write the force equation for the following system b and b are the coefficient of viscious friction and force case by this friction is

The equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex]  tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

Trigοnοmetric equatiοns are equatiοns that invοlve trigοnοmetric functiοns such as sine, cοsine, tangent, etc. These equatiοns usually invοlve finding values οf the unknοwn angle(s) that satisfy the given equatiοn. They can be sοlved using algebraic techniques οr by using the prοperties οf trigοnοmetric functiοns.

Accοrding tο the given infοrmatiοn:

The given functiοn is [tex]f(t) = -5t^2 + 20t[/tex], which mοdels the height οf an οbject in feet as a functiοn οf time in secοnds.

Tο find the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch, we need tο sοlve the equatiοn [tex]-5t^2 + 20t = 18[/tex].

Tο sοlve this quadratic equatiοn using the quadratic fοrmula, we first identify the values οf a, b, and c frοm the general fοrm οf a quadratic equatiοn, [tex]ax^2 + bx + c = 0[/tex].

In this case, a = -5, b = 20, and c = -18. Substituting these values intο the quadratic fοrmula, we get:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

Plugging in the values οf a, b, and c, we get:

[tex]t = (-20 \± \sqrt{+(20^2 - 4(-5)(-18)})) / 2(-5)[/tex]

Simplifying this expressiοn, we get:

[tex]t = (-20 \± \sqrt{(400 - 360))} / (-10)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

[tex]t = 2 \± 0.632[/tex]

Therefοre, the twο pοssible values οf t are:

t = 2 + 0.632 = 2.632 secοnds

t = 2 - 0.632 = 1.368 secοnds

Therefοre, the equatiοn that cοrrectly shοws the quadratic fοrmula being used tο determine the number οf secοnds it will take fοr the οbject tο be at a height οf 18 feet after launch is:

[tex]t = (-b\± \sqrt{(b^2 - 4ac)}) / 2a[/tex]

[tex]t = (-20 \± \sqrt{(20^2 - 4(-5)(-18))}) / 2(-5)[/tex]

[tex]t = (-20\± \sqrt{(40)}) / (-10)[/tex]

[tex]t = (-20 \± 2\sqrt{(10)}) / (-10)[/tex]

t = 2 ± 0.632

Therefοre, the equatiοn is [tex]t = (-20 \± \sqrt{(400 - 4(-5)(-18))}) / 2(-5)[/tex] tο sοlve fοr the time it takes fοr the οbject tο be at a height οf 18 feet.

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Answer:

To calculate the distance between each pair of points given, we can use the distance formula which is derived from the Pythagorean theorem. The formula is:

distance = square root of [(x2 - x1)^2 + (y2 - y1)^2]

Using this formula, we can calculate the following distances:

a. Distance between M and P = 13 units

b. Distance between A and B = 5 units

c. Distance between C and D = 10 units

Answer:

Size 3 ‍♀️

Step-by-step explanation:

In the US, the average shoe size for 10-Year-Old is USA Size 3.

-Jul 12, 2020

The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.

Answer: 0.04

Step-by-step explanation:

In order to get 4% as a decimal, you must divide 4 by 100.

4/100 = 0.04

Thus, the answer to your question is 0.04

The amount of interest earned on $4,000.00 for 4 years, compounding daily at 4.5% APR, is $1,064.08.

To calculate the amount of interest on $4,000.00 for 4 years, compounding daily at 4.5% APR, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we have P = $4,000.00, r = 0.045, n = 365 (since interest is compounded daily), and t = 4. Plugging these values into the formula, we get:

A = $4,000.00(1 + 0.045/365)^(365*4)

A = $4,000.00(1.0001234)^1460

A = $4,889.68

The final amount is $4,889.68, which means that the interest earned is:

Interest = $4,889.68 - $4,000.00 = $889.68

We are given that the monthly interest table shows that $1.197204 in interest is earned for each $1.00 invested. Therefore, to find the interest earned on $4,000.00, we can multiply the interest earned by the factor:

$1.197204 / $1.00 = 1.197204

Interest earned = $889.68 x 1.197204 = $1,064.08

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Answer:

To solve the system of equations:

n + d = 21 ---(1)

0.05n + 0.10d = 1.70 ---(2)

We can use the substitution method by solving for one variable in terms of the other from equation (1) and substituting it into equation (2).

Solving equation (1) for n:

n = 21 - d

Substituting this expression for n into equation (2):

0.05(21 - d) + 0.10d = 1.70

Distributing the 0.05:

1.05 - 0.05d + 0.10d = 1.70

Combining like terms:

0.05d = 0.65

Dividing both sides by 0.05:

d = 13

Substituting this value of d into equation (1):

n + 13 = 21

Solving for n:

n = 8

Therefore, the solution to the system of equations is n = 8 and d = 13.

Answer:

30,000 grams

Step-by-step explanation:

multiply the 30KG by 1,000 (that is the conversion) and you get 30,000g

Answer:

hi I'm really sorry I can't help

The probability of all will fail is the lowest.

The given problem states that a missile guidance system has seven fail-safe components, and the probability of each failing is 0.2. The given variable is binomial. We need to find the following probabilities:

(a) Exactly two will fail.

(b) More than two will fail.

(c) All will fail.

(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.

(a) Exactly two will fail.

The probability of exactly two will fail is given by;

P(exactly two will fail) = (7C2) × (0.2)2 × (0.8)5
= 21 × 0.04 × 0.32768
= 0.2713

Therefore, the probability of exactly two will fail is 0.2713.

(b) More than two will fail.

The probability of more than two will fail is given by;

P(more than two will fail) = P(X > 2)
= 1 - P(X ≤ 2)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2))
= 1 - [(7C0) × (0.2)0 × (0.8)7 + (7C1) × (0.2)1 × (0.8)6 + (7C2) × (0.2)2 × (0.8)5]
= 1 - (0.8)7 × [1 + 7 × 0.2 + 21 × (0.2)2]
= 1 - 0.2097152 × 3.848
= 0.1967

Therefore, the probability of more than two will fail is 0.1967.

(c) All will fail.

The probability of all will fail is given by;

P(all will fail) = P(X = 7) = (7C7) × (0.2)7 × (0.8)0
= 0.00002

Therefore, the probability of all will fail is 0.00002.

(d) Compare the answers for parts a, b, and c, and explain why these results are reasonable.

The probability of exactly two will fail is the highest probability, followed by the probability of more than two will fail. And, the probability of all will fail is the lowest probability. These results are reasonable since the more the number of components that fail, the less likely it is to happen. Therefore, it is reasonable that the probability of exactly two will fail is higher than the probability of more than two will fail, and the probability of all will fail is the lowest.

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The solution to the equation (3√x) - √(9x-17) = 1 is x = 9.

Given the equation in the question (3√x) - √(9x-17) = 1.

To solve for x in the given equation:

(3√x) - √(9x-17) = 1

We can start by isolating the square root term on one side of the equation. Adding √(9x - 17) to both sides, we get:

(3√x) = √(9x - 17) + 1

Squaring both sides of the equation, we get:

(3√x)² = (√(9x - 17) + 1)²

9x = -16 + 2√(9x - 17) + 9x

Solve for 2√(9x - 17)

2√(9x - 17) = 16

36x - 68 = 256

Add 68 to both sides

36x - 68 + 68 = 256 + 68

36x = 324

x = 324/36

x = 9

Therefore, the solution is x = 9.

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The coordinates of your position If we start at the origin, we are moving only along the x-axis  of  a distance of 7 units in positive direction and then only in the negative y-axis direction and  z-coordinate is zero are (7,-6,0).

The origin is the point in space that has a position of (0, 0, 0), which represents the point where the x, y, and z axes intersect.

The first step is to move 7 units in the positive x direction. The positive x direction is the direction in which x values increase. Therefore, we move to the right along the x-axis to the point (7, 0). This means that we have moved 7 units along the x-axis, and our position is now (7, 0, 0).

The second step is to move downward a distance of 6 units. Since we are not moving in the x direction, we are only changing our position along the y-axis. Moving downward in the y direction means decreasing our y-coordinate. Therefore, we move 6 units downward from our current position to the point (7, -6, 0).

Therefore, the coordinates of our position are (7, -6, 0)

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Answer:

2 9/14

Step-by-step explanation:

Answer: Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) ... linear differential equation for x > 0 that satisfies the initial condition.

Step-by-step explanation:

Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

Step-by-step explanation:

The sum of the angles of an N-sided convex figure is (n-2)*180 - a simple proof of which is just to decompose the figure into triangles, each of which has all of its vertices the same as three of the vertices of the original figure. (Cut a quadrilateral into two triangles along a diagonal, for instance).

So, a 7-sided figure has angles totaling 5*180 = 900. Now set up a simple equation:

3x + 4(x+15) = 900

7x + 60 = 900

7x = 840

x = 120

The figure has three angles of 120 degrees, and four angles of 135 degrees.

The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The value of a function, given the value(s) assigned to its argument, is the sum that the function assumes for these input values (s).

For x =7,x+|x| =7+|7| =14

For x =10,x+|x|= 10+|10| =20

For x = 0,x+|x| =0+|0| =0

For x = -3, x + |x| = -3 + |-3| = 0

For x = -8, x + |x| = -8 + |-8| = 0

The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.

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Answer:

x = -2 ,  y = 2

Step-by-step explanation:

hope this helps :)

Answer:

36

Step-by-step explanation:

By answering the presented question, we may conclude that I used the following procedures to produce this graph.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I used the following procedures to produce this graph:

I classified the personnel as full-time, part-time, and temporary.

I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."

I made the segmented bar graph using these percentages.

The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.

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The z-score for the 25th percentile of a standard normal distribution is approximately -0.625. Here option A is the correct answer.

To find the z-score for the 25th percentile of a standard normal distribution, we need to use a standard normal distribution table or calculator. The 25th percentile corresponds to a cumulative area under the standard normal curve of 0.25.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative area of 0.25 is about -0.68. This means that approximately 25% of the area under the standard normal curve lies to the left of -0.625.

So, among the given options, the correct answer is Option A, -0.625, Option D, -0.50, which is also incorrect. Option E, 0.00, is definitely incorrect because the 25th percentile is to the left of the mean.

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Answer:

2x - 13

Step-by-step explanation:

If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:

x + (x - 13) = 2x - 13

Hence, 28 toy soldiers are the correct answer.

A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.

Let's refer to the quantity of toy soldiers as "x".

We are aware that x is within the range of 27 and 54 thanks to the problem.

x can be divided by 4 without any remainders.

The residual is 6 when x is divided by 7.

The leftover after dividing x by five is three.

These criteria allow us to construct an equation system and find x.

Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:

x = 4k, where k is some integer.

Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:

x ≡ 6 (mod 7)

This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:

4k ≡ 6 (mod 7)

We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:

4(1) ≡ 6 (mod 7)

4 ≡ 6 (mod 7)

It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.

k = 2:

4(2) ≡ 6 (mod 7)

1 ≡ 6 (mod 7)

k = 3:

4(3) ≡ 6 (mod 7)

5 ≡ 6 (mod 7)

k = 4:

4(4) ≡ 6 (mod 7)

2 ≡ 6 (mod 7)

k = 5:

4(5) ≡ 6 (mod 7)

6 ≡ 6 (mod 7)

k = 6:

4(6) ≡ 6 (mod 7)

3 ≡ 6 (mod 7)

k = 7:

4(7) ≡ 6 (mod 7)

0 ≡ 6 (mod 7)

We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:

x = 4(7) = 28

This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.

28 toy soldiers are the correct response.

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216 cm2 is the size of the rectangle border.

the translation of the question is

A painting including its frame is 25 cm long and 10 cm wide, what is the area of ​​the frame if it is 4 cm wide?

What is a rectangle's area?

When the dimensions of a rectangle with length and width are multiplied, the area of the rectangle is determined as follows:

A = lw.

The total area is therefore given by:

A = 25 x 10 = 250 cm².

The white region's size is shown by:

A = (25 - 2 x 4) x (10 - 2 x 4) is equal to 17x 2 and 34 cm2.

Hence, the border's area is as follows:

216 cm2 = 250 cm2 - 34 cm2.

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The area of the quadrilateral is 161.24 cm².

We can see that we can divide the quadrilateral into two triangles: ABD and CBD. We know that the height of ABD is 6 cm and the height of CBD is 8 cm. We also know that BD is 15 cm. To find the area of each triangle, we need to find the base of each triangle. We can do this using the Pythagorean theorem.

For triangle ABD:

AB² = AD² + BD²

AB² = (6 cm)² + (15 cm)²

AB² = 261 cm²

AB = [tex]\sqrt(261) cm[/tex]

For triangle CBD:

BC² = CD² + BD²

BC² = (8 cm)² + (15 cm)²

BC² = 289 cm²

BC = 17 cm

Now we can find the areas of the triangles:

Area of ABD =[tex]\frac{1}{2}[/tex] * AB * 6 cm

Area of ABD = [tex]\frac{1}{2}[/tex] * [tex]\sqrt(261) cm[/tex] * 6 cm

Area of ABD = 93.24 cm^2

Area of CBD = [tex]\frac{1}{2}[/tex] * BC * 8 cm

Area of CBD = [tex]\frac{1}{2}[/tex] * 17 cm * 8 cm

Area of CBD = 68 cm²

Finally, we can find the area of the quadrilateral by adding the areas of the triangles:

Area of ABCD = Area of ABD + Area of CBD

Area of ABCD = 93.24 cm² + 68 cm²

Area of ABCD = 161.24 cm²

Therefore, the area of the quadrilateral is 161.24 cm².

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The area is changing at a rate of 28,160 m²/year at that point in time.

The area of the rectangular region is given by:

A = lw

Where l is the length of the rectangular region and w is the width of the rectangular region.

The width of the rectangular region is given to be 220 m. Therefore, we have the width w = 220 m. The length l of the rectangular region can be found knowing that it is twice as long as it is wide. Therefore, the length of the rectangular region is given by:

l = 2w

l = 2 x 220

l = 440

Therefore, the length l of the rectangular region is 440 m.

At the given point in time, the width of the rectangular region is growing at a rate of 32 m per year. Therefore, we have the rate of change of the width dw/dt to be 32 m per year. We need to find how fast the area of the rectangular region is changing at that point in time. Therefore, we need to find the rate of change of the area of the rectangular region dA/dt.

A = lw

dA/dt = w dl/dt + l dw/dt

dA/dt = 220 d/dt(2w) + 440 dw/dt

dA/dt = 220 x 2 dw/dt + 440 dw/dt

dA/dt = 880 dw/dt

Substitute the value of dw/dt to get:

dA/dt = 880 x 32

dA/dt = 28,160 m²/year

Therefore, the area of the rectangular region has a rate of change of 28,160 m² per year at that point in time.

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Answer:

d(0) = -3

Step-by-step explanation:

d(x) = -x + -3                           d(0)

d(0) = 0 - 3

d(0) = -3

So, the answer is d(0) = -3

using the ratio given, the number of computers could be sold by the company last week is: A. 448 desktops, 168 laptops.

To find the actual numbers of desktop and laptop computers sold, we need to choose a common factor for the ratio 8:3.

Let's assume that the total number of computers sold is 33x (where x is a positive integer). Then, the ratio 8:3 corresponds to 8x desktops and 3x laptops. We can check which of the given options satisfies this condition:

A. 8x = 448, 3x = 168 --> This satisfies the condition, as 8:3 = 448:168

B. 8x = 448, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 448:165

C. 8x = 440, 3x = 168 --> This does not satisfy the condition, as 8:3 is not equal to 440:168

D. 8x = 400, 3x = 165 --> This does not satisfy the condition, as 8:3 is not equal to 400:165

Therefore, the answer is option A: 448 desktops and 168 laptops could be the numbers of computers sold by the company last week.

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Answer:

I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.

for the first equation y=-x+6, y intercept is (0,6)

for equation two 2x-y=-9, y intercept is (0,9)

In both of the equations the x value is 1.

Solving for y without graphing. Y=9+2x

and x=-1

Step-by-step explanation:substitute i

HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5

It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.

The value of the additional data point is  [tex]$19.17$[/tex].

Let us first find the mean of the given data:

[tex]Mean = \frac{\sum_{i=1}^{n} x_i}{n}=\frac{39 + 45 + 43 + 42 + 44}{5}= 42.6[/tex]

Now let's find the value of the additional data point. Let the value of the additional data point be x. Therefore, the new sum of data is

[tex]$(39+45+43+42+44+x)$[/tex].

Total numbers of data are 6 (five given in the set and one additional data point).So, the mean of the resulting data set is given by:

[tex]32.083 = \frac{(39+45+43+42+44+x)}{6}[/tex]

Multiplying both sides of the equation by 6 we get:

[tex]6 \times 32.083 = (39+45+43+42+44+x)[/tex]

We have the value of [tex]$39+45+43+42+44$[/tex] which is [tex]$213$[/tex].

Therefore, substituting all the values, we get:

[tex]193.83 + x = 213[/tex]

On subtracting [tex]$193.83$[/tex] from both sides, we get the value of

[tex]x. x = 213 - 193.83 = 19.17[/tex]

Therefore, the value of the additional data point is [tex]$19.17$[/tex]

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