The cost of the polishing, £C, is given by C = 6πr² + 300/r.
The volume of the solid cylinder is 75 m³.
Formula for volume of cylinder = πr²h.
Where R is rhe radius of cylinder and h is the height of the cylinder.
So we can write,
πr²h = 75
h = 75/πr².
So the height of the cylinder is 75/πr² centimeters.
Curved surface area of the cylinder is 2πrh m².
Cost of polishing the curved surface area is £2/cm².
Total cost of polishing the curved surface area = £2×2πrh
Area of the base and the top is 2(πr²).
Cost of polishing base and top is £3/cm².
Cost of polishing 1m² of the base and top,
Cost of area of base and top = £3/cm².
Total Cost of polishing base and top area = £3×2(πr²)
The total cost C of polishing the whole glass,
C = 4πrh + 6πr²
Puting the value of h = 75/πr²
C = 4πr(75/πr²) + 6πr²
C = 6πr² + 300/r.
Hence it is proved that the total cost of polishing is,
C = 6πr² + 300/r.
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can someone help me with this please
Answer:
x=4
Step-by-step explanation:
15-9=6
10-6=4
Answer:
x = 6 cm
Step-by-step explanation:
The two shapes are similar. That means one figure is exactly a multiple of the other figure
We can see that the ration of the length of the bigger rectangle to the length of the smaller rectangle is 15/9 = 5/3
Therefore the ratio of the width of the bigger rectangle to the width of the smaller rectangle must also be 5/3
Given width of big rectangle = 10 and that of small rectangle is x
We get
10/x = 5/3
Multiply by x both sides:
x × 10/x = x × 5/3
10 = 5x/3
Multiply by 3 both sides
30 = 5x
5x = 30
Dividing by 5 both sides
5x/x = 30/5
x = 6 cm
Factorise the following:
a) x^2 + 10x + 16
b) x^2 + 7x + 12
c) x^2 + 13x + 12
Answer:
Step-by-step explanation:
a)
[tex]x^2+10x+16=\\x^2+2x+8x+16=\\x(x+2)+8(x+2)=\\(x+2)(x+8)[/tex]
b)
[tex]x^2+7x+12=\\x^2+3x+4x+12=\\x(x+3)+4(x+3)=\\(x+3)(x+4)\\[/tex]
c)
[tex]x^2+13x+12=\\x^2+x+12x+12=\\x(x+1)+12(x+1)=\\(x+1)(x+12)[/tex]
Answer:
[tex]\textsf{(a)} \quad (x+8)(x+2)[/tex]
[tex]\textsf{(b)} \quad (x+4)(x+3)[/tex]
[tex]\textsf{(c)} \quad (x+12)(x+1)[/tex]
Step-by-step explanation:
Factoring quadratics
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].Rewrite [tex]b[/tex] as the sum of these two numbers.Factor the first two terms and the last two terms separately.Factor out the common term.Part (a)[tex]\textsf{Given}: \quad x^2+10x+16[/tex]
Two numbers that multiply to 16 and sum to 10 are: 2 and 8.
[tex]\implies x^2+2x+8x+16[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+2)+8(x+2)[/tex]
Factor out the common term (x + 2):
[tex]\implies (x+8)(x+2)[/tex]
Part (b)[tex]\textsf{Given}: \quad x^2+7x+12[/tex]
Two numbers that multiply to 12 and sum to 7 are: 3 and 4.
[tex]\implies x^2+3x+4x+12[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+3)+4(x+3)[/tex]
Factor out the common term (x + 3):
[tex]\implies (x+4)(x+3)[/tex]
Part (c)[tex]\textsf{Given}: \quad x^2+13x+12[/tex]
Two numbers that multiply to 12 and sum to 13 are: 1 and 12.
[tex]\implies x^2+x+12x+12[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+1)+12(x+1)[/tex]
Factor out the common term (x + 1):
[tex]\implies (x+12)(x+1)[/tex]
Show the relationship between -5/6 and -7/10. Use an inequality symbol
[repost]
From the inequality concept ( -7 / 10) > ( -5 / 6).
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Given fractional numbers are -5/6 and -7/10. The numbers in the form of inequality will be calculated as:-
-7 / 10 = -0.7
-5 / 6 = -0.84
-0.7 > -0.84
-7 / 10 > -5 / 6
Therefore, from the inequality concept ( -7 / 10) > ( -5 / 6).
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If ATUV is translated to image ATUV, as shown below, by the rule
(x, y) → (x+8, y - 3), what are the coordinates of ATUV?
==========================================================
Explanation:
The given translation rule is (x, y) → (x+8, y - 3) which says "shift 8 units right and 3 units down".
The inverse transformation will undo each to get "8 units left and 3 units up"
So the inverse is (x, y) → (x-8, y + 3)
Use this inverse to determine the preimage of point T'(2,-6)
[tex](\text{x},\text{y})\to(\text{x}-8,\text{y}+3)\\\\(2,-6)\to(2-8,-6+3)\\\\(2,-6)\to(-6,-3)\\\\[/tex]
Therefore, preimage point T is located at (-6,-3) which points us to answer choice B
If we were to apply the rule of "shift 8 units right and 3 units down" to T(-6,-3), you should arrive at T'(2,-6)
help needed asap!! will award brainiest
Please answer asap please and thank you
Answer:
Step-by-step explanation:
Whats 6% of 583! Because its very confusing and if you can help that would be great
Answer:
34.98is the answer ............ .............
Answer: 34.98
Step-by-step explanation:
'Percent (%)' means 'out of one hundred':
6% = 6 'out of one hundred',
p% is read p 'percent',
6% = 6/100 = 6 ÷ 100
What does it mean to calculate the percentage of a number?
6% of 583 = ?
... is equivalent to multiplying them:
6% × 583 = ?
6% of 583 =
6% × 583 =
6/100 × 583 =
(6 ÷ 100) × 583 =
6 × 583 ÷ 100 =
3,498 ÷ 100 =
34.98
5. Which of the following functions has a graph with the largest positive x-intercept?
A. f(x) = 2(x+5)-1
B. f(x) = 8(x+8)
c. f(x) = 2(x-8) +1
D. f(x)=13(x-3)
The function which has a graph with the largest positive x-intercept is C. f(x) = 2(x-8) +1
What is a x-intercept?The value of the x coordinate at the point where the graph crosses the x-axis is known as the x-intercept for any curve. Alternatively, we can say that the x-intercept is the value of the x coordinate at the point where the value of the y coordinate equals zero.
Let y be 0, so lets find the x-intercept of
A. 2(x+5)-1 = 0
⇒ 2(x+5) = 1
⇒ 2x + 10 = 1
⇒ 2x = -9
⇒ x = -9/2
B. 8(x+8) = 0
⇒ x+8 = 0
⇒ x = 0 −8
⇒ x = −8
C. 2(x-8) +1 = 0
⇒ 2x − 15 = 0
⇒ 2x = 15
⇒ x = 15/2
⇒ x = 7.5
D. 13(x-3) = 0
⇒ x − 3 = 0/13
⇒ x − 3 = 0
⇒ x = 0 + 3
⇒ x = 3
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The graph is a function. + O True O False
the provided graph is not a function .
s
What is the product of the common prime factors 24 and 32?
Answer:
2*2*2
That's the prime product of their common factors
x =7, -2, 0, 7
y= 10,0,10,3
Is this a function?
Answer: No, this is not a function.
Functions exist when there are a unique set of x-values and each can match with a y-value. There cannot be a repeating x-value because this creates a discontinuity in the graph. You can have as many repeating y-values as you’d like as long as they each have a unique x-value and are not duplicate plot points.
Since x = 7 repeats in the domain of x-values, this cannot be a function.
Anais bought
2 1/2 yards of ribbon. She had
feet 1
6 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains
The inches of ribbon that Anais use to trim the curtains is 12 inches.
How to illustrate the information?From the information, Anais bought 2 1/2 yards of ribbon and then he had 1 feet 6 inches of ribbon left after trimming some curtains.
It should be noted that 12 inches = 1 feet
Therefore, the inches that will be left will be:
= 2 1/2 - 1 6/12
= 2 1/2 - 1 1/2
= 1 feet
It should be noted that 1 feet = 12 inches.
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What is the relationship between translations, reflections, and ridgid motion?
The relationship between translations, reflections, and rigid motion is that they are all types of rigid motions, which means their size does not change.
What exactly is rigid motion?Rigid motion is the movement of a set in which the distance between points remains constant.
What is translation?Translation is a type of rigid motion in which an object simply slides while maintaining its direction.
What do you mean by reflection?A reflection, like a mirror, causes an image to flip to another location.
We must establish a connection between translations, reflections, and rigid motion.
We can conclude from the above definitions that the size of the object remains constant, but it is undergoing different transitions.
Therefore, Translations, reflections, and rigid motion all belong to the category of transformations that are rigid motions, which means that their sizes don't change.
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PLEASE HELP NOW!!!!!!!!!!! (03.04 MC)
Two exponential functions, f(x) and g(x), are graphed on the same coordinate plane.
Graph of f of x equals 2 to the x power going through points 0 comma 1 and 1 comma 2 and graph of g of x equals 2 to the x power minus 1 going through points 0 comma 0 and 1 comma 1.
What effect does subtracting 1 from the parent function have on the transformed function?
a
Subtracting 1 from the parent function shifts the function up one unit.
b
Subtracting 1 from the parent function shifts the function down one unit.
c
Subtracting 1 from the parent function shifts the function right one unit.
d
Subtracting 1 from the parent function shifts the function left one unit.
Subtracting 1 from the parent function will transform the function in the following way: b Subtracting 1 from the parent function shifts the function down one unit
what is transformation?This refers to as movement of object in an organized way such that the movement can always be calculated from the initial position.
The movement involved in transformation on images is ordered and there are some terms used to classify such movements. some of the terms are:
ReflectionDilationTranslation and so onThe movement done in the question is a translation. This is a linear movement towards a particular direction. the movement is translation is usually:
Up: adding numbers to the y directiondown: subtracting number in the y directionRight: adding number to the x directionLeft: subtracting number or value from the x directionSubtracting 1 from the parent function. the parent function as used refers to the y direction hence option b is the correct answer
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The complement of an angle is half of it’s size. Find the angle
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:The \:\: angles \:\: are \:\: 60° \:\: and \:\:30° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Sum of two complementary angles is 90°
Let's assume one of them to be x, the other one will be x/2 as one of the angles is complementary to other one.
[tex]\qquad \tt \rightarrow \: x + \dfrac{x}{2} = 90[/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{2x + x}{2} = 90[/tex]
[tex]\qquad \tt \rightarrow \: 3x = 90 \times 2[/tex]
[tex]\qquad \tt \rightarrow \: x = 180 \div 3[/tex]
[tex]\qquad \tt \rightarrow \: x = 60 \degree[/tex]
and
[tex]\qquad \tt \rightarrow \: \dfrac{x}{2} = 60 \div 2 = 30 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
You want to drink an average of at least 64 fluid ounces of water each day of the week.
How many fluid ounces of water should you drink on Sunday to reach your goal?
Monday-64
Tuesday-76
Wednesday-66
Thursday-72
Friday-58
Saturday-56
Sunday-56 fluid ounces of water require to reach your goal.
What is a average means?Average: A value that ought to represent the sample is what is meant by the term "Average." The average is calculated by dividing the total number of values in a given set by the sum of all the values in that set. Additionally called the arithmetic mean.In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. If we want to calculate the average for a set of data, we add up all the values and divide this sum by the total number of values.To learn more about : Arithmetic mean.
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19. the sum of twelve and sixteen divided by the sum of three and four
20.the difference of twenty-two and six divided by the sum of five and three
21.the sum of thirty-six and fourteen divided by the product of two and five
22.the quotient of thirty-two and four divided by the sum of one and three
23.the sum of six and fifteen divided by 24.the difference of thirteen and nine
25.the difference of thirty-one and seventeen divided by the product of ten
Answer:
they require the use of fractions.
Step-by-step explanation:
sum means to add both numbers
difference means to subtract the small number from the big number
quotient means to divide
product means to multiply
24. 13-9= 4
not sure what you meant by q23 and q25.
19. the sum of twelve and sixteen divided by the sum of three and four = 4
20. the difference of twenty-two and six divided by the sum of five and three = 2
21. the sum of thirty-six and fourteen divided by the product of two and five = 4
22. the quotient of thirty-two and four divided by the sum of one and three = 2
23. the sum of six and fifteen divided by 24 = 21/24
24. the difference of thirteen and nine = 4
25. the difference of thirty-one and seventeen divided by the product of ten = 7/5 = 1.4
Will plays a game at a theme park.
There are 20 cards numbered from 1 to 20.
Will takes a card at random.
He wins if the card he chooses shows a prime number.
Work out the probability that Will wins.
Give your answer as a fraction in its simplest form.
Answer:
find prime numbers between 1-20:
= 2,3,5,7,11,13,17,19
=8 prime numbers
probability of winning = 8/20=2/5
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assuming the ocean’s level is currently rising at about 1.6 millimeters per year, create an application that displays the number of millimeters that the ocean will have risen each year for the next 25 years.
40 millimeters; the ocean will have risen each year for the next 25 years.
ocean’s level is currently rising at about 1.6 millimeters per year.
create an application that displays the number of millimeters that the ocean will have risen each year for the next 25 years.
IN, 1 year —> 1.6 millimeters;
25 years —> 25*1.6 millimeters;
= 40 millimeters;
40 millimeters; the ocean will have risen each year for the next 25 years.
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Simplify.
Rewrite the expression in the form z^n
z^7/z^-14
In the form exponent function zⁿ, the above equation z⁷/z⁻¹⁴ would equal z²¹.
What are exponential functions?The term "exponential function" refers to a function whose expression calls for the input to exist as an exponent (power) of some constant. The following describes their typical form. There are numerous equivalent forms in which they are written.
Briefing:The negative exponent rule instructs us to place a number with a negative exponent in the denominator and the opposite is also true.
State product of power property of exponents.
Keep the bases the same when multiplying two bases with the same value, and then add the exponents to find the answer.
[tex]\frac{z^7}{z^{-14}}[/tex]
[tex]\frac{z^7}{z^{-14}}[/tex]
[tex]z^{7-(-14)}[/tex]
z²¹.
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A drilling crew dug to a depth of 26 ½ feet during their first day of drilling. On the second day, the crew dug down 9½ feet more than on the first day. Describe the depth of the bottom of the hole after the second day.
The depth of the bottom of the hole after the second day is 36 feet using addition operation.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the sum refers to the outcome of the operation.
Given the depth on the first day is 26 ½ feet.
Depth on the second day = 9½ feet more than on the first day i.e. 9½ feet + depth on the first day
This implies, depth on the second day = 9½ + 26 ½
= 36 feet
Therefore, the depth of the bottom of the hole after the second day is 36 feet.
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please help me quickly
Answer:
80 degrees
Step-by-step explanation:
A line has a slope of 1/3 and includes the points (6,1) and (9,j). What is the value of j?
Answer:
j = 2
Step-by-step explanation:
Slope of a line is given by:
[tex]\medium \text{$\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}[/tex]
where (x₁, y₁) and (x₂, y₂) are two points on the line
This is commonly referred to as rise/run
Given the two points (6, 1) corresponding to (x₁, y₁) and (9, j) corresponding to (x₂, y₂)
[tex]\text{Slope = }\dfrac{\ensuremath{j}-1}{9-6}=\dfrac{j-1}{3}[/tex]
But we are given the slope as 1/3
So we get
[tex]\dfrac{j-1}{3} = \dfrac{1}{3}[/tex]
Multiplying by 2 on both sides gives us:
j - 1 = 1
Adding 1 to both sides gives us
j - 1 + 1 = 1 + 1
j = 2
Function g is a transformation of function f.
-6 -5
4
g(x) =
لا
-2 -1
-1
f(x)
-2
-3
What is the equation of function g?
-5
-6
2
For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5
As per the question statement, We are given f(x) = 2x + 3 and g(x)=x^2+1
and we are supposed to find the composite function defined by (f o g)(x)
(f o g)(x) = f(g(x))
(f o g)(x) = 2 (g(x)) + 3
(f o g)(x) = 2( -x^2 + 1 ) + 3
(f o g)(x) = - 2 x^2 + 5
Hence, For f(x) = 2x + 3 and g(x) = -x^2 + 1, The composite function defined by (f o g)(x) is equal to (f o g)(x) = - 2 x^2 + 5
Composite Function: A function that is composed of further functions, each of which serves as the input to the next.To learn more about composite functions, click on the link given below:
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Choose the number line that correctly compares 24−−√ and 4.256.
The number line that correctly compares √24 and 4.256 is number line C.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used for the comparison of two or more numbers such as √24 and 4.256. Also, a number line typically decreases in numerical value towards the left and increases in numerical value towards the right.
Taking the square root of √24, we have:
√24 = 4.899
In this context, we can reasonably and logically deduce that 4.899 is greater than 4.256 (4.899 > 4.256) and would be placed at the right hand side of the number line and further from 4.899 as shown in number line C in the image attached below.
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Each droplet that you sneeze is approximately 7 x 10-3 mm in diameter. If you wear an N95 mask, which filters virus particles as small as 8 x 10-5, will you sufficiently protect those around you? Explain your reasoning.
Answer:
Yes, 7 x [tex]10^{-3}[/tex] in standard form is 0.007mm
8 x [tex]10^{-5}[/tex] in standard form is 0.00008 mm. The mask will catch particles that are much smaller than 0.007 in diameter.
Step-by-step explanation:
x y
7 11
8 13
9 15
10 17
27
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
The correct answer is that y does not vary directly with x.
If y and x are directly related, then the equation y=kx would be true for each point in the set.
What is the explanation:
If y is directly related to x, then every point in the set would fit the equation y=kx.
For the first point, we would have 11=7k, which would imply that k=11/7.
For the second point, we would have 13=8k, which would imply that k=13/8.
By utilizing proportions to check, we can see that 11/7 does not equal 13/8.
Cross multiplying yields 11*8=7*13, or 88=91
Since this is untrue, k is not a constant and y does not change in accordance with x.
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write the mixed expression as a rational expression: 2+9/g
mixed expression as a rational expression will be [tex]\frac{2g+9}{g}[/tex]
WHAT IS FRACTION ?In mathematics, a fraction is a number that is expressed as a quotient in which the numerator and denominator are divided. In a simple fraction, both are integers. A complicated fraction contains a fraction in either the numerator or denominator. Any fraction that is right has a numerator that is less than its denominator.
CALCULATIONto convert mixed fraction into rational fraction
we multiply denominator with whole number and add it with numerator and the result of this gives numerator . and the denominator is same as mixed fraction .
so for the given expression ,
2 * g + 9 is numerator
and g is denominator .
= [tex]\frac{2g+9}{g}[/tex]
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Write an equation for the line parallel to the given line that contains C.
5
C(1,7); y=x+4
The equation of the line parallel to the given line that contains C is obtained as y = x + 6.
What is termed as the parallel lines?Parallel lines are two or more lines which lie within the same plane but never intersect. They are equal in distance and have the same slope. Parallel lines have been straight lines which never meet, no matter how far they are extended. Numerous pairs of angles are formed when two parallel lines have been intersected by another line known as a transversal.For the given question;
The equation of the line is given as;
y = x + 4
The standard form of the equation of line in slope intercept form is;
y = m x + c
where, m is the slope and c is the y intercept.
On comparing;
m₁ = 1
Now, the other lien is parallel to the given line.
Thus, slopes of both lines will be equal.
m₁ = m₂ = 1
The passing points of the line are;
(x₁, y₁) = C(1, 7)
Now, the equation of lien will be;
y - y₁ = m₂(x - x₁)
Put the values;
y - 7 = 1(x - 1)
Simplifying.
y = x + 6
Thus, the equation of the line parallel to the given line that contains C is obtained as y = x + 6.
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let in the region where . explain why must have a global minimum at some point in (note that is unbounded---how does this influence your explanation?). then find the global minimum. minimu
the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10) is y= 5е¹ ⁻ ˣ +5 x
We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:
First Derivative Test
-a .е⁻ˣ +b = 0 (1)
b=a .е⁻ˣ
Second Derivative Test
y''= a . .е⁻ˣ (2)
Where y'' >0
If we know that ( x,y) = 9 1,10) , then we have the following system:
10 = a е⁻¹ +b (3)
b= a е⁻¹ (4)
y'' = a е⁻¹ (5)
By (4) in (3):
10= 2aе⁻¹
a=10/2е⁻¹
a= 5е
By (5) we prove that y''>0, and we get the value of by (4):
b=5
Thus, the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10) is . y= 5е¹ ⁻ ˣ +5 x
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