The radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].
How to find volume of the cone?
Given
metal radius = R = 20
cone base radius = r
cone height = h
First, we can use Pythagoras theorem
R^2 = r^2 + h^2
r^2 = R^2 - h^2
r^2 = 400 - h^2
Then, we use volume of cone formula
V = 1/3[tex]\pi[/tex] * r^2 * h
V = 1/3[tex]\pi[/tex] * (400 - h^2) * h
V = 1/3[tex]\pi[/tex] * 400h - h^3
To get maximum volume of cone, V'(h) must be 0. So,
1/3[tex]\pi[/tex] * 400 - 3h^2 = 0
400 - 3h^2 = 0
3h^2 = 400
h^2 = 400/3
h = [tex]\frac{20}{\sqrt{3}}[/tex] or 11.55
Next, we find the r with substitution method. So,
r^2 = 400 - ([tex]\frac{20}{\sqrt{3}}[/tex] )^2
r^2 = 400 - [tex]\frac{400}{3}[/tex]
r^2 = [tex]\frac{800}{3}[/tex]
r = [tex]\frac{20\sqrt{2}}{\sqrt{3}}[/tex] or 16.33
Now, we can get maximum volume of cone.
V = 1/3[tex]\pi[/tex] * 16.33^2 * 11.55
V = 1,026.67[tex]\pi[/tex]
Thus, the radius of the cone is 16.33, the height of the cone is 11.55, and the maximum volume of the cone is 1,026.67[tex]\pi[/tex].
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The base of the parallelogram has a length
of 10 cm. What is the height?
10 cm
12cm
14cm
The height is either 10 cm,12 cm,14 cm.
Given:
The base of the parallelogram has a length of 10 cm.
Here area is not given so the height may be anything.
suppose h = 10
area = base * height
= 10 * 10
= 100 cm^2
if h = 12
area = 10 * 12
= 120 cm^2
if h = 14
area = 10 * 14
= 140 cm^2
Therefore the height is either 10 cm,12 cm,14 cm.
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Describe the relationship between <1 and <5
Angles 1 and 5 constitutes one of the pairs
Step-by-step explanation:
What is the slope of the line that passes through the points (2, 3) and (0, 11)
Answer:
-4
Step-by-step explanation:
m= y2-y1/x2-x1
m= 11-3/0-2
m= 8/-2
m= -4
Answer: The slope is -4
Step-by-step explanation: The general formula for calculating the slope is [tex]\frac{y2-y1}{x2-x1}[/tex].
x1 = 2, y1 = 3, x2 = 0, y2 = 11
So we have [tex]\frac{11-3}{0-2}[/tex] = [tex]\frac{8}{-2}[/tex] = -4.
At the penalty apr rate of 28. 99% and a balance of about $1800, approximately how much interest would you owe in one month?.
The interest rate for one month is 2.42% and the interest amount is $40 approximately.
Given,
The penalty APR rate = 28.99%
Balance amount = $1800
We have to find the interest for one month;
Here,
The APR of 28.99% is the yearly interest. To find the monthly rate:
= Rate / 12 months
= 28.99% / 12
= 2.42%
The amount owed is therefore;
= 1,800 x 2.42%
= $43.56
= $40.00 approximately
That is,
The interest rate for one month is 2.42% and the interest amount is $40 approximately.
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Write a sine function that has an amplitude of 3, a midline of 5 and a period of pie
The sine function is y = 5 sin ([tex]16\pi x[/tex] ) + 3.
What is Sine function?The function y =[tex]sin x[/tex] defines a sine wave as a geometric waveform that oscillates (moves up, down, or side to side) frequently.
It is an s-shaped, smooth wave that oscillates above and below zero, to put it another way.
In its most general form, the sine wave can be described using the function y=[tex]a sin (bx)[/tex]
Given:
Amplitude = 3
midline= 5
As, we know
General sine function: a sin b[tex](x- c)[/tex] + d
and, amplitude = absolute value of a
b = 2π / period
c = phase shift (horizontal shift)
d = vertical shift (i/e., midline is y = d)
So,
a = 5, d = 3, and b = 2π / (1/8) = 16π, c = 0
Substituting the above value in Sine function we get
Thus, y = 5 sin ([tex]16\pi x[/tex]) + 3
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A vending machine i deigned to dipene a mean of 7. 5 oz of coffee into an 8-oz cup. If the tandard deviation of the amount of coffee dipened i 0. 5 oz and the amount i normally ditributed, find the percent of time the machine will dipene le than 7. 75 oz
The percent of times the machine will dispense less than 7.75 oz. is 69.15%.
In the given question we have to find the percent of time the machine will dispene less than 7.75 oz.
A vending machine we deigned to dipene a mean of 7.5 oz of coffee into an 8-oz cup.
If the standard deviation of the amount of coffee dipened is 0.5 oz and the amount is normally ditributed.
Mean = 7.5 ,
Standard Deviation = 0.5
P(z< 7.5) = P(z<(X-Mean)/Standard Deviation)
P(z< 7.5) = P(z<(7.75-7.5)/0.5)
P(z< 7.5) = P(z<0.25/0.5)
P(z< 7.5) = P(z< 0.5)
P(z< 7.5) = 0.6915
P(z< 7.5) = 69.15%
Hence, the percent of times the machine will dispense less than 7.75 oz. is 69.15%.
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What is the formula for Circumcentre?
There is no definite formula for calculation of circumcenter of a triangle but a process for calculation of circumcenter has been described here.
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)
We need to find the length of AB, BC and AC
The length will be obtained in terms of x and y
On solving the equations, we will obtain the value of x and y
The value of x and y is the required coordinate of the circumcenter.
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Determine the equation of the line that is parallel to the given line, through the given point
y = -5x + 1 ; (-2,3)
The equation of the line that is parallel to the given line, through the given point is y = -5x - 7
Given equation,
y = -5x + 1
Slope = m
= -5
For two lines to be parallel, slope is equal.
Therefore, m = -5 for another line.
Let the equation of the line be y = mx + c
This line passes through A(-2,3)
Therefore, 3 = -5(-2) + c
3 = 10 + c
c = 3 - 10
= -7
Hence, equation of line is y = -5x - 7.
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What statement about the graph is true?
The true statement about the graph is
It is a function with the domain {-6 < x < 0} and the range {0 ≤ y ≤ 5}.
What is range?The range refers to all possible value in the out put of a graph.
The out put is the y coordinate and the possible values here is within the interval
0 ≤ y ≤ 5
What is domain?The domain refers to all possible value in the input of a graph.
The input is the x coordinate and the possible values here is within the interval
-6 ≤ x ≤ 0
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a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 400 gram setting. based on a 25 bag sample where the mean is 399 grams and the variance is 400, is there sufficient evidence at the 0.025 level that the bags are underfilled? assume the population distribution is approximately normal. find the value of the test statistic. round your answer to three decimal places.
Using the t test statistic, the value of the test statistic is 1.25.
In the given question we have to find the value of the test statistic.
A manufacturer of chocolate potato chips would like to know whether its bag filling machine works correctly at the 400 gram setting.
= 400
A 25 bag sample had a mean of 399 grams and the variance is 400.
There is sufficient evidence at the 0.025 level that the bags are underfilled.
Sample size(n) = 25
sample Mean = 399
Sample Variance = 400
Standard Deviation = √Sample Variance
Standard Deviation = √400
Standard Deviation = 20
Population Mean = 400
So , the null and alternative hypothesis are
H0 : μ = 400
Ha : μ < 400
Using the sample t test statistic
t = (Population Mean - Sample Mean)/(Standard Deviation/Sample size)
t = (400 - 399)/(20/25)
t = 1*25/20
t = 1.25
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then m = -3,
(2m + 3)² =?
Answer:
9
Step-by-step explanation:
(2(-3)+3)^2
(-6+3)^2
(-3)^2
since the power of 2 is even it will be a positive result (if its a odd number like 3 it will be a negative result)
3^2
=9
Find the length x.
HELPPP PLSSSS
Answer: My answer is 4. You may want another answer.
Step-by-step explanation:
visual studying
Solve for y:
-3 + 18iy = x + 9i
A) -3
B) 0.5
C) 2
D) 4
Answer:
Step-by-step explanation:
someone please help me.
72/6 = 12
Write a situation for this equation and draw a picture that goes with it.
The picture for the condition is attached below.
What is factors of number?
A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.
Let, the factors of 72 are
72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24 36, 72.
When we divide 72 by 6 we get 12.
⇒ [tex]\frac{72}{6} = 12[/tex]
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Write the linear equation in standard form. Do not use any spaces in your answer.
2 + (1/2)x = y
By writing both variables in the same side of the linear equation, we will get the standard form:
2y + (-1)*x = 4
How to write the linear equation in standard form?A linear equation between two variables x and y written in standard form is:
a*x + b*y = c
Where the coefficients a, b, and c, are all real numbers.
In this case, we have the linear equation:
2 + (1/2)*x = y
If we multiply both sides by 2, we get:
2*(2 + (1/2)*x) = 2*y
4 + x = 2y
Now we subtract x in both sides to get:
4 + x - x = 2y - x
4 = 2y - x
This is the linear equation in standard form:
2y + (-1)*x = 4
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HEY 55 POINTS!!!!
Complete the sentence.
The greatest amount of sap collected from any one tree is ?
times as great as the least amount of sap collected from
any one tree.
The greatest amount of sap collected from any one tree is ?
times as great as the least amount of sap collected from
any one tree. = 2 times
a) Work out (5 × 10³) × (9 × 10')
Give your answer in standard form.
b) Work out (7 × 105) + (2 × 10²)
Give your answer in standard form.
Pls help due tomorrow!!!!!
Answer:
[tex]\left(m+2\right)\left(n^2+2n+m+1\right)[/tex]
Step-by-step explanation:
Hoooo boy.
This is a long one.
But let's do it!!!!
Apply exponent rule: [tex]\:a^{b+c}=a^ba^c[/tex]
Today, the mountain that contains Mount Rushmore is approximately 5,675 feet high. The height of the mountain is 622.5 feet less than 1.1 times its height before construction began.
The equation to find the height of the mountain prior to construction, represented by the variable h, is
1.1h – 622.5 = 5,675
Solve an equation to find the height of the mountain prior to construction, represented by the variable h.
h =
feet
5761.4 feet is the height of the mountain prior to construction
How to solve an equation to find the height of the mountain?
Given: 1.1h – 622.5 = 5,675
This is an algebraic equation, we need to solve for h
1.1h – 622.5 = 5675
collect like terms:
1.1h = 5675 + 622.5
Add like terms:
1.1h = 6337.5
Divide both sides by 1.1:
h = 6337.5/1.1
h = 5761.4 feet
Therefore, the height of the mountain prior to construction is 5761.4 feet
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100 points if you answer this correctly
Since triangle P'Q'R' is the result of a transformation of triangle PQR, an algebraic representation which best describes this transformation is: C. (x, y) → (5x/2, 5y/2).
What is a transformation?In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.
From the information provided above, we can logically deduce the following coordinates:
Point P = (-1, 1)Point Q = (2, 0)Point R = (-1, -2)Point P' = (-5/2, 5/2)Point Q' = (5, 0)Point R' = (--5/2, -5)Therefore, the transformation rule is given by:
P (x, y) → P' (x, y)
Point P = (-1, 1) → Point P' = ((5/2 × -1), (5/2 × 1)) = Point P' = (-5/2, 5/2).
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solve polynomial equations by factoring
2x³ + 12x² = 0
The value of x is -6 or 0 which is obtained by solving the giving equation using factoring.
What exactly is a polynomial equation? Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree.How can a polynomial equation be solved?Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. Factoring cannot always be used to solve polynomial problems.The original equations' answers are the solutions to the derived equations.Given equation: 2x³ + 12x² = 0
Solving this equation by factoring as follows:
2x³ + 12x² = 0
= 2x²(x+6) = 0
So, x + 6 = 0 or 2x² = 0
x = -6 or x = 0
Therefore, the value of x is -6 or 0 which is obtained by solving the giving equation using factoring.
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i need help pls
PLEASE GIVE ME THE CORRECT ANSWERS FOR ALL 3 PROBLEMS IM BEGGING
The values of the function when x = 3 are -10. -1 and -3, respectively
The values of the functionFunction 1
The equation of the function is given as
y = -4x + 2
We have the value of x to be 3
So, we have
y = -4 x 3 + 2
Evaluate
y = -10
Function 2
The graph represents the notation of the function
On the graph, we have the value of y to be -1, when x = 3
This means that
y = -1
Function 3
The table represents the notation of the function
On the table, we have the value of y to be -3, when x = 3
This means that
y = -3
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the pizza costs £6.40
this is 20% less than the original price.
what was the original price of the pizza?
Answer:
8
Step-by-step explanation:
Price : %
[tex]x[/tex] : 100
6.4 : 80 (Got 80 by 100 - 20)
Cross multiply
100*6.4 = 80[tex]x[/tex]
640 = 80[tex]x[/tex]
640/80 = [tex]x[/tex]
[tex]x[/tex] = 8
7. The basketball team is selling hats and gloves. They will earn $10 for every hat they sell and $8 for every pair of gloves. They want to sell a total of 40 items. Create two unique equations that model the number of hats, h, and the number of gloves, y, that the team is selling.
Answer:
5h+35y=390$
20h+20y=360$
Step-by-step explanation:
there are many answers possible.
The following are just examples:
5h+35y=390$
20h+20y=360$
It takes 5 minutes for your printer to print 40 papers
How long does it take for your printer to print 12 papers?
It will take 1.5 minutes for printer to print 12 papers.
Given,
Time taken to print 40 papers=5 minutes
then,
Time taken to print 1 paper =[tex]\frac{5}{40}=\frac{1}{8}[/tex] minutes
then to find time taken to print 12 papers, multiply 12
Time taken to print 12 paper,
[tex]Time=\frac{1}{8}*12\\\\Time=1.5\ minutes[/tex]
Thus, it will take 1.5 minutes for printer to print 12 papers.
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O is the center of the circle, if ∠OPQ = 25° & ∠ORQ = 20°, find ∠PQR and ∠POR
The values of ∠PQR = 45° and ∠POR = 90°.
The circumference of a circle is defined as its linear distance around it. In other words, if a circle is opened to form a straight line, the length of that line equals the circumference of the circle.
The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually denoted by the letters 'R' or 'r'.
Given that
O is the center of the circle, if ∠OPQ = 25° &∠ORQ = 20°
We have to determine the values of ∠PQR and ∠POR
Sol. OP = OQ
⇒∠OQP = ∠OPQ = 25° [Radii of the same circle]
Similarly, ∠OQR = 20°
∠PQR = 25° + 20°
∠PQR = 45°
Furthermore ∠POR = 2 ∠PQR [the angle at the centre is twice the angle at the circumference].
⇒∠POR = 2 × 45°
∠POR = 90°.
Therefore the values of ∠PQR = 45° and ∠POR = 90°.
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In a cookie recipe, 1 2/3 cups of milk makes 16 cookies. How many cups of milk are needed to make 24 cookies?
2 ft
2 ft
5 ft
4 ft
4 ft
2 ft
2 ft
Answer:
22ft
Step-by-step explanation:
2+2+5+4+4+2+2= 22
answer the problems shown
The 65 represents the speed.
97.5 miles covered in 1.5 hours.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given: d= 65t
We know the Formula of Speed- distance
speed= Distance / time
and, distance = speed x time
So, comparing it with given equation
distance =d , time= t and speed= 65
Now, t=1.5 hours
Distance = 1.5 x 65 = 97.5 miles
and, d= 26 miles
t= 26 / 65
t= 0.4
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how to solve and answer:1
1/3(9-6x)=-11
Answer:
x = 2.875
Step-by-step explanation:
1 1/3 (9 - 6x) = -11
12 - 8x = -11
- 8x = -23
x = 2.875