Answer:
5 units
Step-by-step explanation:
The volume of the cylinder is the area of the circle multiplied by it's height. Therefore, the volume of the cylinder is πr² × h, which when simplified, gives us πr²h. Let's substitute the volume and the radius in the formula to find the height.
⇒ πr²h = Volume of cylinder
⇒ (π)(3²)(h) = 45π
Now, simplify the equation to evaluate the area of the cylinder.
⇒ (π)(3²)(h)/(3²)(π) = 45π/(3²)(π)
⇒ (h) = 45π/(9)(π) = 45/(9) = 5 units
You have a cup of lemonade. Each ice cube has a length of 2 cm, a width of 1 1/4 cm and a height of 3 cm. What is the volume of one of the ice cubes? Show your steps and Explain how you used math to come to your decision. / 100 points if you answer and ill give you brianliest and 5 stars\
So
Volume:-
[tex]\\ \rm\rightarrowtail LBH[/tex]
[tex]\\ \rm\rightarrowtail 2(5/4)(3)[/tex]
[tex]\\ \rm\rightarrowtail 5/2(3)[/tex]
[tex]\\ \rm\rightarrowtail 15/2[/tex]
[tex]\\ \rm\rightarrowtail 7.5cm^3[/tex]
You fill the entire fish tank with water. Then you dump out some of the water. The volume of the water in the tank decreases by 96 cubic inches. How deep is the water now? (The height is 12 inches, the base is 48)
Answer:
1. 6/10 – 2/5 =
Ans: 2/10, which can be reduced to 1/5.
2. If a tank is 5/8 filled with solution, how much of the tank is empty?
Ans: 3/8 of the tank is empty. Since the whole tank would equal 8/8, or 1, and 5/8 of it is filled, then that
means 3/8 of it remains empty.
3. 1/2 x 3/5 x2/3 =
Ans: 6/30, which can be reduced to 1/5.
4. 5/9 ÷ 4/11 =
Ans: 55/36. You cannot reduce this fraction any further.
5. Convert 27/4 to a decimal.
Ans: 6.75. This answer is arrived at by dividing 4 into 27.
6. Convert 0.45 to a fraction.
Ans: 45/100, which can be reduced to 9/20.
7. 4.27 x 1.6 =
Ans: 6.832
8. 6.5 ÷ 0.8 =
Ans: 8.125
9. 12 + 4.52 + 245.621 =
Ans: 262.141
Step-by-step explanation:
I hope this helps
need it ASAP If a graph shows intersecting lines that represent a system of equations, how many solutions does that system of equations have?
Infinite solutions
No solution
Two solutions
One solution
Answer: Well, the answer really depends. But here are a few ways you can figure this out.
Step-by-step explanation:
If the two lines intersect once, then they have one solution.
If they intersect twice there are two solutions
If the lines never intersect, there are no solutions
And if the lines are identical, meaning that their equation is exactly the same. There are infinite solutions.
A solution with systems of equations is determined by the point of intersection. Your answer is the point of intersection
I hope this is helpful! : )
Answer:
no s
Step-by-step explanation:
Pls help asap I need step by step pls I’ll give brainliest
Answer:
it would be 12
Step-by-step explanation:
Answer:
area = 100 inches^2
Step-by-step explanation:
width = x
length = 4x
x + x + 4x + 4x = 50
10x = 50
x = 5
width = 5
length = 4 × 5 = 20
area = length x width
= 20 x 5 = 100
Please help me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: A is (arithmetic sequence)
and D is 1 2 3 4 5 6 7
Unfortunately, I only know the answer to those two.
Sorry.
Write a congruence statement for the pair of triangles shown.
Answer:
Triangle UTS is congruent to Triangle RST.
Step-by-step explanation:
When stating congruence, the corresponding angles and sides must be listed in order. In triangle uts, based on the points, the angle is U, and the side is US. This means that for the other triangle, the first point needs to be the angle, and the last one needs to be the other point for the side. This gives us Triangle UTS is congruent to triangle RST. Hope this helps!
If y = sin(x)
Prove that dy/dx = y cot(x)
[tex]y=sin(x)\implies \cfrac{dy}{dx}=\boxed{cos(x)} \\\\[-0.35em] ~\dotfill\\\\ ycot(x)\implies \stackrel{y}{~~\begin{matrix} sin(x) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cfrac{cos(x)}{~~\begin{matrix} sin(x) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \boxed{cos(x)}[/tex]
1. What is the center of dilation used to dilate quadrilateral WXYZ to quadrilateral W'X'Y'Z'?
Answer:
The answer that makes sence to me is C (-3, 4)
Step-by-step explanation:
work out
3/7 + 9/11
Give your answer as an improper fraction
Answer:
60/77 the answer is not able to be an improper fraction
Step-by-step explanation:
3/7+9/11
33/77+27/77
60/77
divide the sum of 39 and product of 18 and 6 by the difference of 50 and 14
Answer:
the imino acid found in protein strcjure
PLEASE HELP W PRECALC QUESTION
Answer: [tex]2tan(theta)[/tex]
Step-by-step explanation:
I know this is pre-calculus, but I want to let you know what this is actually used for in real calculus. This is a method of integration called "u-substitution" which tranforms the function of 'x' into a function of 'theta'. If we allow the value of 'x' to equal 2sec(theta), we can plug this into the function to get:
[tex]\sqrt{x^2-4} =\sqrt{(2sec(theta)^2-4} =\sqrt{4sec^2(theta)-4}[/tex]
Factor out a 4 to get:
[tex]\sqrt{4(sec^2(theta)-1)}[/tex]
Take the square root of 4 to get a 2 on the outside of the radical:
[tex]\sqrt{4(sec^2(theta)-1)}=2\sqrt{sec^2(theta)-1}[/tex]
Use the trig identity below to convert the secant to tangent:
[tex]tan^2(theta)+1=sec^2(theta)[/tex]
[tex]tan^2(theta)=sec^2(theta)-1[/tex]
Therefore our expression becomes:
[tex]2\sqrt{sec^2(theta)-1}=2\sqrt{tan^2(theta)}[/tex]
The square root of tangent is simply tangent:
[tex]2\sqrt{tan^2(theta)} =2tan(theta)[/tex]
Find the square number
5
8
15
30
36
Hello ! Here's a calculus question!
Find that value of
[tex]\\ \rm\Rrightarrow {\displaystyle{\int\limits_{\pi}^{2\pi}}}\dfrac{sin^6x+cos^6x}{sin^3xcos^3x}[/tex]
Note:-
Answer must include all steps properly .
Kindly don't waste time here if you don't know the answer .
All the best !
Answer:
Undefined.
Formula's used:
[tex]\longrightarrow \bold{sec(x) = \dfrac{1}{cos(x)} }[/tex]
[tex]\longrightarrow \bold{cosec(x) = \dfrac{1}{sin(x)} }[/tex]
[tex]\longrightarrow \bold{cot(x) = \dfrac{1}{tan(x)} }[/tex]
[tex]\longrightarrow \bold{tan(x) = \dfrac{sinx}{cos(x)} }[/tex]
[tex]\longrightarrow \bold{sin^2x + cos^2 x = 1 }[/tex]
[tex]\longrightarrow \sf \bold{Sum \ Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx}[/tex]
[tex]\longrightarrow \bold{ \int \:{sec^2(ax+b) = \dfrac{1}{a}tan(ax+b)+c }}[/tex]
[tex]\longrightarrow \bold{\int \:\dfrac{1}{ax+b} =\dfrac{1}{a} ln|ax+b|+c}[/tex]
Explanation:
[tex]\sf \Longrightarrow \int _{\pi }^{2\pi }\:\dfrac{sin^6(x)+cos^6(x)}{sin^3(x) \ * \ cos^3\left(x)}[/tex]
[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)} +\dfrac{cos^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)}[/tex]
[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^3\left(x\right)}{\:cos^3\left(x\right)} +\dfrac{cos^3\left(x\right)}{sin^3\left(x\right)}[/tex]
[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\ tan^3(x)+ cot^3(x)[/tex]
[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi } \tan ^3(x)dx+\int _{\pi }^{2\pi } \cot ^3 (x)dx[/tex]
[tex]\Longrightarrow \sf \bold{ [ }-\ln |\sec \left(x\right) |+\dfrac{\sec ^2(x)}{2}-\dfrac{\cot ^2 (x)}{2}-\ln |\sin(x)| \bold{ ] }^{2\pi }_\pi[/tex]
apply limits
[tex]\sf \Longrightarrow \sf -\ln \left|\sec \left(2\pi \right)\right|+\dfrac{\sec ^2\left(2\pi\right)}{2}-\dfrac{\cot ^2\left(2\pi\right)}{2}-\ln \left|\sin \left(2\pi\right)\right|-(-\ln \left|\sec \left(\pi \right)\right|+\dfrac{\sec ^2\left(\pi\right)}{2}-\dfrac{\cot ^2\left(\pi\right)}{2}-\ln \left|\sin \left(\pi\right)\right|)[/tex]
simplify using trigonometric basic functions
[tex]\Longrightarrow \sf -\ln \left|\dfrac{1}{\cos \left(2\pi \right)}\right|+\dfrac{\left(\dfrac{1}{\cos \left(2\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(2\pi \right)}{2}-\ln \left|\sin \left(2\pi \right)\right|- ( -\ln \left|\dfrac{1}{\cos \left(\pi \right)}\right|+\dfrac{\left(\frac{1}{\cos \left(\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(\pi \right)}{2}-\ln \left|\sin \left(\pi \right)\right|)[/tex]
The value of cot(2π) is not defined. [ cot(2π) = ∞ ]⇒ Undefined
Answer:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \boxed{\text{un} \text{de} \text{f}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationIntegration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Methods: U-Substitution + U-Solve
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite:
Step 3: Integrate Pt. 2
Step 4: Integrate Pt. 3
Identify variables for u-solve.
1st Integral
Set u:2nd Integral
Set v:Step 5: Integrate Pt. 4
[Integrals] Apply Integration Method [U-Solve]:∴ we have found the value of the given integral.
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Learn more about integration: https://brainly.com/question/14413972
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
name the two operations used for converting weight measurement
Answer:
grams and kilograms it got delted for some reason
Step-by-step explanation:
what us the circumference of circular ground of diameter d m ? find it.
answer:
[tex]\pi d \: m[/tex]
can you explain me how?
Here the diameter = dm
Formula of circumference for circle: 2πr or πd
where "d" is diameter and "r" is radius
diameter = 2(radius)For this question:
circumference:
π(d)π(dm)πdmYour friend leaves your house. She later calls you on her cell phone, saying that she's been driving at 60 miles an hour directly away from you the whole time and is now 60 miles away. How long has she been gone?
Answer: 1hr
Step-by-step explanation: Distance = speed × time
Time = Distance / Speed = 60/60
help me find the area please
Answer:
I'm not a hundred percent sure how to answer this one, because you need the height to solve but the other two tick marks would also be twenty because all of the sides are equal to one another.
In which quadrant is the point (4, -5)? II I IV III
Answer:
Quadrant IV
Step-by-step explanation:
You can easily find in which quadrant a point lies using this key :
Quadrant I = (+ , +)Quadrant II = (- , +)Quadrant III = (-, -)Quadrant IV = (+, -)We have the coordinate (4, -5)
x-coordinate is positivey-coordinate is negativeIt lies in Quadrant IVAnswer:
Quadrant IV
Step-by-step explanation:
The Cartesian plane is divided into 4 quadrants.
Quadrant I is the top right quadrant, where x and y are positive.
We then move in a counterclockwise direction for quadrants II, III and IV.
Therefore:
Quadrant I: (x, y)Quadrant II: (-x, y)Quadrant III: (-x, -y)Quadrant IV: (x, -y)As point (4, -5) has a positive x-value and a negative y-value, it will lie in Quadrant IV
Xavier opened a savings account with a deposit of $12,000. the account earned simple interest. he did not make any additional deposits or withdrawals. at the end of 3 years, the account balance was $12,324. what is the annual interest rate on this account? question 5 options: 0.9% 1.8% 2.7% 3.6%
Answer:
0.9%
Step-by-step explanation:
I took the test
Twice a number added to their half of itself equals 20 find the number
Answer:
[tex]x(2) + 5\\[/tex]
The number is 8 because [tex]8 * 2 = 16[/tex]
And if you add 4, you get 20
Hence, the number is 8
Answer:
8
Step-by-step explanation:
let the number be x
=> 2x+(x/2) = 20
=> 4x+x/2 = 20
=> 5x/2 = 20
=> 5x = 20*2
=> 5x = 40
=> x = 40/5
=> x = 8
can i get brainliest
Give full working and explanation
And I reward you with stars.
Answer this easy question ;-)
Answer:
1309 marbles
Step-by-step explanation:
Kadon has 727 marbles.Simon has: 727 - 145 = 582 marblesAll together:
Kadon marbles + Simon marbles727 marbles + 582 marbles1309 marbles
An event has a probability of 2/7. How would you best describe the likelihood of this event? (Hint: Change it to a decimal)
A. Impossible
B. Less likely
C. Equally likely
D. More likely
E. Certain
Answer:
Less Likely
Step-by-step explanation:
A 2/7 probability means that it will happen less than half the time.
The eliminates equally likely, more likely, and certain as those are 50% or greater.
The probability is also greater than 0%, so it's not "impossible"
Therefore, the answer must be B, Less Likely.
It happens less than half the time, but can at times happen.
Hope this helps!
The solution is, Less Likely, best describe the likelihood of this event.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
An event has a probability of 2/7.
now, we get,
A 2/7 probability means that it will happen less than half the time.
The eliminates equally likely, more likely, and certain as those are 50% or greater.
The probability is also greater than 0%, so it's not "impossible"
It happens less than half the time, but can at times happen.
Therefore, the answer must be B, Less Likely.
To learn more on probability click:
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Jina makes eight dollars for each hour of work. Write an equation to represent her total pay ‘p’ after working ‘h’ hours
Answer:
p = 8h
Step-by-step explanation:
Simple math my guy
Answer:
p=8h
Step-by-step explanation:
For each hour, she gets paid $8. So the total pay would be the number of hours multiplied by 8.
which type of function describes her total savings after m months and why?
Answer:
A.
Step-by-step explanation:
I would advise finding the difference between 300 and 200 and 450 and 300:
[tex]300-200=100\\450-300=150[/tex]
We can eliminate C and D since she saves 100 the first month and 150 the second month.
The next step would be to find the increase every month:
[tex]\frac{Final value}{initial value}=x\\\\\frac{300}{200}=1.5 \\\\\frac{450}{300} = 1.5[/tex]
If we would write the increase as a function, we would get:
[tex]y= 1.5x[/tex]
we can check this by substituting values:
[tex]y=1.5*200\\y=300\\\\\\y=1.5*300\\y=450[/tex]
An exponential function looks like this:
[tex]y= a^x[/tex]
A linear function looks like this:
[tex]y=mx+b[/tex]
Our m is 1.5, a linear increase by 150% and our b is 0, which can be written like:
[tex]y=1.5x+0\\y=1.5x[/tex]
Therefore our function resembles a linear function more than an exponential function, eliminating answer B.
help me!
[tex]\frac{x}{3}+10=\frac{3x-8}{2}[/tex]
Answer:
[tex] \frac{x}{3} + 10 = \frac{3x - 8}{2} \\ \\ \frac{3x - 8}{2} - \frac{x}{3} = 10 \\ \\ taking \: lcm \\ \\ \frac{9x - 24 - 2x}{6} = 10 \\ \\ 9x - 24 - 2x = 60 \\ \\ 7x = 60 + 24 \\ \\ 7x = 84 \\ \\ x = \cancel\frac{84}{7} \\ \\\fbox{ x = 12}[/tex]
hope helpful ~
Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
[tex] \frac{x + 30}{3} = \frac{3x - 8}{2} [/tex]
[tex]2x + 60 = 9x - 24[/tex]
[tex]60 + 24 = 9x - 2x[/tex]
[tex]84 = 7x[/tex]
[tex]x = 12[/tex]
I hope it will be helpful
CHOOSING BRAINLIEST PLEASE HELP
Answer:
The answer is the 2nd 1
Step-by-step explanation:
It's a basic graph
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
There are two mystery numbers. The sum of 10 times the first number and 5 times the second number is -15. The sum of 6 times the first number and 2 times the second number is -10. What are the two numbers? please explain
Answer:
-2 and 1
Step-by-step explanation:
The two "mystery numbers" are described by two relations. We can assign variables to those numbers, and write a system of equations that express the given relations.
__
Let x and y represent the first and second mystery numbers, respectively. The first relation tells us ...
10x +5y = -15
The second relation tells us ...
6x +2y = -10
We can reduce both of these equations to lowest terms by factoring out the common factor of 5 from the first one and 2 from the second one:
2x +y = -33x +y = -5__
We are told to solve this using elimination. We can eliminate the y-variable by subtracting the first equation from the second:
(3x +y) -(2x +y) = (-5) -(-3)
x = -2 . . . . . . . . . . simplify
2(-2) +y = -3 . . . . substitute for y
y = 1 . . . . . . . . . . add 4
The two numbers are -2 and 1.
find the missing number?
IF
3+4 = 19
4+5 = 29
5+ 6=41
1+9 = 19
then 1+3= ?
please help me if you know the answer
Roger has a rope that is 3 feet long.He needs to cut it into 12 equal length pieces.How many feet loń should each piece of the rope be?
Answer:
0.25
Step-by-step explanation:
3/12 is 0.25
3 divided by 12 when simplified or reduced
The fraction 3/12 is equal to the exact decimal number.
Can someone help me understand on how to simplify this ?
Answer:
So first you have to make all the denominaters (bottom #s) the same so we would get 12/20-8/20+5/20 and you would solve this to equal 9/20 and to divide it by 1/6 would equal 2 7/10.
Hope this helps! (pls read the comment for free gift cards)