According to Pythagoras theorem, the value of the third side of the triangle is 38.6mm
In math Pythagoras theorem states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
Here we have given that the triangular pendant has two sides of length 23 mm and 31 mm.
And we need to find the possible lengths (in whole mm) for the third side.
Here in the given question, we have the values of the two sides are 23mm and 31mm.
Then we have to apply the values on the Pythagoras theorem formula,
=> hypotenuse² = adjacent² + opposite²
Now, we have to apply the values as opposite and adjacent on it, then we get,
=> hypotenuse²= 23² + 31²
=> hypotenuse² = 529 + 961
=> hypotenuse² = 1490
Therefore, the value of the third side is 38.6mm
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Three people build a rectangular shed 6 m wide, 4 m long, and 5 m high. How many cubic meters is the shed?.
120 m³ is cubic meters is the shed.
Given :
What in math is a cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. Also said to be a conventional hexahedron. Due to the fact that a cube is three dimensional, the space it occupies will also be three dimensional.
Six square faces surround a cube, hence combining the areas of all six square faces will yield the surface area. The cube formula's surface area is as a result. Cube surface area equals 6 (sides).
w = 6 m
l = 4 m
h = 5 m
a rectangular shed = 6 * 4 * 5
= 120 m³
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What is the mode of 12345?
If we answer yes, then 1, 2, 3, 4, and 5. No phrase is used more than once in this passage. Therefore, there is currently no most prevalent phrase. Thus, this data does not contain a mode.
How can I locate the mode?The mode calculation is a rather simple process. Organize the numbers in a set in whatever order—from lowest to highest as well as highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequently.
The purpose of mode calculation?When the mean, as well as median, as well as median cannot be employed, the mode informs us of the most prevalent value in categorical data. The mode provides insight into the location of a dataset's "center".
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How do you find the x-intercept of a linear equation in two variables?
To find the x-intercept of a linear equation in two variables we set y intercept to 0.
When we are given with a two variable linear equation, we plug 0 in place of y and solve the equation to get the x-intercept of that linear equation.
For example, let us consider the linear equation 2x + 3y = 4
To get the x-intercept of the equation 2x + 3y = 4 we would plug y = 0.
Therefore, 2x + 3(0) = 0
⇒ 2x + 0 = 4
⇒ x = 4/2 = 2
Thus, the x-intercept of the linear equation 2x + 3y = 4 is 2.
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What is the maximum value of this function f x )= − 16x2 32x 20?
On solving the provided question, we can say that - the maximum value or maxima of the given function is 36.
What is maxima?Maximum describes a high point (plural maxima). The term "minimum" refers to a low point (plural minima). Extremum is the Latin term used to describe the greatest or minimum (plural extrema). When greater points are possible elsewhere but not close by, we say local maximum (or minimum). The greatest and smallest values of a function in either a specified range or throughout the whole domain are referred to as a function's maxima and minima, generally known as extrema, in mathematical analysis.
The vertex is used to determine that the function's maximum value is 36.
Function is provided by:
f(x) = [tex]16x^2 + 32x + 20[/tex]
coefficients -
[tex]a = -16, b = 32 , c =20[/tex]
[tex]f_{max} = \frac{32^2 - 4(-16)(20)}{4(-16)}[/tex] = 36
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What is the nature of roots of quadratic equation 4x2 5x 3 0?
The nature of the roots of the quadratic equation 4x² - 5x + 3 is complex.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
4x² - 5x + 3
This is in the form of ax² + bx + c
a = 4
b = -5
c = 3
Now,
D = b² - 4ac
If D < 0 there will be complex roots.
Now,
D = (-5)² - 4 x 4 x 3 = 25 - 48 = -23
D < 0
This means,
The roots are complex.
Thus,
The equation has complex roots.
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How many of these numbers are divisible by 3?
The numbers which are divisible by 3 are countless. We determine it by the divisibility rules.
What is divisible in mathematics?
A number is called divisible by others whenever it is divided properly and obtain a whole number as an outcome. As example 125 can be divided by 5 and we get the whole number 25 so 125 is said divisible by 5.
On the other hand, 225 cannot be divided by 10 and we get a decimal number. So, 225 is not divisible by 10.
How many numbers are divisible by 3?A number is said to be divisible by 3 if the sum of the digits is divided by 3. Suppose we are given two number 308 and 492.
At first, we will sum the digit of each number, 3+0+8 = 11
the sum of the digit of 492 = 4+9+2 = 15
we cannot divide 11 by 3 but 15 is divided by 3. Hence, 492 is divisible by 3.
So, there are countless number which are divisible by 3.
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What is the inverse function calculator?
The inverse of the function that is provided is calculated using the inverse function calculator. When a function, f(x), is given, its inverse, x=f(y), is calculated by switching the variables ( y ).
Given,
Inverse function;
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f1.
Inverse function calculator;
The calculator for inverse functions determines the inverse of the supplied function. If a function, f(x), is supplied, then the inverse of the function, x=f(y), is determined by exchanging the variables ( y ).
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Estimate fx and fy at point B. 70 50 30 y 4 - -30 2 С 10 B -10- 0 - 00 30 50 10 -10 A -70 -2 -20 -4 (Use decimal notation. Give your answer to one decimal place.)
It is difficult to accurately estimate the values of fx and fy at point B without more information. In order to estimate the values of the partial derivatives at a point, you typically need to have a contour map or some other representation of the function in the neighborhood of that point.
A contour map is a graphical representation of a function that shows the values of the function at different points in the xy plane. The lines on the map, called contour lines, represent the values of the function, and the spacing between the lines indicates the rate of change of the function.
To estimate the values of the partial derivatives at a point using a contour map, you can:
Identify the contour line that passes through the point of interest.Look for nearby points on the map that have coordinates that differ only in the x or y direction from the point of interest.Calculate the difference in the function values at these points and divide by the difference in the x or y coordinate, depending on which partial derivative you are estimating.For example, to estimate fx at point B, you could:
Identify the contour line that passes through point B.Look for nearby points on the map that have y-coordinates that are the same as point B but x-coordinates that are different.Calculate the difference in the function values at these points and divide by the difference in the x-coordinates to estimate fx at point B.Without a contour map or other representation of the function in the neighborhood of point B, it is not possible to accurately estimate the values of fx and fy.
Since the question is incomplete and there is no similar one found, the answer is general.
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How do you solve inequality questions?
An inequality like the statement, x + 3 > 5, can be solved by finding the value of the variable, "x", which is x > 2.
How to Solve an Inequality Question?Inequalities are used to express relationships between quantities or values that are not equal. They can be used to describe constraints or limitations on a solution to a problem, or to represent a range of possible values.
Inequality can also be used to describe relationships between variables in algebraic expressions or equations.
To solve an inequality, we need to isolate the variable in the given statement to determine the value of the variable.
For example, given the inequality, x + 3 > 5, in order to solve this inequality, we need to find the value of x by subtracting 3 from both sides:
x + 3 - 3 > 5 - 3
x > 2.
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What is a multiplicity example?
A multiplicity example in mathematics is when a function has multiple solutions to a given equation.
For example, when solving the equation x2 + 4x + 3 = 0, there are two solutions, x = -3 and x = -1. This means that the equation has a multiplicity of two. This can be seen in the graph of the equation, which has two points of intersection on the x-axis.
The multiplicity is a measure of how many solutions a given equation has. It can be determined by using the discriminant, which is the difference between the square of the coefficient of the highest degree term, and four times the product of the coefficients of the lower degree terms, and the constant. In the example above, the discriminant is 16 - 12, which is 4. The multiplicity of the equation is determined by the sign of the discriminant: if it is positive, the equation has two solutions; if it is zero, the equation has one solution; and if it is negative, the equation has no solutions.
The multiplicity of an equation can also be used to determine the nature of the graph of the equation. If the equation has a multiplicity of two, the graph is a parabola, which is a curved line that has two points of intersection on the x-axis. If the equation has a multiplicity of one, the graph is a line, which has only one point of intersection on the x-axis. If the equation has a multiplicity of zero, the graph is a circle, which has no points of intersection on the x-axis.
The concept of multiplicity is important in mathematics, as it can be used to determine the number of solutions an equation may have, as well as the nature of the graph of the equation. Knowing the multiplicity of an equation can help to simplify the process of solving the equation.
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How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour? 100 hours 150 hours 180 hours 200 hours.
It will take 180 Hours to fill the pool if both hoses are used.
In our question, one data is missing. You require the pool's volume or some information that enables you to calculate it. The same statement given by you is part of a problem where you know a series of data that shows the time required to fill the pool at different flow rates:
flow rate time
60 gal/h 300 h => 60 gal/h * 300 h = 18,000 gal
45 gal/h 400 h => 45 gal/h * 400 h = 18,000 gal
36 gal/h 500 h => 36 gal/h * 500 h = 18,000 gal
30 gal/h 600 h => 30 gal/h * 600 h = 18,000 gal
So for this pool to calculate (several times) that the volume is 18,000 gal.
You now possess two hoses, one of which has a flow rate of 40 gals per hour and the other of which has a flow rate of 60 gals per hour.
The total flow rate is the sum of the two flow rates"
total flow rate = 40 gal/h + 60 gal/h = 100 gal/h
And you just must divide the volume of the pool (18,000 gals) by the total flow rate (100 gal/h) to get the time to fill the pool:
time = volume / flow rate = 18,000 gal / 100 gal/h = 180 hours.
So, finally, our answer to fill the pool will be about 180 hours.
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flow rate time
60 gal/h 300 h => 60 gal/h * 300 h = 18,000 gal
45 gal/h 400 h => 45 gal/h * 400 h = 18,000 gal
36 gal/h 500 h => 36 gal/h * 500 h = 18,000 gal
30 gal/h 600 h => 30 gal/h * 600 h = 18,000 gal
So for this pool to calculate (several times) that the volume is 18,000 gal.
You now possess two hoses, one of which has a flow rate of 40 gals per hour and the other of which has a flow rate of 60 gals per hour.
The total flow rate is the sum of the two flow rates"
total flow rate = 40 gal/h + 60 gal/h = 100 gal/h
And you just must divide the volume of the pool (18,000 gals) by the total flow rate (100 gal/h) to get the time to fill the pool:
time = volume / flow rate = 18,000 gal / 100 gal/h = 180 hours.
24 / 18/9 + 4
I don’t understand how to solve the problem at all.
Answer:4.1
Step-by-step explanation:
What is set and example?
Set is the collection of objects with defined property and represented in curly brackets {} . Example: A = { 2, 4, 6 }.
Set is defined as:
The collection of objects in an organized manner with some defined property.It is represented by curly brackets {}.Two ways to represents the given set is set builder form and the roaster form.If we defined collection of books it is not considered as set as here no well defined property is mentioned.If it is collection of books written by any particular writer than it is a set.Example of set is defined as collection of even numbers less than 8 is written as A = { 2. 4, 6 }Learn more about set here
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Do the one you would like please show work
Step-by-step explanation:
I am not what the answer My teacher
A force of 343.8 N is used to push a car 38.5 m horizontally in 4.86 s. Calculate the power developed.
Important Formulas:
[tex]w=Fd[/tex]
[tex]p=\dfrac{w}{t}[/tex]
w = work (Measured in Joules)
F = Force (Measured in Newtons)
d = distance (Measured in meters)
p = power (Measured in watts)
t = time (measured in seconds)
______________________________
Given:
[tex]f=343.8N[/tex]
[tex]d=38.5m[/tex]
[tex]t=4.86s[/tex]
[tex]p=?[/tex]
______________________________
Finding Work:
[tex]w=Fd[/tex]
[tex]w=(343.8)(38.5)[/tex]
[tex]w=13236.3J[/tex]
______________________________
Finding Power:
[tex]p=\dfrac{w}{t}[/tex]
[tex]p=\dfrac{13236.3}{4.86}[/tex]
[tex]\fbox{p = 2723.52 watts}[/tex]
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answer: "approximately nine years
explanation : if an investment scheme promises an 8% annual compounded rate of return, it will take approximately nine years (72 / 8 = 9) to double the invested money.
hope this helps!!
Question 5
Ethan put $1,250 into a savings account. The account pays 4.5% simple interest on an annual basis. If he does not add or withdraw money
from the account, how much interest will he earn after 2 years? Round to the nearest cent.
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Answer:
To calculate the interest earned on a savings account, you first need to determine the interest rate per year and the time the money is invested. In this case, the interest rate is 4.5% and the time is 2 years.
The formula for simple interest is I=Prt, where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the time. Plugging in the values from the problem, we get I = 1250 * 0.045 * 2 = $112.50.
Therefore, Ethan will earn $112.50 in interest after 2 years if he does not add or withdraw any money from the account. Rounded to the nearest cent, this is $112.00.
Step-by-step explanation:
your company makes game parts using 3-d printers. one customer wants a circular game coin that is 2.0 centimeters across and 0.5 centimeters thick, as shown below. you need to estimate the amount of plastic you will need for each batch of 50 coins. how many cubic centimeters is that, rounded up if necessary to be a multiple of 10 cubic centimeters?
The amount of plastic needed for each batch of 50 coins is equal to the volume of 50 coins that is 80 cu.cm.
The diameter of the coin is 2.0 cm.
As radius is half of the diameter, so its radius will be 1.0 cm.
It is given that the coin is circular in shape, so the area of the circular surface will be πr² = 3.14 × 1² = 3.14 sq. cm. (π = 3.14)
The thickness of the coin is 0.5 cm, which will be considered as the height of the coin.
So, the volume of each coin will be = 3.14 × 0.5 = 1.57 cu. cm.
Therefore, the plastic needed for the batch of 50 coins is,
1.57 × 50 = 78.5 cu.cm and in multiple of 10 it will be 80 cu.cm.
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What is the range () function give example?
Here we can say that - A series of integers can be generated over time using the range() method.
What is Range?Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value the minimum. The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.
given,
20, 25, 30, 45, 55, 90, 110,115,120
so range will be 120 - 20 = 100
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What is the mean of the given set of data 12 20 8 15 16 14 7 5 11 8 14?
11.81 is the required mean of the given data set.
What is mean?The mean (also known as the arithmetic mean, which varies from the geometric mean) of a dataset is calculated as the sum of all values divided by the total number of values.
This measure of central tendency is usually referred to as the "average".
Thus, the data set is as follows:
12, 20, 8, 15, 16, 14, 7, 5, 11, 8, 14
Mean formula: Sum of terms / Number of terms
The mean will now be determined as follows:
Mean: Sum of terms / Number of terms
Mean: 130/11
Mean: 11.81
Therefore, 11.81 is the required mean of the given data set.
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f(x) = 10 –
f(134) :
X
134
Answer: -1/34
Step-by-step explanation:
Answer:
f(134) = 9
Step-by-step explanation:
substitute x = 134 into f(x) and evaluate
f(x) = 10 - [tex]\frac{x}{134}[/tex] , then
f(134) = 10 - [tex]\frac{134}{134}[/tex] = 10 - 1 = 9
Guided practice (page 4)
Previous page
Distance from the ground in floors
11+
10+
of
8+
74
1
...
C
8 9 10
Which of the following statements are true about the elevator? Select all that apply.
Elapsed time in seconds
The elevator stayed 3 floors above the ground initially, then went to a lower floor.
The elevator stayed 3 floors above the ground initially, then went to a higher floor.
The elevator appeared to be moving faster when going up than when going down.
The elevator stayed 7 floors above the ground for 2 seconds.
Hint
Submit Answer
The correct statements of the given statements are -
The elevator stayed 3 floors above the ground initially, then went to a lower floor.The elevator appeared to be moving faster when going up than when going down.What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is the distance of the elevator from the ground in floors.
The elevator stayed 3 floors above the ground initially, then went to a lower floor.The elevator appeared to be moving faster when going up than when going down.Therefore, the correct statements of the given statements are -
The elevator stayed 3 floors above the ground initially, then went to a lower floor.The elevator appeared to be moving faster when going up than when going down.To solve more questions on functions, expressions and polynomials, visit the link below -
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Determine the domain of the following graph
Answer:
-1
Step-by-step explanation:
I got -1 by getting two points from the graph where the line touches. The two points I got were (0,-3) and (1, -4). When it asks you to find the domain it's asking you to find for the slope. The domain and the slope are the same thing. To find slope you use the slope formula which is y2-y1 over x2-x1. Once you set up your equation you should get -4-(-3) over 1-0. When you solve it you should get -1/1 and -1 divided by 1 is -1. So then the slope is -1....
(hope you were able to understand it... I might've not chosen the right points but hopefully I did...I'm sorry if you get it wrong)
Can you do formulas in prism?
The formula for a prism is as follow,
The surface area of a prism = (2×Base Area) +Lateral Surface Area
The volume of a prism =Base Area× Height
A prism is a solid whose perimeter is defined by a number of congruent parallel plane polygons, two of which are known as the ends, and two of which are known as the side faces.
The polyhedron known as a prism has two parallel polygonal bases. A prism is a transparent optical device with flat, polished surfaces that refract light. The two polygonal bases are connected by their lateral faces. Longitudinally, the faces are primarily rectangular. It could even be a parallelogram occasionally.
The surface area of a prism is made up of the combined areas of the lateral faces and the two polygonal bases.
The total area that a prism takes up in three dimensions is known as its volume.
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In which triangle all the sides are equal and all the angles are also equal *?
brine flows into a conical tank at a constant rate of 3 cubic feet per minute. the radius of the cone is 5 feet and its height is 12 feet. how fast is the radius increasing when the radius is 2 feet?
Applying derivative on the formula of volume of cone and using the provided values, The answer is 0.059 feet per minute.
What do you mean by derivative?The rate at which a function changes in relation to a variable in mathematics.
What is a cone and it's formula for volume?A cone is a three-dimensional geometric structure with a smooth transition from a flat base often but not always circular to the point at the top, also known as the apex or vertex.
Formula for volume of cone is:
[tex]V= \pi r^{2}\frac{h}{3}[/tex]
derivate the formula for volume of cone , we get,
[tex]\frac{dV}{dt} = 2\pi r * \frac h3 * \frac {dr}{dt}[/tex]
dV / dt = 3
r=2
h=12
dr/dt = 0.059 feet per minute.
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How do you find the maximum value of a parabola using calculus?
You can use calculus to find the maximum value of a parabola by these steps which are given in the solution part.
What is Parabola?A parabola is a U-shaped curve this is drawn for a quadratic function,
To find the maximum value of a parabola using calculus, you can follow these steps:
1. Identify the equation of the parabola in the form "y = ax² + bx + c," where "a," "b," and "c" are constants.
2. Take the derivative of the equation with respect to x.
3. Set the derivative equal to 0 and solve for x. This will give you the value of x at the vertex of the parabola.
Substitute the value of x that you found in step 3 back into the original equation to find the corresponding y-value. This y-value is the maximum or minimum value of the parabola, depending on the value of a. If a is positive, the parabola opens upwards and the y-value is the maximum. If a is negative, the parabola opens downwards and the y-value is the minimum.
For example, suppose you want to find the maximum value of the parabola y = 2x² - 4x + 3. First, take the derivative of the equation: y' = 4x - 4. Set this equal to 0 and solve for x: 0 = 4x - 4, x = 1.
Substituting this value back into the original equation gives us y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1.
Therefore, the maximum value of the parabola is 1.
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What is the nature of roots of 2x² 6x 3 0?
The roots of the given equation are real and distinct because the value of b2-4ac is greater than 0
where a, b, and c are the coefficients in the standard form of the quadratic equation ax²+bx+c=0
Given quadratic equation is 2x²-6x+3=0 on comparing with the standard form of the quadratic equation ax²+bx+c=0
We have a=2, b=(-6) ,c=3
Hence b²-4ac,
Here b²-4ac is also known as discriminant.
=(-6)²-(4×2×3)
=36-24
=12≥0
12 (Twelve) is obviously greater than zero (0)
here value of b²-4ac>0
Hence the nature of the roots of the given equation is real and distinct.
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Question
What is the nature of roots of 2x²- 6x+ 3= 0?
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 14 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Conainter B is completely full.
After the pumping is complete, what is the volume of the empty space inside Container A, to the nearest tenth of a cubic foot?
After the pumping is complete, the volume of the empty space inside container [A] will be 1147.72 ft³.
What is volume of a cylinder? What is equation modelling? What is a mathematical equation and expression?The volume of the cylinder is equivalent to -v{c} = πr²h = π(d/2)²h
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given are two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 12 feet and a height of 19 feet. Container B has a diameter of 14 feet and a height of 13 feet. Container A is full of water and the water is pumped into Container B until Container B is completely full.
Volume of container [A] -
V{A} = (22/7) x (12/2)² x 19
V{A} = (22/7) x 6 x 6 x 19
V{A} = 3149.72 ft³
Volume of container [B] -
V{A} = (22/7) x (14/2)² x 13
V{A} = (22/7) x 7 x 7 x 13
V{B} = 2002 ft³
V{A} - V{B} → Empty space = 3149.72 ft³ - 2002 ft³ = 1147.72 ft³
Therefore, the free space inside the container A will be 1147.72 ft³.
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