The net of a right circular cylinder is shown.

net of a cylinder where the radius of each circle is labeled 5 meters and the height of the rectangle is labeled 9 meters

What is the surface area of the cylinder? Use π = 3.14 and round to the nearest whole number.

225 m2
298 m2
440 m2
707 m2

The height of the object after 3 seconds is 73.5 meters

A model function is a way of describing a real-life system or situation using mathematical concepts and language

Since the equation for the height of the object is given by:

s(t) = -4.9t² + 19.6t + 58.8 and t is the t in seconds

Thus, in order to find the height of the object after 3 seconds, you need to substitute  t = 3 into the equation. That is:

s(t) = -4.9t² + 19.6t + 58.8

s(t) = -4.9×(3)² + 19.6(3) + 58.8

s(t) = 73.5 meters

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The length of the curve y (x) = ₁∫ˣ √(t³ − 1) dt , 4 ≤ x ≤ 9, is 211/4.

In calculus, arc length of curve is the distance between two points along a portion of the curve. Finding the length of an irregular arc segment by approximating the arc segments as connected (straight) line segments is also known as the integral variation of the curve-corrected distance formula. Arc length formula is

ₐ∫ᵇ√[ 1 + (dy/dx)²] dx --(*)

Where, x is the arc length,

We have calculate the length of curve means the length of arc of curve.

Now, y = y (x) = ₁∫ˣ √(t³ − 1) dt

differentiate both sides with respect to x

=> dy/dx= d/dx( ₁∫ˣ√(t³ − 1 ) dt)

Using the fundamental theorem of calculus,

=> dy/dx = dy/dt × dt/dx

let t = x => dt/dx = 1

dy/dt = √x³ - 1 ( from leibnitz rule )

dy/dx = √x³ - 1

Required length of curve = ₄∫⁹√[ 1 + (√x³ - 1)²] dx

= ₄∫⁹√[ 1 + x³ - 1] dx

= ₄∫⁹√x³ dx

[tex] = ₄∫⁹{x}^{ \frac{3}{2} } dx[/tex]

[tex] = \frac{2}{5} ( {9}^{ \frac{5}{2} } - {4}^{ \frac{5}{2} } )[/tex]

[tex]= 211/4[/tex]

So, the required length is 211/4.

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Complete question:

Find out length of the curve

y (x) = ₁∫ˣ √(t³ − 1) dt , 4 ≤ x ≤ 9.

Answer: microscope

Step-by-step explanation:

a camera is equipment for a photographer

a microscope is equipment to a biologist

After the dilation, the coordinates will become (- 9, 12).

Given is the coordinate of point (- 3, 4).

The given coordinate is -

(-3, 4)

After the dilation, the coordinates will become -

(x, y) → (Kx, Ky)

The coordinates after the dilation will be -

(3 x - 3, 3 x 4)

(- 9, 12)

Therefore, after the dilation, the coordinates will become (- 9, 12).

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Answer:

(6.25,2.5)

Step-by-step explanation:

Answer:

m = -1/2

Step-by-step explanation:

Slope can be calculated using the following formula

slope(m) = (y2 - y1) / (x2 - x1)

Where the values of x and y derive from points (x1,y1) and (x2,y2) which can be found in the table.

Here the values of x and y may vary depending on the chosen points however I have chosen (-4,3) and (-2,2)

If we use these points then (x1,y1) = (-4,3) and (x2,y2) = (-2,2)

So, x1 = -4, y1 = 3, x2 = -2 and y2 = 2

We now plug these values into the formula

m = (y2 - y1) / (x2 - x1)

plug in x1 = -4, y1 = 3, x2 = -2 and y2 = 2

m = (2-3) / (-2-(-4)

==> simplify parenthesis

m = -1/2

No further simplification can be done so m = -1/2 is the final answer

Answer:

2 obv

Step-by-step explanation:

slope of -4 and 3 is 2

because -xcoefficient/ycoefficient

and the - × - becomes +

so it will be 4/2 and the answer is 2

Answer:B

Step-by-step explanation: i got it right

By solving an equation for general taxes, we will find that the percent sales tax on the pair of sneakers is 5%.

We know that for an object with a price P, and a tax of X (where X is in a percentage) the price after the tax is:

P' = P*(1 + X/100%)

Here we know that the initial price is $48 and the price after tax is $50.40, so we will get:

$50.40 = $48*(1 + X/100%)

Now we can solve this for X.

($50.40/$48) = 1 + X/100%

(($50.40/$48) - 1)*100% = X

5% = X

So the percent sales tax is 5%.

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Answer:

Step-by-step explanation:

t

The standard form of the quadratic inequality represented by the description is; y <  -2x² + 160x - 2400

An inequality with a quadratic expression is referred to as a quadratic inequality.

It is of the form y = ax² + bx + c (or substitute <,≥ or ≤ for > ) represents a region of the plane that a parabola encircles.

Let's assume that the equation is y = a(x - h)² + k

Where (h, k) is the coordinate of the vertex. Thus;

y = a(x - 40)² + 800

Put the point (60, 0) in the equation

0 = a(60 - 40)² + 800

0 = a(20)² + 800

-800 = 400a

a = -800/400

a = -2

Thus, the equation is;

y = -2(x - 40)² + 800

The inequality is a dashed line and shaded below the parabola and is;

y <  -2(x - 40)² + 800

= y <  -2(x² - 80x + 1600) + 800

y <  -2x² + 160x - 3200 + 800

y <  -2x² + 160x - 2400

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The limit is evaluated by using the series expansion of 1 - cos(2x) and 1 + 2x - e^2x. The series expansion of 1 - cos(2x) is 2x^2 - (2/3)x^4 + (1/5)x^6 - (1/42)x^8 + ... and the series expansion of 1 + 2x - e^2x is 2x - (2/3)x^3 + (2/5)x^5 - (4/21)x^7 + ... Therefore, the limit of both series is 0 as x approaches 0.

The limit of 1 - cos(2x) as x approaches 0 is calculated by taking the series expansion of 1 - cos(2x), which is

2x^2 - (2/3)x^4 + (1/5)x^6 - (1/42)x^8 + ...

When x is 0, all terms in the series are 0, so the limit is 0. Similarly, the limit of 1 + 2x - e^2x as x approaches 0 is calculated by taking the series expansion of 1 + 2x - e^2x, which is

2x - (2/3)x^3 + (2/5)x^5 - (4/21)x^7 + ....

When x is 0, all terms in the series are 0, so the limit is also 0.

The limit of 1 - cos(2x) as x approaches 0 is also calculated numerically. When x is

0.0001, 1 - cos(2x) is 0.000399980.

When x is 0.00001, 1 - cos(2x) is 0.0000039998.

As x becomes closer to 0, the value of 1 - cos(2x) approaches 0. The same is true for

1 + 2x - e^2x.

When x is 0.0001, 1 + 2x - e^2x is 0.000399980.

When x is 0.00001, 1 + 2x - e^2x is 0.0000039998.

As x becomes closer to 0, the value of

1 + 2x - e^2x also approaches 0.

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Answer:

x = 49

Step-by-step explanation:

the figure inside the circle is a cyclic quadrilateral.

the opposite vertices of a cyclic quadrilateral sum to 180° , then

x + 68 + 63 = 180

x + 131 = 180 ( subtract 131 from both sides )

x = 49

The investment scenario that I will choose to would be = option 1 .

An investment is an official asset or item acquired with the goal of generating income or appreciation. Therefore,the investment scenario that is best chosen should be the one with a greater appreciation at Tue end of the end of the day.

Option 1 = $20 × 2 = $40 / day

Option 2 = $0.20 × 3 = $0.6/day

Option 3 = $0.01 × 4 = $0.04/day

Therefore, the best investment scenario would be = option 1 investment scenario.

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Total possible ways that they can sit around a circular table if all the members of each party all sit next to each other are equals to 14,400.

We have , A Senate committee,

Total Democrats = 5

Republicans = 5

We have to calculate the number of ways

can they sit around a circular table if each member sits next to two members of the other party.

We can use counting principle, which helps to count all the possible outcomes and the total possible ways different events can be occur. For this ,choose any 5 consecutive seats to place the Democrats, it doesn't matter which 5 consecutive seats that we choose, since we can rotate the table. Then there are 5 ways to place first member out of 5 democrats. The places available for 2nd member is 4 i.e 4 ways , similarly total ways to place the democrats in their seats. Thus, the Democrats occupy the other 5 seats and they can be arranged in the same muber of ways = 5! = 120 ways. Similarly, total ways to arrange the 5 republicans are 5! = 120 ways. So, the total arrangemets ways are (i.e Ways to arrange the Republicans) x ( Ways to arrange the Democrats) equals to 120 x 120 = 14,400.

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Complete question:

A Senate committee has $5$ Democrats, $5$ Republicans, and $1$ Independent. In how many ways can they sit around a circular table if all the members of each party all sit next to each other? (Two seatings are considered equivalent if one is a rotation of the other.)

The circumcenter of triangle ABC is (-5, 2)

What is the circumcenter?

The circumcenter of a triangle is the point that is equidistant from all three vertices of the triangle. It is the center of the circle that passes through all three vertices of the triangle.

To find the circumcenter of the triangle ABC with vertices A(-5,3), B(5, 8), C(-5.8) we can substitute the values of the coordinates into the formulas above:

x = (8 - 3) * (-5.8^2 + 3^2 - 5^2 - 8^2) - (3 - 8) * (-5^2 + 3^2 - (-5)^2 -3^2) / 2 * (3 - (-5)) * (8 - 3) - (3 - 8) * (-5.8 - (-5))

x = (-5)

y = (3 - (-5.8)) * (-5^2 + 3^2 - (-5)^2 -3^2) - (-5 - (-5)) * (3^2 + 3^2 - (-5.8)^2 - 8^2) / 2 * (3 - 8) * (-5 - (-5)) - (3 - 8) * (3 - (-5.8))

y = 2

Hence, the circumcenter of triangle ABC is (-5, 2)

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Answer:

(0, 5.5)

Step-by-step explanation:

Midpoint of BC: ([-5 + 5]/2, (8 + 8)/2) = (0, 8)

Perpendicular bisector of BC has equation: x = 0

Midpoint of AC: ([-5 + (-5)]/2, (3 + 8)/2) = (-5, 5.5)

Perpendicular bisector of AC has equation y = 5.5

Point of intersection of the two perpendicular bisectors:

(0, 5.5)

Answer: (0, 5.5)

Answer:

0.56

Step-by-step explanation:  

24/43 as decimal is approximately: 0.55814 (Rounded to fifth decimal place)

Answer:

Square root of 85

Step-by-step explanation:

Answer:

Step-by-step explanation: (Don't read this if you are taking a test, please! I don't want you to get in trouble!)

The formula to find a hypotenuse is a^2 + b^2 = c^2 (a squared plus b squared = c squared).

The hypotenuse is the diagonal leg (line WH).

The line WJ = 7, and the line JH = 6.  Let's make line WJ a, and line JH b.

7^2 + 6^2 = c^2.  When you square a number, you multiply that number by itself.  7x7 + 6x6 = c^2.  7x7 = 49 and 6x6 = 36.  Now you have 49 + 36 = c^2

49 + 36 = 85.  85 = c^2.  Square root both sides.  The square root of 85 = the square root of c^2 (c). c = 9.21954446.  If you have to round the hypotenuse to the nearest hundredth, then your answer is 9.22.  The answer for the length of the hypotenuse is 9.22

I hope this helps, but please don't use this on a test!

It would take Jay 21 minutes to clear the driveway of the snow working alone.

What is factorization ?

In math, factorization is when you break a number down into smaller numbers that, multiplied together, give you that original number. When you split a number into its factors or divisors, that's factorization. For example, factorization of the number 12 might look like 3 times 4.

Have given the equation ,

[tex]\frac{1}{j} +\frac{1}{j+21} = \frac{1}{14} \\\frac{j+21+j}{j(j+21)} = \frac{1}{14} \\\\\frac{2j+21}{j^{2}+21j } = \frac{1}{14} \\\\28j+391 = j^{2}+21j\\ j^{2}-7j-391=0\\ j^{2}-21j+14j-391=0\\[/tex]

j(j - 21) +14(j - 21) = 0

(j - 21) (j + 14) = 0

j - 21 = 0                  ,   j + 14 = 0

j = 21                         ,   j = -14

The value of j cannot be negative, because of the context.

So, it would take Jay 21 minutes to clear the driveway of the snow working alone

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Answer:

Step-by-step explanation:

21 min PLATO

Midpoints are A(a, b), B(a+c, b+d), C(2c, d), D(c, 0)

slope AB = slope DC = d/c

slope AD = slope BC = b/(a-c)

Given that Quadrilateral R S T V is in a coordinate plane with vertex and R(0, 0), S(2a, 2b), T(2c, 2d), V(2c, 0).

A is the midpoint of RS, B is the midpoint of ST

C is the midpoint of TV, and D is the midpoint of RV

The midpoint M of segment PQ:

M = (P +Q)/2

A = (R +S)/2 = ((0, 0) +(2a, 2B))/2 = (a, b)

B = (S +T)/2 = ((2a, 2b) +(2c, 2d))/2 = (a+c, b+d)

C = (T +V)/2 = ((2c, 2d) +(2c, 0))/2 = (2c, d)

D = (R +V)/2 = ((0, 0) +(2c, 0))/2 = (c, 0)

The slope of various segments can be found using the slope formula:

m = (y2 -y1)/(x2 -x1)

So, the slopes of the various segments are ...

slope of AB = (b +d -b)/(a +c -a) = d/c

slope of DC = (0 -d)/(c -2c) = -d/-c = d/c . . . . same as slope AB

slope of AD = (0 -b)/(c -a) = -b/(c -a) = b/(a-c)

slope of BC = (d -(b+d))/(2c -(a+c)) = -b/(c -a) = b/(a-c) same as slope AD

Pairs of opposite sides of ABCD are parallel, so quadrilateral ABCD is a parallelogram.

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Answer:

5/3

Step-by-step explanation:

The formula of finding slopes are:

Change in y over change in x, which is:

(10 - 5) / (4 - 1)

= 5/3

Answer: 1/5

Step-by-step explanation:

7/10 - w = 1/2

7/10 - w = 5/10

7-5 = 2

2/10 = 1/5

Answer w=.2

Explanation: −w+7/10=1/2

−

Answer:

∠HKJ = 180 (STRAIGHT ANGLE)

∠HKI = 180-106 = 74

The general solution of the differential equation is y(x) = (c1 + c2x)e^(-x) + (1/5)e^(-x)(sin(ex) - (cos(ex)/e^x))

To solve the differential equation y'' + 3y' + 2y = cos(ex) using variation of parameters, we first need to find a particular solution of the form yp = u(x)e^(rx), where u(x) is a function of x and r is a constant.

The characteristic equation of the homogeneous equation is r^2 + 3r + 2 = 0, which has roots r1 = -1, r2 = -2. Thus, the general solution of the homogeneous equation is yh = c1e^(-x) + c2e^(-2x).

To find a particular solution, we use the method of variation of parameters. Let yp = u(x)e^(-x), where u(x) is a function of x. Then, y'p = u'(x)e^(-x) - u(x)e^(-x) and y''p = u''(x)e^(-x) - 2u'(x)e^(-x) + u(x)e^(-x).

Substituting yp, y'p, and y''p into the original equation and simplifying, we get:

u''(x)e^(-x) - 2u'(x)e^(-x) + u(x)e^(-x) = cos(ex)

We can solve for u(x) by dividing both sides of the equation by e^(-x)

u''(x) - 2u'(x) + u(x) = cos(ex)e^x

Now we need to find W(x) = W(y1,y2) = e^(-x)e^(-2x) = e^(-3x)

Integrating W'(x) cos(ex)e^x dx = -(1/5)e^(-x)(sin(ex) - (cos(ex)/e^x))

Hence we get the  general solution of the differential equation is

y(x) = (c1 + c2x)e^(-x) + (1/5)e^(-x)(sin(ex) - (cos(ex)/e^x))

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No, Barbara does not have enough money.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

Using the words here, we can create the expression 20d+7 where d is the number of days.

We can now substitute 15 in as d, to see how much this will cost.

20*15+7

=300+7 = 307

So the total cost will be $307.

Since $307 is more than $250, she does not have enough money.

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Question:

Susan plans to rent a bike in New Orleans to tour the city. The cost of the rental is $20 per day. The cost of a helmet is $7 for as long as Susan needs the bike. Barbara has $250 to rent a bike for 15 days. Does Barbara have enough money? Explain. First answer gets Brainiest and 48 points hurry please tho

Step-by-step explanation:

6x + 2y = 10

2y = -6x + 10

y=-6/2x +10/2

y= -3x + 5

x + 2y = 4

2y = -x + 4

y= -1/2x + 4/2

y=-1/2x +2

Answer:

1/3

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

1 1/3 = 4/3        4 = 4/1

4/3  /  4/1     = 4/3  X 1/4  =  4/12 = 1/3

To prove that angle 1 is supplementary to angle 3, we must demonstrate that the two angles add up to 180 degrees.

Angle is a term used to describe the shape formed when two straight lines cross or intersect. It is measured in degrees, and is typically represented by the symbol ∠. Angles are important in geometry, architecture, engineering and construction. They are also used in navigation and astronomy. Angles are a fundamental part of understanding the physical world around us.

Since line m is parallel to line n, then the two lines are essentially parallel lines, meaning that all of the angles made with the lines are the same. In this case, the angles made with line m and line n are both 90 degrees. Since the two angles are the same, then that means that angle 1 and angle 3 are also the same.

Since angle 1 and angle 3 are the same, then that means that the two angles add up to 180 degrees. Therefore, angle 1 is supplementary to angle 3.

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An equation of the line that passes through the point (1,7) and perpendicular to the line x+6y=42 is y = 6x + 1

In this question we have been given an equation of line x + 6y = 42

We need to find an equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y = 42

Let m be tha slope of the required line.

We write  equation of line x + 6y = 42 in slope-intercept form.

y = (42 - x)/7

y = 6 - x/6

y = -1/6 x + 6

Let m1 be the slope of line x + 6y = 42

m1 = -1/6

We know that the product of slopes of perpendicular lines is -1.

So, m * m1 = -1

m * (-1/6) = -1

m = (-1) * (-6)

m = 6

So, the slope of the required line is 6

We know that the point - slope form of equation of line is:

(y - y1) = m(x - x1)

Let (x1, y1) = (1, 7)

Substituting values in above equation,

(y - 7) = 6(x - 1)

y - 7 = 6x - 6

y = 6x - 6 + 7

y = 6x + 1

Therefore, equation of the required line is y = 6x + 1

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The equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42 is y = -6x - 5.

The equation of a line that passes through the given point (1,7) and is perpendicular to the line x+6y=42 can be determined by using the slope-intercept form of the equation of a line.

The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope of the line, and b is the y-intercept.

First, we need to determine the slope of the line x+6y=42. To determine the slope, we can solve for y by subtracting x from both sides of the equation, yielding 6y = -x + 42. Then, we can divide both sides of the equation by 6 to obtain y = -x/6 + 7. Thus, the slope of the line x+6y=42 is -x/6.

Now, the slope of a line perpendicular to the line x+6y=42 is the negative reciprocal of the slope of x+6y=42, which is 6/-x.

The equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42 can then be determined using the point-slope form of the equation of a line, which is given by y - y1 = m(x - x1). Substituting the coordinates of the point (1,7) and the slope 6/-x, we obtain

y - 7 = 6/(-x)(x - 1)

Simplifying, we obtain

y = -6x - 5

Thus, the equation of the line that passes through the point (1,7) and is perpendicular to the line x+6y=42 is y = -6x - 5.

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102,566,767, 1,9044828e-10, and 297,060 are the answers to the questions.

The questions above use addition and multiplication to solve the problem.

101,455,348 + 1,111,419 = 102,566,767

0.000000612 x 0.00031119 = 1,9044828e-10

297,060 + 0.0004839 = 297,060

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The probability that the next coin flip will yield a head is 50%, as each coin flip has an equal chance of landing either heads or tails.

Probability is an incredibly important concept to understand in our everyday lives. Understanding probability helps us make informed decisions about the chances of something happening. For example, when playing a game of chance, understanding probabilities can give us a better idea of the likelihood of winning or losing. Knowing the probability of an event happening can also help us make decisions in other areas of life, such as investing.

In the context of coin flipping, it is important to remember that the probability of a coin landing on heads or tails is always 50%. This means that no matter how many times the coin is flipped and no matter what the previous outcome, the probability of the next flip being heads or tails remains the same. This concept is the basis of probability theory, which can be applied to many other areas of life.

Understanding probabilities is also useful in understanding the chances of certain events occurring in the world. For example, understanding the probability of an earthquake happening in a certain area can help us make decisions about where to live or how to prepare for a potential disaster. Similarly, understanding the probability of a successful business venture can help us decide whether or not to invest in it.

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Answer: cant read it

Step-by-step explanation: