A linear programming problem with two decision variables can be solved by a graphical solution method. In this method, the constraints and the objective function of the linear programming problem are graphed on a two-dimensional coordinate plane, and the optimal solution is found at the intersection of the feasible region (the area defined by the constraints) and the level curve of the objective function.
The graphical solution method is a simple and intuitive way to solve linear programming problems with few decision variables, but it becomes impractical as the number of decision variables and constraints increase. In such cases, more complex algorithms, such as the simplex method or interior point methods, are used to find the optimal solution.
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Evaluate the following expression.
25
1/25
-25
-1/25
The expression is evaluated to 1/25. Option B
What are index forms?Index forms are simply described as distinct mathematical forms that are used in the representation of variables or numbers that are too large or too small in more convenient forms.
These index forms are also referred to as scientific notations or standard forms.
Some rules of index forms are;
Add the exponent value of variables or number that have the same bases and are being multipliedSubtract the exponent value of variables or number that have the same bases and are being dividedThe value of a number with negative power is its inverseFrom the information given, we have that;
1/5⁻²
Take the inverse power
1/25
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You deposit $400 in an account that pays 2.34% annual
compounded monthly. What is the balance after
interest
10 years?
A=
The balance after 10 years, considering monthly compounding, would be approximately $512.69.
To calculate the balance after 10 years, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{(nt)[/tex]
A is the final balance
P is the principal amount (initial deposit)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $400, the annual interest rate (r) is 2.34% or 0.0234, the interest is compounded monthly (n = 12), and the number of years (t) is 10.
Using these values, we can calculate the final balance (A):
A = $400(1 + 0.0234/12)⁽¹²ˣ¹⁰⁾
A = $400(1.00195)¹²⁰
A ≈ $400(1.28172)
A ≈ $512.69
We may use the compound interest calculation to determine the balance after 10 years:
A = [tex]P(1 + r/n)^{(nt)[/tex]
The ultimate balance is A.
P stands for the initial deposit's principal.
The yearly interest rate is represented by the decimal r, while the number of times it is compounded annually is represented by n.
The number of years is t.
In the above scenario, the principle (P) is $400, the annual interest rate (r) is 2.34%, or 0.0234, the interest is compounded on a monthly basis (n = 12), and the time (t) is 10.
These numbers allow us to determine the final balance (A):
A = $400(1 + 0.0234/12)⁽¹²ˣ¹⁰⁾
A = $400(1.00195)¹²⁰
A ≈ $400(1.28172)
A ≈ $512.69
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After heating up in a teapot, a cup of hot water is poured at a temperature of
20
3
∘
203
∘
F. The cup sits to cool in a room at a temperature of
6
9
∘
69
∘
F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
�
=
�
�
+
(
�
0
−
�
�
)
�
−
�
�
T=T
a
+(T
0
−T
a
)e
−kt
�
�
=
T
a
= the temperature surrounding the object
�
0
=
T
0
= the initial temperature of the object
�
=
t= the time in minutes
�
=
T= the temperature of the object after
�
t minutes
�
=
k= decay constant
The cup of water reaches the temperature of
18
5
∘
185
∘
F after 1.5 minutes. Using this information, find the value of
�
k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.
Enter only the final temperature into the input box.
The cup of water reaches a temperature of 173 F after 4.5 minutes.
What is temperature?Temperature is a measure of the average kinetic energy of particles in a system. It is an important physical quantity used to describe the state of a system and is widely used in science, engineering, and everyday life. Temperature is a thermodynamic property of a system that shows how much energy is available to do work. In everyday terms, temperature is a measure of how hot or cold something is.
k = -0.2416
The equation for the cooling rate of the cup of water is:
T(t) = 203- 0.2416t
After 4.5 minutes, the temperature of the cup of water can be found by substituting t = 4.5 into the equation:
T(5) = 203- 0.2416(4.5 ) = 173.08 F
Therefore, the cup of water reaches a temperature of 173 F after 4.5 minutes.
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Please helppp. What’s the area and circumference??!
The value of EF is 26
What is segment of a circle?A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord's endpoints.There is minor segment and major segment.
Since the two arcs are equal, i.e arc EF = arc CD, therefore,
chord EF = chord CD
9x-1 = 41 - 5x
collecting like terms
9x +5x = 41+1
14x = 42
divide both sides by 14
x = 42/14
x = 3
Therefore EF = 41-5x
= 41-5×3
= 41-15
= 26
therefore the value of EF is 26
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Help with my math please
Answer:
Step-by-step explanation:
x+y=5; x-y=3Adding both equations, we get:
2x = 8
x = 4Substituting the value of x in any of the equations:
x+y=5
4+y=5
y=1So the solution to this system of equations is: x=4, y=1.3x+y=11; y=x+3Substituting y=x+3 in the first equation:
3x+x+3=11
4x=8
x=2Substituting x=2 in the second equation:
y=x+3
y=2+3
y=5So the solution to this system of equations is: x=2, y=5.x+3y=0; 2x-y=-7Multiplying the second equation by 3 to eliminate y:
6x-3y=-21Adding both equations, we get:
7x=-21
x=-3Substituting x=-3 in the first equation:
x+3y=0
-3+3y=0
y=1So the solution to this system of equations is: x=-3, y=1.y=-3x-2; 6x+2y=-4Substituting y=-3x-2 in the second equation:
6x+2(-3x-2)=-4
6x-6x-4=-4
-4=-4This means that the two equations are equivalent and represent the same line. Therefore, there are infinitely many solutions to this system of equations.-4x+5y=27; x-6y=-2Multiplying the second equation by 5 to eliminate y:
5x-30y=-10Adding both equations, we get:
x-4x+5y-30y=-2+27
-x-25y=25
25y=-x-25
y=-(1/25)x-1Substituting y=-(1/25)x-1 in the first equation:
-4x+5(-(1/25)x-1)=27
-4x-5/5x-5=27
-9x=32
x=-32/9Substituting x=-32/9 in the expression for y:
y=-(1/25)(-32/9)-1
y=83/225So the solution to this system of equations is: x=-32/9, y=83/225.
The terminal side of theta in standard position contains the point (-2, -6). Find the exact value of sin theta.
The exact value of sin theta as required to be determined in the task content is; sin theta = -3 / 2√10.
What is the exact value of sin theta as required?It follows from the task content that the exact value of sin theta is required to be determined from the given information.
Since the given terminal side of theta is; (-2, -6) it follows that the length of the hypothenuse in the arrangement is;
= √((-2)² + (-6)²)
= √(4 + 36)
= √40
= 4√10.
Therefore, since sin theta = opposite / adjacent;
Sin theta = -6 / 4√10
sin theta = -3 / 2√10.
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Can someone help me solve question number 14? I've tried to solve it and got 3426 while the answers in the book say it's 2,6. Can someone pls explain why it's wrong?
Answer:
f(x) = x^3 - 12x^2 + 6x - 8
f'(x) = 3x^2 - 24x + 6 = -30
3x^2 - 24x + 36 = 0
x^2 - 8x + 12 = 0
(x - 2)(x - 6) = 0, so x = 2, 6
Answer:
the values of x are :
x = 2
x = 6
[tex]\frac{2x-1}{3} -\frac{3x}{4} =\frac{5}{6}[/tex]
The value of the variable is -14
What are fractions?Fractions are simple defined as the part of a whole number or variable.
From the information given, we have that;
2x - 1/3 - 3x/4 = 5/6
Find the LCM, we have;
4(2x - 1) - 3(3x) /12 = 5/6
expand the bracket, we get;
8x - 4 - 9x/12 = 5/6
collect the like terms
-x - 4/12 = 5/6
cross multiply the values
-6x - 24 = 60
collect like terms
-6x = 84
make 'x' the subject
x = -14
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how many units is -1+(-4) from -1
The expression -1 + (-4) is 4 units away from -1.
How to find the unitsThis can be solved using the concept of number line.
A number line is a visual representation of all real numbers placed on a straight line with an arbitrary point as the origin the origin is usually represented as zero and the numbers increase from left to right or from right to left
Another way is to find how many units -1 + (-4) is from -1, we need to subtract -1 from -1 + (-4) this is done below
= -1 + (-4) - (-1)
= -1 - 4 + 1
= -4
we can say that, -1 + (-4 ) is 4 units away from -1.
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The graph of function fis shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.
g(x)=f(x + 2)
Drawing Tools
Select
Line
Click on a tool to begin drawing.
-6
-2
Delete
Undo
8
Reset
A graph representing the function g(x) = -1/2f(x + 2) is shown in the image below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 0)/(5 - 3)
Slope (m) = 4/2
Slope (m) = 2.
At data point (3, 0) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 2(x - 3)
y = f(x) = 2x - 6
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The slope of the line tangent to the graph of y = \ln \left( {1 - x} \right) at x=-1 is
(A) -1
(B) - \frac{1}{2}
(C) \frac{1}{2}
(D) \ln \left( 2 \right)
(E) 1
To find the slope of the line tangent to the graph of y = ln(1 - x) at x = -1, we can use the derivative of the function.
The derivative of y with respect to x can be found using the chain rule:
dy/dx = d/dx[ln(1 - x)] = 1 / (1 - x) * (-1) = -1 / (1 - x)
Substituting x = -1 into the derivative, we have:
dy/dx = -1 / (1 - (-1)) = -1 / 2
Therefore, the slope of the line tangent to the graph at x = -1 is -1/2.
The correct answer is (B) -1/2.
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A 2-pint bottle of salad dressing costs $13.76. What is the price per cup?
Submit
The price per cup of salad dressing in a 2-pint bottle that costs $13.76 is $0.86.
To calculate the price per cup of salad dressing, we need to know that there are 2 cups in a pint. Therefore, there are 4 cups in a 2-pint bottle of salad dressing.
To find the price per cup, we divide the total cost of the bottle by the number of cups in the bottle.
$13.76 ÷ 4 cups = $3.44 per cup
Therefore, the price per cup of salad dressing is $0.86, which is obtained by dividing $3.44 by 4.
It is important to know the price per unit, whether it is per ounce, per pound, per liter, or per cup, to be able to compare the cost of different products accurately.
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Factorize a2 - b2
[tex]a {?}^{2} - b {?}^{2} \\ \\ [/tex]
The factorization of the given expression, a² - b², is (a + b)(a - b)
Factorizing an expressionFrom the question, we are to factorize the given expression.
From the given information, the given expression is
a² - b²
This is a special case in the factorization of polynomials. This is called difference of two squares.
Given the expression
x² - y²
The above expression can be written in the factorized form as
(x + y)(x - y)
Check:
Check by expanding the above factored form
(x + y)(x - y)
Applying the distributive property
x(x - y) + y(x - y)
x² - xy + xy - y²
Simplify further
x² - y²
Thus,
x² - y² = (x + y)(x - y)
In the same manner,
a² - b² = (a + b)(a - b)
Hence, the factorization of a² - b² is (a + b)(a - b)
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a rectangular lot is 135 yards long and 100 yards wide, give the length and width of another rectangular lot that has the same perimeter but a larger area.
Will make brainiest if two people answer ૮ ˶ᵔ ᵕ ᵔ˶ ა
The length of side LJ as shown in the similar shapes is 12.92.
What is similar shapes?Similar shapes are enlargements of each other using a scale factor.
To calculate the length of side LJ, we use the formula below
Formula:
XZ/XY = KJ/KL....................... Equation 1From the diagram,
Given:
/XZ/ = 8.2/XY/ = 8.7/KJ/ = 12.18Substitute these values into equation 1 and solve for KL
8.2/8.7 = 12.18/KLKL = 8.7×12.18/8.2KL = 12.92Hence, the right option is 12.92.
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What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
The range of the given function is {y|y>9}. Therefore, option B is the correct answer.
The given function is f(x)=3x+9.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Substitute x=0, 1, 2, 3, 4,....in y=3x+9, We get
When x=0
y=9
When x=1
y=12
When x=2
y=15
When x=3
y=18
So, the range is {9, 12, 15, 18,.....}
Therefore, option B is the correct answer.
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Which composite figure is made up of a cylinder and a half sphere?
a simple random sample of 50 adults was surveyed, and it was found that the mean amount of time that they spend surfing the internet per day is 54.2 minutes, with a standard deviation of 14.0 minutes. what is the 99% confidence interval (z-score
The 99% confidence interval for the population mean time spent on the internet, in minutes, is given as follows:
(48.9, 59.5).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 50 - 1 = 49 df, is t = 2.68.
The parameter values are given as follows:
[tex]\overline{x} = 54.2, s = 14, n = 50[/tex]
Then the lower bound of the interval is given as follows:
[tex]54.2 - 2.68\frac{14}{\sqrt{50}} = 48.9[/tex]
The upper bound of the interval is given as follows:
[tex]54.2 + 2.68\frac{14}{\sqrt{50}} = 59.5[/tex]
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How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.)
A. 0
B. 1
C. 2
D. 3
E. 4
The number of horizontal asymptotes that graph of y = f(x) can have is (c) 2.
As x approaches negative infinity, the function f(x) approaches the horizontal-asymptote y = 0 because the term 1/x becomes negligible compared to other terms. This occurs in the portion of the function defined as 1/x when x < 0.
As x approaches positive infinity, the function f(x) approaches the horizontal-asymptote y = 2 because the term 2x becomes dominant compared to other terms. This occurs in the portion of the function defined as 2x - 1 when x ≥ 0.
Therefore, the graph of y = f(x) has two horizontal asymptotes: y = 0 as x approaches negative infinity and y = 2 as x approaches positive infinity. The correct answer is (c) 2.
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The given question is incomplete, the complete question is
How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.)
f(x) = {1/x , if x<0,
= {2x - 1 , if x≥0.
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
A restaurant put out small dishes of butter at each table.
They divided 1/6 of a pound of butter evenly between
5 dishes.
Answer:
Step-by-step explanation:
Hello!
1. Start by Plugging your numbers in. now all you have to do is 5 divided by 6! Use a calculator but anything works.
A store sells packages of 3 pens for $1.50, 8 pens for $4.00, and 12 pens for $6.00. Let c represent the total cost and p represent the number of pens. Write an
equation to represent this situation.
The equation for the total cost and p represent the number of pens is c = 3p + 8p + 12p
Which equation represents the situation?3 pens for $1.50
8 pens for $4.00
12 pens for $6.00
Where,
c represent the total cost
p represent the number of pens
Total cost, c = 1.50 + 4.00 + 6.00
= $11.50
Number of pens, p = 3 + 8 + 12
= 23
c = 3p + 8p + 12p
$11.50 = 23p
Hence, c = 3p + 8p + 12p is the equation that represents the situation.
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The quadratic equation h=-16t^2+32t+2
represents the height, h (in feet), of a ball kicked after t seconds. Answer each question. Express each answer as a decimal rounded to the nearest hundredth.
How long will it take the ball to reach 18 feet?
When will the object be at 10 feet?
When will the ball hit the ground?
By solving the quadratic equations,
It will take the ball 1 second to reach 18 feet
It will take the ball 1.71 seconds to be at 10 feet
It will take the ball 2.06 seconds to hit the ground
Solving quadratic equations: Determining how long it would take the ball to reach a heightFrom the question, we are to determine how long it would take the ball to reach 18 feet
To determine how long it would take the ball to reach 18 feet, we will set h = 18 in the equation
The given equation is
h = -16t² + 32t + 2
Put h = 18
18 = -16t² + 32t + 2
Rearrange
16t² - 32t - 2 + 18 = 0
16t² - 32t + 16 = 0
16t² - 16t - 16t + 16 = 0
16t(t - 1) -16(t - 1) = 0
(16t - 16)(t - 1) = 0
16t - 16 = 0 OR t - 1 = 0
16t = 16 OR t = 1
t = 16/16 OR t = 1
t = 1 OR t = 1
Hence,
t = 1 second
Hence, it will take the ball 1 second to reach 18 feet
To determine how long it will take the ball to reach 10 feet, we will set h = 10
h = -16t² + 32t + 2
Put h = 10
10 = -16t² + 32t + 2
Rearrange
16t² - 32t - 2 + 10 = 0
16t² - 32t + 8 = 0
Using the quadratic formula,
t = 0.29 second OR t = 1.71 seconds
The ball will hit the ground when h = 0
Set h = 0 in the equation
h = -16t² + 32t + 2
0 = -16t² + 32t + 2
16t² - 32t - 2 = 0
Using the quadratic formula,
t = -0.06 OR t = 2.06
Since t cannot be negative,
t = 2.06 seconds
Hence, it will take 2.06 seconds for the ball to hit the ground
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = - + 7.
The Equation for Table I is y= 1/3x + 5.
The solution of the Equation is (3, 6).
Equation for Table II
y= -1/3 x +7
Table I:
Slope = (6-5)/ (3-0)
slope = 1/3
and, using slope intercept form
y - 5 = 1/3 (x - 0)
y-5 = 1/3x
y = 1/3x + 5
Now, solving the equation for both table we get
x= 3 and y= 6
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kimberly sent gifts to her friends. for each gift she used either a rectangular gift box or a cylindrical gift box. each box contains exactly one gift: either a fragrant soap or a pack of spicy roasted almonds. if half of the boxes she sent were cylindrical, and a third of the rectangular boxes contained soap, then how many cylindrical boxes contained soap?
Kimberly sent approximately 34 cylindrical boxes that contained soap
Let's assume Kimberly sent a total of 100 gift boxes. Since half of the boxes were cylindrical, that means she sent 50 cylindrical boxes.
If a third of the rectangular boxes contained soap, then 1/3 * (100 - 50) = 1/3 * 50 = 50/3 ≈ 16.7 rectangular boxes contained soap. Since we cannot have a fraction of a box, let's round it down to 16 rectangular boxes containing soap.
Now, since each box contains exactly one gift, the remaining cylindrical boxes must contain the pack of spicy roasted almonds. Therefore, out of the 50 cylindrical boxes, 50 - 16 = 34 cylindrical boxes contain soap.
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.
The number of times 100 groups took a
selfie is as follows.
Takes
1 2 3
4
Frequency 27 29 18 14
5
12
Find the probability a group will take their
selfie exactly 3 times.
P(3) = [?]
The probability a group will take their selfie exactly 3 times is 0.18.
We have,
The total groups = 100
The number of groups that took selfies 3 times = 18
Now,
The probability a group will take their selfie exactly 3 times.
= 18/100
= 0.18
Thus,
The probability a group will take their selfie exactly 3 times is 0.18.
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PQR is a tangent to circle QABCD. AB || QD. CB=CD. Let 2, -30° and D₂ =70°. P A 1.1 Calculate Q₁. 1.2 Prove that C=110 A 1.3 Calculate B1
The points (7,-5) and (r,5) lie on a line with slope . Find the missing coordinate .
The missing coordinate is equal to 15.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
5/4 = (5 + 5)/(r - 7)
5/4 = 10/(r - 7)
5(r - 7) = 40
5r - 35 = 40
5r = 75
r = 75/5
r = 15.
Based on the information provided, the slope is the change in y-axis with respect to the x-axis and it is equal to 5/4.
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Complete Question:
The points (7,-5) and (r,5) lie on a line with slope 5/4. Find the missing coordinate
Solve 2x(3x+5)+3(3x+5)=ax 2 +bx+c
Answer:
6x² + 19x + 15
Step-by-step explanation:
2x(3x+5)+3(3x+5)
= (3x + 5) (2x + 3)
= 6x² + 9x + 10x + 15
= 6x² + 19x + 15
So, the answer is 6x² + 19x + 15
We can start by simplifying the left side of the equation using the distributive property:
2x(3x+5)+3(3x+5) = (2x)(3x) + (2x)(5) + (3)(3x) + (3)(5)
= 6x^2 + 10x + 9x + 15
= 6x^2 + 19x + 15
Now we can compare this expression with the right side of the equation, which is a polynomial in x with unknown coefficients a, b, and c:
ax^2 + bx + c
Since the two sides are equal, their corresponding coefficients must be equal as well. This gives us a system of three equations in three unknowns:
a = 6 (the coefficient of x^2)
b = 19 (the coefficient of x)
c = 15 (the constant term)
Therefore, the solution to the equation 2x(3x+5)+3(3x+5)=ax^2+bx+c is:
2x(3x+5)+3(3x+5) = 6x^2 + 19x + 15
15 Points PLEASE HELP ME OUT.
Algebra 1 honors
Answer: A C(t) = -(x-5)^2
Step-by-step explanation:
Answer:
C(t) = -x^2 + 5
Step-by-step explanation:
Notice how C(t) = 5 when t = 0. This means that (0, 5) is a point on C(t) and is the y-intercept, thus making the constant term (term without variable in standard form) 5. Next, notice how C(t) decreases as t increases and decreases. This means that C(t) is reflected over the x-axis such that it looks like an upside-down U shape. Thus, a negative must be applied to the term of the highest degree.
An athlete throws a shot put with an initial vertical velocity of 40 feet per second. He releases the shot put at a height of 5.69 feet.
Use an equation that models the height h (in feet) of the shot put as a function of the time t (in seconds) after it is thrown to find the time that the shot put is in the air.
Round your answers to the nearest whole numbers.
The shot put is in the air for approximately 3 seconds.
The height h (in feet) of the shot put as a function of the time t (in seconds) after it is thrown can be modeled by the equation:
h(t) = h + vt - (1/2)gt²
where v is the initial vertical velocity in feet per second, and s is the initial height in feet.
Here, the initial vertical velocity is 40 feet per second, and the initial height is 5.69 feet. Therefore, we can plug in these values to get:
h = -16t² + 40t + 5.69
To find the time that the shot put is in the air, we need to find the value of t when h = 0, since the shot put will hit the ground when its height is 0.
Therefore, we can set the equation equal to 0 and solve for t:
0 = -16t² + 40t + 5.69
Using the quadratic formula, we get:
t = (-b ± √(b² - 4ac)) / 2a
where a = -16, b = 40, and c = 5.69.
Plugging in these values, we get:
t = (-40 ± √(40² - 4(-16)(5.69))) / 2(-16)
Simplifying, we get:
t ≈ 3 or t ≈ 0.2
Since the shot put cannot be in the air for negative time, the only possible answer is t ≈ 3.
Therefore, the shot put is in the air for approximately 3 seconds.
Learn more about quadratic function here:
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