Body design, muscular power and steadiness, flexibility and cardio-respiratory endurance are the components of fitness. Fitness is a major component of a healthy lifestyle.
What are these skill-related components?While performing tasks during gymnastics she needs balance so that she can maintain and control a particular position.
Body design, muscular power and steadiness, flexibility and cardio-respiratory endurance are the components of fitness. Fitness is a major component of a healthy lifestyle.
Balances are of two types dynamic and static. Balance used while moving and performing the task is dynamic balance while performing in a standing position is static balance.
Gymnasts require balancing as the main component cause they use poles and beams to perform their tasks.
Therefore, balance is the skill mainly required in gymnastics.
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if f(x) = 4x - 3 and g(x) = x + 4, find (f - g)(x)
Answer:
3x - 7
Step-by-step explanation:
This questions asks about the subtraction of functions. To find the answer, we can subtract the same way we would subtract polynomials.
Subtracting Expressions
First, set up the subtraction problem by taking the expression for f(x) and subtracting the expression equal to g(x) from it.
This looks like:
(4x - 3) - (x + 4)Next, distribute the negative to the second binomial
4x - 3 - x - 4Then, combine like terms
3x - 7Since we are not given a x-value, this is the final answer.
Solving for an X-Value
If you are given an x-value, the best way to solve the equation is to first solve each function and then subtract.
For example, using the same rules for each function let's solve (f-g)(2).
First, solve for f(2) and g(2)
f(2) = 5g(2) = 6Then, subtract the 2 values
5 - 6 = -1Can 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]
Addison and Kelsey are running on a path modeled by x2 + y2 – 14x – 16y – 287 = 0, where the distance is in meters. What is the maximum distance between the runners at any given time?
20 meters
32 meters
40 meters
140 meters
Answer:
40 meters
Step-by-step explanation:
The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.
Given that, Addison and Kelsey are running on a path modeled by x² + y² - 14x - 16y - 287 = 0.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x1,y1) and radius r is (x-x1)²+(y-y1)²=r²
Here, the circular path is modeled by x² + y² - 14x - 16y - 287 = 0
We complete the squares to place it in the standard format, thus:
x² - 14x + 49 + y² - 16y +64 = 287+49+64
⇒ (x-7)² + (y-8)² = 400
⇒ (x-7)² + (y-8)² = 20²
So, r² = 20²
⇒ r = 20 meters
Maximum distance = d = 2r
= 40 meters
The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.
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50 cm
1.5
Path
Vegetables
50 cm
50 cm
2
5.5m
This plan shows a vegetable garden.
The width of the path is 50 cm throughout.
4.5m
Step-by-step explanation:
b because you have to multiply
Emily is shopping at the toy store. In that store all dolls are sold at the same price and all dresses are sold at the same price. If Emily buys one doll and one dress, it will cost her $21.00. If Emily buys two dolls and three dresses, it will cost her $51.00. What is the price of one doll at that store?
Answer:
$12.
Step-by-step explanation:
1) if price of one doll is 'x', of one dress is 'y', then the condition 'buys one doll and one dress, it will cost her $21.00' can be written as x+y=21;
2) the condition 'buys two dolls and three dresses, it will cost her $51.00' can be written as 2x+3y=51;
3) it is possible to make up the system:
[tex]\left \{ {{x+y=21} \atop {2x+3y=51}} \right. \ = > \ \left \{ {{x=12} \atop {y=9}} \right.[/tex]
4) the price of one doll is 12$.
Write an equation for the polynomial graphed below
The expression for the polynomial graphed will be y(x) = (x + 3)(x - 1 )(x - 4 ).
How to factor the polynomial?From the graph, the zeros of the polynomial of given graph are:
x = -3
x = 1
x = 4
Equate the above equations to zero
x + 3 = 0
x - 1 = 0
x - 4 = 0
Multiply the equations
(x + 3)(x - 1 )(x - 4 ) = 0
Express as a function gives;
y = (x + 3)(x - 1 )(x - 4 )
Hence, the factored form of the polynomial will be y = (x + 3)(x - 1 )(x - 4 ) .
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I need a walk through please 1
Answer:
[tex]f(x) = \frac{\sqrt{x+2}} 9[/tex]
Step-by-step explanation:
You work in the order you have: you start with your number x, so your first step will be [tex]f_0(x)=x[/tex]. then you add 2: [tex]f_1(x) =x+2[/tex]. Then you take the square root of what you have in the previous step: [tex]f_2(x) = \sqrt {x+2}[/tex]. Finally, you divide by 9: [tex]f(x) = \frac{\sqrt{x+2}} 9[/tex]
A sample has a sample proportion of 0.3. Which sample size will produce the
widest 95% confidence interval when estimating the population parameter?
A. 46
B. 68
C. 56
D. 36
Using the z-distribution, the sample size that will produce the widest confidence interval is given by:
D. 36.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The widest interval has the highest margin of error, and since the margin of error is inversely proportional to the sample size, a lower sample size generates a higher margin of error, hence option D is correct.
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Somebody help please!!
Find the minimum sample size n needed to estimate u for the given values of c, o, and e. C=.95, O=6.4, E= 2
what is (4-¹)(2³-4-2) 4 - ¹ ) ( 2³ - 4-2 )
Answer:
[tex](4-¹)(2³-4-2) 4 - ¹ ) ( 2³ - 4-2 )[/tex]
[tex]4 {}^{ - 2} (2 {}^{3 } - 4 - 2)(2 {}^{3} - 4 - 2)[/tex]
[tex]4 {}^{ - 2} (2 {}^{3} - 4 - 2) {}^{2} [/tex]
[tex] \frac{1}{16} (8 - 4 - 2) {}^{2} [/tex]
[tex] \frac{1}{16} (4 - 2) {}^{2} [/tex]
[tex] \frac{1}{16} \times 4[/tex]
[tex] \frac{1}{4} [/tex]
The equation of a circle is x² + y²-6y+1=0. What are the coordinates of
the center and the length of the radius of this circle?
(1) center (0,3) and radius 2√2
(2) center (0,-3) and radius 2√2
(3) center (0.6) and radius √35
(4) center (0,-6) and radius √35
Answer:
center (0, 3) and radius 2√2
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven equation:
[tex]x^2+y^2-6y+1=0[/tex]
Subtract 1 from both sides:
[tex]\implies x^2+y^2-6y=-1[/tex]
To create a trinomial with variable y, add the square of half the coefficient of the y term to both sides:
[tex]\implies x^2+y^2-6y+\left(\dfrac{-6}{2}\right)^2=-1+\left(\dfrac{-6}{2}\right)^2[/tex]
[tex]\implies x^2+y^2-6y+9=8[/tex]
Factor the trinomial with variable y:
[tex]\implies x^2+(y^2-6y+9)=8[/tex]
[tex]\implies x^2+(y-3)^2=8[/tex]
Factor [tex]x^2[/tex] to match the general form for the equation of a circle:
[tex]\implies (x-0)^2+(y-3)^2=8[/tex]
Compare with the general form of the equation for a circle:
[tex]\implies a=0[/tex]
[tex]\implies b=3[/tex]
[tex]\implies r^2=8 \implies r=2\sqrt{2}{[/tex]
Therefore, the center is (0, 3) and the radius is 2√2
Another day, another math problem 2
Answer:
-7
Step-by-step explanation:
you can use power rule of derivatives for that.
HELP! ASAP!
2.A cube-shaped plant box has edges that are 13 cm long. The plant box is filled with potting soil that has a density of 1.33 g/cm³.
(a) Is it safe to place the plant box on a window ledge that can support a maximum weight of 2400 grams? Explain why or why not.
(b) Would the density of the soil change if the plant box was only half full? Explain.
Step-by-step explanation:
2.
the volume of the box is
length × width × height = 13×13×13 = 13³ = 2197 cm³
the ratio of the density indignation tells us that every cm³ of soil weighs 1.33 g (or every unit of 1.33g soil fits into 1 cm³).
we have 2197 cm³.
their weight is
2197 × 1.33 = 2,922.01 g
so, the filled box clearly exceeds the max. weight of the window ledge, and it is NOT safe to put it there.
b
yes, it would be a little bit less dense.
because every bit of weight you put on top of something increases the pressure on and therefore the density of that something.
The adjusted trial balance columns of the worksheet for Whispering Winds Company are as follows.
Answer:
Question?
Step-by-step explanation:
Waiting for answer, could u help?
Answer:
The practical domain of function is , Roscoe can ride his bike only from 10 miles to 30 miles.
Domain of function is defined as the set of input values for which the function is defined i.e. the set of its possible inputs,
The amount of time it takes for Roscoe to ride his bike m miles is represented by a function.
Where m represent, number of miles he can ride.
Above function is defined for every value of m . But in question it is mention that Roscoe rides his bike at least 10 miles but not more than 30 miles.
Therefore, Domain of function is from 10 miles to 30 miles
Step-by-step explanation:
If you receive a 25% MARKUP on an item costing $60.00, how much money do you pay in total?
Answer:
Money Paid in Total = $45
Step-by-step explanation:
Firstly, the term Mark-up refers to the amount added to the cost price to cover the overheads and realize a profit.
A mark-up percentage is a percentage (%) that is used as a basis to determine the mark-up value.
Given
Cost of an Item = 60$
Markup % = 25% on cost
Hence, Mark up in $ = 60$*25%
= 15$
Therefore, Actual cost of an item = Cost of an item - Mark up on Item
= 60$ - 15$
= 45$
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How to find x and y
he value of x and y from the given figure are 49/5 and 49/15
Similarity theorem of trianglesFrom the given similar triangles, the following expression is true
21/30 = 7/15 = k
Also, x/21 = y/7 = 7/15
Equate
x/21 = 7/15
15x = 7 * 21
5x = 7 * 7
x = 49/5
Similarly
y/7 = 7/15
15y = 49
y = 49/15
Hence the value of x and y from the given figure are 49/5 and 49/15
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4. At what coordinates does the terminal side of a -420° angle intersect the unit circle?
Answer:
[tex]\left(\dfrac{1}{2},-\dfrac{\sqrt{3}}{2}\right)[/tex]
Step-by-step explanation:
An angle is co-terminal with the same angle that has any multiple of 360° added to it.
__
The angle -420° is co-terminal with (-420° +720°) = 300°. The attached unit circle chart shows the coordinates of the terminal side of that angle.
These coordinates are ...
(x, y) = (cos(300°), sin(300°))
(x, y) = (1/2, -√3/2)
2. The length of a rectangle exceeds its breadth by 5m.If the perimeter of the rectangle is 74m,find the length and breadth of the rectangle. Plss answer thiissss
Step-by-step explanation:
length = breadth + 5
the perimeter is a rectangle is
2×length + 2×breadth
in our case
2×length + 2×breadth = 74
so, we use the first equation in the second equation :
2×(breadth + 5) + 2×breadth = 74
2× breadth + 10 + 2× breadth = 74
4×breadth = 64
breadth = 16 m
length = breadth + 5 = 16 + 5 = 21 m
What is the value of
(X+Y) (X-Y) when x=3.5,y=-8.7
Answer:
[tex](x + y)(x - y)[/tex]
[tex](3.5 - 8.7)(3.5 + 8.7)[/tex]
[tex](-5.2)( 12.2)[/tex]
[tex]-63.44 [/tex]
On January 1, 2021, Princess Corporation leased equipment to King Company. The lease term is 12 years. The first payment of $716,000 was made on January 1, 2021. The equipment cost Princess Corporation $5,188,466. The present value of the lease payments is $5,588,516. The lease is appropriately classified as a sales-type lease. Assuming the interest rate for this lease is 9%, how much interest revenue will Princess record in 2022 on this lease? (Round your answer to the nearest whole dollar amount.)
The amount of the interest revenue that Princess will record in 2022 on this lease is:$413,553.82.
Interest revenue
First step
Lease value payments after first payment:
Lease value payments= $5,588,516- $716,000
Lease value payments= $4,872,516
Second step
Lease value payments after second payment:
Lease value payments=$4,872,516+ ($4,872,516×9%) - $716,000
Lease value payments=$4,872,516+$438,526.44-$716,000
Lease value payments=$4,595,042.44
Third step
2022 Interest revenue=$4,643,787.6×9%
2022 Interest revenue=$413,553.8196
2022 Interest revenue=$413,553.82 (Approximately)
Therefore the amount of the interest revenue that Princess will record in 2022 on this lease is:$413,553.82.
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i tried can you help me
Answer:
question 1
the ticket price which results in the greatest revenue is 14+8=22$
question 2
the greatest revenue we get is 22*(7500-250*8)= 22*5500=121000$
Step-by-step explanation:
the cost of a ticket to music concert is 14$
capacity of people for concert = 7500
for every increase in price attendance decreases by 250
so the required equation for getting revenue is
y = (14+x)(7500-250x)
= 105000+7500x-3500x-250x^2
by differentiating the above equation with respect to x we can find the local maxima which gives us the price for getting more revenue
dy/dx = 7500 -3500 - 500x =0
4000=500x
x= 8
from the above equation we got that if the increase in price was 8$ we will be getting the most revenue out of the concert
question 1
the ticket price which results in the greatest revenue is 14+8=22$
question 2
the greatest revenue we get is 22*(7500-250*8)= 22*5500=121000$
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The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of ten automobile insurance liability claims is under study.
The mean will be 10.08 and the standard deviation will be 1.27.
The complete question is given below:-
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of twelve automobile insurance liability claims is under study.
Find the mean and standard deviation of this probability distribution.
For samples of size 12, what is the expected number of claims made by people under 25 years of age?
What is mean?Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
Given that:-
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age.We need to find For samples of size 12, what is the expected number of claims made by people under 25 years of age?The mean will be calculated by the formula below:-
Mean = [tex]\mu[/tex] = np = 12 x 0.84 = 10.08
The standard deviation will be calculated as:-
Standard deviation = [tex]\sqrt{npq}[/tex] = [tex]\sqrt{12\times 0.84\times 0.16}[/tex] = 1.27
Therefore the mean will be 10.08 and the standard deviation will be 1.27.
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which of the following statements is/are true
Using Venn probabilities, the correct statement is given by:
ii) [tex]|A \cup B| = |A| + |B| - |A cap B|[/tex]
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Hence, statement ii is correct.
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Please answer all four of the questions please I will mark u brainliest
Answer:
1: 8 ft
2: 10 cm
3: c is approximately 127.2 or exactly equal to 90 * sqrt(2)
4: sqrt(133)
Step-by-step explanation:
(1) Kevin tries to climb a wall with a ladder. The length of a ladder is 17 feet and it reaches only 15 feet up the wall. What is the distance between the base of the ladder and the wall? :
Here you can use the Pythagorean Theorem to find the length of the base.
the equation is a^2 + b^2 = c^2 where c is the hypotenuse. In this case 17 is the hypotenuse which is c, 15 is a or b it doesn't really matter where you put it.
a^2 + (15)^2 = 17^2
a^2 + 225= 289
a^2 = 64
a = 8
(2) In a right triangle, if the length of one leg is 8 cm and the length of the other leg is 5 cm, what is the length of the hypotenuse? :
The same formula can be used except you don't have to move anything around.
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
10 = c
10 cm
A baseball field is a square with sides of length 90 feet. What is the shortest distance between the first base and the third base?:
So if you look at the image provided, the shortest distance is just a straight line, but more specifically that straight line forms two triangles with the same lengths, That line is the hypotenuse so you can use the same equation as the previous equations
90^2 + 90^2 = c^2
16,200 = c^2
c is approximately 127.2 or exactly equal to 90 * sqrt(2)
(4) How far up a wall will a 13-meter ladder reach, if the foot of the ladder is 6 meters away from the base of the wall?:
6^2 + b^2 = 13^2
36 + b^2 = 169
b^2 = 133
b = sqrt(133)
Fill in the blank. In the triangle below, x=?. Round your answer to two decimal places.
Answer:
Hello
DiinoMahFill in the blank. In the triangle below, x=?. Round your answer to two decimal places.
tim earns 42pounds for 7 hours of work. how much does he earn in 16 hours
Answer:
96
Step-by-step explanation:
divide 42/7
=6
6x16=
96
Answer:
The answer is 96 pounds
Step-by-step explanation:
Multiply 16 with 42 and divide it by 7 and you get the answer 96 pounds
Can you please help meee
Answer: y = 4x + 5/4
Step-by-step explanation: Plug in the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y-intercept, and such that m, b ≠ 0.
What is the area of the rectangle below
Answer:
130 sq. units
Step-by-step explanation:
Any number multiplied by 10 is the same number with a 0 added at the end.
Answer:
1300
Step-by-step explanation:
1. calculator
2.putreef Iub numbers
3 solve