So the price that would maximize revenue is $2.75.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically contains one or more variables, which represent unknown values that can be solved for using algebraic methods. An equation can be represented symbolically using mathematical notation, such as using letters, numbers, and mathematical symbols like +, -, x, /, and =. Equations can be used to model and solve a wide variety of problems in mathematics, science, engineering, and other fields.
Here,
We can start by finding the linear equation that relates price and monthly sales. Let's use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where y is the monthly sales, x is the price, m is the slope, and (x1, y1) is a point on the line.
Using the two points we have:
(10, 19000) and (7, 25000)
We can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (25000 - 19000) / (7 - 10)
m = 2000
Now we have:
y - 19000 = 2000(x - 10)
Simplifying:
y = 2000x - 11000
This equation represents the relationship between price and monthly sales.
To maximize revenue, we need to find the price that gives the highest value for the product of price and monthly sales. In other words, we need to find the maximum value of the function:
R(x) = x * y = x(2000x - 11000)
Expanding and simplifying:
R(x) = 2000x² - 11000x
To find the maximum, we need to take the derivative and set it equal to zero:
R'(x) = 4000x - 11000 = 0
Solving for x:
4000x = 11000
x = 2.75
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What is the equation of the circle with center (3, 2) that passes through the point (10, 6)?
Answer:
7,3
Step-by-step explanation:
its 7,3
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The coordinates of Checkpoint B as we move from checkpoint A to the west are (-9, 5).
What is cartesian coordinate system?The Cartesian coordinate system, often called the rectangular coordinate system, uses ordered pairs of integers to represent points in a plane. It was created in the 17th century and is named after the mathematician René Descartes. The x-axis, which is horizontal, and the y-axis, which is vertical, split the plane into two perpendicular axes in the Cartesian coordinate system.
First, Hurdle 1 is 4 units west of Checkpoint A, so its x-coordinate is:
0 - 4 = -4
Hurdle 2 is 3 units west of Hurdle 1, so its x-coordinate is:
-4 - 3 = -7
Checkpoint B is 2 units west of Hurdle 2, so its x-coordinate is:
-7 - 2 = -9
The y-coordinate for all remain the same.
Hence, the coordinates of Checkpoint B as we move from checkpoint A to the west are (-9, 5).
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81^3/4 / 81^1/2 =
A. (81/3)^ -1/2
B. 27
c. 9
d. 3
How can I find the domain and Range of k(x)=3(2)*-8 that little star is a x
In the function k(x) = 3(2^(-8x)), the domain is all real numbers (-∞, +∞) and the range is all positive real numbers (0, +∞).
Hi! I'd be happy to help you find the domain and range of the function k(x) = 3(2^(-8x)). The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values) that the function can produce.
For k(x) = 3(2^(-8x)), the function is an exponential function, and exponential functions are defined for all real numbers. This means that you can input any real number value for x, and the function will produce a valid output. Therefore, the domain of k(x) is all real numbers, which can be represented as (-∞, +∞) or R.
To find the range, we need to consider the behavior of the exponential function as x increases and decreases. As x goes to negative infinity, 2^(-8x) approaches infinity, and thus 3(2^(-8x)) also approaches infinity. As x goes to positive infinity, 2^(-8x) approaches 0, but since we are multiplying by 3, the minimum value of k(x) is 0. However, the function never actually reaches 0, so the range is all positive real numbers, which can be represented as (0, +∞).
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The first time you have a chance at the game you can see that the player has been in
A data that appears to be an outlier has been circled as shown in the image attached below.
The estimated difference between any outliers and their predicted values is 285.
What is an outlier?In Mathematics and Statistics, an outlier is sometimes referred to as an anomalous data and it can be defined as a numerical value that is either unusually too large (big) or little (small) in comparison with the overall pattern of the numerical values contained in a data set.
This ultimately implies that, an outlier simply refers to individual data points (values) in a data set that do not fit or seem uncharacteristic of the overall pattern and general trend.
Based on the scatter plot, the predicted outliers are 150 and 435;
Difference = 435 - 150
Difference = 285.
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B The owner of a roadside fruit stand prices his peaches to obtain 52% of his cost as If he expects to start with 50 boxes that cost him 45c each and to sell 90% become overripe and cannot be sold, at what price should he mark the 3. markup. before they peaches?
The owner should mark the price of each box of peaches at 68.4 cents.
How to find the price that the owner should mark the 3. markup before they peaches?The cost of one box of peaches is 45 cents. The owner wants to mark them up by 52%, which means he wants to sell them at 152% of their cost.
So, the selling price of one box of peaches would be:
0.52 x 45 cents = 23.4 cents
However, since 90% of the peaches become overripe and cannot be sold, the owner needs to factor this into his pricing. He wants to make sure he covers the cost of all 50 boxes and still makes a profit on the 10% that he can sell.
The number of boxes that will be sold is:
50 x 0.1 = 5 boxes
So, the selling price of one box of peaches needs to cover the cost of 10 boxes (5 boxes that will be sold and 5 boxes that will be wasted):
10 x 45 cents = 4.50 dollars
The total selling price of 10 boxes of peaches is:
10 boxes x 23.4 cents per box = 2.34 dollars
To cover the cost of all 50 boxes and still make a profit, the selling price of the 10 boxes that can be sold needs to be:
4.50 dollars + 2.34 dollars = 6.84 dollars
Since there are 10 boxes to be sold, the selling price of each box needs to be:
6.84 dollars ÷ 10 boxes = 68.4 cents
Therefore, the owner should mark the price of each box of peaches at 68.4 cents.
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Find the surface area (in square meters) of the prism formed by the net.
7m
28 m
14 m
7m
7m
14 m
Surface area of the prism = 2 x 98m2 + (42m x 28m) = 1372m2.
What is surface area?Surface area is the total area of the exposed sides of a three-dimensional object. It is a measure of how much exposed area an object has, and is the sum of the areas of all its exposed faces. Surface area can be calculated for both regular and irregular shapes, and is a critical measurement for many everyday objects such as buildings, containers, and other objects.
Calculation:
The prism formed by the given net has a rectangular base with dimensions 7m x 14m and a height of 28m.
Surface area of a prism = 2 x (area of base) + (perimeter of base) x height
Area of base = 7m x 14m = 98m2
Perimeter of base = (2 x 7m) + (2 x 14m) = 42m
Surface area of the prism = 2 x 98m2 + (42m x 28m) = 1372m2.
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Area of a prism's surface = [tex]2\times 98m^{2}[/tex] + (42m x 28m)
= [tex]= 1372m^2[/tex].
What is surface area?The conclusions that can be taken from this experiment depend on the research question and the tested hypothesis. The medium noise condition recorded the lowest scores, according to the available data, but there is a variation in the output scores among the three conditions.
However, without additional study or experimental manipulation, we are unable to make any inferences about how noise affects production.
The prism created by the provided net has a 28-meter height and a 7-meter * 14-meter rectangle base.
Area of a prism's surface = 2 x (area of base) + (perimeter of base) x height
Area of base = 7m x 14m
= [tex]98m^{2}[/tex]
Perimeter of base = (2 x 7m) + (2 x 14m)
= 42m
Area of a prism's surface = [tex]2\times 98m^{2}[/tex] + (42m x 28m)
[tex]= 1372m^2[/tex]
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The points (0, 1) and (1, 4) are contained in the graph of an equation with only two variables, 2 and y.
Select all of the true statements.
There is exactly one equation in the form y = max + b that contains these points.
There are two equations in the form y = m + b that contain these points.
There are no equations in the form y = a - b* that contain these points.
There is exactly one equation in the form y - a - b° that contains these points.
There is more than one equation in the form y = a - b° that contains these points.
There are no equations in the form [tex]a * b^{x}[/tex] that contains m = 3 and b=1 points.
What is slope-intercept form?The slope-intercept form can be used to determine the equation of a line that goes through two specific points:
y = mx + b
where m denotes the slope and b is its y-intercept.
It is possible to determine the slope of the line using the coordinates (0, 1) and (1, 4).
[tex]= \frac{y2 - y1}{x2 - x1} =\frac{4 - 1 }{1-0} \\= \frac{3}{1} \\= 3[/tex]
As a result, the line's equation can be expressed as:
y = 3x + b
We can use either location to determine b:
1 = 3(0) + b
b = 1
The line's solution is as follows:
y = 3x + 1
The following assertions can be evaluated using this equation:
1) These values can be found in only one equation with the form y = mx + b.
False. The formula y = 3x + 1 is expressed as y = mx + b rather than y = max + b.
2) These points are included in two equations of the type y = m + b.
False. These points are only present in one equation of the type y = mx + b.
3) These points do not appear in any equations of the type y = [tex]a * b^{x}[/tex].
True. The coordinates (0, 1) and cannot be passed through by any equations in this form. (1, 4).
4) These points are contained in precisely one equation with the form y = [tex]a * b^{x}[/tex].
False. For a line in two variables, the equation form y - a - b° is invalid.
5) These points can be found in multiple equations with the shape y = [tex]a * b^{x}[/tex].
False. For a line in two variables, the equation form y = [tex]a - b^{x}[/tex] is invalid.
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Evaluate this table.
X 5 10 15 25 40
Y 1 2 3 5 8
The table represents a(n)
relationship.
The table of values when evaluated as a function a(n) has the equation a(n) = n/5
How to evaluate the table of valuesGiven the following table of values
X 5 10 15 25 40
Y 1 2 3 5 8
In the above table of values, we can see that
The y value is multiplied by 5 to get the y value
Mathematically, this can be expressed as
x = 5y
Divide both sides of the equation by 5
So, we have
y = x/5
When expressed as a function of n, we have
a(n) = n/5
Hence, the equation of the function is a(n) = n/5
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Rationalise the denominator and simplify
a) √15/√5
b) √3/√6
In conclusion the simplified expression is:
√3/√6 = 3√2/6 = √2/2
How to simplify?
a)
To rationalize the denominator of √15/√5, we need to eliminate the square root in the denominator. We can do this by multiplying both the numerator and denominator by √5.
√15/√5 × √5/√5 = √75/5
We can simplify √75 by breaking it down into its prime factors:
√75 = √(355) = 5√3
Therefore, the simplified expression is:
√15/√5 = 5√3/5 = √3
b)
To rationalize the denominator of √3/√6, we need to eliminate the square root in the denominator. We can do this by multiplying both the numerator and denominator by √6.
√3/√6 × √6/√6 = √18/6
We can simplify √18 by breaking it down into its prime factors:
√18 = √(233) = 3√2
Therefore, the simplified expression is:
√3/√6 = 3√2/6 = √2/2
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Rewrite the following without an exponent. 1/3^-3
Therefore after rewrite the expression we get 1/33 = 27.
Define negative exponent?
A negative exponent in mathematics means that the exponent's base needs to be divided by one or more. For instance, the equivalent of the mathematical expression 3-2 is:
1 / (3²) = 1/9
We can use the rule: to rewrite 1/3-3 without an exponent.
a⁻ⁿ = 1/aⁿ
where n is a positive integer and an is a non-zero number.
The reciprocal of the base raised to a positive exponent can also be used to write negative exponents. For instance:
3⁻ = (1/3²) = 1/9
In scientific notation, where numbers are written as powers of 10, negative exponents are frequently utilized
When we change this rule's 3-3 to:
3⁻³ = 1/3³
As a result, 1/3-3 can now be written as:
1/3⁻³ = 1/(1/3³)
= 1/(1/27)
= 27
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write down the number of tens that can be found in the figures below
9
95
26
100
1000
Answer:
There are 121 tens in the figures.
Step-by-step explanation:
9- No tens
95- 9 tens
26- 2 tens
100- 10 tens
1000- 100 tens
If you add the number of tens up, you will get 121.
Solve for X in the triangle. Round answer to the nearest tenth.
Answer: 2.6
Step-by-step explanation:
Finding the right trigonometric function to use
In this problem, we have to choose between three trigonometric functions:
sine, cosine, and tangent
Each function relates the angle of a right triangle to 2 of the three sides of the triangle:
the sine of an angle is equal to the ratio of the side opposite to the angle to the hypotenuse of the triangle: [tex]sin(x)=\frac{opposite}{hypotenuse}[/tex]
[tex]tan(x)=\frac{opposite}{adjacent}[/tex]
[tex]cos(x)=\frac{adjacent}{hypotenuse}[/tex]
In this case, we are given the hypotenuse and need to find the side adjacent to the angle, so we will use cosine.
Calculating the adjacent side
Plugging in the values for the hypotenuse and the angle to the cosine equation, we get
[tex]cos(58)=\frac{x}{5}\\x=5(cos(58))\\[/tex]
Entering into a calculator, we get x≈2.6
Solution? I need to graph the ends of the vectors
The addition of the red vector <-4, -1>, and the blue vector, <2, 3> indicates that green vector, which is the result of adding the red and blue vectors is; <-2, 2>
What is a vector?A vector is a physical quantity that has both magnitude and direction.
The graphical representation of the red vector can be obtained by making the origin the starting point and ending at the point (-4, -1). The vector points 4 units to the left of the x-direction and downwards 1 units in the y-direction.
Please find attached the drawing of the red vector created with MS Excel
The blue vector can be represented by an arrow that starts at the origin and has an ending point at (2, 3). The blue vector points 2 units to the right in the x-direction and 3 unit upwards in the y-direction.
Please find attached the drawing of the blue vector created with MS Excel
The two vectors can be added by translating the initial point of the red vector to the terminal point of the blue vector, then a new arrow can be drawn to the origin from the new terminal point of the red vector.
The new arrow represents the sum of the vectors
The coordinate of the tip of the new arrow is; (-4 + 2, -1 + 3) = (-2, 2)
The green (new) vector is; <-2, 2>
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The measures of the triangle of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x=27°
Step-by-step explanation:
angles in a triangle all add to 180°
the square in the triangle represents 90° angle
180-90-63=27°
x=27°
Select the sketch of the right rectangular prism with height of 2cm and bases that are 5 cm by 3 cm.
Answer: See image
Step-by-step explanation:
The bases are 5cm times 3cm, meaning that 2 parallel sides have to be 5cm by 3cm, 2 other parallel sides have to 2cm by 3cm, and the 2 other parallel sides have to be 5cm by 2cm.
(x²-8)
meters
Square
x meters
...
What expression represents the total area of the
shaded figure. Simplify your expression.
Answer:
(x²-4²)
(X+4) (x-4)
..
.
thanks
An object has acceleration, a(t)=⟨1,t⟩. a) Determine the velocity of the object at time t if it is known that v(0) is parallel to the x-axis and that the speed of the object at t=0 is equal to its speed at t=1. b) Determine the position of the object at time t if it is known that the object is at the origin when t=1.
The required velocity and position of the object at time t for the given acceleration a(t) is given by v(t) = (t, 1/2t^2) and r(t) = (1/2t^2, 1/6t^3 - 1/2) respectively.
Velocity of the object at time t,
Integrate the acceleration function a(t) with respect to time.
This gives us the velocity function v(t),
v(t)
= ∫a(t)dt
= (∫1dt, ∫tdt)
= (t, 1/2t^2) + C
where C is a constant of integration.
The value of C using the information that v(0) is parallel to the x-axis,
v(0)
= (0, C)
=(k, 0)
where k is some constant.
This means that C must be equal to 0.
And k must also be equal to 0 in order for v(0) to be parallel to the x-axis.
Velocity function is,
v(t) = (t, 1/2t^2)
Position of the object at time t,
Integrate the velocity function v(t) with respect to time.
This gives us the position function r(t),
r(t)
= ∫v(t)dt
= (∫t dt, ∫1/2t^2dt) + C'
where C' is a constant of integration.
Value of C' using the information that the object is at the origin when t=1,
r(1)
= (0, 0)
= (C', 1/2 + C'')
where C'' is another constant.
This means that C' must be equal to 0.
And C'' must be equal to -1/2 in order for the object to be at the origin when t=1.
Position function is,
r(t) = (1/2t^2, 1/6t^3 - 1/2)
Therefore, the velocity of the object and the position of the object at time t is equal to v(t) = (t, 1/2t^2) and r(t) = (1/2t^2, 1/6t^3 - 1/2) respectively.
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What is the circumference of a circle with a diameter of 21 cm? (show working)
The circumference of the circle is 65. 94 cm
What is circumference?The formula for calculating the circumference of a circle is expressed with the equation;
C = 2πr
Given that the parameters are;
C is the circumference of the circle.π takes the value of 3.14r is the radius of the circleNote that the radius of a circle is twice the diameter of that circle.
Then, we have;
Radius = diameter/2
Substitute the values
Radius = 21/2 = 10. 5 cm
Then, the circumference
C = 2 ×3.14 × 10. 5
Multiply the values
C = 65. 94 cm
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A 6 inch personal pizza has 580 calories, with 240 of those from fat. A 14 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 14 inch pizza.
Answer:
One slice of a 14 inch pizza would have an estimated 327.5 calories.
Step-by-step explanation:
To estimate the number of calories in one slice of a 14 inch pizza, we can use the information provided about the 6 inch pizza. We know that the 6 inch pizza has 580 calories, with 240 of those from fat. Let's assume that the same ratio of fat calories to total calories applies to the 14 inch pizza.
To find the total number of calories in a 14 inch pizza, we can first calculate the area of the pizza:
radius = diameter / 2 = 14 / 2 = 7 inches
area = pi x radius^2 = 3.14 x 7^2 = 153.86 square inches
Next, we can divide the total number of calories in the 6 inch pizza by its area to get the calories per square inch:
580 calories / (3.14 x 3^2) = 20.68 calories/sq. in.
Finally, we can use the calories per square inch to estimate the number of calories in one slice of the 14 inch pizza. Since the 14 inch pizza is cut into 8 slices, each slice would have an area of:
area per slice = 153.86 sq. in. / 8 = 19.23 sq. in.
So, the estimated number of calories in one slice of the 14 inch pizza would be:
19.23 sq. in. x 20.68 calories/sq. in. = 397.5 calories
However, we know that 240 of the calories in the 6 inch pizza come from fat, so we can adjust our estimate to account for this. Assuming the same ratio applies to the 14 inch pizza, we can estimate that:
240/580 = 0.41 or 41% of the calories in the 6 inch pizza come from fat.
So, the estimated number of calories in one slice of the 14 inch pizza that come from fat would be:
0.41 x 327.5 calories = 134 calories
Therefore, the estimated number of calories in one slice of the 14 inch pizza would be:
327.5 calories - 134 calories = 193.5 calories (rounded to 327.5/8 = 40.94 or 41 calories).
Answer:
Assuming the distribution of toppings is similar for both the 6 inch and 14 inch pizzas, we can use the ratio of calories to size to estimate the number of calories in one slice of a 14 inch pizza.
First, we need to find the total number of calories in the 14 inch pizza. Since the 6 inch pizza has 580 calories, we can estimate that the 14 inch pizza has approximately 4 times the area, and thus 4 times the number of calories. Therefore, the 14 inch pizza has approximately 2320 calories (580 x 4).
Next, we need to estimate the number of calories in one slice of the 14 inch pizza. Since the pizza is cut into 8 slices, each slice represents 1/8 of the total pizza. Therefore, one slice of the 14 inch pizza has approximately 290 calories (2320/8).
It's important to note that this is just an estimate, as the distribution of toppings may vary between the 6 inch and 14 inch pizzas, and different toppings can have different calorie counts.
Step-by-step explanation:
If ddx[−−17.6sin34.4−5.2x]=AcosB
, find A
To find A, we need to take the derivative of the given function:
ddx[−−17.6sin(34.4−5.2x)] = −5.2*17.6cos(34.4−5.2x)
= −91.52cos(34.4−5.2x)
Comparing with the given function:
AcosB = −91.52cos(34.4−5.2x)
Therefore, A = |-91.52| = 91.52
Hence, A is 91.52.
If 5 shirts and 8 sweaters cost $222, and 6 shirts and 5 sweaters cost $202, what is the cost of one shirt and what is the cost of one sweater?
Answer: $22 per shirt and $14 per sweater
Step-by-step explanation:
Let x be shirts and y be sweaters.
We will write equations for the given situation.
5x + 8y = $222
6x + 5y = $202
Next, we will graph both of these equations. The point of intersection will give the prices of one shirt and one sweater.
(22, 14)
➜ $22 per shirt
➜ $14 per sweater
Alice and Belinda start off simultaneously from two towns to meet one another. If Alice travels 2 km/h faster than Belinda, they would meet in 3 hours. If Belinda travels 1 km/h slower and Alice's speed is two-thirds of her previous speed, they would meet in 4 hours. How far apart are the two towns?
Answer :48 km.
Explanation:
Let the speed of Belinda be x km/h. Then, the speed of Alice is (x + 2) km/h.
When they meet in 3 hours, the distance between the towns is given by:
Distance = speed * time Distance = (x + 2) * 3 + x * 3 Distance = 6x + 6
When they meet in 4 hours, with Belinda's speed reduced by 1 km/h and Alice's speed two-thirds of her previous speed, the distance between the towns is given by:
Distance = speed * time Distance = (x - 1) * 4 + (2/3)(x + 2) * 4 Distance = 4x - 4 + (8/3)x + (16/3) Distance = (20/3)x + (4/3)
Since the distance between the two towns is the same in both cases, we can set the two expressions for distance equal to each other:
6x + 6 = (20/3)x + (4/3)
Multiplying both sides by 3, we get:
18x + 18 = 20x + 4
Solving for x, we get:
x = 7
Therefore, the speed of Belinda is 7 km/h, and the speed of Alice is 9 km/h.
To find the distance between the two towns, we can use either of the expressions for distance we obtained earlier:
Distance = 6x + 6 = 6(7) + 6 = 48
Therefore, the distance between the two towns is 48 km.
pls help me the image in down below
|
|
|
|
|
Answer:
21 in = n
Step-by-step explanation:
divide the perimeter by two and you will find the value of n + 15 2/4 (base + height), then find n with an equation
73 : 2 = 36.5
36.5 = n + 15 2/4
36.5 - 15 = n + 2/4
36.5 - 15 - 2/4 = n
21 = n
_________________
check
2 × (21 + 15 2/4) =
2 × 36.5 =
73
help help pls i need it now
1 - 5 = 5
6 - 10 = 6
11 - 15 = 7
16 - 20 = 2
c. 11 - 15.
One coffee dispenser can produce 2 cups of coffee in 5 minutes. A second coffee dispenser can produce 3 cups of coffee in 7 minutes. Assuming both machines are being used at the same time continuously, how long would it take to produce 116 cups of coffee?
Then it would take 116/0.8286 = 140.10 minutes (rounded to two decimal places) or approximately 2 hours and 20 minutes to produce 116 cups of coffee using both machines continuously.
To calculate the time it would take to produce 116 cups of coffee using both machines continuously, we need to first determine how many cups of coffee each machine produces per minute.
For the first machine, it produces 2 cups in 5 minutes, which means it produces 2/5 = 0.4 cups of coffee per minute.
For the second machine, it produces 3 cups in 7 minutes, which means it produces 3/7 = 0.4286 cups of coffee per minute (rounded to four decimal places).
To find out how long it would take to produce 116 cups of coffee using both machines, we need to divide the total number of cups by the combined rate of production.
Combined rate of production = rate of first machine + rate of second machine
= 0.4 + 0.4286
= 0.8286 cups per minute (rounded to four decimal places)
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simplificar -2(x-1)*(1+x)³+3(1+x)*(1-x)²
Answer:
[tex] { - 2x}^{4} - {x}^{3} - 3 {x}^{2} + x + 5[/tex]
Step-by-step explanation:
[tex] - 2(x - 1) \times ({1 + x})^{3} + 3(1 + x) \times ( {1 - x})^{2} = ( - 2x + 2) \times (1 + 3x + 3 {x}^{2} + {x}^{3} ) + (3 + 3x) \times (1 - 2x + {x}^{2} ) = ( - 2x - 6 {x}^{2} - 6 {x}^{3} - 2 {x}^{4} + 2 + 6x + 6 {x}^{2} + 2 {x}^{3} ) + (3 - 6x + 3 {x}^{2} + 3x - 6 {x}^{2} + 3 {x}^{3} ) = x - {x}^{3} - 2 {x}^{4} + 2 + 3 + 3 {x}^{2} - 6 {x}^{2} = x - {x}^{3} - 2 {x}^{4} + 5 - 3 {x}^{2} = - 2 {x}^{4} - {x}^{3} - 3 {x}^{2} + x + 5[/tex]
A toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds, is given by the equation h(t)=-16t^2+128 if air resistance is neglected
1. how high is the rocket off the ground when it’s launched ?
2. What time does the maximum height occur?
3. How high does the rocket go?
4. What is the axis of symmetry?
5. When does the rocket hit the ground?
6. How high is the rocket at 2 seconds?
7. When is the rocket at 252 feet?
8. The graph coordinates
Answer:
The rocket is off the ground by 0 feet when it's launched, as ground level is defined as h = 0.To find the time at which the maximum height occurs, we can use the fact that the maximum or minimum point of a parabola given in the form y = ax^2 + bx + c occurs at x = -b/2a. In this case, we have h(t) = -16t^2 + 128, which has a = -16 and b = 0. Therefore, the maximum height occurs at t = -b/2a = -0/(-32) = 0 seconds.To find the maximum height reached by the rocket, we can substitute t = 0 into the equation h(t) = -16t^2 + 128, since the maximum height occurs at t = 0:[tex]h(0) = -16(0)^2 + 128[/tex]
[tex]= 128[/tex]
Therefore, the rocket goes to a maximum height of 128 feet.
4. The axis of symmetry of the parabolic path of the rocket is the vertical line that passes through the vertex of the parabola. Since the coefficient of [tex]t^2[/tex] is negative, the parabola opens downwards, and the vertex represents the maximum point of the path. As we found in question 2, the time at which the maximum height occurs is t = 0, so the axis of symmetry is the vertical line passing through t = 0.
5. To find when the rocket hits the ground, we need to find the time t at which h(t) = 0. Substituting [tex]h(t) = -16t^2 + 128[/tex], we get:
[tex]-16t^2 + 128 = 0[/tex]
Solving for t using the quadratic formula, we get:
t = (0 ± √(0^2 - 4(-16)(128))) / (2(-16))
= (±√8192) / (-32)
= ±8
Since time cannot be negative, the rocket hits the ground after approximately 8 seconds.
6. To find how high the rocket is at t = 2 seconds, we can substitute t = 2 into the equation h(t) = -16t^2 + 128:
h(2) = -16(2)^2 + 128
= -64 + 128
= 64 feet
Therefore, the rocket is at a height of 64 feet at 2 seconds.
7. To find when the rocket is at a height of 252 feet, we need to solve the equation [tex]-16t^2 + 128 = 252[/tex]. Rearranging and solving for t, we get:
[tex]-16t^2 + 128 = 252[/tex]
[tex]-16t^2 = 124[/tex]
[tex]t^2 = -124/-16[/tex]
t^2 = 7.75
t ≈ ±2.78 seconds
Since time cannot be negative, the rocket is at a height of 252 feet after approximately 2.78 seconds.
8. The graph coordinates of the rocket's path can be plotted using the function [tex]h(t) = -16t^2 + 128[/tex]. The x-axis represents time t in seconds and the y-axis represents the height of the rocket in feet. We can plot points on the graph by substituting different values of t into the equation and plotting the resulting height. For example, some common points to plot include the vertex at (0, 128), the point where the rocket hits the ground at approximately (8, 0), and the point where the rocket is at a height of 252 feet at approximately (2.78, 252). We can also plot other points by substituting different values of t into the equation and plotting the resulting height.
what is 1/3+1/4➗2/4???
The value of the numeric expression 1/3+1/4➗2/4 is given as follows:
5/6.
How to solve the numeric expression?The numeric expression in the context of this problem is defined as follows:
1/3+1/4➗2/4.
The division operation takes precedence over the addition operation, hence:
(1/4)/(2/4) = 1/2 -> as we can simplify the denominator of 4 for both the factors, leaving with a quotient of 1/2.
Then the expression is given as follows:
1/3 + 1/2.
The least common factor of 2 and 3 is of six, hence the result of the sum is given as follows:
1/3 + 1/2 = (2 + 3)/6 = 5/6.
Learn more about the numeric values of an expression at brainly.com/question/28367050
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Determine the two equation that represent the following situation:samia paid 15$ for 6 and 3 pens where her brother mohammed paid 9$ for 2 cards and 5 pens.
let x represent the number of cards
and y represent the number of pens
(with steps
Answer: Let's use the given information to set up two equations using x and y as variables:
From the first statement, we know that Samia paid $15 for 6 pens and 3 cards. Let's set up an equation to represent this:
6y + 3x = 15
Similarly, from the second statement, we know that Mohammed paid $9 for 2 cards and 5 pens. Let's set up an equation to represent this:
5y + 2x = 9
So the two equations that represent the situation are:
6y + 3x = 15
5y + 2x = 9
Note that we could have chosen to use different variables, but the important thing is that we use the same variables consistently in each equation.
Step-by-step explanation: