The volume of the cone changes by a factor of 27
How does the volume of the cone change
From the question, we have the following parameters that can be used in our computation:
Volume of a cone
The volume of a cone is calculated using
[tex]V = \frac13\pi r^2h[/tex]
When the radius and height are both tripled, we have
R = 3r
H = 3h
So, the new volume is
[tex]V_2 = \frac13\pi R^2H[/tex]
Substitute the known values into the equation
[tex]V_2 = \frac13\pi (3r)^2 * 3h[/tex]
Evaluate
[tex]V_2 = \frac13\pi 9r^2 * 3h[/tex]
So, we have
[tex]V_2 = \frac13\pi r^2h * 27[/tex]
Recall that
[tex]V = \frac13\pi r^2h[/tex]
So, we have
[tex]V_2 = 27V[/tex]
This means that the volume of the cone changes by a factor of 27
Question
How does the volume of a cone change if its radius and height are both tripled? A. 3 B. 9 C. 27 D. 81
What is the slope of the function?
how too solve for x 5x+8
What is the area of the trapezoid?
Enter your answer in the box.
[ in] and two at the top
Each of these circles represents a pizza cut into 10 equal slices, and the yellow slices are the ones eaten by Larry.
If Larry ate L% of the total amount of pizzas, what is the value of L?
Answer:
Where is the pic?
y=x^2-16x+63
[tex]y = x { }^{2} - 16x + 63 \\ [/tex]
The equation provided is a quadratic equation in standard form, which can be solved using methods such as factoring, completing the square, or the quadratic formula to find its roots.
Explanation:The equation y=x^2-16x+63 is a quadratic equation, which is a polynomial equation of the second degree. The standard form of a quadratic equation is ax^2 + bx + c = 0. To solve this equation for x, you can either factor it, complete the square, or use the quadratic formula. If this specific equation was meant to be solved, we would look for values of x that make the equation true. This involves finding the roots of the equation, which are the x-intercepts of the parabola represented by the equation on a graph.
Jorge bought a crate of floor tiles for 95.94. The crate had 6 boxes of floor tiles. Each box contained 20 floor tiles
Write and solve an equation to determine the cost per box, b. Then write and solve a second equation to determine the cost per tile, t, the nearest cent
Answer:
Step-by-step explanation:
6b= 95.94 divide will give you $15.99 then divide 20 into 15.99 will give you .7995 they said nearest cent.
Lee and Lyn both invested their birthday money. Lee put his money in a savings account that earned 8% simple interest annually. Lyn put her money in an account that earned 8% interest compounded annually. Who made the better investment and why?
Use what you learned in the lesson and the online content to answer the following question: Which renewable source of energy should the United States focus its research and development efforts to make this source of energy our country’s main energy source by the year 2050? Why?
Answer:
Renewable electricity
Step-by-step explanation:
Renewable electricity is an option for everybody. Using a small solar panel device can create renewable electricity for your home. Renewable electricity is safer and cleaner.
The renewable source of energy is the generation of energy from naturally extracted resources. These sources are naturally replenishing due to excess consumption and overpopulation.
These renewable sources are virtually inexhaustible. The types of renewable energy sources are: biodiesel, wind, solar, hydropower, and many more.
Renewable electricity is the source of energy upon which the United States must focus its research and development efforts.
Renewable electricity is the most suitable option over which the research and development must focus for making it one of the main sources of energy for the country by the yer 2050.
This can be done by using solar panel devices at homes and factories so that they can generate their own electricity. This will help in saving the electricity supply from the poles.
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Bill was able to walk 2 more than twice as many dogs as his friend Steve. Write an algebraic expression to represent the number of dogs Bill walked compared with Steve.
Hallie hikes 5 miles in 90 minutes. At this pace, how long will it take her to hike the next 2 miles? Enter your answer in the box.
Find two consecutive whole numbers that square root 62 lies between
The square root of 62 lies between the consecutive whole numbers 7 and 8, because 7² is 49 and 8² is 64, and 62 is between these two square numbers.
Explanation:The student is asking for two consecutive whole numbers between which the square root of 62 lies. First, identify the whole numbers whose square roots are immediately less than and greater than √62. Considering square numbers we know, 7² = 49 and 8² = 64. Since 49 < 62 < 64, the square root of 62 must be between 7 and 8. Therefore, the two consecutive whole numbers are 7 and 8, as √62 is greater than 7 but less than 8.
The formula that relates the length of a ladder, L, that leans against a wall with distance d from the base of the wall and the height h that the ladder reaches up the wall is mc024-1.jpg. What height on the wall will a 15-foot ladder reach if it is placed 3.5 feet from the base of a wall? 11.5 feet 13.1 feet 14.6 feet 15.4 feet
Answer: 14.6 feet
Step-by-step explanation:
Since, here a ladder which has the length 15 foot and it is far from the base of the wall by 3.5 feet.
Here L represents the length of the ladder while d represents the distance of the ladder from the base of the wall. ( shown in figure)
While h represents height that the ladder reaches up the wall.
Thus, L= 15 foot, d= 3.5 foot
Then on applying Pythagoras theorem,
[tex]L^2=d^2+h^2[/tex]
⇒[tex]15^2=3.5^2+h^2[/tex]
⇒[tex]225=12.25+h^2[/tex]
⇒[tex]h^2=21.75[/tex]
⇒[tex]h=14.5859521458[/tex]≈ 14.6 foot
Thus,height that the ladder reaches up the wall= 14.6 foot ( approx)
Simplify fully the square root of 1/169
The fully simplified form of √(1/169) is 1/13.
Given that an expression √(1/169), we need to simplify it,
To simplify the square root of 1/169, we can break it down as follows:
√(1/169)
Since 1 is the square of itself (1² = 1), we can rewrite the expression as:
√(1/169) = √(1)/√(169)
The square root of 1 is simply 1:
√(1/169) = 1/√(169)
Now, the square root of 169 is 13:
√(1/169) = 1/13
Therefore, the fully simplified form of √(1/169) is 1/13.
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Complete the compass rose below with the correct bearings, please help ASAP
The front of an a-frame house is in the shape of a triangle.The height of the house is 20 feet.The area of the front of the a-frame is 600 square feet.Write and solve an equation to find the base of the A-frame house
Answer:
60 feet
Step-by-step explanation:
Multiply the area by 2 to get 1200 feet. then, divide by 20 to get 60. The base of the a-frame is 60 feet.
what is the surface area of this triangular prism
The quotient of m and 7
help me please I dont know the answer..
Use the steps to solve the Carbon Dating Problem.
1. Graph the function C(t) = 100•e^-0.000121t using points (t, C(t)).
Use elimination to solve the system of equations given by 3x + 4y = 5 and 21x + 28y = 35.
(0 = 0) is a true statement, it means that the system of equations has infinitely many solutions.
The correct option is (C).
To solve the system of equations using elimination, we'll manipulate one or both equations to eliminate one of the variables, either \(x\) or \(y\). Let's start by using elimination to eliminate \(x\).
Given the system of equations:
[tex]\[ \begin{cases} 3x + 4y = 5 \quad \quad \quad \quad \quad (1) \\21x + 28y = 35 \quad \quad \quad (2)\end{cases} \][/tex]
We can see that if we multiply equation (1) by 7, we can eliminate (x) when we add the equations together:
[tex]\[ 7(3x + 4y) = 7 \times 5 \][/tex]
[tex]\[ 21x + 28y = 35 \][/tex]
Now, we can rewrite equation (1) as:
[tex]\[ 21x + 28y = 35 \quad \quad \quad \quad \quad (3) \][/tex]
Now, we'll subtract equation (2) from equation (3):
[tex]\[ (21x + 28y) - (21x + 28y) = 35 - 35 \][/tex]
[ 0 = 0 ]
Since (0 = 0) is a true statement, it means that the system of equations has infinitely many solutions.
So, the correct answer is option C: Infinitely Many Solutions.
complete question given below:
Use elimination to solve the system of equations given by 3x + 4y = 5 and 21x + 28y = 35.
A. No Solution
B. (5/3, 0)
C. Infinitely Many Solutions
D. (0, 5/4)
the equation of a circle is (x-5)^2+(y+3)^2=25 what are the coordinates of the center of this circle
iT COST $9 TO GO TO PETE'S POTTERY PLACE TO MAKE YOUR OWN BOWLS $3 PER BOWL. NATALIE GOES TO PETE'S POTTERY PLACE AND MAKES B BOWLS. SHE DECIODES TO MAKE BOWLS 5 DAYS THIS MONTH SO SHE CAN SELL THEM AT A CRAFTS FAIR.
Part A:write an expression that will represent Natalite's total costy for this month.
What is the value represented by the letter A on the box plot of the data?
{10, 12, 15, 21, 24, 30}
Enter your answer in the box.
The value of letter A on the box plot is given by A = 10
What is box plot?A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.
here, we have,
we know that,
A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.
It is used when showing the distribution of data points across a selected measure and if the box in a box plot is stretched in one direction or the other, then the data is skewed in that direction.
Given data ,
Let the box plot be represented as Z
Now , the values of the data from the box plot is given by
Z = { 10 , 12 , 15 , 21 , 24 , 30 }
The value of the letter A from the box plot is the first value
where A = 10
Therefore , the value of A is 10
Hence , the box plot is solved
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ASAP
Anthony spent $11.23 on his lunch while Margo spent $8.96 on her lunch. Anthony paid with a twenty dollar bill and gave a $2.25 tip. How much did Anthony have left from his twenty dollar bill?
A. $13.48
B. $8.77
C. $6.52
D. $2.24
the answer is c
sorry if im wrong.
An isosceles trapezoid has a perimeter of 57 millimeters. Its shorter base measures 6 millimeters and its longer base measures 15 millimeters. The two remaining sides have the same length; what is that length?
Translate this sentence into an equality
the quotient of x and 7 is at most -24
which are the roots of the quadratic function f(q) = q^2 - 125? check all that apply.
I hope you can see the picture
BD is the perpendicular bisector of AC. What is the length of AC?
Answer:
AC = 12 units.
Step-by-step explanation:
Given : A triangle ABC with BD is the perpendicular bisector of AC.
To find : What is the length of AC.
Solution : We have given triangle ABC with BD is the perpendicular bisector of AC.
Bisector : Which cut the line equally in to two part.
So , BD cut AC in two equal part AD = DC.
We can write
AC = AD + DC.
Plug the values DC = 6 , AD =DC = 6.
AC = 6 + 6
AC = 12 units.
Therefore , AC = 12 units.
Felicia had made 1/4 gallon if punch and poured an equal amount into 8 glasses.would the amount i n each glass be more ot less than 1/16 gallon?