find an equation of the tangent line to the curve at the given point. y = 6ex cos x, (0, 6)

they belong to high-performance athletes

It may be a sign of a family history of early heart disease.  If one of your close relatives, such as a parent or sibling, has experienced a heart attack, a stroke, or was previously diagnosed with heart disease before the age of 60. Thus, option B, C is correct.

The CDC's Response to the Risk Factors in the Country. Leading causes of heart disease and stroke risk factors include high blood pressure, high levels of low-density lipoprotein (LDL) cholesterol, diabetes, smoking, exposure to second-hand smoke, obesity, a poor diet, and inactivity.

People who are aware of their situation make wiser decisions, live longer, and experience greater well-being. Even if you have heart failure, it is still possible to lead a regular life. The secret to success is realizing heart failure and taking charge of it.

Therefore, They are from well-trained professional athletes, and They are from individuals with a history of heart disease.

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The question is incomplete, complete question with option given below:

Three hearts are dissected from individuals with unknown histories. Two of the three hearts are enlarged. Select all of the possible reasons the two hearts may be enlarged.

A. They are from individuals who had low blood pressure histories.

B. They are from well-trained professional athletes.

C. They are from individuals with a history of heart disease.

D. They are from individuals who had arthritis issues.

The value of y in the equation 14.25y = 99.75 is C. 7.00.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the equation is given as:

14.25y = 99.75

Divide through by 14.25

y = 99.75 / 14.25

y = 7

The value of y is 7.

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Answer:

Marker = $0.50

Pencil = $0.15

Step-by-step explanation:

The cost of 3 markers and 2 pencils can be represented as 3M + 2P = $1.80.

The cost of 4 markers and 6 pencils can be represented as 4M + 6P = $2.90.

Now that we have our two equations, we can solve for M and P. To do this, we can eliminate one of the variables by multiplying one equation by a constant and adding the two equations together.

For example, if we multiply the first equation by 4 and the second equation by -3, we get:

12M + 8P = $7.20

-12M - 18P = -$8.70

Adding these two equations together, we get:

-10P = -$1.50

Dividing both sides by -10, we get:

P = $0.15

Now that we have found the value of P, we can substitute it back into one of our original equations to find the value of M. If we substitute P = $0.15 into the first equation, we get:

3M + 2($0.15) = $1.80

3M + $0.30 = $1.80

3M = $1.50

M = $0.50

So, the cost of 1 marker is $0.50, and the cost of 1 pencil is $0.15.

Answer:

-5/4

Step-by-step explanation:

the main answer is -5/4

The area of centroid of the region in the first quadrant bounded by the given curves. y = x6, x = y6 is 17 units.

The centroid can be found if we will integrate the result obtained by subtracting the given two functions .

∫ f(x) - g(x) dx

The limits will be a and b where a = 0 and b =1.

f(x )= x⁶

g(x) =y⁶

= ∫ x⁶ -  y⁶dx

=∫ x⁶dx -  ∫  y⁶dx

= 1/7 x⁷ -  1/7 x⁷  

Now since limits are 0 and 1 ,

1/7 1⁷ -  1/7 0⁷  

=17 units

The central point of any geometric figure is known as centroid.

Different figure have different centroid and the all have unique properties.

Integration is a branch of calculus which means to add things up to form a whole.

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4000 N  is the work done .

In math, what is a distance?

The length of the segment of the line that connects the supplied two points determines the distance between them. The length of the shortest line segment connecting a point to a line represents the distance between them.

                               Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.

m = 80 kg

d = 5m

g = 10 m/s²

work done = force × distance

                   = mgh

                    =  80 × 10 × 5

                    =  4000 N

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Answer:

6i-4

Step-by-step explanation:

To simplify the expression 4i+(8-3i) - 12+√-25, you can start by combining like terms.

First, you can combine the terms 4i and -3i to get 1i. You can also combine the constants 8 and -12 to get -4.

So, the expression becomes 1i - 4 + √-25.

Next, you can simplify the square root. √-25 is the same as √(-25) which is the same as √(5*-5), which is the same as 5√(-1). √(-1) is equal to i, so 5√(-1) is equal to 5i.

Therefore, the final simplified form of the expression is 1i - 4 + 5i, which is equal to 6i - 4.

Answer:

The observation in the upper right corner of the plot is influential for the least-squares regression line.

Step-by-step explanation:

The length of the curve x = 1/3 √y (y − 3)  is 64/3.

The distance between two point along a segment of a curve is known as the arc length.

The equation of the curve is given by:

x = 1/3 √y (y − 3), 16 ≤ y ≤ 25

Length of the curve y = f(x) between point  x =a to x = b is given by:  

[tex]\int\limits^b_a {\sqrt{1+[f'(x)]^2} } \, dx[/tex]

 √1 + [f′(x)]2 dx.

x = 1/3 √y (y − 3)

x = 1/3 * [tex]y^\frac{3}{2}[/tex] - [tex]y^\frac{1}{2}[/tex]

Let's find the first derivative of x.

dx/dy = 1/3. 3/2.  [tex]y^\frac{1}{2}[/tex]- 1/2 .  [tex]y^\frac{1}{2}[/tex]

dx/ dy = 1/2 ( [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])

(dx/dy)^2= 1/4 (  [tex]y^\frac{1}{2}[/tex] - [tex]y^\frac{-1}{2}[/tex])^2

= 1/4(y + [tex]y^-^1[/tex]-2)

1 + {f′(x)}2 = 1 + 1/4(y +[tex]y^-^1[/tex]-2)

= 1/4 y + 1/4[tex]y^-^1[/tex]+ 1/2

1 + {f′(x)}2= 1/4 (y + [tex]y^-^1[/tex] + 2)

√[1 + {f′(x)}2] = 1/2 (  [tex]y^\frac{1}{2}[/tex] +  [tex]y^\frac{-1}{2}[/tex])

Length of curve  is given by:  

25

∫   [tex]\frac{\sqrt{y} }{2} +\frac{1}{2\sqrt{y} }[/tex] dy

16

= [tex]\left \{ {{y=25} \atop {x=16}} \right.[/tex] [[tex]y^\frac{3}{2}[/tex]/3 + √y]

= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]

= [125/3 + 5] - [64/3 + 4]

= 140/3 - 76/3

= (140 - 76)/3

= 64/3

So the length of the curve is 64/3

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In order to plot the region enclosed by the given graphs we have to find the intersection points of all the 3 graphs taking 2 at a time

so finding intersection point of the y=4/x and y=16x

4/x=16x

=>  = 1/4

=> x = 1/2 as x>0

and y=16x

=> y =8

now finding intersection point of y=4/x and y=1/16x

=> 4/x =x/16

=>  = 64

=> x = 8 as x>0

and y= 4/x

=> y=1/2

now finding intersection point of y=16x and y=1/16x

the intersection point of both line is x=0

so y=16x

=> y=0

so we will get the intersection point of all the lines now after plotting all the points below we will get the graph as attached below.

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Answer:

[tex]\frac{3}{5\pi}[/tex]

Step-by-step explanation:

[tex]\frac{f(5\pi/6)-f(0)}{5\pi/6}=\frac{3}{5\pi}[/tex]

It's equation in point-slope from is -1/6x+5/2.

An equation is a formula that is express the equality of two equation.

Based on the given condition the formula

M= -1/6

Substitute {m -1/6

                        { X= 9

                        {Y = 1

(Into y= mx+b)

1=-1/6×9+b

Reduce the expression into the Lowest term

1=-1/2×3+b

Write as a single fraction

1=-3/2+b

Rearrange variables to the left side of the equation.

-b= -3/2-1

Now we have to find the denominator and write the numerators above common denominator

-b=-3-2/2

Calculate the sum or difference

-b=-5/2

b=5/2

Substitute {m=-1/6 b=5/2 into y mx+b

Y=-1/6x+5/2

Rewrite the equation of the line

Y= -1/6x+5/2 in point-slope

Y-1 = -x-9/6

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Answer:

first equation = red line

second equation = blue line

Step-by-step explanation:

First, we solve for y for both equations

4x + 2y = -12

2y = -12 - 4x

2y = -4x -12

y = -2x - 6

3x - 5y = -35

-5y = -35 - 3x

-5y = -3x - 35

y = (-3/5)x + 7

Answer:

78

Step-by-step explanation:

The answer is 78 or 87 dear friend its a mystery

Answer:

op

Step-by-step explanation:

The two simultaneous equations are 50x + 25y = 250 and x + y = 7

Simultaneous equations are a set of two or more equations that contain variables. The values of the variables can be calculated using either method of elimination or substitution. The values of the variables must then satisfy all the equations

Assuming the bottle of soda has 50 grams of sugar in each bottle (since this information is not given). Let the bottles of soda bought be x and bottles of juice bought be y. Two equations will be formed so that we can solve them simultaneously.

50x = total amount of sugar in soda bottles

25y = total amount of sugar in juice bottles

50x + 25y = 250 (total amount of sugar in all bottles)

x + y = 7 (total number of bottles)

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Answer:

3/5

Step-by-step explanation:

AB = AC · cos A

18 = 30 · cos A

cos A = 18/30

cos A = 3/5

The solution to the equation eˣ + 1 = 2ˣ + 2 is x = 1.2

From the question, we have the following parameters that can be used in our computation:

eˣ + 1 = 2ˣ + 2

Split to system of equations

This gives

y = eˣ + 1

y = 2ˣ + 2

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the curves intersect at (1.2, 4.3)

This means that

x = 1.2 (approximated)

Hence, the solution is x = 1.2

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The most sensible average to use in this case would be the mode, which is the value that appears most frequently in the data set. In this case, the mode is 2, which appears 9 times in the data set. This means that the most common number of children in a family in the class is 2.

In this case, the most sensible average to use would be the mode, which is the number that appears most frequently in the data set. This is because the mode represents the most common number of children in the families of the children in the class, which is likely to be a more accurate representation of the typical family size in the class than the mean or median.

To find the mode, we first need to count how many times each number appears in the data set. In this case, the numbers 1, 2, 3, and 4 appear in the data set as follows:

1: 7 times

2: 11 times

3: 3 times

4: 1 time

We can see that the number 2 appears most frequently, with a count of 11. Therefore, the mode in this case is 2, and this is the most sensible average to use in this situation.

The time that has elapsed since Gerardo started walking away from car will be equal to 5 seconds.

We solve this problem by converting it into a linear equation that has three variables in it. Since we have distance, time and speed the three variables will be d, t and s respectively. The expression which shows the distance of Gerardo will be expressed as

d = (s×t) + 9; we have the constant as 9 because Gerardo was 9 feet away from his car.

Now, we have the distance as d = 24 feet and the speed is constant that is equal to 3 feet per second and we need time which will be

24 = (3×t) + 9

15 = 3×t

=> t = 15/3

=> t = 5 seconds

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The given statement is true that the points on a perpendicular bisector of a line segment are equidistant from the segment’s endpoints.

A line that splits another line segment into two equal halves by intersecting it perpendicularly is known as a perpendicular bisector. A rule, compass, and pencil can be used to create a perpendicular bisector.

When two lines cross at right angles or 90 degrees, they are said to be perpendicular to one another. A line that splits a line into two equally sized parts is known as a bisector. A line segment's perpendicular bisector suggests that it meets the segment at a 90-degree angle and splits it into two equal halves.

"Perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment’s endpoints".

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Both equations y = 0.5x + 2.75 and y – 0.5x = 2.75 are equal. Hence, these systems will have infinite solutions. Hence, Option a is the most suitable answer to this question.

The system of equations having an infinite number of solutions must be the same.

In option a -

we have, y = 0.5x + 2.75 and 2y = x + 2.75

Rewriting the second equation 2y = x + 2.75 in slope-intercept form, we get,

2y = x + 2.75

y = x/2 + 2.75/2

y = 0.5x + 1.375

Both equations are not similar.

Hence this option is not the right choice.

Similarly, we will check for option b -

we have, y = 0.5x + 2.75 and y – 0.5x = 2.75

From the second equation y - 0.5x = 2.75, this can be expressed as y = 0.5x + 2.75 in the slope-intercept form.

Here, we get both equations equal.

Thus,  y = 0.5x + 2.75 and y – 0.5x = 2.75 will have infinite solutions.

Similarly, checking for other options, we do not get any similar equations.

Hence, option b is the correct answer to this question.

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The complete question is -

Which systems have infinite solutions? Check all that apply.

a) y = 0.5x + 2.75 and 2y = x + 2.75

b) y = 0.5x + 2.75 and y – 0.5x = 2.75

c) y = 0.5x + 2.75 and 0.5x + y = 2.75

d) y = 0.5x + 2.75 and y = 0.5(x + 5.5)

e) y = 0.5x + 2.75 and y = –2(–0.25x )+ 2.75

Answer: look at the screenshot below I hope it helps you, my friend

have a lovely day :3 :) :D

UWU

Step-by-step explanation:

A city's citizens cast ballots on whether or not to increase property taxes. There were 8 yes votes and 5 nay votes, in that order. if there were 4955 no votes,The total number of votes was 6,940.

The ratio of yes votes to no votes was 8 to 5, meaning for every 8 yes votes there were 5 no votes.

This ratio can be expressed as a fraction: 8/5.

To calculate the total number of votes, we need to know only the number of no votes, which we know is 4955.

We can then multiply this number by the fraction 8/5. This gives us a total of 6,940 votes.

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The number of classes should be an integer and this value will typically be a fraction. The limit needs to be raised in order to take into account all observations when this calculation yields an integer.

The fixed and variable costs can be determined by solving the system of equations if the variable cost is a fixed charge per unit and the fixed costs stay the same. The high-low method can, however, produce more or less accurate findings based on the distribution of values between the highest and lowest monetary values or quantities, therefore it is important to use caution when applying it.

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[tex]-\cfrac{5}{7}(-42k-56)\implies -\cfrac{5}{7}(-42k)\left[ -\cfrac{5}{7}(-56) \right]\implies +\cfrac{5}{7}(42k)+\left[ \cfrac{5}{7}(56) \right] \\\\\\ \cfrac{5(42k)}{7}+ \cfrac{5(56)}{7}\implies 5\cdot \cfrac{42}{7}k + 5\cdot\cfrac{56}{7}\implies 5\cdot 6k+5\cdot 8\implies {\Large \begin{array}{llll} 30k+40 \end{array}}[/tex]

Answer:

0 Joules (No work)

Step-by-step explanation:

The amount of work done on an object is equal to the force applied to the object times the distance over which the force is applied. In this case, the force applied to the car is 100 newtons, but the car does not move, so the distance over which the force is applied is 0 meters.

Therefore, the amount of work done on the car is 100 newtons * 0 meters = 0 joules. This means that no energy has been transferred to or from the car as a result of the force applied to it.

The features that Michael should include on the graph of the parabola are given as follows:

The parabola for this problem is defined as follows:

y = -0.5(x - 3)² - 1.

Comparing to the vertex form definition, the coordinates of the vertex are given as follows:

(3, -1).

The equation can also be written as follows:

-0.5(x - 3)² = y + 1

(x - 3)² = -2(y + 1).

Then the coefficient p is obtained as follows:

4p = -2

p = -0.5

Then the coordinates of the focus are given as follows:

(3, -1 - 0.5) = (3, -3/2),

The equation of the directrix is then given as follows:

y = 1 - 0.5

y = 1/2.

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Answer:

750 ft

Step-by-step explanation:

the 2 situations are similar ( both right triangles ) with corresponding sides being in proportion.

let h be the height of the cell phone tower

We require the dimensions to be the same, using the conversion

1 foot = 12 inches , then

10 ft = 10 × 12 = 120 in

125 ft = 125 × 12 = 1500 in

then we obtain

[tex]\frac{h}{1500}[/tex] = [tex]\frac{120}{20}[/tex] =  6 ( multiply both sides by 1500 to clear the fraction )

h = 1500 × 6 = 9000 in ( divide by 12 to convert to ft )

h = 9000 in ÷ 12 = 750 ft

that is the cell phone tower is 750 ft tall.

Approximately, Brianne percentage rate of contribution is 0.5%.

Brianne's annual contribution to her union dues is $200. Her salary is $38,500.

Approximately, her percentage rate of contribution can be calculated as follows:

percentage rate of contribution = union dues / salary × 100

union dues = 200 dollars

salary = 38500

percentage rate of contribution = 200 / 38500 × 100

percentage rate of contribution = 20000 / 38500

percentage rate of contribution =  0.51948051948

Therefore,

percentage rate of contribution ≈ 0.5%

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