The dimensions of the circular cylinder of maximum volume inscribed in sphere is r = 20.4 cm , h = 28.86 cm.
What is a sphere ?A sphere is a three dimensional round shaped figure , It has no vertices and the distance form the centre to any point on the sphere is same.
It is given that
A right circular cylinder is inscribed in a sphere
The circular cylinder has the maximum volume
Radius of the sphere is 25 cm.
Dimensions of the cylinder = ?
As it is a right cylinder.
The Pythagoras theorem can be applied
r² + (h/2)² = 25²
r² = 625 - h²/4
volume of the cylinder
= πh(625 - h²/4)
= π(625 h - h³/4)
As the volume is maximum ,
so the derivative of the expression = 0
π(625 - 3h²/4) = 0
so h = 50 /√ 3
so r² = 625 - 2500 / (3 *4 )
r = 20.4 cm
h = 28.86 cm
Therefore the dimensions of the circular cylinder of maximum volume inscribed in a sphere is r = 20.4 cm , h = 28.86 cm.
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which expression is equivalent to 6 to the power of 4 x 6 to the 3rd power
Answer:
6^4 * 6^3
Step-by-step explanation:
How much should you put in an investment paying simple interest rate of 8% if you need 4000 in six months?
The amount you should put is 3846
How to determine the principal amount?The given parameters are:
Amount, A = 4000
Rate, r = 8%
Time = 0.5 year i.e. 6 months
The amount on simple interest is calculated as:
A = P(1 + RT)
This gives
4000 = P * (1 + 8% * 0.5)
Evaluate the product
4000 = P * (1 + 0.04)
Evaluate the sum
4000 = P * (1.04)
Divide both sides by 1.04
P= 3846
Hence, the amount you should put is 3846
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y=x^2 is y a function of x
Round the following items to the nearest £1:
Item
Cost
Cost rounded to nearest £1
Notebook
£2.15
£
Pencil Case
£3.80
£
Colouring Pencil
£1.49
£
Answer:
1. Colouring Pencil 2. Notebook 3. Pencil Case
Step-by-step explanation:
Graph the exponential function g (x) = 4* -1
To do this, plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.
Additionally, give the domain and range of the function using interval notation.
I assume you meant [tex]g(x)=4^x -1[/tex].
The graph is shown in the attached image.
The two points on the graph are (0,0) and (1, 3).The asymptote is y = -1.The domain is [tex](-\infty, \infty)[/tex].The range is [tex](-1, \infty)[/tex].The two points on the graph are (0,0) and (1, 3).
The asymptote is y = -1.
The domain is (-∞,∞)
The range is (-1,∞)
What is an exponential function?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be written as 2 2 2 2=25 for the number 32. This phrase should be understood as "two to the fifth power."
The two points on the graph are (0,0) and (1, 3).
The asymptote is y = -1.
The domain is (-∞,∞)
The range is (-1,∞)
The graph of the function is attached with the answer.
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Can someone help me answer this
Duplicate don't answer!
6 times the sum of a number q and 9
Answer:
6(q + 9)
Step-by-step explanation:
find the magnitude and direction
(WILL GIVE BRANLIEST!!)
The magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.
Resolution of vector A into x and y components
Ax = A cosθ
Ay = A sinθ
Ax = 7.7 x cos(27.8)
Ax = 6.81 m
Ay = 7.7 x sin(27.8)
Ay = 3.59 m
Resolution of vector B into x and y componentsBx = B cosθ
By = B sinθ
θ with respect to x - axis = 90 - 20 = 70⁰
Bx = 16.3 m x cos(70)
Bx = 5.575 m
By = 16.3 m x sin(70)
By = 15.32 m
Sum of vectors in x directionVx = Ax + Bx
Vx = 6.81 m + 5.575 m = 12.385 m
Sum of vectors in y directionVy = Ay + By
Vy = 3.59 m + 15.32 m = 18.91 m
Resultant vectorV = √(Vy² + Vx²)
V = √(18.91² + 12.385²)
V = 22.6 m
Direction of the vectortan θ = Vy/Vx
tan θ = (18.91)/(12.385)
tan θ = 1.527
θ = arc tan (1.527)
θ = 56.8⁰
Thus, the magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.
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Slope is -4/5 and passes through the point (2, -3).
5
Answer:
y = (-4/5)x - 7/5
Step-by-step explanation:
The general equation of the line is slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. You have been given the value of the slope (m = -4/5). To find the y-intercept, use the slope and values from the Point (2,-3) to isolate "b".
y = mx + b <----- Slope-intercept form
y = (-4/5)x + b <------ Plug -4/5 in "m"
-3 = (-4/5)(2) + b <----- Plug in "x" and "y" values from Point
-3 = -8/5 + b <------ Multiply -4/5 and 2
-15/5 = -8/5 + b <----- Assign common denominator
-7/5 = b <----- Add 8/5 to both sides
Now that you have the slope and y-intercept, you can construct the equation.
y = (-4/5)x - 7/5
Which value is a solution to 3y + 4 < 16?
Hello,
3y + 4 < 16
⇔ 3y < 16 - 4
⇔ 3y < 12
⇔ y < 12/3
⇔ y < 4
⇒ S = ] - ∞ ; 4 [
Resuelve la Ecuación 4x-7=1+2x
Answer:x=4
Step-by-step explanation:
tendrías que poner términos similares juntos, asegurándote de cambiar el signo de cualquier figura que cruce el igual al signo. luego restarías o sumarías, resolverías las ecuaciones de cada lado, ya que ahora están agrupadas. luego dividirás tu respuesta por el coeficiente que es 2 (2x). esto te dejaría con 4
4x - 2x = 1+7
4x-2x= 8
2x =8
divisir
x=8
Cost of a CD: $19.95
Markup: 70%
Answer:
$33.915 for the cd
Step-by-step explanation:
70% of 19.95 = 13.965
19.95 + 13.965= 33.91
Which equation can be used to solve the problem? 10 is 50 percent of what number? StartFraction 10 divided by 1 Over 50 divided by 1 EndFraction = StartFraction 10 Over 50 EndFraction StartFraction 100 times 2 Over 50 times 2 EndFraction = StartFraction 200 Over 100 EndFraction StartFraction 10 divided by 2 Over 50 divided by 2 EndFraction = StartFraction 5 Over 25 EndFraction StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction Mark this and return
The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Let x be the number.
According to the problem.
50% of x = 10
x = 10 ÷ 50%
= 10×(50/100)
= (50÷5)/(100÷5) = 10/20
Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
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James has an ice cube tray that makes ice in the shape of spheres rather than cubes. Each sphere of ice has a radius of 2 cm. One tray makes 6 spheres.
What is the total volume of ice the tray can make at one time?
The ice cube tray can make 200.96 cubic centimeters of ice.
How to get the total volume?For a sphere of radius R, the volume is:
[tex]V = \frac{4}{3}*3.14*R^3[/tex]
In this case, we have 6 spheres, each one with a radius of 2cm.
Then the total volume of ice that the ice cube tray can make at one time is:
[tex]volume = 6*V = 6*(\frac{4}{3} *3.14*(2cm)^3) = 200.96cm^3[/tex]
The ice cube tray can make 200.96 cubic centimeters of ice.
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Place the indicated product in the proper location on the grid
(a+b)(a-2b)
The product (a+b)(a-2b) is a^2 - ab - 2b^2
How to evaluate the product?The product expression is given as:
(a+b)(a-2b)
Expand the bracket
a * a - a * 2b + b * a - b * 2b
Evaluate the product
a^2 - 2ab + ab - 2b^2
Evaluate the like terms
a^2 - ab - 2b^2
Hence, the product (a+b)(a-2b) is a^2 - ab - 2b^2
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find the volume of the figure below. pls show solution:)
Answer:
294pi
Step-by-step explanation:
1/3*pi*r^2*h=V
1/3*pi*49*18=V
V=294pi
Consider the given figure. Two right angled triangles R T S, and U T S with their hypotenuse side intersecting at the point Q. The opposite side of both triangle have the same length. Using the SSS congruence criterion, what additional information is needed to show that ΔRST ≅ ΔUTS? A. RT ≅ US B. ∠S ≅ ∠T C. RQ ≅ QS D. ∠R ≅ ∠U\
Two or more triangles are said to be congruent if their length of sides and measure of angles are equal. Thus, the required proof expected in the question is option D. <R ≅ <U
When the length of sides or measure of angles of two or more figures is equal, then we say the figures are congruent.
From the given question, the following can be deduced:
RT ≅ US (given: opposite sides are equal)
and TS is a common side for the two triangles.
<TRS ≅ <RSU (alternate angle property)
<RTS ≅ <UST (right angle property)
<RTU ≅ <SUT (alternate angle property)
Therefore it can be observed that the necessary condition to prove that ΔRST ≅ ΔUTS is option D. <R ≅ <U.
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Answer:
Step-by-step explanation:
Please solve this question
The probability that a randomly selected x-value from the distribution will be in the interval:
P(35 < x < 45) = 0.6827 and,P(30 < x < 40) = 0.47725What is the probability of a normal distribution?The probability of a normal distribution can be determined from the symmetrical curve between 1 to 100%.
From the information given:
Mean = 40Standard deviation = 5To determine the probability that a randomly selected x-value is in the given interval:
P(35<x<45)P(30<x<40)[tex]P(35 < x < 45) = P(\dfrac{35-40}{5} < Z < \dfrac{45-40}{5})[/tex]
[tex]P(35 < x < 45) = P(\dfrac{-5}{5} < Z < \dfrac{5}{5})[/tex]
[tex]P(35 < x < 45) = P(-1 < Z < 1)[/tex]
[tex]\mathbf{P(35 < x < 45) = P[Z\le 1] -P[Z\le -1]}[/tex]
Using normal distribution table:
P(35 < x < 45) = 0.8414 - 0.1587
P(35 < x < 45) = 0.6827
[tex]P(30 < x < 40) = P(\dfrac{30-40}{5} < Z < \dfrac{40-40}{5})[/tex]
[tex]P(30 < x < 40) = P(\dfrac{-10}{5} < Z < \dfrac{0}{5})[/tex]
[tex]P(30 < x < 40) = P(-2 < Z < 0)[/tex]
[tex]\mathbf{P(30 < x < 40) = P[Z\le0]-P[Z\le -2]}[/tex]
Using normal distribution table:
P(30 < x < 40) = 0.5 - 0.02275
P(30 < x < 40) = 0.47725
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The common _____ of two rays that make an angle is called the vertex.
your answer goes here
Answer:
endpoint or straight lines
Step-by-step explanation:
same
what is numrical in math and complex function?
[tex] \sqrt{ - i} [/tex]
Answer:
Step-by-step explanation:
[tex]\sqrt{- i} =\sqrt{(-1)i} =\sqrt{i^2i} =i\sqrt{i}[/tex]
Solve |√2-y| = |y-√2|
Answer:
Step-by-step explanation:
|√2-y|=|y-√2|
√2-y=±(y-√2)
when √2-y=y-√2
y+y=√2+√2
2y=2√2
y=√2
when √2-y=-(y-√2)
√2-y=-y+√2
or 0=0
it gives no value of y.
so only possible value is y=√2
Find integra of xlnxdx
Answer:
[tex]\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
Increase the power by 1, then divide by the new power.
Given indefinite integral:
[tex]\displaystyle \int x \ln x \:\: \text{d}x[/tex]
To integrate the given integral, use Integration by Parts:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]
[tex]\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]
[tex]\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}[/tex]
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Which of the following equations is correctly calculated?
Answer:
d) -8 × 3 = -24
Step-by-step explanation:
a) -18 ÷ 6 = -3
b) 30 ÷ 3 = 10
c) -7 × -7 = 49
d) -8 × 3 = -24
Above from all, option d is done correctly.
Note: when negatives are multiplied together or divided they cancel out to being positive. For example: -1 × -1 = 1
Hello!
Let's solve to verify whether the equations are true.
⇒ -18 ÷ 6 = -3
⇒ Given answer : 3
⇒ Incorrect
⇒ 30 ÷ 3 = 10
⇒ Given answer : -10
⇒ Incorrect
⇒ -7 × -7 = 49
⇒ Given answer = -49
⇒ Incorrect
⇒ -8 × 3 = -24
⇒ Given answer = 24
⇒ Correct
∴ The equation which is correctly calculated is -8 × 3 = -24.
If cos = 3/5 and is in quadrant IV, Sin2=
Using a trigonometric identity, it is found that the sine of the angle is given as follows:
[tex]\sin{\theta} = -\frac{4}{5}[/tex].
Which trigonometric identity relates the sine and the cosine of an angle?Considering an angle [tex]\theta[/tex], the identity is given as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
In this problem, the cosine is given as follows:
[tex]\cos{\theta} = \frac{3}{5}[/tex]
Hence the sine is found as follows:
[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]
[tex]\sin^2{\theta} + \left(\frac{3}{5}\right)^2{\theta} = 1[/tex]
[tex]\sin^2{\theta} + \frac{9}{25} = 1[/tex]
[tex]\sin^2{\theta} = \frac{16}{25}[/tex]
[tex]\sin{\theta} = \pm \sqrt{\frac{16}{25}}[/tex]
In quadrant IV, the sine is negative, hence:
[tex]\sin{\theta} = -\frac{4}{5}[/tex].
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Which equation can be used to solve the problem? 10 is 50 percent of what number? StartFraction 10 divided by 1 Over 50 divided by 1 EndFraction = StartFraction 10 Over 50 EndFraction StartFraction 100 times 2 Over 50 times 2 EndFraction = StartFraction 200 Over 100 EndFraction StartFraction 10 divided by 2 Over 50 divided by 2 EndFraction = StartFraction 5 Over 25 EndFraction StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction Mark this and return
The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Let x be the number.
According to the problem.
50% of x = 10
x = 10 ÷ 50%
= 10×(50/100)
= (50÷5)/(100÷5) = 10/20
Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
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Find the compound amount and the interest earned when the given investment has continuous compounding.
$11,000 at 2.3% for 8 years
The compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
We know the formula for continuous compounding:
[tex]\rm A = P(e)^{rt}[/tex]
[tex]\rm A = 11000(e)^{0.023\times8}[/tex]
A = $13,222.17
I = A - P = 13,222.17 - 11000
I = $2,222.17
Thus, the compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.
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Lynn’s cruise lasted 11 days and 7 hours. Convert the time to hour
Here is conversion chart
1 day=24hr
so the equation to solve this would look like this
(24*11)+7
Therefore the answer is 271 hr
Help me with this question please :)
Explanation:
There are 7 ways to pick the first place position, then 6 ways for second place, 5 for third, and so on. We count down until we get to 1
7,6,5,4,3,2,1
Multiply out those values to get the final answer. On many calculators this can be done using the factorial button, indicated as an exclamation mark
7! = 7*6*5*4*3*2*1 = 5040
Use the function below to find F(-4).
Answer:
D
Step-by-step explanation:
Answer:
1/16
Step-by-step explanation:
To evaluate the function f(-4), we let x =4 in f(x) = [tex]2^{x}[/tex]
f(-4) = [tex]2^{-4}[/tex]
= 1/[tex]2^{4}[/tex]
=1/16
A fair coin is flipped twice. What is the probability of showing heads on both flips?
Answer:
0.25 or 1/4
Step-by-step explanation:
P(coin is flipped as head) = 0.5 or 1/2 (one of 2 sides)
P(coin is flipped as head twice) = P(coin is flipped as head) x P(coin is flipped as head)
= 0.5 x 0.5
= 0.25 or 1/4