Substituting in p = 1/2,
[tex]\frac{1}{2}=\frac{8}{v}\\ \\ v=\boxed{16}[/tex]
The perimeter of an equilateral triangle is 9x + 3, this is greater than the perimeter of a
regular pentagon which is 10x - 5.
Write down an inequality to represent this information.
Answer:
x < 8
Step-by-step explanation:
9x + 3 > 10x - 5
9x - 10x > -5 - 3
-x > -8
x < 8
Can someone check whether its correct or no? this is supposed to be the steps in integration by parts
Answer:
[tex]\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\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.
Given integral:
[tex]\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x[/tex]
[tex]\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:[/tex]
[tex]\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x[/tex]
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]\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)[/tex]
[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]
Substituting the defined parts into the formula:
[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}[/tex]
[tex]\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:[/tex]
[tex]\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)[/tex]
[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]
[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}[/tex]
Therefore:
[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x[/tex]
[tex]\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:[/tex]
[tex]\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}[/tex]
Divide both sides by 2:
[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}[/tex]
Rewrite in the same format as the given integral:
[tex]\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]
Differentiation Rules used:
[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\sin(k)$}\\\\If $y=\sin(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=k\cos(kx)$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\cos(k)$}\\\\If $y=\cos(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=-k\sin(kx)$\\\end{minipage}}[/tex]
Integration Rules used:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $e^{kx}$}\\\\$\displaystyle \int e^{kx}\:\text{d}x=\dfrac{1}{k}e^{kx}+\text{C}$\end{minipage}}[/tex]
A 20-ft by the 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 256 ft2, how wide is the walkway?
========================================================
Explanation:
x = width of the walkway in feet
This is some positive real number.
The dimension of 20 feet bumps up to 20+2x when adding on x from both directions. Similarly, the 40 ft dimension becomes 40+2x
Refer to the diagram below.
The 20 ft by 40 ft pool is surrounded by a larger rectangle that is 20+2x ft by 40+2x ft
The pool itself is 20*40 = 800 sq ft. Add on the walkway area to get 800+256 = 1056 sq ft.
-----------
Area = length*width
1056 = (20+2x)*(40+2x)
1056 = 20*40 + 20*2x + 2x*40 + 2x*2x ... FOIL rule
1056 = 800 + 40x + 80x + 4x^2
0 = 4x^2 + 40x + 80x + 800 - 1056
0 = 4x^2 + 120x - 256
4x^2 + 120x - 256 = 0
4(x^2 + 30x - 64) = 0
x^2 + 30x - 64 = 0
Let's use the quadratic formula to finish solving for x.
Plug in a = 1, b = 30, c = -64
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-30\pm\sqrt{(30)^2-4(1)(-64)}}{2(1)}\\\\x = \frac{-30\pm\sqrt{1156}}{2}\\\\x = \frac{-30\pm34}{2}\\\\x = \frac{-30+34}{2} \ \text{ or } \ x = \frac{-30-34}{2}\\\\x = \frac{4}{2} \ \text{ or } \ x = \frac{-64}{2}\\\\x = 2 \ \text{ or } \ x = -32\\\\[/tex]
Recall we made x be positive. This is because a negative walkway width does not make sense. This means we'll ignore x = -32.
The only practical solution is x = 2
Therefore, the walkway is 2 feet wide
Which is the graph of f,(x) = 0.5(4)*
I assume you meant [tex]f(x)=0.5(4)^{x}[/tex]. The graph is shown below.
Your load is a container full of water. The container measures
1.0m x 1.25m x 1.1m and weighs 50kg when empty. Since 1 cubic
metre of water weighs 1 tonne, find the weight of the load
Answer:
1282kg
Step-by-step explanation:
1.0*1.12*1.1=1.232 tonnes
50kg + 1232kg = 1282kg
Hope this helps :)
The changes in account balances for Elder Company for 2021 are as follows:
Assets $ 480,000 debit
Common stock 250,000 credit
Liabilities 160,000 credit
Paid-in capital—excess of par 30,000 credit
Assuming the only changes in retained earnings in 2021 were for net income and a $50,000 dividend, what was net income for 2021?
The changes in account balances for Elder Company for 2021 are net income will be $160000
We have given debt common stock = $680000
Credit liabilities = 350000
Credit paid in capital = 190000
And an excess of par 30,000 credit Assuming the only changes in retained earnings
So 680000 = 350000+190000+30000+ retained earning
What is the net income?Net income is an entity's income minus the cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.
So retained earning = $110000
Dividend paid = $50000
So Net income = dividend paid + retained earning
Net income = $110000+$50000
Net income = $160000
So option (c) will be the correct answer.
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if f(x)=5^2x-2 and g(x)=x+1, find (f-g) (x)
The function (f-g) (x) is represented as 5^2x - 3 - x .
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
Given;
f(x)=5^2x-2
g(x)=x+1
Then, the function
(f-g) (x) = 5^2x-2 - (x+1)
Distribute the negative;
(f-g) (x) = 5^2x-2 - x - 1
(f-g) (x) = 5^2x - 3 - x
Hence, the function (f-g) (x) is represented as 5^2x - 3 - x .
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8(w-5)=16 solve for w please give working out
Michael went to the game store there was so much games he wanted and if one of them was $42.29 and the other one was $87.99 and he had $142 how much would he have left
Answer:
$11.72
Step-by-step explanation:
Add: $42.29 + $87.99 = $130.28
Subtract: $142 - $130.28 = $11.72
Answer:
he would have spent 131.08 dollars meaning he has 11.72 dollars left.
Step-by-step explanation:
Need help, can't figure this one out:
Find the perimeter of the following rectilinear figure.
The perimeter of the following rectilinear figure is 54 units.
What is Perimeter ?Perimeter of a figure is the distance covered when a person walk one round across its edges .
The given figure is in the form of a rectangle ,
The perimeter is equal to the sum of all sides ,
The bottom base is 13 includes (base of the small extended figure )
The left side is 14(includes left side of the small extended figure)
The right side is 10+5+4 (includes right side of the small extended figure)
The top is 8
Therefore the perimeter is 13+14+10+5+4+8 = 54 units
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-0.38 written as a fraction is
Which of the following expressions are equal to -8/11 - 3/4 - 1/4
In the expressions that we are given, we can note that there is a negative in all of them. This means that we can factor out the negative.
With the negative factored out, it will look like this: [tex]-(\frac{8}{11} + \frac{3}{4} + \frac{1}{4} )[/tex]
The reasoning for this is because you distribute the negative to each term. For example 8/11 is a term, and so is 3/4, and 1/4. So our first answer is D.
Another way we can do this is by combining like terms. We see that in the denominator for -3/4 and -1/4 they both share 4. We can combine it so it becomes -4/4 or -1. It would be E.
The third way we can do this is by rewriting it. Answer A rewrites it so that it is + -, effectively just -. This allows us to treat the equation as if it were the original one.
Hopefully this helps you out, brainliest would help me out.
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If “a” is a non zero constant, what is the maximum number of turns for the graph of
y = x³ + ax² - 7x+10
The maximum number of turns for the graph given by the function is; 2.
What is the maximum number of turns for the graph?It follows from the task content that the graph given is that of a cubic function. On this note, it follows that the graph has 2 turning points.
This follows from the fact that the degree of the polynomial is 3 and hence, the maximum number of turns on the graph is 2.
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Consider the following loan. Complete parts (a)-(c) below
An individual borrowed $88,000 at an APR of 6%, which will be paid off with monthly payments of $667 for 18 years.
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
The amount borrowed is $, the annual interest rate is%, the number of payments per year is the loan term is years, and the payment amount is $
The complete statements are mathematically given as
the amount borrowed= 88000the annual interest rate= 6%the number of payments per year= 12The loan term= 18the payment amount.=8004What is the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.?Generally, The transfer of money, products, or services in return for other goods and services in proportions that have been previously agreed upon and deemed acceptable is what is meant by the term "payment."
In conclusion, the amount borrowed= 88000
the annual interest rate= 6%
the number of payments per year= 12
The loan term= 18
the payment amount.=667*12
the payment amount.=8004
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A movie theater sells up to 10 tickets at a time online.what is the domain of this graph.
The domain of the function is whole numbers from 0 to 10.
How to explain the domain?Given the graph of function represents the tickets sold vs cost. A movie theater sells up to 10 tickets at a time online. we have to find the domain of the graph.
As shown in the graph the number of tickets sold is 0 to 10 and also the number of tickets are always positive and a whole number. It can never be negative or in fraction form.
Hence, the value of x is a positive whole number. The domain of the function is the complete set of possible values of x. The domain of the function is whole numbers from 0 to 10.
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Consider a triangle ABC like the one below. Suppose that B=129°, a=7, and c=42. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
4-C-b-0
DOD
X
No
solution
5
?
The angles are: A =24.7° ; B = 40.6° ; C =114.7°.
What is Cosine law?
The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The cosine law in trigonometry generalizes the Pythagoras theorem, which applies to a right triangle.
Cosine Law
a² = b²+c²-2bc cos A
b² = c²+a² -2ca cos B
Sum of three angles of a triangle is 180°.
a = 34 ; b= 53; c = 74
Substituting the given values in the cosine law, we have
34² = 53² + 74² - 2*53 *74 * cos A
7844 cos A = 2809 + 5476 - 1156 = 7129
cos A = 7129/7844 = 0.9088
A = cos⁻¹ (0.9088) = 24.6600° = 24.7°
53² = 74² + 34² - 2 (74)(34) cos B
5032 cos B = 5476 + 1156 - 2809 = 3823
cos B = 3823/5032 = 0.7597
B = cos⁻¹ (0.7597) = 40.5622° = 40.6°
Also, A + B + C = 180°
24.7 + 40.6 + C =180
C =180 - 65.3 = 114.7°
Thus, the angles are: A =24.7° ; B = 40.6° ; C =114.7°
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What would the following figure look like after a reflection in a horizontal mirror, followed by a rotation 90 degrees counterclockwise?
Answer:
Step-by-step explanation:
To rotate any figure we have to have the CENTER of rotation!!!!
You did not provide us (your helpers) with that point, so I chose point on the horizontal mirror.
Solve the system of equations : y = x/2 , y = -x - 3 . You can use any method you wish for solving systems of equations. Check your answer.
Answer:
x=−2 and y=−1
Step-by-step explanation:
Problem:
Solve y=x2;y=−x−3
Steps:
I will solve your system by substitution.
y=1/2x;y=−x−3
Step: Solve y= 1/2x for y:
Step: Substitute 1/2 x for y in y=−x−3:
y=−x−3
1/2x= =−x−3
1/2x+x=−x−3+x(Add x to both sides)
3/2x = -3
3/2x/3/2 = -3/3/2 (Divide both sides by 3/2)
x=−2
Step: Substitute −2 for x in y=1/2x:
y=1/2x
y=1/2(-2)
y=−1(Simplify both sides of the equation)
Answer:
x=−2 and y=−1
A water sprinkler sends water out in a circular pattern. How large is the watered area if the radius of the watering pattern is 3 feet?
Use 3.14 for pi.
Answer:
28.26 feet squared
Explanation:
Area of circle is determined by : π(radius)²
Here given:
π = 3.14radius = 3 feetSolve for area:
π(radius)²3.14(3)²28.26 feet²Answer:
28.26 feet squared
Step-by-step explanation:
Radius of the watering pattern = 3 feet
Area = π r²
= 3.14 × 3²
= 28.26 feet squared
What is the value of h?
Answer:
h=-2
Step-by-step explanation:
the graph was shifted 2 units left
Homework:Section 5.3 Homework
Question 5, 5.3.21
Part 1 of 2
HW Score: 50%, 4 of 8 points
Points: 0 of 1
Question content area top
Part 1
In airline applications, failure of a component can result in catastrophe. As a result, many airline components utilize something called triple modular redundancy. This means that a critical component has two backup components that may be utilized should the initial component fail. Suppose a certain critical airline component has a probability of failure of 0.0056 and the system that utilizes the component is part of a triple modular redundancy.
(a) Assuming each component's failure/success is independent of the others, what is the probability all three components fail, resulting in disaster for the flight?
(b) What is the probability at least one of the components does not fail?
The probability that all three components fail is 1.756 × 10⁻⁷. The probability of at least one of the components does not fail 0.9999998244.
What is a Probability?Probability is the likelihood for an event to occur. In a given statistical distribution, the probability explains the range of values and probabilities that a randomized variable could have.
From the given information;
Assuming each component's failure/success is independent of the others: the probability that all three components fail is:
P(three components fail) = (0.0056)^3
P(three components fail) = 1.756 × 10⁻⁷
The probability that at least one does not fail is:
P(at least one does not fail) = 1 - P(all three components fail)
P(at least one does not fail) = 1 - 1.756 × 10⁻⁷
P(at least one does not fail) = 0.9999998244
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One person ran 4 miles in 24 minutes. At this rate, how long would it take to run 26 miles?
Divide.
74.48 ÷ 7.6
Enter your answer as a decimal in the box.
determine whether each pair of lines is perpendicular parallel or neither
Answer:
1st set of equations - parallel
2nd set - perpendicular
3rd set - neither
Step-by-step explanation:
First set:
simplify the equation for line 1 by dividing by -4: y = 0.5x + 1
simplify the equation for line 1 by dividing by -6: y = 0.5x - 1.5
Both have the same slope: 0.5 so the lines are parallel.
Second set:
simplify the equation for line 1 by dividing by 3: y = -2/3x + 4
simplify the equation for line 1 by dividing by -4: y = 3/2x - 7/4
-2/3 * 3/2 = -1, so the lines are perpendicular
Third set
simplify the equation for line 1 by dividing by 1/2: y = -2x+4
simplify the equation for line 1 by dividing by 2: y = -1/4x +2
-2x+4=-0.25x+2
-2x+0.25x=2-4
-1.75x=-2
x=1.14
y=-2(1.14)+4 = 1.7143. So there is an intersection point
The pair of lines 2x - 4y = -4 & 3x - 6y = 9, 2x + 3y = 12 & and 6x - 4y = 7, and x + (1/2)y = 2 & (1/2)x + 2y = 4 will be parallel lines, perpendicular lines, and neither parallel nor perpendicular, respectively.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The pair of lines is given as,
2x - 4y = -4 ⇒ y = (1/2)x + 1
3x - 6y = 9 ⇒ y = (1/2)x - 3/2
The pair of lines are parallel to each other because the slope is equal.
2x + 3y = 12 ⇒ y = -(2/3)x + 4
6x - 4y = 7 ⇒ y = (3/2) x - 7/4
The pair of lines are parallel to each other because the product of slopes is -1.
x + (1/2)y = 2 ⇒ 2x + y = 4
(1/2)x + 2y = 4 ⇒ 2x + 4y = 8
The pair of lines are neither parallel nor perpendicular to each other.
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*
Which of the following are situations that can be modeled with a quadratic function? Select all that apply.
O
0
A tree decays 10% every six weeks.
The height of a diver after jumping from a high dive into the water.
The height of a ball rolled down a hill.
A gym charges $15 perfitness class.
An ant bocid eliminates 50% of bacteria every 24 hours
The height of a rocket after it is Bunched
Answer:
Option 2 and 5 are correct. Look down for my explanation↓:
Step-by-step explanation:
So We need to tell which one of them is quadratic function.
Option 1 is exponential decay so, it is not quadratic.
Option 2 is quadratic because the diver will take the parabolic shape when jumps.
Option 3 is not quadratic. Option 4 is not quadratic it is linear.
Option 4 is again exponential not quadratic.
Option 5 is quadratic because it takes the parabolic shape again.
How do I do this? The question is in the picture.
Answer:
Step-by-step explanation:
Which functions have a vertex with a x-value of 0? Select three options.
f(x) = |x|
f(x) = |x| + 3
f(x) = |x + 3|
f(x) = |x| − 6
f(x) = |x + 3| – 6
Answer:
f(x) = |x|f(x) = |x| + 3f(x) = |x| − 6Answer:
A,B,D
Step-by-step explanation:
Math: Evaluating a piece wise function...help!
The values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1
How to evaluate the piece wise function?The function is given as:
[tex]g(x) = \left[\begin{array}{cc}-2&-2.5 < x \le -1.5\\-1&-1.5 < x \le -0.5\\0&-0.5 < x < 0.5&1&0.5 \le x < 1.5\end{array}\right[/tex]
To calculate g(-0.5), we make use of the domain -1.5 < x ≤ -0.5
At this domain;
g(x) = -1
So, the value of g(-0.5) is
g(-0.5) = -1
To calculate g(0.3), we make use of the domain -0.5 < x 0.5
At this domain;
g(x) = 0
So, the value of g(0.3) is
g(0.3) = 0
To calculate g(0.5), we make use of the domain 0.5 ≤ x 1.5
At this domain;
g(x) = 1
So, the value of g(0.5) is
g(0.5) = 1
Hence, the values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1
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In a random sample of 250 students, 150 were in favor of longer hours at the school library. At 98% level of confidence, what is the margin of error?
Select one:
0.051
0.080
0.065
0.072
0.078
0.061
0.072 is the margin of error.
What is standard error?The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation.
According to the question,
In a random sample of 250 students,
p= 0.98 (or 98%) were in favor of longer hours at the school library.
The standard error of p(the sample proportion) is (approximately)
The standard error of p = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
p = 0.98
1 - p = 1 - 0.98 = 0.02
Here,
n = 250
The standard error of p = [tex]\sqrt{ \frac{0.98 (0.02) }{250}[/tex]
The standard error of p ≈ 0.072
Therefore,
The margin of error is 0.072.
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If P(n) and Q(n) are polynomials of degree j and k, respectively, then the series
Infinite
Σ P(n)/Q(n)
n=1
converges if j < k − 1 and diverges if j ≥ k – 1.
Use the polynomial test given above to determine whether the series converges or diverges.
Infinite
Σ 1/(n)^8 +7
n=1
O converges
Odiverges
Answer:
converges
Step-by-step explanation:
well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0 and k = 8. Since 0 < (8-1)
0 < 7 the series converges
