Answer:
The equation for the radius of cone R in terms of the radius of cylinder (r) is,
R = r√3
Step-by-step explanation:
Volume of the cone = πR²H/3 (where Height is H and Radius is R)
Volume of the Cylinder = πr²h (where Height is h and Radius is r)
Now, both are same in height, so H = h and Their volume are same. So,
πR²H/3=πr²h
or, R²/3=r²
or, R²=r²×3
or, R = √(r²×3)
or, R = r√3
Answered by GAUTHMATH
Final answer:
The relationship between the volume of a cylinder and a cone with the same radius and height leads to the equation for the radius of the cone in terms of the cylinder's radius. By equating the volumes and simplifying, we find that the cone's radius R is equal to the square root of 3 times the cylinder's radius r, or R = √3 * r.
Explanation:
We start with the formula for the volume of a cylinder V = πr²h and the volume for a cone, which is a third of the cylinder's volume, V = ⅓πr²h. Since we are given that the volume of a cone equals the volume of a cylinder with the same radius and height, we can set up an equation to find the radius of the cone R in terms of the cylinder's radius r.
We know that the volume of the cone is one third the volume of the cylinder, so when they are equal, the cone must be larger to compensate for this ratio. Therefore, the volume equation becomes V = πR²h, where R is the radius of the cone and h is the height. To find R in terms of r, we equate the two volume formulas: πR²h = 3πr²h. Simplifying, we get R² = 3r² and hence, R = √3 * r.
Solve for x using cross multiplication
Answer:
x = 4
Step-by-step explanation:
cross- multiplying gives
5 × 3x = 4(2x + 7) ← distribute
15x = 8x + 28 ( subtract 8x from both sides )
7x = 28 ( divide both sides by 7 )
x = 4
Cross multiplication is used to solve equations with fractions or ratios. Multiply across the equals sign ('cross multiply'), and then isolate 'x' by adjusting the equation. Replace variable with actual figures to get the exact value.
Explanation:Cross multiplication is a mathematical technique used to solve problems involving fractions or ratios. Let's do an example. Suppose we have a ratio equation like this: a/b = c/ x (x is the variable we need to find).
The first step is to cross multiply. So, you multiply 'a' and 'x', and 'b' and 'c'. This gives us: ax = bc.
Next, we isolate 'x' by dividing both sides of the equation by 'a'. This gives us: x = bc/a.
Now, put the actual numbers into the equation to get the value of 'x'.
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What is the solution of the following system?
{5x + 5y = 15
{6x - 4y = -12
Can someone show me an example of long division?
Answer:
When you have large numbers to divide,
draw a tableau for long division on the side.
Write the steps that will be your guide,
D, M, S, B and R – Abide by to long divide!
Step-by-step explanation:
Answer:
Step-by-step explanation:
HELP ME PLSSS!!!!! I'LL GIVE BRAINLIEST!!!
What is the best approximation of the solution to the system? (Round to the nearest whole number).
Explain what is similar or different about the two lines. Use the key vocabulary words: Slope and Y-Intercept.
For the first question you best estimate would be : (1, 7) because these points are the closest co-ordinates to the real answer
Second question answer will be: The 2 lines have different slope, one is negative and another is positive. The y-intercepts for both equation are different but the x co-ordinate in both intercepts is 0
Answer: fvkglf
Step-by-step explanation: wdkogtrjfigtrkfijpwoeeefkjdmsjlfmhuygbnm,kjliuhyjbnmbgtfrghjklhyughbjnkuyliuynijedju ypour welcomebhf
I WILL AWARD BRAINLIEST!
The Patronete Winery's tastiest wine must have a 12% alcohol content. How many gallons of wine with a 9% alcohol content must be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content?
Answer:
3000 gallons of 12 percent is required
Step-by-step explanation:
We can use the formula
percentage * amount + percentage * amount = percentage*total amount
We have 9 percent and 15 percent wine that we are mixing to get 12 percent wine.
We are adding g gallons and 3000 gallons to get a total of (g+3000) gallons
Substituting this information in
.09 *g + .15 * 3000 = .12 (g+3000)
Distribute
.09g +450 = .12g+360
Subtract .9g from each side
.09g-.09g +450 = .12g-0.09g+360
450 = .03g + 360
Subtract 360 from each side
450-360 = .03g
90 =.03g
Divide each side by .03
90/.03 = .03g/03
3000 = g
find the prime factorization of 3,240
Answer:
Answer: 3240 = 2^3×3^4×5
Factor the following integer:
3240
The last digit of 3240 is 0, which means it is even. Therefore 3240 is divisible by 2:
3240 = 2 1620:
3240 = 2×1620
The last digit of 1620 is 0, which means it is even. Therefore 1620 is divisible by 2:
1620 = 2 810:
3240 = 2×2×810
The last digit of 810 is 0, which means it is even. Therefore 810 is divisible by 2:
810 = 2 405:
3240 = 2×2×2×405
405 is not divisible by 2 since 405 is odd and 2 is even:
3240 = 2×2×2×405 (405 is not divisible by 2)
The sum of the digits of 405 is 4 + 0 + 5 = 9, which is divisible by 3. This means 405 is divisible by 3:
405 = 3 135:
3240 = 2×2×2×3×135 (135 is not divisible by 2 since 405 is not)
The sum of the digits of 135 is 1 + 3 + 5 = 9, which is divisible by 3. This means 135 is divisible by 3:
135 = 3 45:
3240 = 2×2×2×3×3×45 (45 is not divisible by 2 since 135 is not)
The sum of the digits of 45 is 4 + 5 = 9, which is divisible by 3. This means 45 is divisible by 3:
45 = 3 15:
3240 = 2×2×2×3×3×3×15 (15 is not divisible by 2 since 45 is not)
The sum of the digits of 15 is 1 + 5 = 6, which is divisible by 3. This means 15 is divisible by 3:
15 = 3 5:
3240 = 2×2×2×3×3×3×3×5 (5 is not divisible by 2 since 15 is not)
Divide 3 into 5:
| 1 | (quotient)
3 | 5 |
- | 3 |
| 2 | (remainder)
5 is not divisible by 3:
3240 = 2×2×2×3×3×3×3×5 (5 is not divisible by 2 or 3)
No primes less than 5 divide into it. Therefore 5 is prime:
3240 = 2×2×2×3×3×3×3×5
There are 3 copies of 2, 4 copies of 3 and 1 copy of 5 in the product:
Answer: 3240 = 2^3×3^4×5
3,240 =
= 324 × 10 =
= 4 × 81 × 10 =
= 2^2 × 3^4 × 2 × 5 =
= 2^3 × 3^4 × 5Dan's father is an orange farmer and he brought 32 orange it to class today if each child got four oranges and five children did not want oranges how many children are in the class?
Answer: There are 13 children.
Step-by-step explanation:
1. Let's call x the number of children in the classroom. We know that each child received 4 oranges, except 5 of them.
2. There were 32 oranges in total.
3. We can write this problem as an equation that represents the number of oranges distributed, as follows:
[tex]4(x-5)=32[/tex]
4. Now we solve the equation to find the value of x:
[tex]x-5=\frac{32}{4}[/tex]
[tex]x-5=8[/tex]
[tex]x=13[/tex]
5. There are 13 children in the classroom. 8 of them received oranges and the rest did not.
Identify the slope of the line shown in the graph below: slope = -1
Slope = 0
Slope = undefined
Slope = 1
Answer:
Vertical lines have an undefined slope. Horizontal lines have a 0 slope.
So, undefined.
Step-by-step explanation:
Answer:
undefined
Step-by-step explanation:
this slope is undefined because it goes straight down and is vertical. the x and y-coordinates never change and there is no run when doing rise over run.]
pls mark brainliest
1) 3 - 7 x 5 + 2 x 4=
2) 7 - 2 x 5 + 9 x 3=
3) 2 - 8x + 3x When x = 5
4) 4 - 2x + 5x when x= 4
5) z divided 2 - 4z + 3(z-3) when z =8
GEMDAS!
1:
3 - 7 x 5 + 2 x 4
3 - 35 + 2 x 4
3 - 35 + 8
3 - 27
-24
2:
7 - 2 x 5 + 9 x 3
7 - 10 + 9 x 3
7 - 10 + 27
7 + 17
24
3:
2 - 8x + 3x When x = 5
2 - 8(5) + 3(5)
2 - 40 + 15
2 - 25
-23
4:
4 - 2x + 5x when x= 4
4 - 2(4) + 5(4)
4 - 8 + 20
4 + 12
16
5:
z ÷ 2 - 4z + 3(z - 3) when z = 8
8 ÷ 2 - 4(8) + 3(8 - 3)
8 ÷ 2 - 32 + 24 - 9
4 - 32 + 24 - 9
4 - 8 - 9
-13
I might've did #5 incorrect.... Really really sorry...
Find the solutions of the form x=a,y=0and x=0 ,y=b for the following equations: 2x+5y=10 and 2x+3y=6. is there any common solution?
Answer:
see explanation
Step-by-step explanation:
To find the intercepts, that is where the graph of the lines cross the x and y axes.
• let x = 0, in the equation for y-intercept
• let y = 0, in the equation for x-intercept
Consider each equation separately
2x + 5y = 10
x = 0 : 5y = 10 ⇒ y = 2 ⇒ (0, 2) ← y -intercept
y = 0 : 2x = 10 ⇒ x = 5 ⇒ (5, 0) ← x- intercept
2x + 3y = 6
x = 0 : 3y = 6 ⇒ y = 2 ⇒ (0, 2) ← y- intercept
y = 0 : 2x = 6 ⇒ x = 3 ⇒ (3, 0 ) ← x- intercept
The common solution is the y-intercept in both equations (0, 2 )
Write 209 is v divided by 255 as an equation
Answer:
209 = v / 255
Step-by-step explanation:
209 is v divided by 255
The word is means equals
209 = v / 255
Which property is demonstrated?
Answer:
associative property of multiplication
Step-by-step explanation:
edge 2021
I need help can someone please help me
Answer:
its 33 cm
Step-by-step explanation:
Martha states that -6 is a rational number.Wich is a correct explanation for this statement?
A)The number -6 is the opposite of 6
B) The number -6 is a negative integer
C) The number -6 can be written as -6/1
D)The number -6 is less than 0
Answer:
It would be C
Step-by-step explanation:
The number is between integers, so it can't be an integer or a whole number. It's written as a ratio of two integers, so it's a rational number and not irrational.
Answer:
C.
Step-by-step explanation:
because if -6 is a rotational number it should also be able to be translated into a fraction form
Tony went to the candy store and saw that his favorite candy was on sale. The original price is $1.49 per candy bar. Today, the store is selling it for $1.25 per candy bar. How much greater (in dollars) is the original price than the sale price?
Answer:
$0.24
Step-by-step explanation:
1.49 - 1.25 = 0.24
Answer:
$0.24
Step-by-step explanation:
I need help with a and b
if i clock out at 1:46 and i have 30 Minutes what time do i go in?
I will get in 2:16.
Now it is given that I clock out or I got out when the time was 1 hour 46 minutes.
And I have 30 minutes to go in.
So after 30 minutes, the time will be :
1 hour + 46 minutes
+ 30 minutes
1 hour + 76 minutes
Now we know that 60 minutes = 1 hour
So the time will be 2 hours and 16 minutes.
Therefore, the time at which I will get in after 30 minutes is 2:16
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how do you do these problems?? Help please!!!!
Answer:
290 ans 4/5 miles
Step-by-step explanation:
174/24=7.25
7.25X40=290
Next problem
10/2=5
4/5
work out 5/7 of 100
Give your answer correct to the nearest whole number
Answer:
71
Step-by-step explanation:
One way in which to work this out is to multiply 100 by 5, obtaining 500, and then dividing this result by 7. The nearest whole number is 497, or 71.
PLEASE HELP!! what is the units digit of 23^23
HURRY! PLEASE answer in 1 MINUTE!
Thanks!
The units digit of 23^23 is 7. This is found using the power cycle of 3 (the units digit of the base number), which is 3, 9, 7, 1 and the remainder when the exponent 23 is divided by the length of this power cycle (4).
Explanation:To find the units digit of 2323, one needs to understand a pattern in power cycles. For any number, the units digit will repeat in a certain cycle when the number is raised to higher powers. For number 3, every fourth power goes back to the value 1. Thus, the cycle for the number 3 is 3, 9, 7, 1.
Here’s how the calculation works:
For finding the pattern cycle we ignore any digits other than the units digit. This means we only need to look at the pattern in powers of 3 (not 23). Determine which number of the cycle to use. The exponent 23 divided by the length of the cycle (4) leaves a remainder of 3 (because 23/4= 5 remainder 3). So we use the third number in the cycle, which is 7. Hence, the units digit of 2323 is 7.Learn more about Units Digit here:https://brainly.com/question/17038912
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WILL MARK BRAINLIEST! Please help me. :(
Answer:
A
Step-by-step explanation:
Distribute the (-)
6x^3y^3+x^3y^3 + 5x^2y^2 - x^2y^2 - x^2y+x^2y +xy^2 +3x+3x +2-4
Cancel out bold and add:
7x^3y^3 + 4x^2y^2 +xy^2+6x-2
Berto invested in a precious mineral. The value of the mineral tend to increase by about 11% per year. He invest $40,000 in 2015 How much more will he invested be worth in 2020
the difference from 40000 to the future value in 2020, namely 5 years later is simply the yield or interest amount.
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$40000\\ r=rate\to 11\%\to \frac{11}{100}\dotfill &0.11\\ t=years\dotfill &5 \end{cases} \\\\\\ I=(40000)(0.11)(5)\implies I=22000[/tex]
a can of vegetable soup cost $2.88 for 12 oz a can of chicken soup cost $2.25 for 9 oz which kind of soup cost less
Answer:
Vegetable soup costs less because it's only $0.24/oz while chicken soup costs $0.25/oz.
Step-by-step explanation:
Vegetable = $2.88/12 = $0.24/per 1 oz
Chicken = $2.25/9 = $0.25/per 1 oz
3x+5=17 what's the answer
3x+14==11
3x + 5 = 17 subtract 5 from both sides
3x = 12 divide both sides by 3
x = 4
3x + 14 = 11 subtract 14 from both sides
3x = -3 divide both sides by 3
x = -1
Answer:
4 and -1
Step-by-step explanation:3x+5=17, x=4 because 17-5=12 and 12 divided by 3 is 4.
3x=14=11 we need to subtract 14 from both sides which will give us an end result of 3x=-3, so x =-1
help please than you
Does cell division always mean an organism is growing?
write the equation of the line in slope- intercept form:
9y-27x=18
The slope-intercept form:
[tex]y=mx+b[/tex]
[tex]9y-27x=18[/tex] add 27x to both sides
[tex]9y=27x+18[/tex] divide both sides by 9
[tex]\boxed{y=3x+2}[/tex]
alma is finding the measures of the angles in a triangle that have the ratio 1:3:5. circle her mistake and correct it
x + 3x +5x = 180
8x = 180
x = 22.5
Answer:
error in summing terms in x
Step-by-step explanation:
x + 3x + 5x = 180 ( collect like terms on left )
9x = 180 ← ( 9x not 8x )
divide both sides by 9
x = 20
Alma made a calculation error in solving for the angles with a ratio of 1:3:5. The correct values for x, which is the smallest angle, should be 20 degrees with the middle and largest angles being 60 degrees and 100 degrees respectively.
Alma is attempting to solve for the measures of angles in a triangle with a ratio of 1:3:5. However, there seems to be a mistake in her calculation. To correct it, we start with her equation x + 3x + 5x = 180, which represents the fact that the sum of the angles in a triangle is always 180 degrees (Theorem 20).
Combining like terms we do have 9x = 180. Solving for x gives us x = 20.
Therefore, the measure of the smallest angle is 20 degrees, the middle angle is 60 degrees, and the largest angle is 100 degrees.
HELP ASAP! WILL MARK AS BRAINLIEST (if you get answers correct)
1. (-6,-1), (-2,-3)
a. (-4,-2)
b. (2,-5)
c. (-2,1)
d. (-3.5,-2.5)
2. (-4,-5), (2,3)
a. (-4.5, 2.5)
b. (-3,-4)
c. (8,11)
d. (-1,-1)
3. (-3,-1), (3,5)
a. (-2,4)
b. (0,2)
c. (-3,-3)
d. (9,11)
4. What is the midpoint between (-3,-2) and (4,7)?
a. (2.5, 0.5)
b. (3.5, 4.5)
c. (-7, -9)
d. (0.5, 2.5)
Answer:
Step-by-step explanation:
If you want the mid point for these questions then for the 1st
1. add -6 and -2 which is -8 then divide by 2 which is -4, then add -1 and -3 which is -4 and then divide by 2 which is -2. so the mid point is (-4,-2)
2. its the same as above first add -4 and 2 which is -2 then divide by 2 which is -1, then add -5 and 3 which is -2 and divide by 2 which is -1. the point is (-1,-1)
3. -3+3=0 dived by 2 which is 0, -1+5=4 divide by 2 which is 2
point is (0,2)
4. -3+4=1 divide by 2 which is 1/2 =0.5, -2+7=5 then divide by 2 which is 5/2=2.5. point is (0.5,2.5)
What are the factors of x2 – 100?
(x – 50)(x + 50)
(x – 10)(x + 10)
(x – 25)(x + 4)
(x – 5)(x + 20)
Answer:
(x-10)(x+10)
Step-by-step explanation:
Here, the given expression,
[tex]x^2-100[/tex]
[tex]=(x)^2-(10)^2[/tex]
By using the identity [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]=(x+10)(x-10)[/tex]
[tex]=(x-10)(x+10)[/tex] ( By the commutative property )
Since, further factorization is not possible,
Hence, the factors of [tex]x^2-100[/tex] are,
[tex](x-10)(x+10)[/tex]
Second option is correct.