Please help!!! Very confused on my homework.
The tank is completely filled with water and then drains completely into the pool. The volume of the cylindrical tank is v1=36pir2/1 where r1 is the radius of the tank in feet.
PROBLEM IS ON THE ATTACHMENT!
Answers
Step-by-step explanation:
we need to use both equations for the volumes.
the only variables in them are r1 and r2.
when we say both results (volumes) are equal, that means we can create an equation with one formula on one side and the other formula on the other side.
and then we can easily transform the equation into "r1 = ..." or "r2 = ..."
and yes, your teacher made a mistake by hinting to solve for r1 in a. and b. it is r1 in a. and r2 in b.
a.
the goal here is an equation in the form
"r1 = ..."
that means r1 is a function of r2.
36×pi×r1² = 1/2 × 4/3 × pi × r2³ = 4/6 × pi × r2³ =
= 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
r1² = (2/3 / 36) × r2³ = (1/(3×18)) × r2³ = 1/54 × r2³
r1 = sqrt(1/54 × r2³) = 1/3 × sqrt(1/6 × r2³)
b.
the goal here is
"r2 = ..."
again
36×pi×r1² = 2/3 × pi × r2³
36 × r1² = 2/3 × r2³
3×36 × r1² = 2 × r2³
3×18 × r1² = r2³
54 × r1² = r2³
[tex]r2 = \sqrt[3]{54 \times {r1}^{2} } = 3 \times \sqrt[3]{2 \times {r1}^{2} } [/tex]
c.
r2 is doubled.
so, we have to go back to our equation of a.
r1 = sqrt(1/54 × r2³).
when r2 is doubled, we get
r1 = sqrt(1/54 × (2×r2)³) = sqrt(1/54 × 8 × r2³) =
= sqrt(8) × sqrt(1/54 × r2³)
so, when r2 doubles, r1 has to grow by the factor of sqrt(8) to keep the equality intact.
Related Questions
Isaac buys 17 anti-pollution masks for £5. 25 each
He pays with five £20 notes.
a) How much change should Isaac get?
Write your answer in £.
The normal price of an e-scooter is £370
1
In a sale, there is off the normal price of the e-sc
4
hlork out the nice of the e-scooter in the sale
Answers
a) Issac get £10.75 as change after buying all masks
b) The price of the e-scooter in the sale is £277.50
a)
Isaac buys 17 anti-pollution masks for £5.25 each, so the total cost is
17 * 5.25 = £89.25
He pays with five £20 notes, which is a total of 5 * 20 = £100
So, the change he should get is £100 - £89.25 = £10.75
Therefore, Isaac should get £10.75 as change.
b)
In the sale, there is 1/4 off the cost price of the e-scooter, which means that the scooter is discounted by 1/4 * £370 = £92.50.
To work out the price of the e-scooter in the sale, you need to subtract the discount from the normal price, so
£370 - £92.50 = £277.50
Therefore, the price of the e-scooter in the sale is £277.50
To know more about cost price click below:
https://brainly.com/question/29511226#
#SPJ4
How do you find height of a triangle when base is given to you?
Answers
The height of a triangle can be found using the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Therefore, the height of a triangle can be found by rearranging the formula to height = (2 * area) / base.
To find the height of a triangle when the base is given, first use the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Next, rearrange the formula to height = (2 * area) / base so that the height can be found by dividing the area by the given base. Once the area is known, the height can be found by plugging the area and base into the rearranged formula. For example, if the base of a triangle is 8 and the area is 12, then the height of the triangle can be found by dividing 12 by 8, which is equal to 1.5. Therefore, the height of the triangle is 1.5.
Learn more about triangle here
https://brainly.com/question/2773823
#SPJ4
please help: find TZ
Answers
28. Anael cut several boards to build a deck.
The boards must be 100 in. ± 0.25 in. Her
measurements of the boards after cutting
them are shown in the graph. Which boards,
if any, can she not use?
Answers
Anael can not use the fourth board measurement. This can be solved by using the concept of inch scale.
What is inch scale?A centimeter is smaller than an inch. On the other side of the centimeter ruler, inches are denoted by the large, continuous hash marks that are inscribed above the digits. On a ruler, the inch is the largest unit and is denoted by the longest line. There is a number next to each 1-inch line on the ruler that designates.
Since the international yard was adopted in the 1950's and 1960's, standards for the precise length of an inch have fluctuated, but the inch is now based on the metric system and is defined as precisely 25.4 mm.
The question given here,
the first board measurement: [tex]99\frac{3}{4} =[/tex] 99 inch ± 0.75 inch
the second board measurement: [tex]99\frac{7}{8} =[/tex] 99 inch ± 0.875 inch
the third board measurement: [tex]100\frac{1}{6} =[/tex] 100 inch ± 0.16 inch
the fourth board measurement: [tex]100\frac{5}{16} =[/tex] 100 inch ± 0.3125 inch
the fifth board measurement: [tex]99\frac{13}{16} =[/tex] 99 inch ± 0.8125 inch
Thus, Anael can not use the fourth board measurement.
To know more about inch scale refer to:
https://brainly.com/question/261465
#SPJ1
As n ranges over the positive integers, what is the maximum possible value for the greatest common divisor of 11n 3 and 2n 1
Answers
The maximum possible value for the greatest common divisor (GCD) of 11n + 3 and 2n + 1 as n ranges over the positive integers is 1.
The GCD of two integers is the largest integer that divides both integers without leaving a remainder. We can use the Euclidean algorithm to find the GCD of two numbers.
The Euclidean algorithm states that for two integers a and b, we can find the GCD of a and b by repeatedly applying the following steps:
Divide a by b to get a quotient q and a remainder r
Replace a with b and b with r
Repeat the process until r is 0
If we apply this algorithm to 11n + 3 and 2n + 1, we get the following:
GCD(11n+3, 2n+1)
As 11n + 3 = 3(2n + 1) + 5n
= GCD(2n+1, 5n )
As 2n + 1 = (2/5)(5n) + 1
= GCD(5n, 1)
= GCD(1, 0)
= 1
So as n ranges over the positive integers, the maximum possible value for the GCD of 11n + 3 and 2n + 1 is 1.
To know more on Euclidean algorithm
https://brainly.com/question/13266751
#SPJ4
I don’t know this question
Help me
Answers
Answer: Probably negative 69
What is median?
the sum of values in a set of data multiplied by the number of values in the set
the sum of values in a set of data divided by the number of values in the set
the middle value in a data set when the values are put in order
the value that occurs most often in a data set
Answers
the middle value in a data set when the values are put in order
For example, the set {3,1,2} sorts to {1,2,3} where the median is 2.
Another example: The set {1,2,3,4} has 2 and 3 tied for the middle most position. The midpoint is (2+3)/2 = 5/2 = 2.5 which is the median.
Enrique earns 101010 points for each question that he answers correctly on a geography test. Write an equation for the number of points, yyy, Enrique scores on the test when he answers xxx questions correctly.
On his first geography test, Enrique answered 333 questions correctly. On his second test, Enrique answered 777 questions correctly.
Place points on the graph to show Enrique's first and second geography test.
Answers
An equation for the number of points y, and the correct answers x is y = 10x.
Define the term equation?One mathematical expression makes up a term. It could be a single variable (a letter), a single number (negatively or positively), or a number of variables multiplied but just never added as well as subtracted.
For the stated question-
Since Enrique receives 10 points for every question on the a geography test that is answered properly,Again for number of points, "y," Enrique receives on the test if he successfully answers "x" questions, we must formulate an equation.Consequently, the total points earned equal the total points earned for each question. number of questions with accurate responses.
Consequently, points earned = 10x
y = 10x.
First geography test: x = 3
y = 10*3 = 30
Second geography test: x = 7
y = 10*7 = 70
Thus, the graph for the enrique's first and second geography test is plotted.
To know more about the equation, here
https://brainly.com/question/2972832
#SPJ4
The correct question is-
Enrique earns 10 points for each question that he answers correctly on a geography test. Write an equation for the number of points, y Enrique scores on the test when he answers x questions correctly.
On his first geography test, Enrique answered 3 questions correctly. On his second test, Enrique answered 7 questions correctly.
Place points on the graph to show Enrique's first and second geography test.
How the addition of 2 and 2 become 5?
Answers
In the late 19th century, the Russian press used the phrase 2 + 2 = 5 to describe the moral confusion of social decline at the turn of a century, because political violence characterised much of the ideological conflict among proponents of humanist democracy and defenders of tsarist autocracy in Russia
Isabel is shopping for her new car. She identified six models she likes at a local dealership. The table lists
the down payment she would need to make on each car to keep the monthly payment within her budget.
Assume that she's using only the money accumulated in her savings account to make the down payment.
Use this information and the appropriate time value of money formula e to select all the cars that are
within Isabel's budget.
5
choice 1
choice 2
choice 3
down payment: $8,500 down payment: $6,200 down payment: $5,100
choice 4
choice 5
choice 6
down payment: $7,250 down payment: $7. 750 down payment: $7,500
Answers
The value of Isabel's account after three years can be calculated using the future value of the annuity formula.
Isabelle's budget car is:
Choice 2Choice 3Choice 4Reason:
Monthly savings, PMT = $200
Account compound interest, r = 1.7%
t = Account value after 3 years is displayed as increase.
We know that:
[tex]FV =PMT * \frac{[(1+i)^n -1]}{i}[/tex] --------------------- (1)
Where;
i = r/12
⇒ n = 12 × t
From the above equation(1), we get:
[tex]FV =200 * \frac{[(1+\frac{1.7}{2} )^{12*3} -1]}{\frac{1.7}{12} }[/tex]
≈ 7381.4
Therefore,
The budget cars she can buy, those that require a down payment of less than $7,381.4, which are:
The required down payment of choice 02 is $6200.
The required down payment of choice 03 is $5100.
The required down payment of choice 04 is $7250.
Learn more about Future value:
https://brainly.com/question/8286272
#SPJ4
Jane is building a fence around her garden. For every 4 feet of fencing, the cost is 36 Complete the table below showing the length of the fence and the cost.
Answers
The Complete is showing the length of the fence and the cost.
Length of fencing 4 6 7 9 10
Cost: 36 54 63 81 90
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Length of fencing 4 6 7 x 10
Cost: 36 y z 81 w
Now, Using proportion
4/ 36 = 6/y
4y = 36(6)
y = 54
and, 4/36 = 7/z
4z = 36 (7)
z = 63
and, 4/36 = x /81
x = 9
and, 4/36 = 10/w
360 = 4w
w= 90
Learn more about proportion here:
https://brainly.com/question/29774220
#SPJ1
What is the degree of the polynomial 7x³ 5x 4x³ 2x²?
Answers
The degree of the polynomial 7x³ 5x 4x³ 2x² is 3.
The degree of a polynomial is the highest power of x in the polynomial.
In this case, the polynomial is 7x³ 5x 4x³ 2x², and the highest power of x is x³. This means that the degree of this polynomial is 3.
It's important to note that when working with polynomials it's important to pay attention to the signs of the coefficients. In this case, we have 7x³, 5x, 4x³, 2x². The x³ term has the highest degree and it's coefficient is 7, the x term has the second highest degree and it's coefficient is 5, the x³ term has the same degree as the first x³ term, but the coefficient is different, and the x² term has the fourth highest degree and it's coefficient is 2.
Learn more about Polynomials here:
https://brainly.com/question/2833285
#SPJ4
How do you find the sides of a triangle with angles on a 45 45 90?
Answers
the given triangle A 45-45-90 triangle is a right triangle having interior angles measuring 45°, 45°, and 90° in degrees.
A 45-45-90 triangle is also an isosceles triangle, which means that its two legs are equal in length.
All 45-45-90 triangles are similar to each other.
Line segments DE and FG are perpendicular to side AB of the 45-45-90 triangle, ABC. Triangles ADE and AFG are also 45-45-90 triangles now, △ABC~△ADE~△AFG.
The ratio of the side lengths of a 45-45-90 triangle is:
ratio= 1:1: √2
The legs of opposite the 45° angles (the shorter sides) are √2÷2of the length of the hypotenuse (the side opposite the 90° angle)
The hypotenuse is √2 times the length of either leg.
Since a 45-45-90 triangle is also an isosceles triangle, then, the two legs are equal on measuring. Assuming x is the length of the leg and b is the length of the hypotenuse and using the Pythagorean Theorem:
x^2 + x^2= b^2
Thus, the ratio of the side lengths of a 45-45-90 triangle are x:x:√2 or 1:1: √2 respectively.
To know more about Triangle:
brainly.com/question/2773823
#SPJ4
What is a dual of a formula?
Answers
The dual formula is a formula which we get when we replace the symbol ∨ by ∧ , ∧ by ∨ , T by F or F by T.
Basically , we can say that it is obtained by replacing tautology by contradiction.
There are certain rules which are to be followed while applying dual formula which are,
Some symbols, example ¬ remains the same while finding dual.If we will find the dual of a dual we will get the original statement.T (tautology) and F (contradiction) are duals of each other.T is changed to F and vice-versa.S1 is a tautology if and only if S2 is a contradiction.
To learn more about dual
brainly.com/question/28222956
#SPJ4
Compare the means of the shift outputs. The workers in the shift with the highest mean will earn a bonus. Which shift will earn the bonus?
Answers
The workers in shift B earns the bonus.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Mean is found by adding all the data values and then dividing with number of values in the set.
Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}
Number of data in shift A = 12
Mean = (77 + 91 + 82 + 68 + 75 + 72 + 85 + 65 + 70 + 79 + 94 + 86) / 12
= 944 / 12
= 78.67
Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}
Number of data in shift B = 12
Mean = (68 + 93 + 53 + 100 + 77 + 86 + 91 + 88 + 72 + 74 + 66 + 82) / 12
= 950 / 12
= 79.17
The workers in the shift with the highest mean will earn a bonus. It is shift B.
Hence the workers in shift B earn the bonus.
Learn more about Mean here :
https://brainly.com/question/14548171
#SPJ1
The full question is as follows :
The following are daily outputs from shift A and shift B at a factory.
Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}
Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}
Q. Compare the means of the shift outputs. The workers in the shift with the highest mean will earn a bonus. Which shift will earn the bonus?
Molly is building a model roller coaster as part of a school project she chose the millennium force in cedar point which is 94 meters tall to model if molly uses a scale of 1 centimeter = 4 meters what will be the height of the model
Answers
Answer:
23.5 cm
Step-by-step explanation:
You want the height of the model of a 94 m tall roller coaster when the model scale is 1 cm = 4 m.
ProportionThe model dimensions are assumed to be proportional to the real-world dimensions, so the model height h will satisfy the proportion ...
h/(94 m) = (1 cm)/(4 m)
Multiplying by 94 m gives ...
h = (1 cm)(94/4) = 23.5 cm
The height of the model is 23.5 cm.
Select the correct answer.
Which statement about this system of equations is true?
A. The system has no solution.
B. The system has a unique solution at (0,6).
C. The system has a unique solution at (0,-4).
D. The system has infinitely many solutions.
Answers
The statement that is true on the system of equations is that A. The system has no solution.
Why is there no solution ?There is no solution in the given system of equations because the lines formed by the equations are parallel to each other. This means that they will never intersect with each other.
A solution is only derived at the points where the systems of equations intersect with each other. As there is no point where these equations intersect, it means there is no solution for these system of equations.
Find out more on system of equations at https://brainly.com/question/13729904
#SPJ1
I GIVE THANKS AND MARK BRAINLIEST
WHAT ARE THE CORRECT ANSWER(S)?
Answers
Answer:
b and d
Step-by-step explanation:
slope is -0.632 which is quite literally what d is saying, (on terms of graphs) for every 1 square over it goes -0.63 squares down
Find the missing angle. 60° 75° 75° ?
Answers
Answer:
65?
Step-by-step explanation:
im not to sure but maybe 65
Where is the quadrant 1?
Answers
The quadrant 1 of the graph is in the place of upper right quadrant.
the term graph in math is referred as a non-linear kind of data structure made up of nodes or vertices and edges
Here we have given that we have to find the place of quadrant 1.
In order to find that we must know that definition of quadrant in math that is one other than the region/part of a cartesian plane which is obtained when the two axes intersect each other and it is used to determine the position of a point in a plane.
As we all know that the first quadrant is in the upper right-hand corner of the plane.
And here we all also know that both x and y have positive values in this quadrant.
To know more about graph here
https://brainly.com/question/17267403
#SPJ4
will u simplify -164
Answers
Answer:
No, I will not simplify -164
Step-by-step explanation:
You can not Simplify -164
so the answer will be you can not simplify it
Two has 4 2/3 pitches of juice. One glass holds 1/6 of a pitcher. How many glasses can teo fill?
Answers
Teo can fill 28 glasses in 4 2/3 pitches of juice.
Teo has 4 2/3 pitches of juice.
First we write the improper fraction (mixed fraction) as a proper fraction.
4 2/3
= [(4 × 3) + 2] / 3
= (12 + 2) / 3
= 14/3
One glass holds 1/6 of a pitcher.
Let m number of glasses hold 14/3 pitches of juice.
By unitary method,
m × (1/6) = 14/3
To find the value of m we need to divide fractions.
m = (14/3) / (1/6)
m = (14/3) × (6/1)
m = 14 × 2
m = 28
Learn more about the unitary method here:
https://brainly.com/question/22056199
#SPJ4
An octagonal prism (shown) has __________ faces and ___________ vertices. Question 20 options: A) 16, 10 B) 10, 16 C) 8, 10 D) 6, 8
Answers
With 10 faces and 16 vertices, an octagonal prism is depicted.Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape.
Do octagonal prisms have eight vertices?An octagonal prism therefore has 10 faces, 24 vertices, and 16 vertices.Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape. 16 vertices, 10 faces, and 24 edges make up its surface.Eight of the nine vertices of an octagonal pyramid are found where the triangle faces of the base meet, while the ninth vertex is found where the triangular faces of the pyramid's top meet.There are 8 faces on an octahedron, which is a polyhedron. The octahedron shape of a hexagonal prism is defined by its 8 faces, which include its 2 bases and 6 sides.With 10 faces and 16 vertices, an octagonal prism is depicted. Two octagonal bases and eight rectangular sides define an octagonal prism, which has two of each shape.To learn more about octagonal prism refer to:
https://brainly.com/question/11461768
#SPJ4
A population of 210,000 people is increasing by 15% each year. How much will the population be in 5 years?
Answers
According to the compound interest formula, the population is 5 years is 422,385.
The term compound interest in math is defined as the interest calculated on the principal and the interest accumulated over the previous period.
Here we have given that the population of 210,000 people is increasing by 15% each year.
And then while looking into the given question, we have identified that the value of
interest rate = 15%
principal count = 210,000
time period = 5
Here we have to convert R as a percent to r as a decimal, then we get
=> r = R/100
=> r = 15/100
=> r = 0.15 rate per year,
Now, we have to solve the equation for A
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Apply the values on it , then we get,
[tex]A = 210,000.00(1 + \frac{0.15}{1} )^{(1)(5)}[/tex]
When we simplify this one then we get
[tex]A = 210,000.00(1 + 0.15)^5[/tex]
Therefore, the value of A is 422,385.
To know more about compound interest here.
https://brainly.com/question/29335425
#SPJ4
Is 2 a happy number?
Answers
No, 2 is not a happy number because 2 can not become 1 after a series of stages in which each step 2 is replaced by the sum of its squares
Let's try to first comprehend what numbers are.
An arithmetic value that is calculated and utilized to represent a quantity is called a number. Numeral symbols, such as "3" are used in writing to represent numbers. A number system is a methodical technique to express numbers using digits or other symbols. The numerical system is a helpful collection of numbers that illustrates the number's algebraic and mathematical structure. presents an example that is typical.
Happy numbers If a number leads to 1 after a series of stages in which each step's number is replaced by the sum of its squares, it is said to be happy. For example, if we start with a happy number and keep replacing it with the sum of its squares, we eventually reach 1.
So 2 is not a happy number.
To know more about happy numbers here:
https://brainly.com/question/29889128
#SPJ4
Which table shows the function y = -2x + 4?
Answers
Answer:
Slope = -2 Y intercept is (0,4)
Step-by-step explanation:
What is a coordinate plane example?
Answers
A coordinate plane is a two-dimensional surface formed by two number lines
What is coordinate system?In a plane, a Cartesian coordinate system is a system of coordinates that designates each point uniquely by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length. Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. The coordinate plane allows us to graph points, lines, and more. The plane that houses the x- and y-axes is known as the xy-plane, while the y- and z-axes are housed in the yz-plane and the x- and z-axes are housed in the xz-plane.To learn more about coordinate system refer to:
https://brainly.com/question/2141683
#SPJ4
What is 62% of $10.50?
Answers
Answer:
$6.51
Step-by-step explanation:
To make a percent a decimal, divide by 100
62% = .62
.62 x 10.50 = 6.51
We know that half of 10.50 is 5.25 and 625 would be a little higher and 6.51 is a little higher.
felix wants to make a graphic design as a decoration for a new website. His initial idea for the design involves using the shapes of three parabola is graphed on a coordinate plane, as shown.
Answers
Transformation for A to B : Shift 2 unit horizontally.
Transformation for A to C : Shift 1 unit horizontally, 1 unit vertically.
Equation of Parabola A : y = - (x - 1)² + 1
Equation of Parabola B : y = - (x - 3)² + 1
Equation of Parabola C : y = - (x - 2)² + 2
What is parabola?Section of a right circular cone by a plane parallel to a generator of the cone is a parabola. It is a locus of a point, which moves so that distance from a fixed point (focus) is equal to the distance from a fixed line (directrix)
Fixed point is called focus.
Fixed line is called directrix.
Equation of the parabola having vertex (h, k).
y = a(x - h)² + k
Equation of Parabola A with vertex (1,1)
y = a(x - 1)² + 1
parabola A has point (0, 0) on it
0 = a (0 - 1)² + 1
a = -1
Equation of the parabola A
y = - (x - 1)² + 1
Shifting parabola A, 2 unit horizontally, we get parabola B
Equation of the parabola B
y = - (x - 3)² + 1
Shifting Parabola A, 1 unit horizontally and 1 unit vertically, we get parabola C
Equation of the parabola C
y = - (x - 2)² + 2
Hence, shifting 1 unit horizontally and 1 unit vertically in Parabola A we get parabola C and shifting 2 unit horizontally we get parabola B,
y = - (x - 1)² + 1 is equation of Parabola A.
y = - (x - 3)² + 1 is equation of Parabola B.
y = - (x - 2)² + 2 is equation of Parabola C.
Learn more about parabola here:
https://brainly.com/question/21685473
#SPJ1
set an expression negative -4n +3+9n-4 is equivalent to 4N. What error did Maria likely make?
Answers
The error that Maria likely make is that she subtracted 1n from 5n.
How to infer the error?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
The value of the expression will be:
= -4n +3+9n-4
= 5n - 1
The error was because 1n was minus from 5n
Learn more about expressions on:
brainly.com/question/723406
#SPJ1