Answer:
r ≈ 7.963 cm
Step-by-step explanation:
Given the following dimensions of a cylinder:
Volume (V) = 3785 cm³
Height (h) = 19 cm
In order to find the value of the radius, it is necessary to determine the formula for finding the radius of a cylinder.
The formula for finding the volume of a cylinder is: V = πr ²h
To isolate the radius, start by dividing both sides by π × h :
[tex]\mathsf{\frac{V} {\pi\times\:h}\:=\:\frac{\pi\:r^{2}\:h} {\pi\times\:h}}[/tex]
[tex]\mathsf{\frac{V} {\pi\times\:h}\:=\:r^{2}}[/tex]
Next, take the square root of both sides to isolate r :
[tex]\mathsf{\sqrt{\frac{V}{\pi\times\:h}} = \sqrt{r^{2}}}[/tex]
[tex]\mathsf{\:r\:=\:\sqrt{\frac{V}{\pi\times\:h}}}[/tex]
Now, we can finally substitute the given values into the formula for radius, r:
[tex]\mathsf{\:r\:=\:\sqrt{\frac{3785}{\pi\times\:19}}}[/tex]
r ≈ 7.963 cm
Therefore, the radius of the cylinder is 7.963 cm.
Simplify. (−5)^5(−5)^−6
Answer:
Step-by-step explanation:
In exponents multiplication, if bases are same, add the powers
[tex]a^{m}*a^{n} =a^{m+n}\\\\\\(-5)^{5}*(-5)^{-6}=9-5)^{(-5) + (-6)} = (-5)^{-11}[/tex]
Answer:
Your answer would be:
-1/5 or -0.2
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Sue has 18 3/4 cups of sugar Each pie calls for 1 1/2 cup of sugar Sue wants to break 12 pies Does she have enough sugar How much will be left over or how much more does she need
Answer:
she will have 3/4 cups left over
Step-by-step explanation:
1 1/2 times 12 is 18
Which of the following triangles could lie on the graph with the same rise over run in Question # 3?
A. A triangle with a rise of 10 and a run of 30
B. A triangle with a rise of 30 and a run of 10
C. A triangle with a rise of 10 and a run of 40
D. A triangle with a rise of 2 and a run of 5
Answer:
B.
Step-by-step explanation:
2x+3y=5x-y solutions
[tex]2 \times + 3y = 5x - y[/tex]
Solution:[tex]2 \times + 3y = 5x - y
[/tex] Move the variables to the left
[tex]2 \times + 3y - 5 \times + y = 0[/tex]
Collect like terms
[tex] - 3 \times + 4y = 0[/tex]
Change the signs
Answer:[tex]3 \times - 4y = 0[/tex]
Simplify the following.
can someone pls help 25+ Points And BRAINLIEST.
I know the answer so give step by step explanation.
Answer:
(2f-17h)/24k
Step-by-step explanation:
We can make the common denominator for 3k and 8k in the form of 24k, so we get (multiply the first fraction by 8 and the second one by 3 to get 24k on each denominator) (8f-32h)/3k-(6f-15h)/24k. Now we can just subtract the numerators :
8f-32h-6f+15h (sign gets flipped on 6f and 15h), so we get
(2f-17h)/24k
One number is twice another number. The sum of their reciprocals is 6. What are the numbers?
Answer:
8 and 2
Step-by-step explanation:
Answer:
1/4 and 1/2
Step-by-step explanation:
One number is twice another number.
x and 2x
The sum of their reciprocals is 6
[tex]\frac{1}{x}[/tex] + [tex]\frac{1}{2x}[/tex] = 6
Use common denominator of 2x
[tex]\frac{2}{2x}[/tex] + [tex]\frac{1}{2x}[/tex] = 6
[tex]\frac{3}{2x}[/tex] = 6
multiply botn sides by 2x
3 = 12x
Divide both sides by 12
1/4 = x
x = 1/4
2x = 1/2
The numbers are
1/4 and 1/2
A group of 7 students went bowling. Each student rented bowling shoes for $x and spent $15 on snacks. A group of 6 adults also went bowling and paid twice as much to rent bowling shoes as each student. Each adult also spent $12.50 on snacks. If both groups spent the same total amount, what was the cost for each adult to rent bowling shoes?
Answer:
$3.52 (rounded to nearest penny)
Step-by-step explanation:
7x + 15(7) = 12(2x) + 12.5(6)
7x + 105 = 24x + 75
105 = 17x + 75
30 = 17x
1.76 = x
3.52 = 2x
The cost for each adult to rent bowling shoes is $12.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Group I:
Total students= 7
Rent of bowling= $x
Spent on snacks= $15
Then, total amount spent by 7 children = 7x+ 15(7)
Group II:
Total students= 6
Rent of bowling= $2x
Spent on snacks= $12.50
Then, total amount spent by 7 children = 6(2x)+ 6 (12.50)
So, If both groups spent the same total amount
7x+ 105= 12x + 75
12x- 7x = 105- 75
5x = 30
x= 6
Hence, the cost for each adult to rent bowling shoes is $12.
Learn more about equation here:
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The formula for the area of a triangle is A=1/2bh, where b is the base of the triangle and h is the height of the triangle. The area of the triangular sail of a sailboat is 126ft^2. The base is 12 ft. Find the height of the sail.
(Show steps please)
Answer:
H=21ft
Step-by-step explanation:
Height=2•Area/Base
Area=126ft^2
Base=12ft.
H=2•126/12=21ft
H=21ft
Hope this helps :)
Write the word sentence as an equation. Then solve the equation
the difference between a number p and 6 is -14
Answer:
-8
Step-by-step explanation:
The difference between a number P and 6 is -14.
then;
[tex]p - 6 = - 14 \\ p = - 14 + 6 \\ p = - 8[/tex]
Algebraic Proof
Match the justification to each step of the deductive reasoning about this picture. Please Help!
The following are deductive reasoning for each statement in the algebraic proof given:
1. CD + DE = CE (Segment Addition Postulate)
2. 8 + (3x + 7) = 6x (Substitution)
3. 3x + 15 = 6x (Combining like terms)
4. 15 = 3x (Subtraction Property of Equality)
5. x = 5 (Division Property of Equality)
6. CE = 6(5) (Substitution)
Recall:
The Segment Addition Postulate states that when a point lies between two endpoints on a line segment, the length of the larger segment equals the sum of the lengths of the two smaller segments formed.Thus, the following are deductive reasoning for each statement in the algebraic proof given:
1. CD + DE = CE (Segment Addition Postulate)
2. 8 + (3x + 7) = 6x (Substitution)
Rationale: Plug in the values of CD, DE and CE3. 3x + 15 = 6x (Combining like terms)
Rationale: Add 8 and 7 together4. 15 = 3x (Subtraction Property of Equality)
Rationale: Subtract 3x from each side of the equation.5. x = 5 (Division Property of Equality)
Rationale: Divide each side of the equation by 3).6. CE = 6(5) (Substitution)
Rationale: Plugging in the value of x into "6x"Learn more about Segment Addition Postulate on:
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40 pts & Brainliest to first Correct. PLZ HELP ASAP
Answer: [tex]16x^4y^2a^6[/tex]
Step-by-step explanation:
just apply to the power of 2 to every term
-4 times -4 is 16
x^2 to power of 2 is 2 times 2 so x^4
y^2 is y^2
a^3 to power of 2 is 3 x 2 = 6 so a^6
16x^4y^2a^6
Answer:
16x^4y^2a^6
Step-by-step explanation:
Do this step by step
16x^4y^2a^6
Please give brainliest!
What is the measure of _____?
Answer:
95 degrees
Step-by-step explanation:
The sum of all the angles need to come to 360 degrees. We already have 2 90 degree angles, together 180 degrees. Subtract from 360 to get 180, so we know the other two angles together need to equal 180. x + x + 10 = 180
Add common terms, then subtract 10: 2x = 170
Divide by 2: x = 85
So angle F is 85 + 10, or 95 degrees.
Please solve: 7x - 4 = 2
3y-8=3y
solve for y
help asap
step by step please
Answer:
y=4/3
Step-by-step explanation:
3y-8=3y
3y+3y=8
6y=8
y=8/6=4/3
Find the area of the surface generated by revolving x = t y = t^2 1 ≤ t ≤ 2 around the y-axis
Answer:
4^22x
Step-by-step explanation:
will give brainliest
Answer:
Steeper: y=-3/2x+1/2 AND y=-2x+7/3 AND y=-7/4x+3/2
Less Steep: y=-4/3x+2/3 AND y=-8/7x+4/7
Step-by-step explanation:
Hope this helps :)
Divide 35 in the ratio 3:2
[tex]3x + 2x = 35 \\ 5x = -35 \\ x = 7 \\ 3x = 3 \times 7 = 21 \\ 2 x \: \: \: \: 2 \times 7 = 14 \\ 21 \: and \: 14 \: answer[/tex]
hopefully it's helpSimplify 6^-3/6^5
answers:
• 6^8
• 6^-2
• 1/6^8
• 1/6^2
Solve the equation 5.3g + 9 = 2.3g+ 15
a. Find the value of g
Answer:
g=2
Step-by-step explanation:
5.3g+9=2.3g+15
5.3g-2.3g=15-9
3g=6
g=6÷3
=2
Answer:
g = 2
Step-by-step explanation:
5.3g + 9 = 2.3g + 15
Subtract 2.3g from both sides
3g + 9 = 15
Subtract 9 from both sides
3g = 6
Divide both sides by 3
g = 2
At a picnic, 12 people shared 4 large sandwiche
equally. How much of a sandwich did each
person get to eat?
Answer:
1/3
Step-by-step explanation:
Answer:
each person ate 1/3 of a sandwich
Step-by-step explanation:
100 if u get this right!
Answer:
■ y = m x
m = slope
Here m = 4/3
,*,slope is 4/3
Solve. −6.6x=−4 What is the solution to the equation? Enter your answer as a simplified fraction in the box. x =
Answer:
20/33
Step-by-step explanation:
i took the test
Answer:
x = 20/33
Step-by-step explanation:
−6.6x = −4
Divide both sides by -6.6
x = -4/(-6.6)
x = 40/66
x = 20/33
Answer: x = 20/33
A gym is offering a deal to members. Customers can sign up by paying a registration fee of $100 and $28 per month. The function that models this situation is c(m) = 28m + 100, where m is the number of months and c(m) is the cost of becoming a member.
Determine:
6. the shape of the graph
7. the independent and dependent variables
8. the domain and range
9. Interpret the slope and y-intercept values
10. How much will the membership cost for a whole year?
6) The equation given is written in standard form of writing the equation of a line y = mx + b
Hence the shape of the graph that denotes the equation c(m) = 28m + 100 is a straight line
7) The independent variable is a variable that can stand alone while the dependent variable is depending on all other variables in an expression.
From the given equation c(m) = 28m + 100, the independent variable is (m) while the dependent variable is c(m)
8) The domain is the input value for which the equation exists while the rage is the output value for which the equation exists. For the given expression, the value of the expression will exist at a point where c(m) > 0
28m + 100 > 0
28m > -100
m > -100/28
m > --25/7
The domain is m > -25/7 while the range is c(m) > 0
9) The comparing the equation with y = xm+ b
where x is the slope
28m = mx
x = 28
This shows that the rate of change of cost per member is $28
The y-intercept is the point where the number of months is 0
If m = 0
c(0) = 28(0) + 100
c(0) = 100
The initial cost of membership in the first month is $100
10) Given the formula c(m) = 28m + 100
For a whole year, m = 12
c(12) = 28(12) + 100
c(12) = 336 + 100
c(12) = 436
Hence the membership will cost $436 for the whole year
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A box of cereal states that there are 96 calories in a
3
4-cup serving. What is the unit rate for calories per cup? How many calories are there in 3 cups of the cereal?
Answer: 96
Step-by-step explanation:
96/3 = 32 per cup 32 x 3 = 96
How to factor a tri, quad, or polynomial.
Explanation:
Factoring to linear factors generally involves finding the roots of the polynomial.
The two rules that are taught in Algebra courses for finding real roots of polynomials are ...
Descartes' rule of signs: the number of positive real roots is equal to the number of coefficient sign changes when the polynomial is written in standard form.Rational root theorem: possible rational roots will have a numerator magnitude that is a divisor of the constant, and a denominator magnitude that is a divisor of the leading coefficient when the coefficients of the polynomial are rational. (Trial and error will narrow the selection.)In general, it is a difficult problem to find irrational real factors, and even more difficult to find complex factors. The methods for finding complex factors are not generally taught in beginning Algebra courses, but may be taught in some numerical analysis courses.
Formulas exist for finding the roots of quadratic, cubic, and quartic polynomials. Above 2nd degree, they tend to be difficult to use, and may produce results that are less than easy to use. (The real roots of a cubic may be expressed in terms of cube roots of a complex number, for example.)
__
Personally, I find a graphing calculator to be exceptionally useful for finding real roots. A suitable calculator can find irrational roots to calculator precision, and can use that capability to find a pair of complex roots if there is only one such pair.
There are web apps that will find all roots of virtually any polynomial of interest.
_____
Additional comment
Some algebra courses teach iterative methods for finding real zeros. These can include secant methods, bisection, and Newton's method iteration. There are anomalous cases that make use of these methods somewhat difficult, but they generally can work well if an approximate root value can be found.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided 20 ctn 8 Citi 6 Cm 12 CITL 16 cm Drawing not to scale The two triangles above are similar a. Find x using the ratio of the sides 12 cm and 16 cm. 20 T 12 16 Show your work b. Find x using the ratio of the sides 6 cm and 8 cm Show your work C. Explain why the answers to (a) and (b) should be the same
Find the perimeter. Simplify your answer.
Please help me!
give the equation of the horizontal asymptote of the function shown below. g(x)=2x/x+5
Answer:
y=2
Step-by-step explanation:
Because the degrees of the numerator and denominator are equal to each other, then the equation of the horizontal asymptote of the function is y=2 since the end behavior of the function is equal to 2x/x=2.
What is the slope for M(4,-8 negative) N(6,-1 negative)
Answer:
m=7/2
Step-by-step explanation:
The volume of a box is given by V=3x^3 + 33x^2 + 84x. Determine expressions for a possible set of dimensions for this box.
Answer:
(-7,0) (-4,0)(0,0)
Step-by-step explanation:
