1365 batting orders are possible for the game.
Given,
In the question:
In a cricket match, you have a squad of 15 players and you need to select 11 for a game.
To find the how many batting orders are possible for the game?
Let's Know:
What are combination?
Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!
n = the number of items.
r = how many items are taken at a time.
Substitute the values in above formula :
15! / 11! (15 - 11)!
= 15! / 11! 4!
= 15 × 14 × 13 × 12 / 4 × 3 × 2
= 1365 orders
Hence, 1365 batting orders are possible for the game.
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Lauren used the Quantitative Reasoning Process to budget and to start a savings account. Each month she makes about $185 from a part-time job. Lauren's parents also send her $120 per month. The sum of Lauren's paycheck and the money she gets from her parents is 11% more than her total expenses. How much money does Lauren have available to add to her savings account each month?
Lauren can add $30 each month to her savings account
Income made by Lauren from part-time job = $185
Money sent to Lauren by her parents = $120
Total income of Lauren = Money from job+ money received from parents = 120+185 = $305
Let her total expenses be x
Substituting the values in the formula we get:
Sum of Lauren's paycheck + Money she gets from her parents = Total expenses+ 11% more than her total expenses
185 + 120 = x+11% of x
305=x+11/100*x
305 = 1.11x
x=274.77 or 275
Money she can add in her savings account each month = Total money received - Expenses = 305 - 275 = $30
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A 14-foot ladder is leaning against a house with the base of the ladder 6 feet from the house. How high up the house does the ladder reach? If necessary, round to the nearest tenth foot.
The ladder leaning on the house formed a right angled triangle
Using an illustration from the diagram given:
To get the height the house makes with the ladder, we will apply pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
[tex]\begin{gathered} \text{hypotenuse = 14, adjacent = 6, opposite = }? \\ 14^2=opposite^2+6^2 \\ 196\text{ = }opposite^2\text{ + 36} \\ \\ \text{subtract 36 from both sides:} \\ 196\text{ - 36 = }opposite^2 \\ 160\text{ = }opposite^2 \end{gathered}[/tex][tex]\begin{gathered} \text{square root both sides:} \\ \sqrt[]{160}\text{ = }\sqrt[]{opposite^2} \\ \text{opposite = }12.649 \\ \\ \text{To the nearest tenth, the height of the house betw}een\text{ the ladder and base of the house is 12.6 ft (option B)} \end{gathered}[/tex]let k(x)=3h(x)+4x^4/g(x). given the following table of values, find k'(-1)
Given the following table of values, k'(-1) is 3.
What is differentiation?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative. finding a function's derivative, or rate of change, in mathematics. Differentiation is the process of determining a function's derivative. The derivative is the rate at which x changes in relation to y when x and y are two variables.
Given Data
k(x) = -3h(x) + [tex]\frac{4x^{4} }{g(x)}[/tex]
k(x) = -3h'(x) + 4 [tex]\frac{4x^{3}g(x)-x^{4}g'(x) }{gx^{2} }[/tex]
k'(-1) = -3h'(-1) + 4 [tex]\frac{4g(-1)-g'(-1)}{g(-1^{2}) }[/tex]
k'(-1) = -3(-1) + 4(0)
k(-1) = 3 + 0
k'(-1) = 3
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Write the coordinates of the vertices after a reflection over the x-axis.-10-8-6-4-2246810-10-8-6-4-2246810xyDEFG
Solution:
Given the graphed polygon below:
To determine the coordinates of the vertices after reflection over the x-axis,
step 1: Give the coordinates of DEFG.
Thus, we have
[tex]\begin{gathered} D(0,\text{ -10\rparen} \\ E(0,\text{ 0\rparen} \\ F(10,\text{ 0\rparen} \\ G(10,\text{ -10\rparen} \end{gathered}[/tex]step 2: Give the reflection formula, over the x-axis.
For reflection over the x-axis, we have
[tex]D(x,\text{ y\rparen}\rightarrow D^{\prime}(x,\text{ -y\rparen}[/tex]step 3: Give the coordinates after reflection over the x-axis.
From the formula in step 2,
we thus have
[tex]\begin{gathered} D^{\prime}(0,\text{ 10\rparen} \\ E^{\prime}(0,0) \\ F^{\prime}(10,\text{ 0\rparen} \\ G^{\prime}(10,\text{ 10\rparen} \end{gathered}[/tex]f(x)= {4-3x if x [tex]\leq[/tex] 1
{2x if 1
{5x+5 if x[tex]\geq[/tex]9
f(-4)=?
f(1)=?
f(5)=?
f(7)=?
f(9)=?
All the values are;
1) f (-4) = 16
2) f (1) = 1
3) f (5) = 10
4) f (7) = 14
5) f (9) = 50
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The function is;
f (x) = { 4 - 3x ; if x ≤ 1
= { 2x ; if x > 1
= { 5x + 5 ; if x ≥ 9
Now, Find all the values as;
Since - 4 is belong in x ≤ 1, so we get;
f (x) = 4 - 3x
f (-4) = 4 - 3 × -4
f (-4) = 4 + 12
f (-4) = 16
And, Number 1 is belong in x ≤ 1, so we get;
f (x) = 4 - 3x
f (1) = 4 - 3 × 1
f (1) = 4 - 3
f (1) = 1
And, Number 5 is belong in x > 1, so we get;
f (x) = 2x
f (5) = 2 × 5
f (5) = 10
And, Number 7 is belong in x > 1, so we get;
f (x) = 2x
f (7) = 2 × 7
f (7) = 14
And, Number 9 is belong in x ≥ 9, so we get;
f (x) = 5x + 5
f (9) = 5 × 9 + 5
f (9) = 50
Thus, All the values are;
1) f (-4) = 16
2) f (1) = 1
3) f (5) = 10
4) f (7) = 14
5) f (9) = 50
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read Dune Kuta Software - Infinite Algebra 2 Absolute Value Inequalities Solve each inequality and graph its solution. 1 16 = 18 2) pulss 18 boots -34 bane
ANSWER
The solution is: -3 < p < 3.8
EXPLANATION
When we have an absolute value inequality, to "eliminate" the absolute value we have to write the following:
[tex]\begin{gathered} |10p-4|<34 \\ -34<10p-4<34 \end{gathered}[/tex]To solve this we have to add 4 everywhere in the inequality:
[tex]\begin{gathered} -34+4<10p-4+4<34+4 \\ -30<10p<38 \end{gathered}[/tex]And divide everything by 10:
[tex]\begin{gathered} -\frac{30}{10}<\frac{10p}{10}<\frac{38}{10} \\ -3To graph we have to draw a line from -3 to 3.8, with empty circles at the ends - because those values are not included in the solution.
This is a Statistics questions please help
Considering the parameters of the normal distribution for American men's heights, it is found that:
a) The percentage greater than 74 inches is: 2.5%.
b) The proportion between 64 and 71.5 inches is: 0.815.
Normal DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the following equation:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure represented by X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.In the context of this problem, the mean and the standard deviation of the heights of American men are given as follows:
[tex]\mu = 69, \sigma = 2.5[/tex]
The proportion of heights that is greater than 74 inches is one subtracted by the p-value of Z when X = 74, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (74 - 69)/2.5
Z = 2.5
Z = 2.5 has a p-value of 0.9772.
1 - 0.9772 = 0.0228, hence the percentage is of 2.28%. Using the Empirical Rule, this percentage is rounded to 2.5%.
The proportion of heights between 64 inches and 71.5 inches is the p-value of Z when X = 71.5, subtracted by the p-value of Z when X = 64, hence:
X = 71.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (71.5 - 69)/2.5
Z = 1
Z = 1 has a p-value of 0.84. (rounded with the Empirical Rule).
X = 71.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (64 - 69)/2.5
Z = -2
Z = -2 has a p-value of 0.025. (rounded with the Empirical Rule).
Hence the proportion is:
0.84 - 0.025 = 0.815.
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PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!ON NUMBER 4!!!!!
The absolute value function y = 3|x + 1| + 9 is y ≥ (x + 4)/3 when x ≥ 0 and
y > - (x - 2)/3 when x < 0.
What is the absolute value function?The absolute value function always outputs a positive value irrespective of the input.
Given we have to write the absolute value function as a piecewise function.
We know | x | = a implies x ≥ a and - x < a.
y = 3| x + 1 | + 9.
y - 9 = 3| x + 1|.
(y - 9)/3 = | x+ 1 |.
∴ (y - 9)/3 ≥ x + 1.
y/3 - 3 ≥ x + 1.
y/3 ≥ x + 4.
y ≥ (x + 4)/3.
OR
(y - 9)/3 = | x+ 1 |.
- (y - 9)/3 < x + 1.
-y/3 + 3 < x + 1.
-y/3 < x - 2.
-y < (x - 2)/3.
y > - (x - 2)/3.
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can you please help me with this algebra 2 question please
If we consider a, b and c all positive constants and b > 1, a exponential growth in general is represented by a function like:
[tex]f(t)=a\cdot b^{ct}[/tex]In otherwise, a exponential decay can be represent by:
[tex]g(t)=a\cdot b^{-ct}=a\cdot(\frac{1}{b})^{ct}[/tex]Now we can check whose functions are similar to one of these:
h(x) = 3x + 1.3 is a linear function, therefore, this is neither exponential growth or decay;
f = 3*(4.2^x) is an exponential growth;
y = (5/6)*(7^x) is an exponential growth;
T = 0.6*(1.3^x) is an exponential growth;
W(x) = (1/8)*[(3/5)^x] is an exponential decay, since in this case we have 3/5 < 1.
K = 4.2*(0.28^x) is an exponential deacay by the same argument.
What is the x-intercept of the following equation?15x + 5y =30
the Given
[tex]15x+5y=30[/tex]We are asked to find the x-intercept of the linear equation. This can be seen below.
Explanation
To find the x-intercept, we must recall that x-intercept is the point at which the graph of the equation crosses the x-axis. We can find this point by plotting the given equation.
From the graph, we can determine the x-intercept as
Answer: (2,0)
Q:Find the distance from the red point to the origin. Sketch on the graph to convince us.
Distance Between Two Points
We are given two points on the graph attached to the question.
The red point has coordinates (7,3) and the origin is at (0,0)
I'll work out the graph to show the required distance.
The required distance (in the red drawing) is the hypotenuse of a right triangle of lengths 7 and 3, thus the distance is calculated as:
[tex]d=\sqrt[]{7^2+3^2}=\sqrt[]{49+9}=\sqrt[]{58}[/tex]Calculating, we get d is approximately 7.62
the graph of a quadratic function is given. determine the function's equation.
Here, we are given a quadratic equation graph and we are tasked with getting the equation of the quadratic equation from the graph
The first thing we need to note here is the shape of the parabola.
This in the sense that if the parabola opens up or faces down
On the graph we can see that the parabola faces the positive x-direction
Generally, the equation of a quadratic graph is usually in the form below;
[tex]y=ax^2\text{ + bx + c}[/tex]So by identifying the values of a,b and c, we can get the complete equation of the graph
The above form is called the standard form while the form we have in the options is referred to as the vertex form
The vertex form can be written as;
[tex]y=a(x-h)^2\text{ + k}[/tex]Now, looking at the graph, we can see that the graph crosses the y-axis at the point y = 6
At this point, the value of x is 0
The vertex (h,k) represents the center point of the parabola
In the case of this question, the point is (-2,2)
so h =-2 and k is 2
What is left is to get a
we can obtain this from the value of y = 6 and x = 0
Thus;
6 = a(0-(-2))^2 + 2
6 = a(2)^2 + 2
6 = 4a + 2
4a = 6-2
4a = 4
a = 4/4 =1
So the equation in the vertex form is f(x) = (x + 2)^2 + 2
HELP YALL! Suppose you just got a new job that pays ten dollars and 55 cents per hour. You get
paid every two weeks. If you are assured that you will work at least 6 hours per shift
and have 4 shifts per week, then what is the minimum you should expect (before
taxes) in your first paycheck?
Answer:
506.40
Step-by-step explanation:
.
Graph the solution set of the following linear equation
2x+2y<-6
Graph the inequality by finding the boundary line, then shading the appropriate area.
y < −x −3
A car manufacturer announced that next year the price of a certain model car would increase by 3.5%. This year the price is 15,757. Find the increase and the new price. The increase in the price of car is?The new price of car is?
Given:
Initial amount (Base) = 15, 757
Rate of increase = 3.5% or 0.035 in decimal form
Find: new price and the price increase
Solution:
To be able to get the new price, we need to solve for the price increase first. To do that, we need to know what is 3.5% of the old price 15, 757. To calculate that, we will multiply 0.035 by 15,757.
[tex]0.035\times15,757=551.495\approx551.50[/tex]3.5% of 15, 757 is 551.50. This is the price increase of the car next year.
Hence, by next year, the new price will now be 15,757 + 551.50 = 16, 308.50.
An initial population of 350 flying squirrels triples every year. Write an exponential equation to represent the population growth of the flying squirrels after any given number of years, x.
The exponential equation that represents the growth of the flying squirrels is F = 350 X 3^t.
What is the exponential function?An exponential equation can be described as an equation with exponents. The exponent is usually a variable. An exponential equation exhibits a compound growth rate.
The general form of exponential function is f(x) = [tex]e^{x}[/tex]
Where:
x = the variable e = constantThe population of the bird = present population x (1 + growth rate)^number of years
350 x (1 + 2)^t
F = 350 X 3^t
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PLEASE HELP!! I DON'T KNOW THE ANSWER BUT OF I CLOSE IT I CAN'T GET BACK IN I CAN ONLY ACCESS THIS ONE PLEASE HELP!!!!! ⚠⚠⚠⚠⚠⚠
Answer:
The answer is the third one.
Step-by-step explanation:
They show the points plotted correctly.
A spinner has 3 equal sections that are white, yellow, and green. Another spinner has 3 equal sections that are blue, purple, and red. How many different combinations of colors are possible if you spin each spinner once?A. 6B. 9C. 12D. 16
ANSWER
[tex]B)9[/tex]EXPLANATION
We want to find the number of different combinations of colors possible if both spinners are spun at once.
To do this, we have to find the product of the number of colors on each spinner.
That is:
[tex]\begin{gathered} 3\cdot3 \\ \Rightarrow9 \end{gathered}[/tex]The answer is option B.
Which expression has a value of 13?
Answer:
To solve this problem you will have to use PEMDAS (parenthesis, exponents, multiplication, division, addition, and subtraction).
The grounds crew at a college is installing a path around a pond on campus as shown.9x + 10x2 - x4x2 - 7x + 8- x?+ 9x + 12What is the perimeter of the path?A. – 3 + 15x2 + 25% + 20B. 12x2 + 2x + 20C. -13 + 13x2 + 11x + 20D. 1232 + 25x + 20
The perimeter of a figure or shape is the distance around it.
The perimeter of the given path would be
9x + 10x^2 - x^3 + 4x^2 - 7x + 8 - x^2 + 9x + 12
We would collect like terms. It becomes
- x^3 + 10x^2 + 4x^2 - x^2 + 9x + 9x - 7x + 8 + 12
= - x^3 + 13x^2 + 11x + 20
The correct option is C
3. The number of zeroes in the end of perfect square is never_______
(vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number. Q. The number of zeroes at the end of a perfect square is always odd.
I hope it will be helpful for you.
The table shows a proportional relationship. x 14 6 26 y 7 3 13 Describe what the graph of the proportional relationship would look like. A line passes through the point (0, 0) and continues through the point (7, 14). A line passes through the point (0, 0) and continues through the point (14, 7). A line passes through the point (0, 0) and continues through the point (3, 6). A line passes through the point (0, 0) and continues through the point (13, 26).
The proportional relationship graph that represents the table of values given would look like the graph shown below.
What is a Proportional Relationship?A proportional relationship graph always passes through the point of origin, (0, 0). The slope of the graph of a proportional relationship is also called the constant of proportionality, k, which can be calculated by using the coordinates of any point on the line, (x, y).
Constant of proportionality, k = y/x.
The equation for a proportional relationship is given as y = kx.
Given the table of values above which represents a proportional relationship, the graph of the table of values will go through the points below:
(0, 0)
(14, 7)
(6, 3)
(26, 13)
Therefore, the graph of the proportional relationship would look like the graph attached below which passes through:
B. (0, 0) and continues through the point (14, 7).
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Write a mathematical expression for the following statement
x is at least 19
Write a mathematical expression for the following statement: x is at least 19
this means that x > 19
in set builder notation: (19,∞)
I need help its very difficult
Here is the meaning of each statement:
The percentage of households that have the internet in 2007 is 61.7%
The percentage of households that have the internet in 1984 is k%.
The percentage of households that have the internet in 2017 is greater than the percentage of households that have the internet in 2000.
The sum of the percentage of households that have the internet in 1997 and 2001 is approximately equal to the percentage of households that have the internet in 2009.
What is the meaning of each statement?Percentage is the fraction of an amount expressed as a number out of 100. In order to change a number to percentage, multiply the number by 100. The sign that represent percentage is %.
A function is an expression or rule that defines the relationship between the independent variable and the dependent variable. A function could be a linear function or an exponential function.
In this question,
x = is the number of years after 1980
and the independent variable is the percentage of households that use the internet after 1980.
H(27) = 61.7
1980 + 27 = 2007
This means that 61.7% households use the internet 27 years after 1980 or 61.7% households use the internet in 2007
H(4) = k
1980 + 4 = 1984
This means that k% households use the internet 4 years after 1980 or k% households use the internet in 194
H(37) > H(30)
This means that the percentage of households that use the internet 37 years after 1980 is greater than the percentage of households that use the internet 30 years after 1980
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nitrogen has half-life of 15 hours. how much nitrogen will remain in an 18.0 g sample after 60 hours?
If the half-life is 15 hours and there are 18 g, it means that after 15 hours,
18/2 grams would decay, leaving behind 18/2 grams
This means that 9 grams would be left.
After another 15 hours (making a total of 30 hours), 9/2 grams would decay leaving behind 9/2 grams (i.e 4.5 grams.
After another 15 hours (making a total of 45 hours), 4.5/2 grams would decay leaving behind 4.5/2 grams. Hence 2.25 grams are left
After another 15 hours (making a total of 60 hours), 2.25/2 grams would decay leaving behind 2.25/2 grams.
Hence after 60 hours, only 1.125 grams would be left
21. A truck is driving N35oE at a speed of 110 km/h. Determine the components of the vector representing this force.
Solution:
The question will be represented below as
To figure out the horizontal component (x), we will use the trigonometric ratio below
[tex]\begin{gathered} sin\theta=\frac{opp}{hyp} \\ \theta=35^0,opp=x,hyp=110 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} s\imaginaryI n\theta=\frac{opp}{hyp} \\ sin35=\frac{x}{110} \\ x=110\sin35^0 \\ x=63.1\text{ km/h} \end{gathered}[/tex]Step 2:
To figure out the vertical component (y), we will use the trigonometric ratio below
[tex]\begin{gathered} \cos\theta=\frac{adj}{hyp} \\ \theta=35^0,adj=y,hyp=110 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \cos(\theta)=\frac{adj}{hyp} \\ \cos35=\frac{y}{110} \\ y=110cos35^0 \\ y=90.1 \end{gathered}[/tex]Hence,
The horizontal component is = 63.1 km/h
The vertical component is = 90.1 km/h
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Simplify the expression.
the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths
negative 37 over 24 times j minus 17 over 12
negative 37 over 24 times j plus 17 over 12
43 over 24 times j plus 1 over 12
negative 43 over 24 times j plus negative 1 over 12
Which expression is equivalent to 3(−4.5b − 2.1) − (6b + 0.6)?
19.5b + 1.5
−19.5b − 1.5
−19.5b − 6.9
19.5b − 6.9
The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b - 6.9.
What are expressions in math?Expressions in mathematics are mathematical assertions that comprise at least two terms that contain numbers, variables, or both, and are connected by an operator in between.Addition, subtraction, multiplication, and division are examples of mathematical operators. To simplify algebraic statements, like terms might be added or removed. Similar terms have the same variable raised to the same power.Given expression:
3(−4.5b − 2.1) − (6b + 0.6)
To simplify the expression open the brackets and multiply the terms,
-13.5b − 6.3 − 6b - 0.6
Now, combine the like terms together and add them,placing a negative sign in front of the terms
-13.5b − 6b - 0.6 - 6.3
-19.5b - 6.9
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3. Describe the similarities and differences among the following experiments. (a) Slips of paper are marked with the numbers 1, 2, 3, 4, and 5 and placed into a box. After being mixed, two slips are drawn simultaneously. (b) Slips of paper are marked with the numbers 1, 2, 3, 4, and 5 and placed into a box. After being mixed, one slip is drawn then put back into the box, then a second slip is drawn. (c) Slips of paper are marked with the numbers 1, 2, 3, 4, and 5 and placed into a box. After being mixed, one slip is drawn and not put back into the box, then a second slip is drawn.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Describe the first experiment
Two slips were drawn simultaneously, this means that the outcome of the first slip drawn will be multiplied by the outcome of the second slip drawn. The probability will follow the "and rule of probability".
STEP 2: Describe the second experiment
Since one slip is drawn and then put back into the box before a second slip is drawn, this is a PROBABILITY WITH REPLACEMENT. The outcome of the first event will not affect the outcome of the second event since the paper slips are replaced hence not reduced.
STEP 3: Describe the third experiment
Since one slip is drawn and not put back into the box before a second slip is drawn, this is a PROBABILITY WITHOUT REPLACEMENT. The outcome of the first event will affect the outcome of the second event since the paper slips reduce.
Difference between b and c is that b is with replacement and the total outcomes does not change while c is without replacement and the total outcomes change(reduce) after the first slip is drawn.
Bobby read a total of 20 books over 2 months. If Bobby has read 90 books so far, how many months has he been with his book club? Solve using unit rates
Step 1
From the question;
[tex]\begin{gathered} Bobby\text{ reads 20 books in 2 months} \\ \end{gathered}[/tex]We are required to find how many months it will take him to read 90 books
Step 2
We will use the ratio below to solve the problem.
[tex]\begin{gathered} \frac{20\text{ books}}{90\text{ books}}=\frac{2months}{x} \\ x=months\text{ to read 90books} \\ x=\frac{90\times2}{20} \\ x=9\text{ months} \end{gathered}[/tex]Answer; It will take Bobby 9months to read 90 booj
[tex]9\text{ months}[/tex]You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 165 km south and 152 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?
For the constant speed, it take 5 minutes 3 seconds after you depart JBLM will you be the closest to Mt. Rainier.
Speed:
Speed means a rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.
Given,
You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 165 km south and 152 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM.
Here we need to find the time taken after you depart JBLM will you be the closest to Mt. Rainier for the constant speed of 800 km/hr.
Let us consider +x direction is east, and the -y direction is south.
We know that, JBLM is at the origin (0, 0). All distance units are presented in kilometers.
While we consider that, you are flying on line
165x + 152y = 0
We know that the slope of the line
ax + by = c
is given by -a/b, which suggests we can form the equation of a perpendicular line by swapping x and y coefficients and negating one of them.
Then, we get the equation as,
152x - 165y = c
That is perpendicular to the flight path.
Now we need to find c so that this is true at the coordinates of Mt. Rainier.
The perpendicular line through (56, -40) is
152x - 165y - (152(56) - 165(-40)) = 0
When we expand it then we get,
152x - 165y - (8512 + 6600 ) = 0
152x - 165y - 15112 = 0
We know that the distance in km from JBLM (0, 0) to this line is given by
So, when we apply the value of (x,y) as (0,0) then we get,
=> | 152(0) - 165(0) - 15112 |/√(152²+165²)
=> 15112/√50329
=> 15112/224.34
≈ 67.362
Therefore at the constant speed of 800 km/hr, you will have flown that 67. 362 km.
Then for one km you would take,
=> 62.076/800 hr ≈ 0.0842 hr
When we convert this then we get,
=> 0.0842 = 5 minutes 3 seconds.
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