Answers
Answer:
[tex]\displaystyle r = 6 \ cm[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityGeometry
Volume of a Cone Formula: [tex]\displaystyle V = \frac{\pi}{3}r^2h[/tex]
r is radiush is heightStep-by-step explanation:
Step 1: Define
Identify variables
V = 120π cm³
h = 10 cm
Step 2: Solve for r
Substitute in variables [Volume of a Cone Formula]: [tex]\displaystyle 120\pi \ cm^3 = \frac{\pi}{3}r^2(10 \ cm)[/tex]Multiply: [tex]\displaystyle 120\pi \ cm^3 = \frac{10\pi}{3}r^2 \ cm[/tex][Division Property of Equality] Divide [tex]\displaystyle \frac{10\pi}{3} \ cm[/tex] on both sides: [tex]\displaystyle 36 \ cm^2 = r^2[/tex][Equality Property] Square root both sides: [tex]\displaystyle 6 \ cm = r[/tex]Rewrite: [tex]\displaystyle r = 6 \ cm[/tex]Answer:
Radius of cone is 6 cm
Step-by-step explanation:
[tex]\sf\small\underline\purple{Given:-}[/tex]
[tex]\sf{\leadsto Volume\:_{(cone)}=120π \:cm^3}[/tex]
[tex]\sf{\leadsto \: Height\:_{(cone)}=10 cm}[/tex]
[tex]\sf\small\underline\purple{To\: Find:-}[/tex]
[tex]\sf{\leadsto Radius\:_{(cone)}=?}[/tex]
[tex]\sf\small\underline\purple{Solution:-}[/tex]
To calculate the radius of cone . Simply by applying formula of volume of cone. As given in the question that height is 10 cm and it's volume is 120 π cm³.
[tex]\sf\small\underline\purple{Calculation\: begin:-}[/tex]
[tex]\sf{\leadsto Volume\:_{(cone)}=\dfrac{1}{3}\pi\:r^2\:h}[/tex]
[tex] \small \sf \leadsto volume \: of \: cone \: = \frac{1}{3} \pi \times r {}^{2} h \\ [/tex]
[tex] \small \sf \leadsto \: 120 π cm³ \: = \frac{1}{3} \times\pi r {}^{2} \times 10cm \\[/tex]
[tex] \small \sf \leadsto \: 120 π cm³ \: = \frac{10 \: \pi\: cm}{3} \: r {}^{2}[/tex]
[tex] \small \sf \leadsto \frac{ 120\pi \: cm {}^{3} \times 3}{10\pi \: cm} \: = r {}^{2} \\ \\ [/tex]
[tex] \small \sf \leadsto \frac{360\pi cm {}^{3} }{10\pi \: cm} = \: r {}^{2} \\ [/tex]
[tex]\small \sf \leadsto 36 \:cm {}^{2} = r {}^{2} [/tex]
[tex]\small \sf \leadsto \sqrt{36 \: cm {}^{2} } = \sqrt{r {}^{2} } [/tex]
[tex]\small \sf \leadsto6cm = r[/tex]
Related Questions
Helpppp and explain :)
Answers
Answer:
Problem 1: 25
Problem 2: 693
Step-by-step explanation:
Problem 1:
f(x) = -5n + 1
g(x) = -6n + 2
(f + g)(-2) = f(-2) + g(-2)
f(-2) = -5(-2) + 1
f(-2) = 10 + 1
f(-2) = 11
g(-2) = -6(-2) + 2
g(-2) = 12 + 2
g(-2) = 14
(f + g)(-2) = 11 + 14
(f + g)(-2) = 25
Problem 2:
f(x) = 7 + 2x
g(x) = 5x - 2
fg(7) = f(7) × g(7)
f(7) = 7 + 2(7)
f(7) = 7 + 14
f(7) = 21
g(x) = 5(7) - 2
g(x) = 35 - 2
g(x) = 33
Therefore:
fg(7) = 21 × 33
fg(7) = 693
A company has the pay scales below , with the percent of employees receiving that pay listed. Find the best value to represent an average salary at this company. ( round to the nearest dollar ) Job Salary Percent of Employees Entry 23,264 60% 47,480 38% 117,027 2%
Answers
Answer:
$34,341
Step-by-step explanation:
Given :
Job Salary Percent of Employees Entry 23,264 60% 47,480 38% 117,027 2%
To obtain the best value for the mean salary ; we obtain the weighted average ;
Σ(salary * weight factor) / Σ weight
[(23264 * 0.60) + (47480 * 0.38) + (117027 * 0.02)] ÷ (0.60 + 0.38 + 0.02)
= 34341.34 / 1
Average salary = 34341.34
= $34,341 ( nearest dollar)
n is an integer
Write the values of n such that [tex]-8\leq 4n\ \textless \ 12[/tex]
Answers
Answer:
-2, -1, 0, 1, 2,
Step-by-step explanation
Divide the whole thing by 4.
You will have -2 [tex]\leq[/tex] n < 3
The only values that fit range from -2 to 2.
Consider the graph. Which inequality best represents the graph?
Answers
Answer:
y >= x/2 - 1
Step-by-step explanation:
the slope (rise/run) is 1/2 and the y-intercept is -1 so in point-slope form
y = x/2 - 1 but everything above the line (unshaded part) is valid so y is equal to or greater than.
list the integers satisfy the inequality -1 less than 2x - 5 less or equal to 5
Answers
Answer:
integers are { 3 , 4 , 5 }
Step-by-step explanation:
- 1 < 2x - 5 ≤ 5
- 1 + 5 < 2x - 5 + 5 ≤ 5 + 5 [ adding by 5 ]
4 < 2x + 0 ≤ 10
4 < 2x ≤ 10
2 < x ≤ 5 { divide by 2 ]
Therefore, integers are { 3 , 4 , 5 }
Can someone please solve this?
Answers
what is the product of 172837286 and 17368364????
Answers
Answer:
3.0019009e+15
Step-by-step explanation:
the word and is multiplication so multiply the two numbers
Answer:
3.001900896*10^15 is the answer
Pls help me no files just type it in thank you<333
Answers
Answer:
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
We're provided - Number of kids playing soccer = 8 , Number of kids playing basketball = 16. Total number of kids at the park = 8 + 16 = 24. Now , divide 24 by 2 , you'll get 12 and that's your final answer.[tex] \boxed{ \boxed{ \large{ \tt{۵ \: OUR \: FINAL \:ANSWER : \underline{ \tt{12}}}}}}[/tex]
-Yey! We're done ツ
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What is the answer to 12 radius circle
Answers
Answer:
The answer is 113.10 ft²
Step-by-step explanation:
The square feet which is the area of a 12 ft circle is 113.10. If there is a option for that
Answer:
113.04 ft^2
Step-by-step explanation:
use formule A = πr^2
Which expression is the radical form of x^4/5?
Answers
Answer:
The picture is the answer
Step-by-step explanation:
Can i get some help pls!
Answers
Answer:
Graph the system on linear equations.
Step-by-step explanation:
(-4, 4) & (-4, -6)
Find the missing side
Answers
Answer:
x=21
Step-by-step explanation:
they are corresponding to each other
Complete the angle addition postulate for the following angle
Answers
Answer:
measure of angle GEO.....
Simplify completely..........
Answers
Answer:
[tex]\frac{x}{x-1}[/tex]
Step-by-step explanation:
[tex]\frac{3x^2 - 1}{x^2 - 1} - \frac{2x + 1}{x + 1}[/tex] [tex][ \ x^ 2- 1 = (x-1)(x + 1) \ ][/tex]
[tex]= \frac{3x^2 - 1}{(x-1)(x + 1 )} - \frac{2x + 1}{x + 1}\\\\=\frac{(3x^2 - 1)-(2x + 1)(x-1)}{(x + 1)(x-1)}[/tex] [tex][\ Taking \ LCM \ ][/tex]
[tex]= \frac{(3x^2 - 1)- (2x^2 - 2x + x - 1)}{(x+1)(x-1)}\\\\=\frac{3x^2 - 1 - 2x^2 + x + 1 }{(x+1)(x-1)}\\\\=\frac{x^2 +x}{(x+1)(x-1)}\\\\=\frac{x(x+1)}{(x+1)(x-1)}\\\\=\frac{x}{x-1}[/tex]
Finding LCM :
Example :
[tex]\frac{1}{6} + \frac{1}{3}[/tex]
6 = 2 x 3
3 = 1 x 3
[tex]\frac{1}{2 \times 3} + \frac{1}{ 3}[/tex] [tex]= \frac{1}{2 \times 3} + \frac{1 \times 2}{ 3 \times 2}[/tex]
[ To make the denominators same : the second fraction is multiplied and divided by 2 ]
Similarly :
[tex](x^2 - 1 ) = (x -1)(x+1)\\\\(x + 1) = 1 \times (x + 1)[/tex]
Same rule we applied : multiplied the numerator and denominator of the second term with ( x - 1 )
Therefore the second term becomes ,
[tex]\frac{2x + 1}{x + 1} = \frac{(2x + 1)(x - 1)}{(x + 1)( x - 1)}[/tex]
verify that :- 5/8x(7/9-11/6)=(5/8x7/9)-(5/8x11/6)
please answer
Answers
In this example a = 5/8, b = 7/9 and c = 11/6
what is the answer to 11/5 divided by 2/5
Answers
Answer:
The Correct Answer is [tex]\frac{11}{2}[/tex] (11/2)
Decimals Form: 5.5
Answer:
5 1/2 or 5.5
Step-by-step explanation:
11/5 ÷ 2/5
11/5 × 5/2 = 11/2 = 5 1/2
а
The radius
of
a circle is 10cm and
the length of a chord is 12 cm.
Then , calculate the distance between
the chord and centre of
a circle
Answers
Step-by-step explanation:
by referring to the diagram,
a = 8
What are the values of x in the equation x2 - 6x + y =
A)x= -2 or x = 8
B)x= -1 or x = -11
C)x= 1 or x = 11
D)x = 2 or x = -8
Answers
a rule in quadratic equ states that
if summation of the roots should be -b/a of the equa
comparing the equ x² - 6x + y=0
with. ax² + bx +c =0
we see that in the equ, a= 1, b=-6
so the sum of the roots is -(-6)/1= +6
looking the the option the only one that agreed is option A
-2 + 8= 6
there fore the values of x are -2 or 8
will give branliest TO ANY ACTUAL ANSWERS
Which equation does the graph of the systems of equations solve?
two linear functions intersecting at 3, negative 2
Answers
find the value of x and y
Answers
58-14= 44
44+58= 102
180-102= 78
78/2=39
Y=39
Answer:
x = 58
y = 39
Step-by-step explanation:
x = 58 (Vertically opposite angles)
x + 2y + (x-14) = 180 (Angles in a straight line)
=> x + 2y + x - 14 = 180
=> 2x + 2y = 180 + 14
=> 2(58) + 2y = 194
=> 116 + 2y = 194
=> 2y = 194 - 116
=> 2y = 78
=> y = 78/2
=> y = 39
9. Here are two expressions with a missing number: Expression 1: • Expression 2: + 4 Choose the same number to put in both blanks, so that both expressions would result in an irrational answer. You can choose your number from the following list: 3.2, , , and 0.232323... Explain your reasoning. (4 points: 2 points for the answer and 2 points for the explanation)
Answers
All the other options are rational 32/10, 2/3, 23/99
If you multiply two fractions you always get a fraction.
If you add 4 to a fraction it is still rational.
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 4 cos 5θ
Answers
Answer:
y-acis
Step-by-step explanation:
the function graph is symmetric about
- y-axis when it is an even function
-the origin ehen it is an even function
A symmetrical graph about the x-axis is not a function graph
f(×) is a even if and only if f(×) =f(×)
f(×) is a odd if and only f(×)=f(×)
We have the function r(0) = 4cos (50)
(only symmetry about the y-acis or about the origin)
Check r(-0)
r(-0) = 4cos (5-0) = 4cos (-50 = 4 cos (50)
Used cos (-× = cos ×
We have r(0). Therefore the graph of r(0) is symmectric about the y-axis.
NEED HELP; What is the value of x?
X/8=6/12
A. 3
B. 5
C. 4.
D. 0.5
Answers
Answer:
the answer is 4
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the range of the following relation R {(3, -5), (1,2),(-1,-4),(-12)}
Answers
Answer:
The range of the following relation is(-5,2,-4)
Which property of exponents must be used first to solve this expression? (iy2)1/3
Answers
Step-by-step explanation:
"must be used first" is a very hard phrasing. multiplication is commutative.
and I am not sure that the problem is stated correctly.
I read here
(i×y²) to the power of 1/3.
i is the imaginary constant sqrt(-1) ?
exponents brought themselves to the power of something else multiply.
e.g.
[tex]({2}^{3})^{4} = {2}^{12} [/tex]
exponents in multimedia expressions of the same base simply add up.
e.g.
[tex] {2}^{3} \times {2}^{4} = {2}^{7} [/tex]
a negative exponent means that the expression with the same positive exponent is just at the bottom of a division.
e.g.
[tex] {2}^{ - 3} = 1 \div {2}^{3} [/tex]
and a fraction as exponent specifies a root to be taken.
e.g
[tex] {2}^{1 \div 3} = \sqrt[3]{2} [/tex]
so, I would do all the exponent multiplications to simplify the expression.
[tex] \sqrt[3]{i \times {y}^{2} } = ({i \times {y}^{2} })^{1 \div 3} = [/tex]
[tex] = ( { - 1}^{1 \div 2} \times {y}^{2} ) ^{1 \div 3} [/tex]
1/2 × 1/3 = 1/6
2 × 1/3 = 2/3
[tex] = { - 1}^{1 \div 6} \times {y}^{2 \div 3} = \sqrt[6]{ - 1} \times \sqrt[3]{ {y}^{2} } [/tex]
so, as we can see, we can move freely from multiplying the fraction exponents to converting them into root expressions and vice versa.
If you input 3 into the equation below, what is the resulting y-value?
y=9
Answers
Answer:
It will still be 9. y=9 is a horizontal line. No matter the x value, the answer will be the same.
Step-by-step explanation:
Eric was rock climbing. At one point, he stopped and climbed straight down 2\dfrac{1}{2}2 2 1 2, start fraction, 1, divided by, 2, end fraction meters. Then he climbed straight up 6\dfrac{3}{4}6 4 3 6, start fraction, 3, divided by, 4, end fraction meters. Eric was wondering what his change in elevation was after these two moves.
Answers
Answer:
Hence, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above. So after the 2 moves, he is up by [tex]4\frac{1}{4}[/tex] meters.
Step-by-step explanation:
Let us assume "negative" as climbing up and "positive" as climbing up. Here we need to find the change in elevation.
[tex]2\frac{1}{2}[/tex] meters down means [tex]-2\frac{1}{2}[/tex]. [tex]6\frac{3}{4}[/tex] meters up means [tex]+6\frac{3}{4}[/tex].Now we have:
[tex]=-2\frac{1}{2} + 6\frac{3}{4}\\\\=-\frac{5}{2} +\frac{27}{4} \\\\=\frac{-5(2)+27}{4} \\\\=\frac{-10+27}{4} \\\\=\frac{17}{4} = 4\frac{1}{4}[/tex]
Answer:
b
Step-by-step explanation:
convert 4 years to months
Answers
Answer:
48 months
Step-by-step explanation:
12 times 4 48
Answer:
48 months
There's 12 months in 1 year.
So we would multiply 12 months by 4 years to get 48 months
Can someone help me?It's urgent and thank you!
Answers
Answer:
y = square root x2 - 5
Step-by-step explanation:
y=[tex]\sqrt{x} -5[/tex]
(the top option)
Doughnuts are sold in bags and cartons
A bag holds four doughnuts and a carton holds ten doughnuts
Tom buys B bags of doughnuts and C cartons of doughnuts
He buys a total T doughnuts
Writs down a formula for T in terms of B and C
Answers
Answer:
Doughnuts are sold in bags and cartons
A bag holds four doughnuts and a carton holds ten doughnuts
Tom buys B bags of doughnuts and C cartons of doughnuts
He buys a total T doughnuts
Writs down a formula for T in terms of B and C
Step-by-step explanation:
Doughnuts are sold in bags and cartons
A bag holds four doughnuts and a carton holds ten doughnuts
Tom buys B bags of doughnuts and C cartons of doughnuts
He buys a total T doughnuts
Writs down a formula for T in terms of B and C
