5. A sphere and a right circular cylinder have equal volumes. The radius of the sphere equals the radius of the base of the cylinder. Compare the surface area of the sphere with the area of the total surface of the cylinder.
Answers
Given:
The volume of sphere is equal to the volume of cylinder.
The radius of sphere is equal to the radius of the cylinder.
The objective is to compare the surface area of sphere with the total surface area of cylinder.
Explanation:
The general formula of total surfacea area of cylnder is,
\(\begin{gathered} A_C=2\pi r^2+2\pi rh \\ A_C=2\pi r(r+h)\text{ . . . . . . .(1)} \end{gathered}\)SImilarly, the general formula of surface area of sphere is,
\(A_S=4\pi r^2\text{ . . . . . . (2)}\)Now, to compare the surface area of two given shapes, divide equation (2) by (1).
\(\begin{gathered} \frac{A_S}{A_C}=\frac{4\pi r^2_{}}{2\pi r(r+h)} \\ \frac{A_S}{A_C}=\frac{2r}{(r+h)}\text{ . . . . . (3)} \end{gathered}\)To find (h/r):
Since, the volume of sphere is equal to the volume of cylinder,
\(\begin{gathered} \frac{4}{3}\pi r^3=\pi r^2h \\ \frac{4}{3}=\frac{\pi r^2h}{\pi r^3} \\ \frac{4}{3}=\frac{h}{r} \\ r=\frac{3h}{4}\text{ . . . . .(4)} \end{gathered}\)Now, substitute the value of equation (4) in equation (3).
\(\begin{gathered} \frac{A_S}{A_C}=\frac{2(\frac{3h}{4})}{(\frac{3h}{4}+h)} \\ \frac{A_S}{A_C}=\frac{6h}{4(\frac{3h+4h}{4})} \\ \frac{A_S}{A_C}=\frac{6h}{7h} \\ \frac{A_S}{A_C}=\frac{6}{7} \end{gathered}\)Related Questions
I need some help with this problem
Answers
Answer:(-(3x^(3)-x-1))/((x^(2)+1)^(2))
What point lies on the graph y=x2-5
Answers
The point (0, -5) lies on the graph of the quadratic equation y = x² - 5. The shape of the graph is a parabola.
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
The equation y = x² - 5 represents a quadratic equation. A quadratic equation have the shape of a parabola.
When x = 0;
y = 0² - 5
y = -5
The point (0, -5) lies on the graph of y = x² - 5
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The number of free songs downloads is determined using a ratio, when you purchase 40 songs, you get 24
Answers
Answer:
5:3 (simplified)
Step-by-step explanation:
This is a ratio that explains how many free downloads you get when purchasing 40 songs. For every 40 songs you buy, you get 24 songs. Simplify that, and you get 3 free downloads per 5 songs you purchase (5:3).
PLEASE HELP QUICKLY(25 points)!!
Match the description with the correct answer.
(questions)
———————
y-intercept -
slope-
domain-
range-
is this graph increasing, decreasing or both-
x-intercept-
———————
(answer choices)
(4,0), (0,4), (-2,0), (0,-2), +2, -4,
input values, increasing, decreasing,
both increasing and decreasing, output values
———————
please help quickly its worth 10.34 points on my test
Answers
Answer: In that picture the slope is increasing
Step-by-step explanation: positive rise and positive run (uphill from left to right)
April wants to borrow $200 from her father and is willing to pay $9 in Interest. Her father wants to charge an interest rate of 6%. How long can April keep the money?
Answers
Answer:
principle (p)= $200
interest (I) =$9
Rate (R) = 6%
time (T)= ?
we know,
Time(T) = I×100÷P×R
= 9×100÷ 200×6
= 3÷4 years
The figure shown is composed of two cubes.
Which equation shows the surface area
ne figure?
SA = 6(5-5)+6(3-3)-2(3-3)
What is the surface area of
the figure shown?
cm²
3cm
5c
Answers
186 cm³ will be the surface area of the given figure.
To calculate the surface area of the given figure, we need to add the surface area of two cubes and reduce the area of the hidden part.
Thus,
Total surface area = Surface area of bigger cube + surface area of the smaller cube - 2* surface area of the hidden part.
So,
Total surface area = 6*(5*5)+6*(3*3)-2*(3*3)
Total surface area = 150+54-18
Total surface area = 186
Therefore, the surface area of the given figure will be 186 cm³.
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Eric is on diet where he must eat between 1500 and 3000 calories per day.If he already had 750 calories for breakfast, how many can he have the rest of the day?Variable Represents:Inequality:Solve.Sentence:
Answers
Eric has a limit of calories of:
\(1500\leq\text{Eric}\leq300\)The value of calories Eric eats in that day is given by:
\(\text{Eric}=x+750\)Where "x" is the value of the calories he can still eat. The inequality is:
\(1500\leq x+750\leq3000\)To solve it we need to break it into two inequalities.
\(\begin{gathered} x+750\leq3000 \\ x+750\ge1500 \end{gathered}\)We need to solve them individually.
\(\begin{gathered} x+750\leq3000 \\ x\leq3000-750 \\ x\leq2250 \end{gathered}\)\(\begin{gathered} x+750\ge1500 \\ x\ge1500-750 \\ x\ge750 \end{gathered}\)The result is:
\(750\leq x\leq2250\)Eric can eat between 750 and 2250 calories on that day.
Answer: 2240
Step-by-step explanation: 3000-750= 2240
A company makes two products, A and B. Product A requires 12,5 hours of machining time and 30 minutes of finishing time per unit. Product B requires 10 hours of machining time and one hour of finishing time per unit. There are 10000 hours and 600 hours available for machining and finishing respectively. Severe material shortages for the two products will limit their production to a maximum of 700 units for product A and 400 units for product B per day. If x and y are the number of units of product A and B produced per day respectively, choose the system of inequalities that describes the process.
Answers
The system of inequalities that describes the process is 12.5x + 10y ≤ 10000 and 0.5x + y ≤ 600
Inequality
Inequality is an expression that shows the non equal comparison of two or more variables and numbers.
Let x represent the number of products A and y represent the amount of product B, hence:
12.5x + 10y ≤ 10000 (1)
Also:
0.5x + y ≤ 600 (2)
The system of inequalities that describes the process is 12.5x + 10y ≤ 10000 and 0.5x + y ≤ 600
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Holly ate 3 brownies from a pan with nine pieces what two equivalent fractions describe how much she ate?
Answers
An experiment was used to test a new migraine medicine. Each participant took either the new medicine or a placebo
then waited for one hour to see if the headache went away or remained. The results are compiled in the contingency
table below. Use the table to answer the questions.
Went Away| Medicine| Placebo
Remained|. 120. |. 68
18. | 44
Your answers should be exact numerical values.
There were
participants whose headache remained.
The probability of randomly selecting an individual whose headache remained is
There were
participants whose headache remained and took a placebo.
The probability of randomly selecting an individual whose headache remained and took a placebo is
Answers
1) Number of participants whose headache remained is: 62
2) The probability of randomly selecting an individual whose headache remained is: 0.4133
3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933
How to find the probability of random selection?From the table, we have the parameters as:
Number of participants that took medicine and headache went away = 120
Number of participants that took placebo and headache went away = 68
Number of participants that took and headache remained = 18
Number of participants that took placebo and headache remained = 44
1) Number of participants whose headache remained = 18 + 44 = 62
2) The probability of randomly selecting an individual whose headache remained is:
62/(62 + 120 + 68)
= 62/150
= 0.4133
3) The probability of randomly selecting an individual whose headache remained and took a placebo is:
44/150 = 0.2933
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H(p)=p/5 + 15
What is the independent variable in this function
Answers
In the given function H(p) = p/5 + 15, the independent variable is "p" ,
The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.
It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.
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HELP QUICK!!! ANSWER A B C D OR E
Answers
Answer:
It's (E) ..................
Answer:
E
Step-by-step explanation:
Determine the area bounded by the curves f(x) = 4x and g(x) = 3x + 1.
Answers
Answer: 12x^2+4
Step-by-step explanation:
I’m confused !!!!!!!!!!
Answers
Answer:
Ok, so what you have to do is find the range of the number the way you find the range is by writing down the relation. (the relation is the set of the ordered pairs with x and y coordinates). Then you have to list the y-coordinates of the relation. The way to find the range of the relation, you simply have to write down all of the y-coordinates of each ordered pair. Also, make sure to remove any duplicate coordinates so that you only have one of each y-coordinate.
The way you find the ordered pair is by moving a certain amount of steps to the left or right on the x-axis and a certain amount of steps upwards or downwards on the y-axis.
Explanation:
I'm sorry for not giving you the actual range and the ordered pairs for each number but I have to have a graph so I can see and verify an actual answer. I hope that my explanations help you figure out what the answer is! Have a nice day! :)
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help me
Answers
what is the common factors of 4,8,12
Answers
Answer:
the common factors are- 1, 2, 4.
Answer:
1, 2, 4
Step-by-step explanation:
A common factor is a whole number which is a factor of two or more numbers.
Hope it helped!
Is (12 + 12)7 × 37 equivalent to (24 × 3)7?
Answers
Answer:
NO
Step-by-step explanation:
(12+12)7 x 37 (24 x 3)7
(24)7 x 37 (72)7
168 x 37 504
6216 is not equal to 504
so NO
Can I plz have brainliest please
Pedro is solving this number riddle using guess and check. Fourteen less than my number is eleven. What is my number? Which statements about solving the riddle are true? Check all that apply. Less than means subtraction. Subtract 14 from the unknown number to get 11. 14 – 11 = 3 25 – 14 = 11 The unknown number is 25.
Answers
The answer is 1, 2, 4, 5
Have a GREAT day!
(a) Un ángulo mide 47°. ¿Cuál es la medida de su complemento?
(b) Un ángulo mide 149°. ¿Cuál es la medida de su suplemento?
Answers
El supplemento y el complemento de cada ángulo son, respectivamente:
Caso A: m ∠ A' = 43°
Caso B: m ∠ A' = 31°
¿Cómo determinar el complemento y el suplemento de un ángulo?De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:
Ángulo y su complemento
m ∠ A + m ∠ A' = 90°
Ángulo y su suplemento
m ∠ A + m ∠ A' = 90°
Donde:
m ∠ A - Ángulom ∠ A' - Complemento / Suplemento.Ahora procedemos a determinar cada ángulo faltante:
Caso A: Complemento
47° + m ∠ A' = 90°
m ∠ A' = 43°
Caso B: Suplemento
149° + m ∠ A' = 180°
m ∠ A' = 31°
ObservaciónEl enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.
The statement is written in Spanish and its answer is written in the same language.
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What is the slope formula?
Answers
Answer:
(y2-y1)/(x2-x1)
Step-by-step explanation:
The slope is the change in y over the change in x
(y2-y1)/(x2-x1)
where ( x1,y1) and (x2,y2) are two points on the line
Answer:
O A. \(\frac{y2-y1}{x2-x1}\)
Step-by-step explanation:
This is just about how the Slope-Formula works
ok so you get two points off a graph then you use it to plot it in the Slope-Formula like this
for example imma go with (-2, 5) and (3, 7)
I need to subtract 7 - 5 / 3 - -2. so...
m = slope
m = \(\frac{y2-y1}{x2-x1}\)
m = \(\frac{7-5}{3--2}\) Only add the denominators when there's 2 - signs together
m = \(\frac{2}{5}\)
how to differentiate functions
Answers
Answer: see boxed answers below
Step-by-step explanation:
(i) multiply the exponent to the coefficient then subtract 1 from the exponent.
\(y=\dfrac{3}{5x^3}+3x^4+2x^2-20\\\\\\\text{rewrite it as follows}: y=\dfrac{3}{5}x^{-3}+3x^4+2x^2-20x^0\\\\\\y'=(-3)\dfrac{3}{5}x^{-3-1}+(4)3x^{4-1}+(2)2x^{2-1}-(0)20x^{0-1}\\\\\\y'=-\dfrac{9}{5}x^{-4}+12x^3+4x^1-0\\\\\\y'=\large\boxed{-\dfrac{9}{5x^{4}}+12x^3+4x}\)
(ii) Use the division formula: \(y = \dfrac{a}{b}\rightarrow \quad y'=\dfrac{ab'-a'b}{b^2}\)
\(a=5x^3+1\qquad \qquad a'=15x^2\\b=3x^5+4x^2\qquad \quad b'=15x^4+8x\\\\\\y'=\dfrac{(15x^2)(3x^5+4x^2)-(5x^3+1)(15x^4+8x)}{(3x^5+4x^2)^2}\\\\\\.\quad =\dfrac{45x^7+60x^4-75x^7-55x^4-8x}{(3x^5+4x^2)^2}\\\\\\.\quad =\large\boxed{\dfrac{-35x^7+5x^4-8x}{(3x^5+4x^2)^2}}\)
Which of the following statements are true?
Answers
Answer:
D
Step-by-step explanation:
i think it's correct if not I'm sorry
X
What is the multiplicative inverse of 5/6
Answers
The multiplicative inverse of 5/6 as required to be determined in the given task content is 6/5.
What is multiplicative inverse?It follows from the task content that the multiplicative inverse of the given number; 5/6 is required to be determined.
By definition; it follows that the Multiplicative inverse of an expression refers to its reciprocal. It is the value that, when multiplied by the original, give a product of 1 (the multiplicative identity element).
So,
5/6 × 6/5
= 30/30
= 1
Hence, 6/5 is the multiplicative inverse of 5/6
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Triangles ABC and DEF are similar. Find the
perimeter of triangle DEF.
a. 34.7 cm
b. 25.3 cm
c. 15 cm
d. 38 cm
Please show work to help me understand.
Answers
If Both triangles are similar the ratio of sides will be same
\(\\ \sf\longmapsto \dfrac{AB}{AC}=\dfrac{DE}{DF}\)
\(\\ \sf\longmapsto \dfrac{8}{10}=\dfrac{12}{DF}\)
\(\\ \sf\longmapsto 8DF=120\)
\(\\ \sf\longmapsto DF=\dfrac{120}{8}\)
\(\\ \sf\longmapsto DF=15cm\)
Now
\(\\ \sf\longmapsto Perimeter=DF+DE+EF\)
\(\\ \sf\longmapsto Perimeter=15+11+12\)
\(\\ \sf\longmapsto Perimeter=38cm\)
12. Which of the following represents the linear equation 3(x + 2) = 12 - 2y in standard \ A|y=-3/2x+3 [B] y = 3/2x-3 3x - 2y = 10 D 3x + 2y = 6
Answers
Answer: The answer is D. 3x+2y=6, please mark me as brainliest, I want my brainliest back and I want very helpful for good!!!
Step-by-step explanation:
x^4+2x^3-12x^2+14x-5 > 0
Answers
The value of x is (-∞, -5) ∪ (1, ∞).
Given is a polynomial, \(x^4+2x^3-12x^2+14x-5 > 0\),
Solving for x,
Factors =
\(x^4+2x^3-12x^2+14x-5\\ \\= \quad \left(x-1\right)^3\left(x+5\right)\)
Therefore,
\(\left(x-1\right)^3\left(x+5\right) > 0\)
\(x < -5\quad \mathrm{or}\quad \:x > 1\)
Hence the value of x is (-∞, -5) ∪ (1, ∞).
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someone help me pls
Answers
Step-by-step explanation:
this is to be helpful for you
What is the length of x?
Answers
Answer:
25
Step-by-step explanation:
a2+b2=c2
3^2+4^2=c^2
9+16=25
25^2=625
Sqrt of 625 = 25
Answer:
x = 5
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² = 4² + 3² = 16 + 9 = 25 ( take the square root of both sides )
x = \(\sqrt{25}\) = 5
why do the hands on the clock form an angle?
Answers
Answer:
The entire clock measures 360 degrees. As the clock is divided into 12 sections. The distance between each number is equivalent to 30 degrees (360/12)
I hope this helps you!
Use the original price and the markup to find the retail price.
Original price: $60; Markup: 20%
Answers
Answer:
$72 would be the retail price
Step-by-step explanation: