(1405/900) = 10r
r = ln(1405/900)/10 ≈ 0.0445398 ≈ 4.45%
As we found above, the relation between r and doubling time is ...
r = ln(2)/t ⇒ t = ln(2)/r
t = ln(2)/0.0445398 ≈ 15.56 . . . . years
The annual rate is about 4.45%; the doubling time is about 15.56 years.
__
Additional comment
In the first problem, we could find the account balance after 10 years using the found interest rate. In that case, it would be $1452.56. Instead, we chose the doubling time to be the exact value in the problem.
There is a "rule of 70" or sometimes the "rule of 72" that tells you the approximate doubling time in years (y) for an interest rate of r%. It is ...
y = 70/r
The amount of error depends on the interest rate and the way interest is compounded.
When the interest is compounded continuously, a slightly different rule gives the exact doubling time:
y = 100·ln(2)/r ≈ 69.31472/r
This is effectively the rule we used above.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Triangle ABC is defined by the points A(2,9), B(8,4), and C(-3,-2). Complete the following equation for a line passing through point C and perpendicular AB.
The equation of the line passing through point C and perpendicular to line AB is: y = -6/5x - 20/5 + 2
Describe slope using an example.The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Using the coordinates of points A and B, we have:
m = (4 - 9) / (8 - 2) = -5 / 6
The slope of a line perpendicular to this line would be the negative reciprocal of this slope, so:
m= -1 / m = -6 / 5
Next, we can use the point-slope form of a line to find the equation of the line, which is:
y - y1 = m * (x - x1)
Substituting the values for m, x1, and y1 (where x1 and y1 are the coordinates of point C), we have:
y - (-2) = -6/5 * (x + 3)
Simplifying and solving for y, we get:
y = -6/5 * x - 20/5 + 2
So, the equation of the line passing through point C and perpendicular to line AB is: y = -6/5x - 20/5 + 2
Learn more about slope
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Height in P
0
-1
0.5
1
Time in Seconds (t)
function:
2
h(t) = -16t² + 12t
Move the blue lines to indicate where the basketball
player is going UP in the air.
Complete these sentences (reminder: you can click on
the graph to locate certain values).
The player starts going up at
2.25
The player stops going up at
1.76
NC
seconds.
In mathematical terms, when would the player be
rising?
(0,0.375)
seconds.
WELL
TITT
US
Jan 29s
The quadratic function for the height of the player, h(t) = -16·t² + 12·t indicates the following
The player starts going up at 0 seconds
The player stops going up at 0.375 seconds
The player would be rising in the interval [0, 0.375)
What is a quadratic function?A quadratic function is a function that can be expressed as; f(x) = a·x² + b·x + c, with the values of a, (a ≠ 0) b, and c representing numbers.
The function for the height is; h(t) = -16·t² + 12·t
The time the player starts going up can be found as follows;
The minimum height = -1
When h(t) = -1, we get; -1 = -16·t² + 12·t
-16·t² + 12·t + 1 = 0
Therefore, t = (3 ± √13)/8
t ≈ 0.826 and t ≈ -0.076
However, the value of the time is a natural number, therefore;
The player starts going up at t = 0 seconds.The player stops going up at the maximum height, which can be obtained from the value of the maximum point of a quadratic function, which is; t = -12/(2 × (-16)) = 3/8 = 0.375
The player stops going up at 0.375 secondsIn mathematical terms the player will be rising between the interval, 0 ≤ t < 0.375, which can be expressed as; [0, 0.375)
The interval during which the player is rising is; [0, 0.375)Learn more on the evaluation of quadratic functions here: https://brainly.com/question/27910564
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four more than h is no less than 27.
Answer:
Below
Step-by-step explanation:
four more than h is h+4
no less than 27 means it is greater than or equal to 27
h+4 >= 27
