A circle is centered at the point O (0,0) and has a radius of the square root of 38?
Where’s does the K (6,1) lie?

Answer:

23/9

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(a) The initial speed of the projectile - 28.2m/s

(b)The total time interval the projectile was in flight - 4.07s.

a) When a projectile is launched with speed \(v_{i}\) at an angle above the horizontal, the initial velocity components are \(v_{xi}\) = \(v_{i}\) cos\(θ\) and                  \(v_{yi}\)= \(v_{i}\) sin\(θ\) . Neglecting air resistance, the vertical velocity when the projectile returns to the level from which it was launched (in this case, the ground) will be \(v_{y} = - v_{yi}\) .

From this information, the total time of flight is found  \(v_{yf} = v_{yi} + a_{y}\) to be

         \(t_{total} = \frac{v_{yf} - v_{yi} }{a_{y}}\)   = \(\frac{-v_{yi} - v_{yi} }{-g}}\)  = \(\frac{2v_{yi} }{g}\)

         \(t_{total} = \frac{2v_{i}sinθ }{g}\)

Since the velocity of a projectile with no air resistance is constant, the horizontal distance it will travel in this time is given by

R = \(v_{xi} t_{total} = (v_{i} cosθ_{i}) \frac{2v_{i}sinθ }{g}\)  =  \(\frac{v^{2}_{i}}{g}( 2sinθ_{i} cosθ_{i} )\) = \(\frac{v^{2} _{i} (sin2θ_{i} ) }{g}\)

Thus, if the projectile is to have a range of R=81.1m when launched at an angle of \(θ_{i}\)=45.0°, the required initial speed is

\(v_{i} = \sqrt{\frac{81.1 * 9.80}{sin90} }\) = 28.2 m/s

Therefore, the initial speed of the projectile - 28.2m/s

b) With \(v_{i}\)=28.2m/s and \(θ_{i}\) = 45.0°, the total time of flight (as found

above) will be

        \(t_{total} = \frac{2v_{i}sinθ }{g}\)  = \(\frac{2(28.2 m/s) sin45}{9.80m/s^{2}}\) = 4.07s

∴The total time interval the projectile was in flight - was 4.07s.

c) Note that at \(θ_{i}\) =45.0° that sin(2\(θ_{i}\)) will decrease as \(θ_{i}\) is increased above this optimum launch angle. Thus, if the range is to be kept constant while the launch angle is increased above 45.0°, we see from \(v_{i}\) = \(\sqrt{\frac{Rg}{sin2θ_{i}} }\)that the required initial velocity will increase.

Observe that for \(θ_{i}\) <90°, the function sin\(θ_{i}\) increases as \(θ_{i}\) it increased. Thus, increasing the launch angle above 45.0° while keeping the range constant means that both \(v_{i}\) sins will increase. Considering the expression  \(t_{total}\) given above, we see that the total time of flight will increase.

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The correct question is :

The record distance in the sport of throwing cowpats is 81.1m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time interval the projectile was in flight. (c) How would the answers change if the range were the same but the launch angle was greater than 45°? Explain.

Answer:

see below (I hope this helps!)

Step-by-step explanation:

Square roots are usually in the form a√b where a and b are any rational number.

Answer: PR and CK form right angles.

Step-by-step explanation:

By definition, perpendicular lines form right angles, and vice versa (in other words, lines that form right angles are perpendicular). Since we need to show PR is perpendicular to CK, we must first show that PR and CK form right angles.

The data provide sufficient evidence to support the claim that the mean salary for family practitioners in Los Angeles is greater than the national average.

The populace imply earnings for household practitioners in Los Angeles is equal to the country wide average.

Alternative hypothesis: The populace imply revenue for household practitioners in Los Angeles is higher than the country wide average.

We can use the stage of magnitude (alpha) of 0.05 and a one-tailed test, as we are solely fascinated in whether or not the imply earnings in Los Angeles is larger than the countrywide average.

Substituting the given values, we get:

t = ( $210,000 - $175,000 ) / ( $40,000 / √40 )

t = 3.18

Where,

The country wide common is $175,000, as mentioned in the question.

The income for household practitioners in Los Angeles is appreciably higher than the country wide common at the 0.05 degree of significance.

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Answer:

The slope, or m, is equal to 1/2.

Step-by-step explanation:

m = y2 - y1/x2 - x1

m = 2 - 4/3 - 7

m = -2/-4

m = 1/2

The distance between the cars changes by 60.42mph.

Distance is a measurement of how far apart two objects or locations are. Distance in physics or common language can refer to a physical length or an assumption based on other factors. |AB| is a symbol that can be used to represent the distance between two points. "Distance from A to B" and "Distance from B to A" are frequently used interchangeably. A distance function or metric is a technique to describe what it means for elements of some space to be "close to" or "far away" from each other in mathematics. It is a generalization of the idea of physical distance. Through dimensions like time, space, and isolation, an object may be psychologically distanced from itself.

Calculations:

\(d=\sqrt{80^{2}+50^{2} } \\\)

d=94.34

1st car -- 40mph/hr

2nd car-- 50 mph/hr

The positions of cars at 4pm

Distance travelled by 1st car = 80m

Distance travelled by 2nd car = 50m

\(d^{2}=a^{2} +b^{2}\)

2d.dd/dt=2a(da/dt) +2b(db/dt) =d(dd/dt) =a(da/dt)+b(db/dt)=94.34(dd/dt)=50*50+80*40

dd/dt=(2500+3200)(94.34)  =60.419

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In an observational study, the statement that a cause and effect can be determined is false.

Observational studies simply establish associations between predictor and outcome variables. Observational studies cannot confirm that an association contemplates cause and effect.

In observational studies, confounding variables may explain an observed relationship between predictor and outcome variables.

In an observational study, a cause and effect cannot be determined. Observational studies are used to gather data about a particular population or phenomenon, but they do not allow for the determination of cause-and-effect relationships.

This is because observational studies do not control the variables that are being studied and, therefore, cannot determine the relationship between two variables.

In order to determine cause and effect, a controlled experiment is needed in which the variables are manipulated, and their effects are observed.

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Answer:

multiply total weight by unit cost

8.8 x 2.09 = 17.765 = $17.77

Step-by-step explanation:

Answer:

TC(x) = ($2.09/lb)(8.5 lb) = $17.77

Step-by-step explanation:

The total cost is the product of (unit price) and (number of pounds):

TC(x) = ($2.09/lb)(8.5 lb) = $17.77

The required graph is attached below that represents the solution to the system of inequalities.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

For the first inequality, x + y > 1, we can rewrite it as y > -x + 1 and graph the boundary line y = -x + 1. Since the inequality is strictly greater than, we should shade the region above the line.

For the second inequality, -x + y ≤ 3, we can graph the boundary line -x + y = 3, which is the same as y = x + 3. Since the inequality is less than or equal to, we should shade the region below the line.

Point (0, 2) is in the shaded region. Plugging in x = 0 and y = 2 into the inequalities gives:

x + y > 1: 0 + 2 > 1, which is true

-x + y ≤ 3: -0 + 2 ≤ 3, which is true

Therefore, (0, 2) is a solution to the system.

Any point in the shaded region will be a solution to the system, and any point outside the shaded region will not be a solution.

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Using the AND rule of probability and percentage calculations, The answer is 0.0684.

Probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Percentages are fractions with a 100 as the denominator. The percent symbol (%) is used next to the number to denote that it is a percentage.

62% goes to college.

% not going to college = 100%-62%

=38%

on that 38%, 18% gets employment,

probability =  0.38 * 0.18

=0.0684

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Danika walks 50 blocks in one week.

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer. The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier. It is used for combining groups of identical size.

As per the data given,

We have,

Danika lives at 5 blocks from her school.

As Danika walks 5 blocks to and from school, making her round trip

So, total distance covered by Danika will be: 5 blocks + 5 blocks = 10 blocks.

As Danika walks to and from school 5 days a week,

Hence, she walks 10 blocks * 5 days = 50 blocks in one week.

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Answer:

(C)

Step-by-step explanation:

plz give brainlist

Answer:

10x -6

Step-by-step explanation:

f(x) = 5x + 2x  = 7x

g(x) = 3x - 6

f(x) + g(x) = 7x+ 3x-6

                = 10x -6

Answer:

(7-d)(7+d)

Step-by-step explanation:

49 - d^2

Rewriting

7^2 - d^2

We know that a^2 - b^2 = (a-b)(a+b)

(7-d)(7+d)

The answer you are looking for is -(d+7)(d-7).

Answer: 4/5

Step-by-step explanation: It is 8/10, but if you simplify it, it is 4/5.

Step-by-step explanation:

the measure of the segment YZ

\( \sin(30) = \frac{yz}{50} \\ yz = 50 \times \sin(30) = 25\)

YZ= 25 m

Answer:

2 quarters, 2 dimes, and 1 nickel

Step-by-step explanation:

25 times 2 = 50

10 times 2 = 20

1 times 5 = 5       +

____________

0.75

The coins can be distributed in the following manner -

2 quarters (2 x 25) + 2 dimes (2 x 10) + 1 nickel (5) = $0.75

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Michele who has 5 coins Worth 0.75 in all.

We can distribute the coins in the following manner -

2 quarters (2 x 25) + 2 dimes (2 x 10) + 1 nickel (5) = $0.75

Therefore, the coins can be distributed in the following manner -

2 quarters (2 x 25) + 2 dimes (2 x 10) + 1 nickel (5) = $0.75

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Answer:

y = 2/3 x + 6

Step-by-step explanation:

I do not see a point C, so I guess you get to make your own point C.  I will make it at (06,)

The equation of the line seen is

y = 4/6x + 5  If you start at A and count up, you will get 4 unit and then count right you will be 6 units.  This is the slope 4/6.  the 5 is where the line crosses the x axis (0,5)

We can simplify  4/6 to 2/3

y = 2/3 x + 5

When lines are parallel, they have the same slope, but different y intercept.  

Since I made C (0,6)  The equation of this parallel line would be

y = 2/3 x + 6

Draw a line parallel to AB but make sure that it goes through the point (0,6)

Answer:

  252

Step-by-step explanation:

The largest possible value of the second number is the least multiple itself: 252.

Slope: 1/5

Y-intercept: 0

Equation: Y= 5x

The number of ways Link can color the triforce so that it remains recognizable and he doesn't color any two triangles the same color if they share a side is 6 ways.

To find the number of ways Link can color the triforce so that it remains recognizable and he doesn't color any two triangles the same color if they share a side, follow the steps below:

1: Color one of the triangles with any of the three colors. There are 3 ways to do this.

2: Color the other two triangles adjacent to the first one with different colors from the first one. There are 2 ways to do this since only two colors are left.

3: Color the remaining triangle with the color that is different from the colors of the other three. There is only one color left to do this.

Therefore, the total number of ways Link can color the triforce so that it remains recognizable and he doesn't color any two triangles the same color if they share a side is:3 × 2 × 1 = 6 ways

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The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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Answer:

Average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Step-by-step explanation:

The formula for average rate of change of f(x) over [a,b] is

\(m=\dfrac{f(b)-f(a)}{b-a}\)

The given function is

\(r(x)=x^2+2x-5\)

\(r(0)=(0)^2+2(0)-5=-5\)

\(r(3)=(3)^2+2(3)-5=10\)

Now,

\(m_1=\dfrac{r(3)-r(0)}{3-0}\)

\(m_1=\dfrac{10-(-5)}{3}=5\)

From the graph it is clear that q(0)=-4 and q(3)=5.

\(m_2=\dfrac{q(3)-q(0)}{3-0}\)

\(m_2=\dfrac{5-(-4)}{3}=3\)

It is given that  function p has as x-intercept at (3,0) and a y-intercept at (0,6). It menas p(0)=6 and p(3)=0.

\(m_3=\dfrac{p(3)-p(0)}{3-0}\)

\(m_3=\dfrac{0-6}{3}=-2\)

From the given table it is clear that s(0)=-13 and s(3)=5.

\(m_4=\dfrac{s(3)-s(0)}{3-0}\)

\(m_4=\dfrac{5-(-13)}{3}=6\)

Therefore, the average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.

Answer:

7% decrease

Step-by-step explanation:

12500 - 11625 = 875

875/ 12500 = 0.07

0.07 × 100 = 7

Answer:

7%

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The value of an excel formula that will square this number is,

⇒ N²

We have to given that;

A number is stored in cell a1.

Hence, We can formulate;

Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.

And, We also get;

To display the square of the value in cell A1 into cell B1,

We can type = A1² into cell B1.

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Answer:

10.375

Step-by-step explanation:

3/8ths equal 0.375 and then you have ten as the whole number therefore you add the lower number onto the whole number and then you get your answer.

Answer:

40 cm

Step-by-step explanation:

Since the triangles are similar then the ratio of corresponding sides are equal.

Compare the ratio of the 2 smallest sides

\(\frac{12}{3}\) = 4 ← scale factor

Thus the longest side of the other triangle is 4 times the longest side of the first triangle , that is

longest side = 4 × 10 = 40 cm

Answer:

y=3x-2

Step-by-step explanation:

y-y0=m(x-x0)

y-4=3x-6

y=3x-2

\(\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)

Find the equation of a line that passes through (2,4) and has a gradient of 3.

\(\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\)

First, let's take a look at our provided information.

| Provided information:-

\(\bigstar\) On simplification,

\(\bigstar\) On further simplification,

Which results in:-

\(\rule{300}{1}\)