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A cone has a volume V, radius r, and a height of 12 cm. A cone has the same height and 1/3 of the radius of the original cone. Write an expression for its volume.
Answer:
[tex]\displaystyle \frac{4r^2\pi }{9} \text{ cm}^3[/tex]
Step-by-step explanation:
We will write an expression for the second cone's volume. Let r be equal to the radius of the first cone.
The volume of a cone can be found with the following formula. Here, h is the height, r is the radius, and V is the volume.
[tex]\displaystyle V=\frac{1}{3} \pi r^2h[/tex]
We will substitute our given values and simplify.
[tex]\displaystyle V=\frac{1}{3} \pi (\frac{1}{3}*r )^2(12)[/tex]
Square.
[tex]\displaystyle V=\frac{1}{3} \pi \frac{r^2}{9} (12)[/tex]
Divide 12 by 3.
[tex]\displaystyle V=\pi \frac{4r^2}{9}[/tex]
Move π to the numerator.
[tex]\displaystyle V=\frac{4r^2\pi }{9}[/tex]
The volume of the new cone, with the same height but one-third of the original radius, is represented by the expression (4 / 9)πr².
The volume of a cone is given by the formula V = (1/3)πr²h.
For a cone with a radius r and height 12 cm, its volume can be expressed as:
[tex]V = (\frac{1}{3})\pi r^2(12) = 4\pi r^2[/tex]
Now, consider a cone with the same height, but with 1/3 of the original radius. Let the new radius be (1/3)r. Using the volume formula again:
[tex]V = (\frac{1}{3})\pi (\frac{1}{3}r)^2(12) = (\frac{1}{3})\pi(\frac{1}{9}r^2)(12) = (\frac{12}{27})\pi r^2 = \frac{4}{9}\pi r^2.[/tex]
Thus, the expression for the volume of the new cone is (4 / 9) πr².
Antonio drove 26 miles north, and then drives west. At the end of his drive, it is determined that he is 50 miles from where he started. How far did he drive west
Answer:
42.7
Step-by-step explanation:
Final answer:
To find out how far Antonio drove west, we can use the Pythagorean theorem. The distance driven north (26 miles) and the distance west form the two legs of a right triangle, with the total displacement from starting point (50 miles) as the hypotenuse. Solving the equation, we find Antonio drove approximately 42.70 miles west.
Explanation:
The question asks to determine how far Antonio drove west given that he first drove 26 miles north and then drove west, ending up 50 miles from where he started. This can be solved using the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this scenario, the distance Antonio drove north and the distance he drove west form the two legs of a right triangle, with the overall displacement from his starting point being the hypotenuse.
To solve the problem, let x be the distance Antonio drove west. We already know the northward distance is 26 miles, and the hypotenuse is 50 miles. Setting up the equation based on the Pythagorean theorem gives us:
26² + x² = 50²
Solving for x:
x² = 50² - 26²
x² = 2500 - 676
x² = 1824
x = √(1824)
x = 42.70 miles
So, Antonio drove approximately 42.70 miles west.
what is the value of N? N+ 2 1/3=4 2/3
Answer:
N = 2 1/3
Step-by-step explanation:
N + 2 1/3 = 4 2/3 (Given)
N = 2 1/3 (Subtract 2 1/3 on both sides.)
pls help I will mark brainlist if correct !! :)
Answer:
a and b
Step-by-step explanation:
Write the equation that represents the data in the table shown. Explain your answer.
The equation that represents the data in the table is y = 4x – 2.
Solution:
Take any two point from the table.
Let the points taken are (0, –2) and (3, 10).
[tex]x_1=0, y_1=-2, x_2=3, y_2=10[/tex]
Slope of the line:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$m=\frac{10-(-2)}{3-0}[/tex]
[tex]$m=\frac{12}{3}[/tex]
m = 4
Using point-slope formula,
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-2)=4(x-0)[/tex]
[tex]y+2=4x[/tex]
Subtract 2 from both sides, we get
y = 4x – 2
The equation that represents the data in the table is y = 4x – 2.
How many meters are equivalent to 247 centimeters?
Answer:
2.47 m
Step-by-step explanation:
247 cm /100 = 2.47 m
1 m = 100 cm
247 centimeters is equivalent to 2.47 meters
To convert centimeters to meters, we use the conversion factor that 100 centimeters equal 1 meter. This is because the prefix 'centi' in centimeter means 'one hundredth', so 100 centimeters make up 1 meter.
To find the number of meters in 247 centimeters, we divide 247 by 100, because there are 100 centimeters in a meter. This gives us:
247 cm ÷ 100 = 2.47 meters
Therefore, 247 centimeters is equivalent to 2.47 meters.
Please help ASAP! Will give brainlyest to best answer!
Option B:
m∠C = 35°
Solution:
Given data:
m(ar BD) = 30° and m(ar AE) = 100°
To find the measure of angle C:
We know that,
Angle formed by two intersecting secants outside the circle is equal to half of the difference between the intercepted arcs.
[tex]$m \angle C=\frac{1}{2}({arc} \ AE-{arc} \ BD)[/tex]
[tex]$=\frac{1}{2}{( 100^\circ-30^\circ )[/tex]
[tex]$=\frac{1}{2}\times {70^\circ[/tex]
= 35°
m∠C = 35°
Option B is the correct answer.
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7 - 9 = 7+(-9)
Add.
The required sum of 7 and -9 is -2. Adding a negative number to a positive number results in a negative sum.
When adding the numbers 7 and -9, we follow the rules of addition with positive and negative numbers. To add a positive number and a negative number, we can think of it as subtraction. In this case, we have 7 + (-9), which is the same as 7 - 9.
To perform the addition, we subtract 9 from 7:
7 - 9 = -2
Therefore, the sum of 7 and -9 is -2. Adding a negative number to a positive number results in a negative sum. In this case, subtracting 9 from 7 gives us -2.
Learn more about sum here;
https://brainly.com/question/17684163
#SPJ6
Evaluate 14 - 2xy when x=-6 and y= 2.
10
28
384
52
Answer:
I got 38
Step-by-step explanation:
14 - 2 (-6) (2) = 38
Answer:
thats a great answer i got the same
Step-by-step explanation:
Darlene has eaten three eights of the pizza what fraction of the pizza remains?
Answer:
5/8
Step-by-step explanation:
1-3/8=5/8
Determine whether the given length can be side lengths of a right triangle. 12m, 60m, 61m
Answer:
No
Step-by-step explanation:
Using the converse of Pythagoras' identity.
If the longest side squared is equal to the sum of the squares of the other 2 sides then the triangle is right.
The longest side = 61, thus
61² = 3721
12² + 60² = 144 + 3600 = 3744 ≠ 3721
Thus these sides do not form a right triangle.
Planes Q and R are parallel. Lines a and b are shown on planes Q and R, respectively.
Planes Q and R are parallel. Plane Q contains line a and plane R contains line b. Both lines are going in different directions.
Which statement is true about lines a and b?
They are parallel lines.
They are perpendicular lines.
They are skew lines.
They will intersect.
Answer: I have included an image of the correct answer.
They are skew lines
Answer:
C: They are skew
if you cant read upside down.
Step-by-step explanation:
Edge 2021
Consider the equation, -5x+10x+3 = 5x+6
Answer: No value for x
Step-by-step explanation:
-5x+10x+3 = 5x+6
5x + 3= 5x +6
Step 1: Combine like terms
5x - 5x = 6-3
0=3
A souvenir of the Eiffel Tower is scaled at 1/80 inch to 1 foot. If the first-story platform of the tower is 189 ft high, find the height of the first-story platform of the souvenir of the Eiffel Tower. 0.42 in 2.36 in 15,120 in 0.2 in
Answer:
2.36 in.
Step-by-step explanation:
1 foot is equivalent to 1/80 in.
So 189 feet is equivalent to 189/80 in = 2.36 in.
What is the GCF of 5 , 6 , and 8
Answer:
The GCF of 5, 6, and 8 would be 1.
Step-by-step explanation:
To find the GCF (Greatest Common Factor) of any amount on numbers, you would find the factors of the numbers and find which is the greatest one that they have in common.
To find the GCF of 5, 6, and 8, we must first find the factors of 5, 6, and 8.
Factors of 5: 1, 5
Factors of 6: 1, 2, 3, 6
Factors of 8: 1, 2, 4, 8
Now we found the factors of 5, 6, and 8. to find the GCF, we must now find which factors they have in common.
The factors 5, 6, and 8 have in common is 1. Since they have no other factors in common, 1 would be the GCF.
The GCF of 5, 6, and 8 would be 1.
I hope this helps. :)
Final answer:
The Greatest Common Factor (GCF) of the numbers 5, 6, and 8 is 1, as it is the only common factor among all the numbers.
Explanation:
The Greatest Common Factor (GCF) of the numbers 5, 6, and 8 is found by determining the largest number that divides each of the given numbers without leaving a remainder. To find the GCF, we can list the factors of each number:
Factors of 5: 1, 5Factors of 6: 1, 2, 3, 6Factors of 8: 1, 2, 4, 8Looking at the factors, 1 is the only number that is common to all three, making it the GCF.
Hence, the GCF of 5, 6, and 8 is 1. This methodically derived GCF encapsulates the common factor that unifies the numerical trio.
the half-life of isotope X is 2.0 years. How many years would it take for a 4.0mg sample of X to decay and have only 0.50 mg of it remain
After 2.0 years, the 4.0 mg sample decays to 2.0 mg.
After another 2.0 years (total 4.0 years), the 2.0 mg sample decays to 1.0 mg.
And after another 2.0 years (total 6.0 years), the 1.0 mg sample decays to 0.50 mg.
So it takes 6.0 years for 4.0 mg to decay to 0.50 mg.
It takes for a 4.0 mg sample of X to decay and have only 0.50 mg of it remain is 6 years.
What is half-life?It is the continuous disintegration of the matter by the emission of highly penetrating radiation associated with the nucleus.
Given
The half-life of isotope X is 2.0 years.
How to find the years would it take for a 4.0 mg sample of X to decay and have only 0.50 mg?The half-life of isotope X is 2.0 years.
Mass Time period
4.0 mg 0
2.0 mg 2
1.0 mg 4
0.5 mg 6
Thus, 6 years would it take for a 4.0 mg sample of X to decay and have only 0.50 mg of it remain.
More about the half-life link is given below.
https://brainly.com/question/24710827
9. The height of a plane is a function of the time since take off. Identify the dependent variable? *
A Height
B Speed
C Time
D Acceleration
answer please !!! i need help asap
Answer:
A. Undefined will be your answer
Step-by-step explanation:
approximate √29 as a decimal to the tenths place.
Answer:
the correct answer is 5.4
There are 250 cells in Petri dish.the cells are increasing at a rate of 4% per hour.Model this situation with an equation .
Answer:
250÷4%= x per hour
Step-by-step explanation:
Final answer:
The situation where 250 cells in a Petri dish are increasing at a rate of 4% per hour can be modeled using the equation is 260 cells.
Explanation:
To model the situation where 250 cells in a Petri dish are increasing at a rate of 4% per hour, we use the formula for exponential growth:
N = N0ert
Where N is the future population size after time t, N0 is the initial population size, e is the base of the natural logarithm (approximately equal to 2.71828), r is the growth rate per unit of time, and t is the number of time units.
Here, N0=250 cells, r=0.04 (4% growth per hour, converted to decimal), and t will be the number of hours passed. Let's make t equal to 1 to see the number of cells after one hour:
N = 250e0.04(1)
After one hour, the Petri dish would have:
N = 250e0.04 ≈ 250(1.04081) ≈ 260 cells
Thus, this equation models the exponential growth of the cell population in the Petri dish over time.
you have to loan Rs 75000 for 2 years for a purpose. if a finance company A lends money at 10% per annum compounded annually and Finance Company B lends money at 8% per annum compounded semi annually for which Finance Company will you take the loan and why give your reason with calculation
He will take the loan from Company B.
Step-by-step explanation:
Given,
For Company A
Principal (P) = Rs 75000
Time (T) = 2 years
Rate of interest (R) = 10%
For Company B
Principal (P) = Rs 75000
Time (T) = 2 years
Rate of interest (R) = 8%
To find the amount of the loan he has to pay for both the companies.
Formula
Amount =P [tex](1+\frac{R}{100} )^{T}[/tex]
Amount= P[tex](1+\frac{R}{100Xn} )^{nT}[/tex]
For Company A
Amount = 75000[tex](1+\frac{10}{100}) ^{2}[/tex] [ Here, P= 75000, T=2 and R = 10%]
= 194530 (approx)
For Company B
Amount = 75000([tex](1+\frac{8}{200} )^{4}[/tex] [ Here, P= 75000, T=2, n = 2 and R = 8%]
= 87739 (approx)
Hence,
He will take the loan from Company B, because he has to pay less money for this company.
what is -4.5= a - 8
Answer:
Step-by-step explanation: -4.5=a-8
1. add 8 to both sides -4.5+8= 3.5
2. since you added 8 to negative 8 you get zero so it just goes away
3. ANSWER= 3.5=a
Find the length of the third side of the right triangle.
To calculate the length of the hypotenuse in a right triangle, apply the Pythagorean theorem: c = √(a² + b²). In an example with sides of 9 and 5 blocks, the hypotenuse would be approximately 10.3 blocks, accurate to three significant figures.
Explanation:To find the length of the third side of a right triangle, known as the hypotenuse, we can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Therefore, the formula to calculate the length of the hypotenuse is c = √(a² + b²).
For example, if the lengths of the two sides are 9 blocks and 5 blocks, we can use this formula to find the length of the hypotenuse:
c = √(9 blocks)² + (5 blocks)²c = √(81 + 25)c = √106c ≈ 10.3 blocksNote that the result is presented with three significant figures for precision. In real-world applications, such as finding the distance walked in city blocks, this provides a more accurate depiction of the distance.
A magazine contains thirteen pages. You
open to a random page. The page number
is two or ten.
If a magazine contains thirteen pages, it means that the pages are numbered from 1 to 13. When you open the magazine to a random page, there are two possibilities for the page number: it can either be two or ten.
Page number in a magazine
In the context of a magazine, the page number refers to the physical numbering of the pages within the publication.
The page number is typically printed near the top or bottom of each page, allowing readers to navigate through the content.
In this case, if you randomly open the magazine to page two, you will find the content printed on that page. Similarly, if you randomly open the magazine to page ten, you will find different content printed on that page.
Is x greater than less than or equal to 110
Based on the image you sent, the correct answer is: C. x = 110°
Here's why:
The image shows a diagram with two angles marked. One angle is labeled 110°, and the question asks about the measure of angle x.
Since there are no markings or indications otherwise, we can assume that angle x is congruent to the labeled angle.
Therefore, the measure of angle x is also 110°.
The other answer choices are not supported by the information in the image:
A. x > 110°: There's no evidence to suggest that angle x is greater than 110°.
B. x < 110°: There's no evidence to suggest that angle x is less than 110°.
So, angle z will be equal to 110° by vertically opposite angles.
Hence, the correct option will be C. z = 110°.
ANSWER IN ONE MINUTE AND YOU WILL BE THE BRAINLIEST!
Sabrina and four friends share 3 1/4 pizzas. If they all ate the same amount, which expression could be one of the steps in determining how much pizza each person ate?
A. 5/1 X 13/4
B. 13/4 X 1/5
C. 13/4 X 5/1
D. 5/1 X 4/13
Answer:
B
Step-by-step explanation:
Kevin is twice as old as Sean. Together their ages add up to 75.
Answer:
Kevin would be 50 and Sean would be 25
Step-by-step explanation:
Assuming that there is no other information given,
and Kevin is twice as old as sean, and they gotta add up to 75 total
50 + 25 = 75
25x2 = 50
Hope this helped!
Answer:
Kevin is 50 and Sean is 25.
Step-by-step explanation:
Add 25 + 50 = 75
Multiply 25 x 2 = 50
Hope this helps
-Amelia The Unknown
h(x)=x+5/8
find the inverse
Answer:
X=8y-5
Step-by-step explanation:
Let y be the inverse of x+5/8
Y=x+5/8
Cross multiply
8y=x+5
Substrate 5 from both sides
8y-5=x
Therefore x=8y-5
PLEASE ANSWERRRRRRRRR
A student is making a model of the electromagnetic spectrum.
Which text should the student use for label 1 to describe other properties of waves shown?
A. HIGH FREQUENCY, LOW ENERGY
B. LOW FREQUENCY, LOW ENERGY
C. LOW FREQUENCY, HIGH ENERGY
D. HIGH FREQUENCY, HIGH ENERGY
Yo sup??
the correct answer to this question is option B ie
low frequency and low energy because
it's wavelenght is high so it's frequency will be low and
E=hv
where v is frequency
Hope this helps
When Madiha was born, her aunt opened a certificate of deposit in her honor to help send her to college someday. now at the age of 18, there is $31,066 in Madiha's account. how much did her aunt originally invest if the interest rate was 6.5%? (round to the nearest dollar)
A.$375
B.$12,500
C.$10,000
D.$8,000
Answer:
C.$10,000
Step-by-step explanation:
Let X be the amount of initial investment, 6.5% be the compound interest, n=18years and $31,066 as the final amount:
#Using compound interest:
[tex]A=P(1+i)^n\\\\\Where \ A=31066,i=6.5\%, n=18,P=X\\\\31066=P(1+6.5\%)^{18}\\\\31066=P(1.065)^{18}\\\\P=\frac{31066}{3.106654}\\\\P\approx10000[/tex]
Hence, the amount initially ionvested is $10,000