Answer:
Step-by-step explanation:
(a²-2ab+b²)=(a-b)²
a²+2ab+b²=(a+b)²
i solve b and d
(b)
9x²-36x+36=0
(3x)²+2×3x×-6+(-6)²=(3x-6)²
(d)
a²-b²=(a+b)(a-b)
4x²-81=0
4x²-81=(2x)²-9²=(2x+9)(2x-9)
The Ferris wheel shown makes 14 revolutions per ride. How far would someone travel during one ride? Round your final answer to the nearest whole number. Use 3.14 for π.
diameter 67 feet
Someone would travel about
feet during one ride on the Ferris wheel.
Answer:
2,945 feet
Step-by-step explanation:
Find the circumference.
C = dπ
C = 67(3.14)
C = 210.38
Since there are 14 revolutions, multiply the circumference by 14.
210.38 x 14 = 2945.32
Round
2,945
Hello, can u help me out please i will give brainlist :)
Answer:
$5.75
Step-by-step explanation:
Find the difference between the weeks as this will give you the difference hence the amount deposited each week
0->1
is 12.00->17.75
diffrence is $5.75
1->2
is 17.75->23.50
diffrence is $5.75
the amount saved each week is $5.75
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
Learn more about calculus: https://brainly.com/question/20197752
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
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:
A tank in the shape of a hemisphere has a radius of 3 feet. If the liquid that fills the tank has a density of 88.2 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
4988 pounds
Step-by-step explanation:
Volume of Hemisphere
4/3 x π x r^3 = 4/3 x 3^3 x π = 4/3 x 27π = 36π = Volume of Sphere
To calculate volume of Hemisphere = 36π / 2 = 18π foot^3
Weight of the liquid
88.2 pounds / foot^3 means that every cubic foot weighs 88.2 pounds so
88.2 pounds x 18π = 4987.5925 which to the nearest pound = 4988 pounds.
i do not know this answer
Answer:
9 millimeters is the answer.
Find the value of x. (25 points!)
Answer:
22.5
Step-by-step explanation:
By the angle bisectors theorem,
30/32 = x/24
x=24(30/32) =22.5
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:
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]
Which answer choice correctly represents 0.4121212…?
A. 0.412
B.
C.
D.
the on with the line over the 2 only
Step-by-step explanation:
Find the solution set of the inequality
4.7 -1 <11.
Answer:
4x-1<11
4x<11+1
4x<12
x<12/4
x<3
A radioactive compound with mass of 260 grams decays at a rate of 3.8% per hour. Which equation represents how many grams of the compound will remain after 8 hours?
A: C=260(1.038)^8C=260(1.038)^8
B: C=260(0.962)^8C=260(0.962)^8
C: C=260(0.038)^8C=260(0.038)^8
D: C=260(1-0.38)^8C=260(1−0.38)^8
The exponential equation that represents how many grams of the compound will remain after 8 hours is:
B: C=260(0.962)^8
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.A radioactive compound with mass of 260 grams decays at a rate of 3.8% per hour, hence the equation for the mass after t hours is given by:
[tex]A(t) = 260(1 - 0.038)^t[/tex]
[tex]A(t) = 260(0.962)^t[/tex]
After 8 hours, the amount is given by:
[tex]A(t) = 260(0.962)^8[/tex]
Hence option B is correct.
More can be learned about exponential equations at https://brainly.com/question/25537936
What are the solutions to the quadratic equation (x + 4)(3x - 5) = 0?
Answer:
x = 4x = 5/3Step-by-step explanation:
Given :
⇒ (x + 4)(3x - 5) = 0
The solutions will make the answer 0.
Therefore,
x + 4 = 0 3x - 5 = 0⇒ x = 4
⇒ 3x = 5 ⇒ x = 5/3
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]
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
Solve for x. Leave your answer in simplest radical form.
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER
Answer:
x = 7
Step-by-step explanation:
I used the formula c^2 = a^2 + b^2
if you need further explanation,let me know
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)πdmwhich 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.
What is x. Please show *all* the steps.
The equation 5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0 is a quadratic equation
The value of x is 8 or 1
How to determine the value of x?The equation is given as:
5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0
Rewrite as:
-5/x - 2 + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0
Take the LCM
[-5(x + 2) + (x -5)(x- 2)]\[x^2 - 4 + [3x + 8]/[x^2 - 4] = 0
Expand
[-5x - 10 + x^2 - 7x + 10]/[x^2 - 4] + [3x + 8]/[x^2 - 4] = 0
Evaluate the like terms
[x^2 - 12x]/[x^2 - 4] + [3x + 8]/[x^2 - 4 = 0
Multiply through by x^2 - 4
x^2 - 12x+ 3x + 8 = 0
Evaluate the like terms
x^2 -9x + 8 = 0
Expand
x^2 -x - 8x + 8 = 0
Factorize
x(x -1) - 8(x - 1) = 0
Factor out x - 1
(x -8)(x - 1) = 0
Solve for x
x = 8 or x = 1
Hence, the value of x is 8 or 1
Read more about equations at:
https://brainly.com/question/2972832
Scott has 6 T-shirts and 10 dress shirts in his wardrobe. What is the probability of selecting a dress shirt from his wardrobe?
a-3/8
b-3/5
c-5/8
d-8/5
Answer:
B
Step-by-step explanation:
6 divided by 10 = 0.6
0.6 = 6/10
6/10 = 3/5
kevin completed 10 problems of his homework during lunch this is 2/7 of the total assignment how many problem was Kevin assigned for homework
Answer:
35 problems
Step-by-step explanation:
We know that 10 problems are 2/7 of his total assignment, so we can set up the following equation,
[tex]\frac{10}{x\\} = \frac{2}{7}[/tex]
(side note: x is the denominator because we don't know how many problems it is out of yet)
We can cross multiply which gives us: (7x10) and 2(x)
70 = 2x (set them equal)
x = 35 (divide 70 by 2)
Hope this helps!
Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are. N A B M
Answer:
Step-by-step explanation:
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
The circumference of a circular ice
skating rink is 408.2 m.
What is the
approximate are of the skating rink? Use
3.14 for Pi. (10 points)
Answer:
13259.77 meters squared
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
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.
someone please answer these 3 questions
Answer:
5 prism all have same volume
Step-by-step explanation:
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.
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.
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