Answer:
I. Radius, r = 2.90 cm
II. Height, h = 4.10 cm
Step-by-step explanation:
Given the following data;
Volume of cone = 24 cm³
To find the height and radius of the cup that will use the smallest amount of paper;
Mathematically, the volume of a cone is given by the formula;
[tex] V = \frac{1}{3} \pi r^{2}h[/tex] ......equation 1
Where;
V is the volume of the cone.
r is the radius of the base of the cone.
h is the height of the cone.
Substituting into the formula, we have;
[tex] 36 = \frac{1}{3} \pi r^{2}h[/tex]
Multiplying both sides by 3, we have;
[tex] 108 = \pi r^{2}h[/tex]
Making radius, r the subject of formula, we have;
[tex] r^{2} = \frac {108}{ \pi h} [/tex]
Taking the square root of both sides, we have;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
Mathematically, the lateral surface area of a cone is given by the formula;
[tex] LSA = \pi rl [/tex] ......equation 2
Where;
r is the radius of a cone
l is the slant height of a cone.
To find the slant height, we would apply the Pythagorean' theorem;
[tex] l = \sqrt {r^{2} + h^{2}} [/tex]
Substituting r into the above equation, we have;
[tex] l = \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Substituting the values of r and l into eqn 2, we have;
[tex] LSA = \pi * \sqrt { \frac {108}{ \pi h}} * \sqrt {\frac {108}{\pi h} + h^{2}} [/tex]
Simplifying further, we have;
[tex] LSA = \sqrt {108} * \sqrt { \frac {\pi h^{3} + 108}{\pi h}} [/tex]
[tex] LSA = \sqrt {108} * \sqrt { \frac {108}{ h^{2}} + \pi h}} [/tex]
Next, to find the value of h, we differentiate the above mathematical equation with respect to h;
[tex] \frac {dS}{dh} = \sqrt {108} * (\pi - \frac {216}{h^{3}}) * (\pi h + \frac {108}{h^{2}}) [/tex]
Limiting [tex] \frac {dS}{dh} [/tex] w.r.t 0;
[tex] \frac {dS}{dh} = 0 [/tex]
[tex] (\pi - \frac {216}{h^{3}}) = 0 [/tex]
Rearranging the equation, we have;
[tex] \pi = \frac {216}{h^{3}} [/tex]
We know that π = 3.142
[tex] 3.142 = \frac {216}{h^{3}} [/tex]
Cross-multiplying, we have;
[tex] 3.142h^{3} = 216 [/tex]
[tex] h^{3} = \frac {216}{3.142} [/tex]
[tex] h^{3} = 68.75 [/tex]
Taking the cube root of both sides, we have;
Height, h = 4.10 cm
Lastly, we find the value of r;
[tex] r = \sqrt { \frac {108}{ \pi h}} [/tex]
[tex] r = \sqrt { \frac {108}{3.142 * 4.10}} [/tex]
[tex] r = \sqrt { \frac {108}{12.88}} [/tex]
[tex] r = \sqrt {8.39} [/tex]
Radius, r = 2.90 cm
The height and radius of the cup that will use the smallest amount of paper is;
Radius = 2.52 cm
Radius = 2.52 cmHeight = 3.58 cm
Let us first state some relevant formulas;
Volume of a cone is;
V = ⅓πr²h
Surface area of a cone is;
S = πrL
Where L is Slant height and has a formula;
L = √(h² + r²)
We are told that the cone is to hold 24 cm³. Thus; V = 24 cm³
24 = ⅓πr²h
πr²h = 72
r = √(72/πh)
Putting √(72/πh) for r in the Slant height equation gives;
L = √(h² + (72/πh))
Thus;
S = π × √(72/πh) × √(h² + (72/πh))
Differentiating with respect to h gives;
dS/dh = √72 × (π - 144/h³) × 1/√(πh + 72/h²)
At dS/dh = 0,we will have;
(π - 144/h³) = 0
Thus;
h³ = 144/π
h = 3.58 cm
Thus, from r = √(72/πh);
r = √(72/(π × 3.58))
r = 2.52 cm
Read more at; https://brainly.com/question/4405937
Jalen plots two integers on a horizontal number line. The leftmost integer is negative. Which must be true of the second integer
Answer:
The second integer is greater than the first.
Step-by-step explanation:
Since the first integer is the leftmost out of the two, this means that the second one must be greater than the first since it is to the right of it.
Answer:
c
Step-by-step explanation:
The following are the last 10 run scores Colin got in cricket:
34, 26, 11, 9, 20, 19, 31, 6, 33, 35
a) Work out Colin's mean score.
b) Colin plays cricket again on Sunday. He gets 29 runs.
What is his new mean score?
Give your answers as decimals.
HELPPPO
Answer:
a)18.8
b)20
Step-by-step explanation:
Basically, you have to add all the numbers from the data set (188) then divide them by 10 and that equals 18.8
The second part you have to add 32 to 188 ( which equals 210) and that by 11 which equals 20
23 points help plzzz
Which number is an integer?
O -3/4
O 1/5
O 2
O 4 2/3
The answer is 2 ez.
Answer:
2
Step-by-step explanation:
hope i helped :))
Pythagorean Theorem
A rectangular park is 8 miles long and 6 miles wide. How
long is a pedestrian route that runs diagonally across the
park?
In this discussion, you will need to provide the solution
to the problem explaining the intermediate steps you
used in the process.
Answer:
10 miles
Step-by-step explanation:
The Pythagorean Theorem states a^2+b^2=c^2
So, (8^2)+(6^2)=c^2
64+36=100
Square root of 100=10
Determine whether the function is linear or quadratic.
y = (x + 1)(8x - 8) - 8x2
a) Linear
b) Quadratic
Answer:
it's a linear
since when you expand the equation (x+1)(8x-8) the x is equal to zero which is left for y to be the subject
8x²-24= y
Express tan J as a fraction in simplest form
Answer:
Tan J = 3/4
Step-by-step explanation:
Recall, SOH CAH TOA
TOA means:
Tan J = Opp/Adj
Reference angle = <J
Opposite = 15
Adjacent = 20
Plug in the vakues
Tan J = 15/20
Simplify
Tan J = 3/4
Ray invested $300 in Stock A
and $750 in Stock B. Since then,
the value of Stock A has increased
by 15% each year and the value of
Stock B has decreased by 12% each
year. After 4 years, which statement
is true regarding the value of
his investments?
A) Stock A is worth $55.15 more than Stock B.
(they won a radio contest)
B) Stock A is worth $74.93 more than Stock B.
(they are best friends)
C) Stock B is worth $55.15 more than Stock A.
(they wanted to get attention)
D) Stock B is worth $74.93 more than Stock A.
(they were training for a marathon)
CADRUG
Answer:
i think its b
Step-by-step explanation:
LM is the midsegment of ABC is AC is 28 centimeters long , how long is LM?
Answer:
LM = 14
Step-by-step explanation:
LM = AC/2
LM = 28/2
LM = 14
Hope this helps!
The measure of LM is 14 cm.
What is Mid - segment?A triangle midsegment is a line segment that connects the midpoints or centres of two opposite or adjacent triangle sides.
The midsegment theorem asserts that a line segment connecting the midpoints of any two sides of a triangle is parallel to and half of the third side.
According to mid segment is
LM = AC/2
We have AC = 28 cm
Now, substitute the value of AC we get
LM = 28/2
LM = 14
Thus, the measure of LM is 14 cm.
Learn more about Mid- segment here:
https://brainly.com/question/15381486
#SPJ5
el vector desplazamiento de un objeto en movimiento inicialmente en el origen tiene una magnitud de 12.5 cm y está en un ángulo de 210 grados en relación con el eje de las x en determinado instante Cuáles son las coordenadas del objeto en ese instante ? una pelota rueda con velocidad constante a 2.40 m por segundo con un ángulo de 37 grados en relación al eje de las x del cuadro cuadrante si sabemos que la pelota está en el origen en tiempo igual iniciar cuáles son sus coordenadas x 1.75 segundos
Answer:
hey mate
which laungage is this
Find the volume of the cubes or rectangular prisms in cubic centimeters.
Answer:1st cube 2nd box 2nd cube 3rd box 4th cube 1st box and 1st cube 1st box
Step-by-step explanation:
The asked volumes are 36/125 cm³, 6/125 cm³, 1/125 cm³ and 8/125 cm³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Given are dimensions of cuboid and cubes, we are asked to find their volumes.
We know that, volume of cube = side³
Volume of cuboid = length · width · height
1) Dimensions of the cuboid = 3/5, 4/5, 3/5
Volume = 3/5×3/5×4/5 = 36/125 cm³
2) Dimensions of the cuboid = 1/5, 2/5, 3/5
Volume = 1/5×2/5×3/5 = 6/125 cm³
3) Side of the cube = 1/5 cm
Volume = (1/5)³ = 1/125 cm³
4) Side of the cube = 2/5 cm
Volume = (2/5)³ = 8/125 cm³
Hence, the asked volumes are 36/125 cm³, 6/125 cm³, 1/125 cm³ and 8/125 cm³
For more references on volume, click;
https://brainly.com/question/28058531
#SPJ2
i have 6 eggs, i broke 2, i cooked 2, and i ate 2, so how many are left?
Answer:
I can't tell if this is a joke or not haha but you would have four eggs left because you broke two, cooked and ate the same two eggs.
Plz help me with is question, ill try to give brainliest
Answer:
[tex]\text{B. } (8,6)[/tex]
Step-by-step explanation:
In slope-intercept form [tex]y=mx+b[/tex]:
[tex]m[/tex] represents slope[tex]b[/tex] represents the y-intercept [tex](x,y)[/tex] represent the coordinates of any point the line passes throughIn slope-intercept form, the equation for the table is given by [tex]y=x-2[/tex], and the equation for the second line is given by [tex]y=\frac{1}{4}x+4[/tex].
To find the point of intersection, set those two equations equal to each other and solve:
[tex]x-2=\frac{1}{4}x+4,\\x-2=0.25x+4,\\0.75x=6,\\x=8[/tex]
[tex]y=x-2,\\y=8-2,\\y=6[/tex]
Therefore, these two lines intersect [tex]\boxed{\text{B. (8,6)}}[/tex]
Why is this graph proportional?
Answer:
The graph represents a linear function that passes through the origin.
Step-by-step explanation:
Proportional functions can be represented by [tex]y=kx[/tex], where [tex]k[/tex] is some constant. They form a straight line that always pass through the origin (0,0). We can see all these characteristics in the graph, thus the graph is proportional.
Solve for t, 0 < t < 27.
21 sin(t)cos(t) = 12 sin(t)
Answer:i
Step-by-step explanation:i
ASAP PLSSSS HELP!!!!!!!!!!!!!!
Find the length of the missing side in the right triangle shown below.
A)144
B)313
C)169
D)5
E)None of these answers are correct
Answer:
the answer is d or e i think its d but its one of the 2
Step-by-step explanation:
Please I need help and thx
please show how you did it
Answer:
1.) 9.2
2.)
625
633
the dealer
8.81
Step-by-step explanation:
I'm gonna assume that cm= compounded monthly
1.)
effective rate: .153/12= .01275
x= payments
[tex]2590.67=300*\frac{1-(1+.01275)^{-x}}{.01275}\\.110103476=1-1.01275^{-x}\\.889896525=1.01275^{-x}\\\log_{1.01275}.889896525=-x\\x=9.207[/tex]
2.)
If there is no interest rate attached to financing through the deal the payment is just
37500/60 = 625
The monthly payment from the bank has a present value of 37500-3000=34500
and the effective rate is .039/12= .00325
[tex]34500=x\frac{1-(1.00325)^{-60}}{.00325}\\34500=54.43234738x\\x=633.81[/tex]
Finally, the amount we save is just the difference
633.81-625=8.81
Answer:
1.) 9.2
2.)
625
633
the dealer
8.81
Step-by-step explanation:
I'm gonna assume that cm= compounded monthly
1.)
effective rate: .153/12= .01275
x= payments
\begin{gathered}2590.67=300*\frac{1-(1+.01275)^{-x}}{.01275}\\.110103476=1-1.01275^{-x}\\.889896525=1.01275^{-x}\\\log_{1.01275}.889896525=-x\\x=9.207\end{gathered}
2590.67=300∗
.01275
1−(1+.01275)
−x
.110103476=1−1.01275
−x
.889896525=1.01275
−x
log
1.01275
.889896525=−x
x=9.207
2.)
If there is no interest rate attached to financing through the deal the payment is just
37500/60 = 625
The monthly payment from the bank has a present value of 37500-3000=34500
and the effective rate is .039/12= .00325
\begin{gathered}34500=x\frac{1-(1.00325)^{-60}}{.00325}\\34500=54.43234738x\\x=633.81\end{gathered}
34500=x
.00325
1−(1.00325)
−60
34500=54.43234738x
x=633.81
Finally, the amount we save is just the difference
633.81-625=8.81
What is the thirteenth number in the Fibonacci sequence
Answer:
The 13th number in the Fibonacci sequence is 144.
Step-by-step explanation:
The sequence from the first to the 13th number is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
[tex]\huge\boxed{\sf 144}[/tex]
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
[tex]\sf 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, \boxed{144}, 233, 377,...[/tex]
It represents the set of traits, competencies and values an individual would like to possess.
a. Perceived Self
b. The Ideal Self
c. Self-Identities
d. Self Esteem
Answer:
The correct answer is - d. Self Esteem
Explanation:
Self-esteem is how we value and perceive ourselves. It based on the believes and opinions we make for ourselves. It represents various traits and characteristics such as self-confidence, identity, feeling of belonging, and competency.
Values are the principle or opinions we make to follow and values provide a sense of identity and uniqunessgive you a clearer sense of self, meaning, more energy, focus, and self-esteem.
The option that represents the set of traits, competencies and values an individual would like to possess is;
Option B; The Ideal Self
Let us access all the given options;
Option A; Perceived self is simply defined as how an individual sees himself or herself. Option B; The Ideal Self is defined as how an individual would like himself or herself to be. This means such an individual will wish he or she possessed certain traits or values.Option C; Self Identities are simply how individuals identify and define themselves. For example an athlete, a Pastor, a doctor, a lecturer e.t.c.Option D; Self esteem is simply defined as the worth or value individuals place on themselvesLooking at the definitions above, in conclusion we can see that the only one that fits the description given in the question is The Ideal Self.
Read more at; https://brainly.com/question/13832207
what is the vertex of y=x²+14x-9
Margo borrows $1600, agreeing to pay it back with 3% annual interest after 11 months. How much interest will she pay?
Round your answer to the nearest cent, if necessary.
Answer:
Margo will pay $ 44 in interest.
Step-by-step explanation:
Given that Margo borrows $ 1600, agreeing to pay it back with 3% annual interest after 11 months, to determine how much interest will she pay, the following calculation must be performed:
3/12 x 11 = 0.25 x 11 = 2.75
1600 x 1.0275 = X
1644 = X
1644 - 1600 = 44
Therefore, Margo will pay $ 44 in interest.
What is the value of x?
Answer:
x=15 degree
Step-by-step explanation:
5x +5+6x -1+3x+5x+3+4x+8 =360 degree (exterior angles of pentagon is 360 degree)
23x +15 =360
23x=360-15
x=345
x=345/23
x=15 degree
if the equation 2x^2+ bx+ 5=0 has no real solutions, which of the following must be true A. b^2 < 10 B. b^2> 10 C. b^240
Answer:
C. b²< 40
Step-by-step explanation:
2x²+ bx + 5=0 has no real solutions
=> D< 0
b² < 4ac
b²< 4(2)(5)
b²< 40
Express in the form 1: n.
Give n as a decimal.
16 : 12
Answer: n will be 4
Step-by-step explanation:
Identifying a Proportional Relationship in a Table
Which takle represents a proportional relationship?
x
y
4
*
.
09
y
8
5
2
12
7
18
20
26
12
28
60
84
18
20
9514 1404 393
Answer:
see below
Step-by-step explanation:
A proportional relationship is one in which the ratio of y to x is a constant for all non-zero values of x and y.
Of the tables shown here, this is the case only for the one shown below. It has ...
y = 1.4x
Answer:
The middle one
Step-by-step explanation:
The middle one
y = (7/5)x
x y
5 7
20 28
60 84
in a system of equations why is the intersection the solution
9514 1404 393
Answer:
It satisfies both equations.
Step-by-step explanation:
The points on the graph of an equation are the values of the variables that satisfy the equation (make it true).
In a system of equations, you're generally looking for values of the variables that satisfy all of the equations in the system. That is, the solution will be a point on the graph of every equation in the system.
For a point to be on more than one graph, it must lie at a point of intersection of the graphs. If all of the graphs of a system go through the point of intersection, that point satisfies all of the equations, so is a solution of the system of equations.
Graph the image of square CDEF after a reflection across the x-axis
Answer:
If you have a general point (x, y), and you reflect it across the x-axis, the coordinates of the new point will be:
(x,-y)
So we only change the sign of the y-component.
Now, if we do a reflection across the x-axis of a whole figure, then we apply the reflection to all the points that make the figure.
Then, we could just apply the reflection to the vertices of the square, then graph the new vertices, and then connect them, that is equivalent to graph the image of the square after the reflection.
The original vertices are:
C = (-3, 7)
D = (0, 7)
E = (0, 10)
F = (-3, 10)
Now we apply the reflection, remember that this only changes the sign of the y-component, then the new vertices are:
C' = (-3, -7)
D' = (0, -7)
E' = (0, - 10)
F' = (0, - 10)
Now we need to graph these points and connect them to get the reflected figure, the image can be seen below.
In the equation 2x+4=y, what is the value of y when x=5?
9514 1404 393
Answer:
y = 14
Step-by-step explanation:
Put the value of x where x is and do the arithmetic.
2x + 4 = y
2·5 + 4 = y . . . . . . substitute for x
10 + 4 = y . . . . . . . multiply
14 = y . . . . . . . . . . add
The value of y is 14 when x = 5.
Easy question 34.8 + 6.879 =?
Answer: Easy Answer: 41.679
Step-by-step explanation:
y= 2x + 1
y = -3x +6
Solve the solution to this system of linear equations
(Please help)
Answer:
yeahh, i'm proud of you
Step-by-step explanation:
3. Basket A had 7 times as many plums as basket B at first. Zoe put 58 more plums in each
basket. Now Basket A has three times as many plums as basket B. How many more
plums are there in basket A than basket B now.
Answer:
87 many more plums are there in Basket A than Basket B
Step-by-step explanation:
Before
N = 58/2
Basket A = N x 7 + 58
Basket B = N x 7
Now
Basket A = 29 x 7 + 58
= 261/3
= 87
Basket B = 29 x 7
= 203 + 58
= 261/3
= 87
Basket A and B has a difference of 87 Plums
:) Thank you!!