A- The maximum vertical distance from the water surface to the diver’s
shoulders are 12.061 meters.
B- The time that the diver’s shoulders enter the water is 1.936 seconds.
C- The total distance traveled by the diver’s shoulders from the time
she leaps from the platform until the time her shoulders enter the water is 12.946 meters.
D- The angle, θ between the path of the diver and the water at the instant the diver’s shoulders enter the water is 1.519.
A-
[tex]\frac{dy}{dx} =0[/tex] only when [tex]t=0.36735[/tex]. Let [tex]b=0.36735[/tex]
The maximum vertical distance from the water surface to the diver’s
shoulders is y(b)=11.4 + [tex]\int\limits^b_0 \frac{dy}{dT} dt = 12.061[/tex] meters.
B-
[tex]y(A)=11.4+\int\limits^A_0 \frac{dy}{dt} dt = 11.4+3.6A- 4.9A^{2} =0[/tex]
when A= 1.936 seconds.
C-
[tex]\int\limits^A_0 {\sqrt{(\frac{dx}{dt} )^{2} + (\frac{dy}{dt} )^{2} } } \, dt = 12.946 m[/tex]
At time A, dy/dx = [tex]\frac{dy/dt}{dx/dt} | _{t=A} = -19.21913[/tex]
D- The angle between the path of the diver and the water is [tex]tan^{-1} (19.21913) = 1.518 or 1.519[/tex]
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How is exponential function used in population growth?
The population grows exponentially as the population size increases because the growth rate per capita (per person) growth rate remains constant. The availability of resources will eventually stop populations in nature from growing exponentially.
what is exponential function?An exponential function is defined by the equation f(x) = ax, in which the exponent of the input variable x is used. The exponential curve affects both the value of x and the exponential function. The exponential function, with the form, is a crucial mathematical function. f(x) = ax.
Population growth or decline that is ongoing and whose pace of change is inversely correlated with the total number of people in the population at any given time.
The population grows exponentially as the population size increases because the growth rate per capita (per person) growth rate remains constant. The availability of resources will eventually stop populations in nature from growing exponentially.
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two numbers have a sum of 10 and a product of 20 what is the sum of the reciprocal of the numbers
HELP
The sum of the reciprocals of the two numbers is 0.5
How to find the reciprocal of the numbersLet the two numbers be x and y such that
x + y = 10
xy = 20
In x + y = 10, x = 10 - y
plugging in in xy = 20
(10 - y)y = 20
10y - y² - 20 = 0
y² - 10y + 20 = 0
solving the quadratic equation gives
y = 2.76 OR 7.24
sum of the reciprocal of the numbers
= 2.76⁻¹ + 7.24⁻¹
= 0.5
the sum is 0.5
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somebody please help me
Answer:
Divided both sides by 2
Step-by-step explanation:
The equation is
2 (t +7) = 16
t + 7 = 8
To get to the second step, they divided bot sides by 2
How old is a 12th grader?
Frequently between the ages of 17 and 18, students. Seniors are students in the twelfth grade. The 12th grade, or senior year of high school, is frequently considered by students.
what do you mean grader ?Exams, projects, and academic assignments are evaluated by graders, who also issue grades. They create test materials, quizzes, and other things. They develop or implement the grading criteria and system. Either hand grading or the usage of an electronic evaluation and grading application are options for them.
here ,
Students are typically between the ages of 17 and 18. Seniors are the term for students in the twelfth grade.
Twelveth grade, or senior year of high school, is often seen by students as a time to unwind and get ready to leave their old lives behind and enter either college or the workforce.
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What are the actual parameters in C++ Mcq?
Actual parameters are those that are supplied into a function when it is called or those that are used to make a function call.
Using parameters, subprograms pass information. The variables or expressions listed in a subprogram call's parameter list are the real parameters.
For instance, the procedure call that follows lists the two real parameters amount and emp num:
raise_salary(emp_num, amount);
The parameters that are used when calling a function at any point in the code are the actual parameters. It is the real value that a caller has given the process. When a subroutine like Functions is invited, the parameters are what you decide.
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What are the 4 types of values?
Thousands, hundreds, tens and ones are four types of values and there are many more.
What is value?Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.
What is the value of 4?The number 4 is in this case in the tens column. As a result, the place value of the number four is tens or tens.
Thousands, hundreds ,tens and ones are four types of values and there are many more like ones etc. Moreover after solving any problem for unknown variable the resulting numerical solution can also be termed as value.
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Solve: 2y - 4 = 14
:))
Answer:
y=9
Step-by-step explanation:
[tex]2y-4=14\\(2y-4)+4=(14)+4\\2y=18\\\frac{2y}{2}=\frac{18}{2}\\y=9[/tex]
Answer:
y=9
Step-by-step explanation:
add the 4 on both sides: 2y-4+4=14+4
2y=18
divide by 2: 18/2= 9
What is division example?
Answer:
42 divided by 2
Step-by-step explanation:
42 divided by 2 equals 21 and how to find if it is correct is to add it together 21+21 or multiply it by what it was divided by 21x2
If x² + 6x = 40, what are the values of x-6?
Answer:
-2
Step-by-step explanation:
x² + 6x = 40
This equation has the value of x as 4
Let's test
(4)^2 + 6(4) = 40
16 + 24 = 40
So, x is 4 in this equation
Now for the question, what is the value of x-6
We know x is 4
4 - 6 = -2
pls help me and explain how to do this
The slope of the line is -3/4.
What is a line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
The points on the line are (-4, 5), (0,2), (4, -1).
The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of the line is
(2 - 5)/(0 - (-4)) = -3/4
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i have a pie. if i give two pieces to joe, one piece to mary, and another piece to joe, how many pieces of pie does joe have?
Answer: 3 pieces of pie
Step-by-step explanation:
You gave Joe two pieces at first, then you gave joe another piece of pie
2 + 1 = 3 pieces of pie
Where accurate measurement is necessary?
While measuring mass of precious substances, such as gold, silver, etc., we need to be accurate in our measurement. in competitions and events, a difference of second can make you lose or win the game. Thus, accurate time measurement in such cases is very important.
Precision measures the reproducibility of measurements, even when they are far from the acceptable value, whereas accuracy measures how near a measurement is to a known or accepted value. Repeatable measurements that are reliable and precise are extremely near to the real values.
How closely a measured value resembles the real (or "true") value is referred to as accuracy. For instance, an accurate reading for the weight would be as near to 100g as feasible if you weighed a typical 100g weight on a scale.
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Find the area of the shape 1/4 circle 8 radius
Answer:
16 pi
Step-by-step explanation:
Area of a circle is pi*radius^2. In this case, the area of the full circle would be pi*8^2 which is 64pi. The area of a quarter circle would be one fourth of that, so 16pi
Find the slope of the line that passes through (4, 7) and (2, 10).
The Slope of the Line passing through (4, 7) and (2, 10) is -3/2
What is Slope?
The slope formula is used to compute the inclination or steepness of a line. The slope of the lines is calculated using the x and y coordinates of the lines. It is the ratio of the y-axis change to the x-axis change.
Solution:
A(4, 7) and B(2, 10)
Slope = y2 - y1 / x2 - x1
Slope = 10 - 7 / 2 - 4
Slope = 3 / -2
Slope = -3/2
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How do you find the reflecting on a coordinate plane( x-axis or y-axis )?
A transformative process turns a figure into a reflection.
How do you determine the reflecting on an x-axis or y-axis coordinate plane?If you want to reflect a point across the x-axis, multiply its y-coordinate by -1. If you want to reflect a point across the y-axis, multiply its x-coordinate by -1.A transformative process turns a figure into a reflection.When a point is reflected across the x-axis, the x-coordinate stays constant, but the y-coordinate is thought to be the additive inverse. The x-axis shows a reflection of the point (x, y) as (x, -y).The y-coordinate remains constant when a point is mirrored across the y-axis, while the x-coordinate is thought to be the additive inverse. The point (x, y) is reflected on the y-axis as (-x, y).(x, y)(x, y) is the formula for a reflection over the x-axis.
(x,y)(x,y) is the formula for a reflection across the y-axis.
The formula is (x,y)(y,x) for a reflection in the line y=x.
(x, y)(y, x) is the formula for a reflection in the origin.
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How do you graph a linear inequality steps?
The steps to graph the linear inequality is shown. (Refer to the steps below)
What is linear inequality?A linear inequality in mathematics is an inequality involving a linear function.
One of the symbols for inequality is found in linear inequality.
It displays non-equal data in graph style.
These steps will be used to graphically solve a set of linear inequalities:
1. Find y's inequality solution.
2. Represent the inequality as a linear equation and, depending on the inequality sign, graph the line as either a solid line or a dashed line.
3. Darken the area when the inequality is satisfied.
4. For every disparity, repeat steps 1 through 3.
5. The region where all of the inequalities intersect will be the solution set.
Therefore, steps to graph the linear inequality is shown.
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Does (7, –5) make the equation y = x + –2 true?
Answer:
no
Step-by-step explanation:
-5 = 7 + -2
7 + -2 = 5
no
Answer:
No
Step-by-step explanation:
7,-5 is not a point on the line
-5, -7 is on the line
What is the formula for finding the circumcenter of a triangle?
Answer:
P(X, Y) = [(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)]
Step-by-step explanation:
How to Construct Circumcenter of a Triangle?
The circumcenter of any triangle can be constructed by drawing the perpendicular bisector of any of the two sides of that triangle. The steps to construct the circumcenter are:
Step 1: Draw the perpendicular bisector of any two sides of the given triangle.
Step 2: Using a ruler, extend the perpendicular bisectors until they intersect each other.
Step 3: Mark the intersecting point as P which will be the circumcenter of the triangle. It should be noted that, even the bisector of the third side will also intersect at P.
5. For each scenario, fill in numbers in the blanks to create a scenario that
can be solved using a system of equations. Make sure the scenario that you
provide has ONE solution. Then, answer the questions that follow.
Scenario 1
There are
some are cows. There are
total animals in the barn. Some of the animals are chickens and
legs in all.
a. What is the system of equations that represents the scenario you created?
B. Prove your solution is correct.
The scenario in this problem is described as follows:
There are 50 total animals in the barn, and there are 160 legs in total.
The system of equations that describes this situation is given as follows:
x + y = 50.4x + 2y = 160.What is the system of equations that describes this scenario?The variables that describe the system of equations are given as follows;
Variable x: number of cows in the barn.Variable y: number of chickens in the barn.There are 50 total animals in the barn, hence:
x + y = 50.
There are 160 legs in total. Considering that each cow has four legs, while each chicken has two legs, we have that:
4x + 2y = 160.
The system of equations is composed by these two equations and can be solved using any method to identify the amounts of each animal.
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(g) sin² A+ cos² A + tan² A+ 1 = 4
that is the solution to the questions well. thank you, you can contact me for any further enquiry
is the integer r divisible by 3 ? (1) r is the product of 4 consecutive positive integers. (2) r < 25
Yes, the integer is divisible by 3.
To determine if r is divisible by 3, we must first determine the value of r. According to statement 1, r is the product of 4 consecutive positive integers.
This means that the 4 integers must be increasing by 1 each time. The smallest integer must be 1, and the 4th integer must be 4 higher than the first, making it 5.
The product of these 4 integers is 1 x 2 x 3 x 4 = 24, which is less than 25.
Since 24 is divisible by 3, r is also divisible by 3.
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What does fit () do?
When using supervised learning, the fit() technique requires two arrays of training data, but unsupervised learning only requires one array.
What does fit () do in regression?After the model is initialised, the "fit" method runs the algorithm on the training data. That is all it does, in essence. Thus, the machine learning model is trained using the training data by the sklearn fit approach. In the manufacturing industry, the term "form-fit-function" (FFF) refers to a part's distinguishing features (a single component that goes into the final build of your product, typically kept on an item master).
model.fit(): fit practise data This accepts the data X and the labels y as two arguments for supervised learning applications (e.g., model. fit(X, y)). Function at Cost. The cost function for linear regression is the Sum of Squares of Errors with the lowest value. Calculate the squared error sum for each and every available line.
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The area of a right triangle is 44 m². Find the lengths of its legs if one of the legs is 3 m longer than the other.
Answer:
[tex]Lengths:8m and 11m[/tex]
Step-by-step explanation:
Area of a triangle is [tex]\frac{1}{2}bh[/tex]
[tex]44=\frac{1}{2} (x+3)(x)\\[/tex]
[tex]44=\frac{1}{2} (x_{2 +3x)[/tex]
[tex]88=x^{2} +3x[/tex]
[tex]x^{2} +3x-88=0[/tex]
[tex](x+11)(x-8)=0[/tex]
[tex]x=8[/tex]
[tex]Lengths:8m and 11m[/tex]
the ratio of milk to water in a mixture is 12:5.if there is 144liters of waterinth mixture. find d amount of milk
The ratio of milk to water in the mixture is 12:5, which means that for every 12 parts of milk, there are 5 parts of water. We can set up a proportion to solve for the amount of milk in the mixture. Let's call the amount of milk x.Then the proportion is:(12 parts milk) / (5 parts water) = (x liters milk) / (144 liters water)To solve for x, we can cross-multiply and simplify:12x = 5 * 144
x = (5 * 144) / 12
x = 60 litersThus, the amount of milk in the mixture is 60 liters.
According to the question,
ratio amount of water : milk is 5:12
given amount of water in the mixture is 144 litre,
then we have to find the value of x,
as given, 12x=144
x=144/12
x=12
or, 5(12) = 60litre.
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Are AAA triangles solvable?
Yes, they are solvable.
In geometry, a triangle is considered to be an "AAA" triangle (or "AAA similarity") if all three of its angles are equal. Such a triangle is also known as an equilateral triangle.
An equilateral triangle is a type of triangle that has all three sides of equal length and all three angles of equal measure (60 degrees). It is a regular polygon, and it is one of the few geometric shapes that has this property.
Because all three angles in an equilateral triangle are equal, it is relatively easy to solve for various properties of the triangle. For example, the length of each side can be found if the measure of one angle and the length of one side are known. Similarly, the measure of an angle can be found if the length of one side and the measure of one angle are known.
In summary, AAA triangles are solvable because they have a consistent and predictable structure, with all sides and angles being equal.
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How do you translate an entire triangle?
To translate an entire triangle, you need to first identify the coordinates of the triangle's vertices.
calculate the vector of the translation by subtracting the coordinates of the original triangle from the coordinates of the translated triangle. Finally, apply the vector to each of the triangle's vertices to move the entire triangle.
1. Identify the coordinates of the triangle's vertices (x1, y1, x2, y2, x3, y3).
2. Calculate the translation vector by subtracting the coordinates of the original triangle from the coordinates of the translated triangle (x1T, y1T, x2T, y2T, x3T, y3T).
3. Apply the vector to each of the triangle's vertices to translate the entire triangle. This can be done by adding or subtracting the vector from the original coordinates of the triangle's vertices.
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what is the value of u
The value of u = 56.78 degree
What is the value of angle?Any triangle's three angles sum up to 180 degrees when added together. Therefore, the sum of angles A, B, and C is 180 degrees. Any triangle in the field of geometry has this property. This concept can be used to determine the measure of an angle or angles in which the degree measure is absent or not provided.
A, B, and C is 180 degrees
in a triangle <u- 40 degree <u+50 degree so <u is
<u- 40 degree
<u+50 degree
so
<u =
(u - 40 ) + (u+50 ) + u = 180
3u - (170.3) =180
u = 170.3/3 = 56.78.
The value of u = 56.78 degree
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How do you solve inverse ratios and proportions?
Assuming that x and y be inversely proportionate, we can denote their relationship as x ∝1/y. It follows that as the value of x rises, the value of y falls, and vice versa.
Define the term inverse ratios and proportions?When the product of two values, x and y, is a constant, they remain inversely proportional to one another (always remains the same). Accordingly, as x rises, y falls, and conversely, by a certain amount so that x and y remain constant.Making an equation to determine the value of a new variable is also made possible by understanding that product does not change.We must first establish the connection between the two variables in order to calculate the value of the variable that's also inversely proportionate to the other.We need to figure out the proportionality constant k, which is similar to the a directly proportional connection.
Thus, x ∝1/y
x = k/y
k = xy.
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9. Determine the end behavior of the given polynomial function: f(x) = -x-2x³ +3x+9.
Answer:
The graph increases as it approaches -∞.
The graph decreases as it approaches ∞.
Step-by-step explanation:
f(x) = -x - 2x³ + 3x + 9
f(x) = -2x³ + 3x - x+ 9
f(x) = -2x³ + 2x+ 9
Look at the highest exponent(which is 3).
SInce the highest exponent is odd, that means that the graph approaches infinity in a different direction as per negative infinity. Since the highest exponent has a negative sign:
The graph is going UP as x-values get SMALLER ( To -∞)
The graph is going DOWN as x-values get LARGER ( To ∞)
Hence:
The graph increases as it approaches -∞.
The graph decreases as it approaches ∞.
Answer:
Since the degree is odd, the ends of the function will point in the opposite directions.
Odd
What are the three primary kinds of parameters Mcq?
The three primary kinds of parameters are Input parameters, Output parameters, and Input/Output parameters.
One of the bits of data supplied as input to a function is referred to by a parameter, a special sort of variable. These bits of information represent the values of the arguments that will be used to call or invoke the function. Functions may have one or more parameters or none at all.
A function is typically defined with an ordered list of parameters so that each time it is called, the arguments are evaluated for that call and the results can be assigned to the associated parameters.
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