The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.
How do you find the maximum volume of a cone?The cone has a volume of
V=πr2h/3
Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.
R is the cone's slant height, and it serves as the hypotenuse of a right triangle.
R2 = h2 + r2, or r2 = R2-h2.
So V = (1/3)π
[R2-h2]
h = (π/3)[R2h-h3]
You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.
dV/dh=(π/3)[R2-3h2]
R2-3h2=0 --> h2=R2/3 -> h = R/√3
Now we can determine r:
r2=R2-R2/3 = (2/3)R2
The volume formula with r and h substituted:
V = (π/3)
r2h = (π/3)(2R2/3)
(R/√3)
V(R)=2πR3/(9√3)
The complete question is:
A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).
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50 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!50 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!50 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Select the correct answer. The graph of function f is shown. Function g is represented by the table. x -2 -1 0 1 2 g(x) -32 -16 -8 -4 -2 Which statement correctly compares the two functions on the interval [0, 2]? A. Both functions are increasing, but function g is increasing faster. B. Both functions are increasing, but function f is increasing faster. C. Function f is increasing, and function g is decreasing. D. Both functions are increasing at the same rate.
Answer:
B
Step-by-step explanation:
Please help if you want brianleist!! :) uhm don't mind update- NO LINkS- Thank you to those who help! :)
Answer: 107ft^2
Step-by-step explanation:
Calculate the area of both squares and add together.
Area =
(5x7) + (8x9) = 107ft^2
Calculate the area of a rectangle with the base of 12 feet and height of 3 feet.
(I need the answer as fast as possible so if anybody could help that would be greatly appreciated)
A: 9 square feet
B: 15 square feet
C: 30 square feet
D: 36 square feet
Find the area of the following color regions
A 30 foot ladder leans against a house. The angle between the base of the ladder and the ground is 83º. Find the distance from the base of the ladder to the house. (Show work!)
Answer:
3.656 ft
Round as needed
Step-by-step explanation:
cos∅ = adj/hyp
cos 83 = adj/30
multiply both sides by 30
30 * cos83 = adj
30 * 0.121869343405147 = adj
3.6560803022 = adj
≈ 3.656 ft
please help me if you can!!
( links = report )
Answer: 3150
Step-by-step explanation:
V = lwh
V = 25 x 7 x 18
V = 3150
What is the solution of x^2 7x 4?
The answer to the given question is x = -2, x = 2. The given problem can be solved by the following steps :
Step 1: Rewrite the equation in standard form: x2 + 7x - 4 = 0
Step 2: Find the factors of the coefficient of x and the constant term: -4 = -2 x -2, 7 = 7
Step 3: Set up the factors to solve the equation: (x + 2)(x - 2) = 0
Step 4: Solve each factor: x + 2 = 0, x - 2 = 0
Step 5: Find the solutions: x = -2, x = 2
Therefore, the final answer is x = -2, x = 2.
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What is 2/3 + 1/6 + 2/8
Answer:
2/3 + 1/6 + 2/8
=(2×8+1×4+2×3)/24
=(16+4+6)/24
=26/24
=13/12
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What is 3 6 equivalent to in fractions?
Answer:
1/2
Step-by-step explanation:
The circumference of a circle B is 80% of the circumference of circle A.
a) Find the ratio of the area of circle A to the area of circle B, giving your
answer in the form 100:n
100 :
(2)
Square E has sides of length e cm.
Square F has sides of length fcm.
The area of square E is 69% greater than the area of square F.
b) Work out the ratio of e:f
Your final line should say, Ratio of e:f is
(2)
The area of circle A to the area of circle B ratio is 100: 64, and the ratio of e: f is 13: 10.
The area of the circle is equal to the multiplication of the square of the circle's radius and π.
A = πr²
where 'r' is the radius
Circumference of circle A × 0.8 = circumference of circle B
So, taking r as the radius of A,
2πr = circumference of circle A
2πr × 0.8 = circumference of circle B
So the radius of B is r × 0.8.
Now we can substitute that in the area equations :
Area of A = π×r²
Area of B = π × (r × 0.8)² = π × r² × 0.64
The circumferences of the A to B ratio is
Circumference of A : Circumference of B = (2 × π × r)/(2 × π × r × 0.8)
= 1: 0.8 = 100: 80,
The areas of circle A to circle B ratio is
Area of A : Area of B = (π × r²)/(π × r² × 0.64) = 1: 0.64 = 100: 64
e² = f² × 1.69
69% larger shows that f² is the 100% to which we must add 69% to obtain e². 100% + 69% Equals 169%, obtaining a factor of 1.69.
We have this equation:
e² = f² × 1.69
Apply the square root on both sides.
e = f × √(1.69) = f × 1.3
e/f = 1.3 = 1.3/1 = 13/10
the ratio e:f = 13: 10
Thus, the ratio of circle A's area to circle B's area is 100: 64 and the ratio of e: f is 13: 10.
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Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these
-2n^4-5n-10
Explanation is[tex]^{}[/tex] in a file
bit.[tex]^{}[/tex]ly/3gVQKw3
Which equation below is using the correct set up to solve for x?
Answer:
A is your answer
Step-by-step explanation:
Answer:
8²+16²=x²
Step-by-step explanation:
because h²=base²+perpendicular ²
What is the solution to the system of linear equations 3x minus 2y equals 14 5x plus y equals 32?
The solution to the system of linear equations is x = 10 and y = 22.
To solve this system of linear equations, we can use the substitution method.
First, we want to isolate one of the variables in either equation. Let's start with equation 1:
3x - 2y = 14
Add 2y to both sides to isolate x:
3x = 14 + 2y
Divide both sides by 3 to solve for x:
x = (14 + 2y) / 3
Now, substitute this expression for x into equation 2:
5x + y = 32
5(14 + 2y) / 3 + y = 32
Simplify:
70 + 10y + y = 32
Combine like terms:
11y = -38
Divide both sides by 11 to solve for y:
y = -38 / 11
y = -3.45454545...
Now, substitute -3.45454545... for y in the expression for x:
x = (14 + 2(-3.45454545...)) / 3
x = (14 - 6.9090909...) / 3
x = 7.09090909... / 3
x = 2.36363636...
x = 2.4 (rounded to nearest tenth)
Now that we have both x and y, the solution to the system of linear equations is x = 2.4 and y = -3.5.
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What is the measure of xº?
A. 10°
B. 16°
C. 34°
D. 70°
A 5 m 60 cm high vertical pole cat a hadow 3 m 20 cm long. Find at the ame time
(i) the length of the hadow cat by another pole 10 m 50 cm high,
On solving the provided question we can say that equation formed is x/y = k, x = ky => y₂ = (10.5 × 3.2) / 5.6 => y₂ = 6
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x/y = k, x = ky
where k is a constant.
Thus, x₁ / y₁ = x₂ / y₂
5.6 / 3.2 = 10.5 / y₂
5.6 × y₂ = 10.5 × 3.2
y₂ = (10.5 × 3.2) / 5.6
y₂ = 6
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Find the value of xif V√81 = 3.
OA) 4
OB) 2
OC) 8
OD) 27
The value of exponent x, if [tex]$\sqrt[\text X]{81} = 3[/tex], is 4, in the given equation.
What is exponent?
Exponent is the process of expressing large numbers as powers, according to the definition. Accordingly, the exponent describes the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6×6×6×6. 6⁴ can be used to represent this. In this case, the base is 6 and the exponent is 4. You can interpret this as 6 raised to the power of 4.
Exponents are represented by the symbol. The word "carrot" refers to this symbol (). 4 raised to a power of two, for instance, can be expressed as 4^2 or 4². Thus, 4^2 = 4 × 4 = 16. A few exponent-based numerical expressions are represented in the table below.
The value of x, if [tex]$\sqrt[\text X]{81} = 3[/tex]
3 × 3 = 9
9 × 3 = 27
27 × 3 = 81
Thus, The value of x, if [tex]$\sqrt[\text X]{81} = 3[/tex], is 4.
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The number of views on a viral video can be modeled by the function
G(t) = 2500(5) 2-4. Write an equivalent function of the form G(t) = ab.
The equivalent expression would be; function G(t) = 86,400•3^t
What is a function in simple definition?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
The number of views on a viral video can be modeled by the function
G(t) = 2500(5) 2-4.
we have to find out an equivalent function of the form G(t) = ab.
Here, we want to make a transformation
From what we have;
G(t) = 2500(5)^(t - 4)
From indices, we know that;
x^(a + b) = x^a•x^b
Thus, we have it that;
G(t) = 2500•3^t•3^2
G(t) = (9 * 9600) * 3^t
G(t) = 86,400•3^t
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HELP ASAP PLEASE!!!!!!! NO LINKS!!!!!!!
Answer:
x=8
Step-by-step explanation:
Add up the angles to 90 because angle GHI and angle IHJ should add up to 90°
3x+66=90
-66=-66
Solve for x.
3x = 24
3 = 3
x =8
Hope this helps.
it costs $12.50 to enter the amusement park and $1.50 to play each game. Write and solve an inequality to fin the number of games g Cole can play if he has $35 to spend at the park
Answer:
g=1.50x+12.50 / Cole can play 15 games
Step-by-step explanation:
Once writing the equation place 35 for the variable.( 35=1.50x+12.50) Then you would have to solve for x.(x=15) I hope this is correct
How do you represent a number line on a class 7?
Draw a line and locate the origin '0', mark the positive numbers on the right and the negative number on the left of '0' at an equal distance.
A number line is a horizontal straight line in which the integers are placed in equal intervals. All the numbers can be represented in a number line. This line can be extended indefinitely at both ends.
A number line is a graphical representation of numbers on a straight line. It is used for comparing and ordering numbers. It can be used for representing any real number that includes every whole number and natural number.
Draw a line and locate the point ‘0’. This point is known as the origin. If the given number is positive, draw it on the right side of the origin. If it is a negative number, draw it on the left side of zero. Divide each unit into the values equal to the denominator of the given fraction.
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A parade route is 3/4 mile long.There will be a Refreshment add the standAlso be eight refreshment stand at the end of the route. How far are the refreshment stands in feet
Answer: 440 ft
Step-by-step explanation:
Given
A parade route is [tex]\frac{3}{4}[/tex] mile long
There are 8 refreshment stand at the end of the route
Suppose there are two refreshment stand, so the route is divided into 3 parts, similarly for three stands, the route is divided into 4 parts
For 8 stands, the route is divided into 9 parts
Distance between two stands is
[tex]\Rightarrow \dfrac{\frac{3}{4}}{9}\\\\\Rightarrow \dfrac{1}{12}\ \text{miles}[/tex]
We know, [tex]1\ \text{mile}\equiv 5280\ ft[/tex]
convert miles to feet
[tex]\Rightarrow \dfrac{1}{12}\times 5280\\\\\Rightarrow 440\ ft[/tex]
Need help with this lesson is Graphing Polynomials
Answer:
Step-by-step explanation:
y = [tex]\sqrt{x+4}[/tex] + 5
Find the value of x.
Answer:
4
Step-by-step explanation:
Solve the equation for all real solutions in simplest form. 2p? – 3p - 7=0
Answer:
p = -7
Step-by-step explanation:
1) added up the like therms
-p -7 = 0
2) multiply by -1
p+7 = 0
3) add at both members -7
p+7-7 = -7
p= -7
a taxi charges $2.35 fee plus $0.55 per mile. melissa has no more than $15 to spend on her taxi ride how many miles can she go?
Answer:
2.35 + 0.55 × 15 = 10.6
Therefore, she can go 10.6 miles.
Answer:
10.6
Step-by-step explanation:
2.35 + 0.55 x 15 = 10.6
how does the value of A determine the range for f(x) = a|x|
HELP PLEASE ASAP
Answer:
It will either invert the graph or stretch/compress the horizontal
Step-by-step explanation:
When a is negative It will invert the graph, and reflect it over the x-axis
By plugging in a=1 you get a normal absolute value function of x ( a V on the graph)
If a>1 then your graph will compress
If a<1 then your graph will stretch
How many prime numbers are between $30$ and $40$?
Answer:
2 prime numbers: 31 and 37
Step-by-step explanation:
31 and 37 are the only prime numbers between 30 and 40
Triangle STU is a right triangle.
Write an equation that relates the lengths of sides s, t, and u? (5 points)
Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².
What is the triangle?Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.
Here,
Given : Triangle STU is a right triangle.
Thus,
We find :
sides s,t and u
the relationship between them is :
As it is a right triangle
So,
According to the pythagoras theorem,
=>u²= t²+s²
Therefore , the solution of the given problem of triangle comes out to be the relationship between s,t and u is u²= t²+s².
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Lol I’m bad at math can someone help me with #5?
Answer:
21/5
Step-by-step explanation:
cross multiply
21=5x
flip
5x= 21
divide both sides
Rene makes $38,000 per year and pays about 35% of
his gross monthly income in federal and state taxes.
He wants to find an apartment to rent. Estimate how
much he can afford to pay for rent each month. Then
determine how much money he will have after taxes
and rent are paid.
PLEASE HELP
After the taxes and rent, the remaining amount in his gross pay is $5,700
The term gross income is defined as also known as gross pay when it’s on a paycheck is an individual’s total earnings before taxes or other deductions.
Here we have given that Rene makes $38,000 per year and pays about 35% of his gross monthly income in federal and state taxes.
And as we all know that If you live in a metropolitan city, your HRA is equivalent to 50% of your basic salary.
Therefore, the remaining amount in his hand is calculated as,
=> $38000 - [35% of income + 50% of income]
Here the 35% of income is
=> 38000 x 35/100
=> 380 x 35
=> 13300
Similarly, the 50 percent of the income is
=> 38000 x 50/100
=> 380 x 50
=> 19000
Then the remaining amount is calculated by apply the values on it, then we get,
=> $38000 - [$13300 + $19000]
=> $3800 - $32300
=> $5700
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