Answer:
Para un vaso de [tex]V = 25\pi\,cm^{3}[/tex], las dimensiones del vaso son [tex]r \approx 2.321\,cm[/tex] y [tex]h \approx 4.642\,cm[/tex].
Para un vaso de [tex]V = 1000\,cm^{3}[/tex], las dimensiones del vaso son [tex]r \approx 5.419\,cm[/tex] y [tex]h \approx 10.839\,cm[/tex].
Step-by-step explanation:
El vaso se puede modelar como un cilindro recto. El enunciado pregunta por las dimensiones del vaso tal que su área superficial ([tex]A_{s}[/tex]), en centímetros cuadrados, sea mínima para el volumen dado ([tex]V[/tex]), en centímetros cúbicos. Las ecuaciones de volumen y área superficial son, respectivamente:
[tex]V = \pi\cdot r^{2}\cdot h[/tex] (1)
[tex]A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r\cdot h[/tex] (2)
De (1):
[tex]h = \frac{V}{\pi\cdot r^{2}}[/tex]
En (2):
[tex]A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot \left(\frac{V}{\pi\cdot r} \right)[/tex]
[tex]A_{s} = 2\cdot \left(\pi\cdot r^{2}+V\cdot r^{-1} \right)[/tex]
Asumamos que [tex]V[/tex] es constante, la primera y segunda derivadas de la función son, respectivamente:
[tex]A'_{s} = 2\cdot (2\pi\cdot r -V\cdot r^{-2})[/tex]
[tex]A'_{s} = 4\pi\cdot r - 2\cdot V\cdot r^{-2}[/tex] (3)
[tex]A''_{s} = 4\pi + 4\cdot V \cdot r^{-3}[/tex] (4)
Si igualamos [tex]A'_{s}[/tex] a cero, entonces hallamos los siguientes puntos críticos:
[tex]4\pi\cdot r - 2\cdot V\cdot r^{-2} = 0[/tex]
[tex]4\pi\cdot r = 2\cdot V\cdot r^{-2}[/tex]
[tex]4\pi\cdot r^{3} = 2\cdot V[/tex]
[tex]r^{3} = \frac{V}{2\pi}[/tex]
[tex]r = \sqrt[3]{\frac{V}{2\pi} }[/tex] (5)
Ahora, si aplicamos este valor a (4), tenemos que:
[tex]A_{s}'' = 4\pi + \frac{4\cdot V}{\frac{V}{2\pi} }[/tex]
[tex]A''_{s} = 4\pi + 8\pi[/tex]
[tex]A_{s}'' = 12\pi[/tex] (6)
De acuerdo con este resultado, el valor crítico está asociado al área superficial mínima. Ahora, la altura se calcula a partir de (5) y (1):
[tex]h = \frac{V}{\pi\cdot \left(\frac{V}{2\pi} \right)^{2/3} }[/tex]
[tex]h = \frac{2^{2/3}\cdot \pi^{2/3}\cdot V}{\pi\cdot V^{2/3}}[/tex]
[tex]h = \frac{2^{2/3}\cdot V^{1/3}}{\pi^{1/3}}[/tex]
Si [tex]V = 25\pi\,cm^{3}[/tex], entonces las dimensiones del vaso son:
[tex]r = \sqrt[3]{\frac{25\pi\,cm^{3}}{2\pi} }[/tex]
[tex]r \approx 2.321\,cm[/tex]
[tex]h = \frac{2^{2/3}\cdot (25\pi\,cm^{3})^{1/3}}{\pi^{1/3}}[/tex]
[tex]h \approx 4.642\,cm[/tex]
Un litro equivale a 1000 centímetros cúbicos, las dimensiones del vaso son:
[tex]r = \sqrt[3]{\frac{1000\,cm^{3}}{2\pi} }[/tex]
[tex]r \approx 5.419\,cm[/tex]
[tex]h = \frac{2^{2/3}\cdot (1000\,cm^{3})^{1/3}}{\pi^{1/3}}[/tex]
[tex]h \approx 10.839\,cm[/tex]
what is 24.65 cubed?
Answer:
14,977.8946
Step-by-step explanation:
please help will give brainliest
Answer:
B
Step-by-step explanation:
In ΔQRS, the measure of ∠S=90°, SR = 7, QS = 24, and RQ = 25. What is the value of the tangent of ∠Q to the nearest hundredth?
Answer:tanQ=
adjacent
opposite
=
24
7
≈0.2917≈0.29
Step-by-step explanation:
trust me bro
The value of the tangent of ∠Q is 0.96.
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
We have,
∠S=90°, SR = 7, QS = 24, and RQ = 25.
Using Trigonometry
tan Q = P/ B
tan Q= 24/ 25
tan Q = 0.96
Thus, the value of tan Q is 0.96.
Learn more about Trigonometry here:
https://brainly.com/question/29002217
#SPJ2
prove that √3cosec20° - sec20° = 4
Answer:
LHS,
√3cosec20°-sec20°hope it helps.
stay safe healthy and happy.PLEASE ANSWER IMMEDIATELY!!!
Answer:
w
Step-by-step explanation:
The inputs (x) have the different variables in order for it to be a function.
Find the sum of the geometric series if n=6, r= 1/4, a = 2.
Sn = a(1-r^n)/(1-r)
Sn= 8(1-1/4096)/3= 2.67
green foods purchases packages of noodles by the carton. each carton contains 36 packages and costs $43.20. green foods sells the noodles for $2.29 per package. what is the markup per carton?
Answer:
91% markup
Step-by-step explanation:
$43.20 divided by 36 is $1.20 per package
if Green Foods is selling one package for $2.29 then they are marking each package up by $1.19
if you take the difference of the per carton prices (82.44-43.20) and divide it by 43.20, you get a 91% markup
Help me ask me if you want brainly
Answer:
the answer is a!
Step-by-step explanation:
if f(x)=5x-12, what is f(2)
Answer:
f
−
1
(
x
)
=
x
−
12
5
Step-by-step explanation:
Х
Leila is buying a dinosaur model. The price of the model is 2 dollars, and she also has to pay a 7% tax
Which of the following expressions could represent how much Leila pays in total for the model?
Choose 2 answers:
107
1
100
B
0.70 + 2
1.07.2
D
7
+ 1
10
1.72
Answer: 107/100x
1.07x
Step-by-step explanation:
Since the price of the model is x dollars, and she also has to pay a 7% tax, the amount that Leila will pay in total for the model will be the addition of the price of the model and the tax. This will be:
= x + (7% × x)
= x + (7/100 × x)
= x + (0.07 × x)
= x + 0.07x
= 1.07x
This can also be 107/100x
4.
x-10
= 30
12
Solve for x.
Answer:
40-10=30
Step-by-step explanation:
x-10=30
we are going to flip the problem which would make it addition so you would do 10+30=X and we can fill in the blank of x equalling 40 because 10+30 is 40
Answer:
x = 40
Step-by-step explanation:
x - 10 = 30
=> x = 30 + 10
=> x = 40
(Click the picture to see math question) please help I’ll mark brainliest
Answer:
g(x) = f(x + 2)
Step-by-step explanation:
The x value has been translated by 2
Feel free to mark it as brainliest :D
find the radius of a circle
if the circumference is 66cm
Answer:
10.5
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the side length of the base is 14.7 and the height of the pyramid is 17.2 in. Round your answer to the nearest tenth of a cubic inch.
Answer: 1238.916
Step-by-step explanation:
A = (Bh)/3
B = 14.7 x 14.7
The area of a pyramid is the formula at the top. B in the formula at the top is the Base. The reason it is capitalized is because B is also a formula. You need to find the area of the base of the pyramid and plug it into the equation. It this case, the base is equal to the second equation above.
Match each expression to its equivalent expression
Answer:
Step-by-step explanation:
first: x+(1/4)
second: (-1/3 )x +1/4
third: (3/4)x +1/3
Solve each equation over the interval [0°, 360°). If a decimal approximation is necessary, round to four decimal places. cos 2x -cos x-2 = 0
Answer:earthy
Step-by-step explanation:vuinh
Could u have this for me please it's a laser sub
Answer:
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ slope = \frac{10 - 5}{20 - 15} \\ = \frac{5}{5} \\ = 1[/tex]
Use the net to find the lateral area of the prism. 15 m 3 m 6 m 3 m 6 m
Answer:
270 m²
Step-by-step explanation:
LA = (3+6+3+6)×15
= 18×15 = 270 m²
Which expression has the same value as the one below? 87 + (-12)
Answer:
75
Step-by-step explanation:
Given data
First term= 87
Second term= -12
Hence,
87 + (-12)
open bracket
+*-= -
= 87 -12
=75
Therefore the equivalent is 75
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x=28.8
Step-by-step explanation:
using cosine
cos x= adjacent/hypotenuse
cos x = 71/81
cos x = 0.8765
make x subject of the formula
x= cos^-1 0.8765
x= 28.77699973
x≈ 28.8
The required value of x is 28.8 degrees for the right triangle.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
The right triangle is given in the question, as shown
We have to determine the value of x for the triangle.
As we know the cosine ratio is:
cos x = adjacent/hypotenuse
As per the question, substitute the known values in the above ratio,
cos x = 71/81
Apply the division operation,
cos x = 0.8765
Solve for x, and we get
x= cos⁻¹ (0.8765)
x = 28.77699973
x ≈ 28.8
Thus, the required value of x is 28.8 degrees.
Learn more about the right triangle here:
brainly.com/question/6322314
#SPJ2
A circle fits inside a semi-circle with the diameter of 24mm.
Cauculate the shaded area.
Sorry I could not get the image
Answer:
Area of shaded part = 113 mm² (Approx.)
Step-by-step explanation:
Given:
Diameter of Semi-circle = 24 mm
Find:
Area of shaded part
Computation:
Radius of semi-cicrle = Diameter of Semi-circle / 2
Radius of semi-cicrle = 24 / 2
Radius of semi-cicrle = 12 mm
So,
Radius of small circle = 12 / 2
Radius of small circle = 6 mm
Area of shaded part = Area of semi circle - Area of small circle
Area of shaded part = [πR² / 2] - [πr²]
Area of shaded part = [(3.14)(12)² / 2] - [(3.14)(6)²]
Area of shaded part = [(3.14)(144) / 2] - [(3.14)(36)]
Area of shaded part = 226.08 - 113.04
Area of shaded part = 113.04
Area of shaded part = 113 mm² (Approx.)
Ahmad deposits $3000 into an account that pays simple interest at a rate of 3% per year. How much interest will he be paid in the first 4 years?
Answer:
.......
Step-by-step explanation:
Jahlan, simple interest means that interest is paid every year on the original $4000.
To find 2% of 4000, you multiply 4000(.02) = $80.
Since the interest is the same, 3(80) = $240.
Which equation is true for the value a=7
A. a+2(a-3)= 15
B. 4a-4(14)-a=24
C. 2a+47=105
D.3a+2(a-3)=34
E. 4a-2a=18
Answer:
The answer is just re look at the question A
Answer
THE ANSWER IS A
Step-by-step explanation:
Need 3 and 4 for those who are up to the task
Answer:
x = 18.4
y = 35º
Step-by-step explanation:
cos∅ = adj/hyp
cos49 = x/28
28cos49 = x
x = 18.4
tany = opp/adj
tany = 19/27
y = arctan19/27
y = 35º
can I get some help with these please...
Answer: b d a
Step-by-step explanation:
B
D
A
Find the area of following rhombuses. Round your answers to the nearest tenth if
necessary.
Answer:
[tex]Area =55.4ft^2[/tex]
Step-by-step explanation:
Given
The attached rhombus
Required
The area
First, calculate the length of half the vertical diagonal (x).
Length x is represented as the adjacent to 60 degrees
So, we have:
[tex]\tan(60) = \frac{4\sqrt 3}{x}[/tex]
Solve for x
[tex]x = \frac{4\sqrt 3}{\tan(60)}[/tex]
[tex]\tan(60) = \sqrt 3[/tex]
So:
[tex]x = \frac{4\sqrt 3}{\sqrt 3}[/tex]
[tex]x = 4[/tex]
At this point, we have established that the rhombus is made up 4 triangles of the following dimensions
[tex]Base = 4\sqrt 3[/tex]
[tex]Height = 4[/tex]
So, the area of the rhombus is 4 times the area of 1 triangle
[tex]Area = 4 * \frac{1}{2} * Base * Height[/tex]
[tex]Area = 4 * \frac{1}{2} * 4\sqrt 3 * 4[/tex]
[tex]Area =2 * 4\sqrt 3 * 4[/tex]
[tex]Area =55.4ft^2[/tex]
What are the steps to multiplying a decimal times a decimal?
Solve for y: 3y - x = a
A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than
12
centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of
76
bolts. The sample mean bolt length was
12.07
centimeters. The population standard deviation is known to be
σ
=
0.28
centimeters.
What is the test statistic
z
?
What is the
p
-value?
Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of
α
=
0.1
?
Answer:i dont know
Step-by-step explanation:
how to find the vat on 14% of 1800
Answer:
[tex]14 \ 100 \1800[/tex]