So we have two planes flying toward each other. Let's use v for the speed of the slower plane. Then the speed of the faster plane is v+40. If we pass to the reference system of the slower plane we have that its speed is 0 and the speed of the other plane is v+v+40=2v+40. So basically we have a problem where one of the planes is stationary whereas the other approaches at 2v+40mph and it takes it 2 hours to travel 1180 miles. Remember that the speed is equal to the distance traveled divided by the time it took the plane to travel that distance. Then we get:
[tex]\begin{gathered} 2v+40\frac{mi}{h}=\frac{1180mi}{2h}=590\frac{mi}{h} \\ 2v=590\frac{mi}{h}-40\frac{mi}{h}=550\frac{mi}{h} \\ v=\frac{550\frac{mi}{h}}{2}=275\frac{mi}{h} \end{gathered}[/tex]Then we get:
[tex]v+40\frac{mi}{h}=275\frac{mi}{h}+40\frac{mi}{h}=315\frac{mi}{h}[/tex]Then the speeds of the planes are 275mph and 315mph.
what is the area of the Shaded region used 3.14
In this problem, the area of the shaded region is equal to the area of the complete square, minus the area of the four circles
so
REmember that
The length side of the complete square is equal to two times the diameter of one circle
A=(2*12)^2-4*pi*(12/2)^2
assume pi=3.14
A=576-4(3.14)(36)
the area of the Shaded region is A=123.84 ft^2solve for y. 2x-y=12
Answer:
2x - 12 = y
Step-by-step explanation:
→ Add y to both sides
2x = 12 + y
→ Minus 12 from both sides
2x - 12 = y
Show instructionsQuestion 1 (1 point)Does the point (0,5) satisfy the equation y = x + 5?TrueFalse
The equation is
[tex]y=x+5[/tex]The point given is:
[tex](x,y)=(0,5)[/tex]The x coordinate given is 0 and the y coordinate given is 5.
We put the respective point and see if the equation holds true or not.
Thus,
[tex]undefined[/tex]A student council president wants to learn about the preferred theme for the upcoming spring dance. Select all the samples that are representative of the population.
The idea of being representative of the population is actually reflecting the characteristics (features) we want to study of the whole population.
In this case, the samples that better represent the whole population are B and D. Why? Because they give us the possibility of taking a student of every grade. The other options, excluding the "bus option" and the first option, fail doing that. Finally, these options (bus option and lunch option) are related to the council president.
The deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is $150, and the deposit for month 5 is %180. Answer the questions below and show all work.1. What is the common difference for the deposits made each month?2. Write an explicit formula for this arithmetic sequence. 3. What is the amount of Ginny's deposit in the 12th month?4. At what month will Ginny first make a deposit that is at least $500?
SOLUTION
The deposits Ginny makes at her bank each month form an arithmetic sequence. The deposit for month 3 is $150, and the deposit for month 5 is $ 180.
Since it follows an arithmetic sequence, T n = a + ( n- 1 ) d
Month 3 , T 3 = a+ ( 3 - 1 ) d = 150
a + 2 d = 150 --------------------- equ 1
Month 5 , T 5 = a + ( 5 - 1 ) d = 180
a + 4 d = 180 ...........................equ 2
Solving the two equations, we have :
a - a + 4 d - 2 d = 180 - 150
2 d = 30
Divide both sides by 2 , we have:
d = 15
Let us put d = 15 in equ 1 , we have a + 2 d = 150
a + 2 ( 15 ) = 150
a + 30 = 150
a = 150 - 30
a = 120
From the solution,
Month 1 = 120
Month 2 = 120 + 15 = 135
Month 3 = 135 + 15 = 150
Month 4 = 150 + 15 = 165
Month 5 = 165 + 15 = 180
1. What is the common difference for the deposits made each month? d = 15
2. Write an explicit formula for this arithmetic sequence.
Recall that Tn = a + ( n - 1 ) d
Tn = 120 + ( n - 1 ) 15
Tn = 120 + 15 n - 15
Tn = 120 - 15 + 5n
Tn = 105 + 15n
3. What is the amount of Ginny's deposit in the 12th month?
Tn = 105 + 15n
T 12 = 105 + 15 ( 12 )
T 12 = 105 + 180 = 285
4. At what month will Ginny first make a deposit that is at least $500?
Using Tn = 105 + 15 n = 500
105 + 15 n = 500
15 n = 500 - 105
15 n = 395
Divide both sides by 15 , we have :
n = 26 . 33
n = 27
what is the slope of the line represented by y = -5 + 2?
Question:
Find the slope of
[tex]y=-5x+2[/tex]Answer:
Remember that when we have the equation of a line in the form
[tex]y=mx+b[/tex]The slope of the line is the number that accompanies x (A.K.A Coefficient)
Therefore, the slope of the line is -5
Una clase tiene 42 alumnos. Se puede determinar que 3/9 son niños y 4 6 son niñas, ¿Cuántos niños y cuantas niñas hay en la clase?
The number of boys and girls that are in this class is equal to 28 students and 14 students respectively.
How to determine the number of boys?In order to determine the number of boys that are in this class with a total population of 42 students, we would have to multiply the total number of students by the fraction representing only the number of boys as follows:
Number of boys, B = 4/6 × Total number of students
Substituting the given parameters into the formula, we have;
Number of boys, B = 4/6 × 42
Number of boys, B = 4 × 7
Number of boys, B = 28 students.
Similarly, we we would have to multiply the total number of students by the fraction representing only the number of girls as follows:
Number of girls, G = 3/9 × Total number of students
Number of girls, G = 3/9 × 42
Number of girls, G = 1/3 × 42
Number of girls, G = 42/3
Number of girls, G = 14 students.
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Complete Question:
A class has 42 students. It can be determined that 3/9 are boys and 4/6 are girls, how many boys and girls are there in the class?
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Given 4 h + 6 = 30
4 h = 30 - 6
4 h = 24
Divide both sides by 4, we have:
h = 24 /4
h = 6
Which probem situation can be represented by the equation below?3x +3 <11F Joe and Hannah together got less than 11 questions correct on their quizzes. Joe got 3 more questions correct than Hannah. What is x, the number of quiz questions Hannah got 3 correct?G A coin collection of dimes and quarters has less than 11 coins. The collection has more than 3 times as many quarters as dimes. How many dimes, x, is in the collection?H Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?J The length of a rectangle is 3 inches more than the width, x. Three times the length is less than 11. What is the width of the rectangle?
Let x be correct questions of Joe and y be correct quiz question of Joe. The in equality for Joe and Hannah together questions is,
[tex]x+y<11[/tex]Joe got 3 more questions correct than Hannah, means equaltion is,
[tex]y=x+3[/tex]So inequality obtained is,
[tex]\begin{gathered} x+x+3<11 \\ 2x+3<11 \end{gathered}[/tex]Thus option F is incorrect.
Let x be number of dimes and y be number of quarters. So inequality for collection of coins is,
[tex]x+y<11[/tex]The number of quarters are,
[tex]y=3x[/tex]So resultant inequality is,
[tex]\begin{gathered} x+3x<11 \\ 4x<11 \end{gathered}[/tex]Thus option G is incorrect.
Let larger number be y. So sum of numbers is less than 11, means
[tex]x+y<11[/tex]The equation of larger number in terms of smaller number is,
[tex]y=2x+3[/tex]Substitute the value of y in the inequality to obtain the desired inequality.
[tex]\begin{gathered} x+2x+3<11 \\ 3x+3<11 \end{gathered}[/tex]Thus inequality obtained is 3x + 3 < 11.
Thus option H is correct.
Correct option : Two numbers have a sum that is less than 11. The larger number is 3 more than twice he smaller number. What s the smaller number, x?
what is P(x) = 2x^3 + 5x^2 + 5x + 6 as a product of two factors.
So we have to write the following polynomial expression as a product of two factors:
[tex]P(x)=2x^3+5x^2+5x+6[/tex]In order to do this we should find one of its roots first i.e. a x value that makes P(x)=0. If we use r to label this root we can write P like:
[tex]P(x)=(x-r)\cdot(ax^2+bx+c)[/tex]Where a, b and c are numbers that we can find using Ruffini's rule. So first of all let's find a root. We can use the rational root theorem. It states that if P(x) has rational roots then they are given by the quotient between a factor of the constant term (i.e. the number not multplied by powers of x) and a factor of the leading coefficient (i.e. the number multiplying the biggest power of x). In this case we have to look for the factors of 6 and 2 respectively. Their factors are:
[tex]\begin{gathered} 6\colon6,-6,3,-3,2,-2,1,-1 \\ 2\colon2,-2,1,-1 \end{gathered}[/tex]And the quotients and possible values for r are:
[tex]6,-6,3,-3,2,-2,\frac{3}{2},-\frac{3}{2},1,-1,\frac{1}{2},-\frac{1}{2}[/tex]So one of these numbers make P(x) equal to zero. For example if we take x=-2 we get:
[tex]\begin{gathered} P(-2)=2\cdot(-2)^3+5\cdot(-2)^2+5\cdot(-2)+6 \\ P(-2)=-16+20-10+6=0 \end{gathered}[/tex]So -2 is a root of P(x) which means that we can take r=-2.
Now we can use Ruffini's law. On the first row we write the coefficients of P(x). Then the first one is repeated in the third row:
Now we multiply 2 by -2 and we write the result under the second coefficient. Then we add them:
Now we do the same with the 1:
And then we multiply 3 and -2 and add the result ot the last coefficient:
The numbers 2, 1 and 3 are the values of a,b and c respectively. Then we can write P(x) as a product of two factors and the answer is:
[tex]P(x)=(x+2)(2x^2+x+3)[/tex]In how many ways can Joe, Mary, Steve, Tina and Brenda be seated around a round table?241220
The number of people to be seated around the table, n=5.
Now, n=5 people can be seated in a circle in (n-1)! ways.
[tex](n-1)!=(5-1)=4!\text{ =4}\times3\times2\times1=24[/tex]Therefore, Joe, Mary, Steve, Tina and Brenda can be seated around the round table in 24 ways.
Find the equation of a line parallel to y=x+6 that passes through the point (8,7)(8,7).
The equation of the line which is parallel to the line y = x + 6, and which passes through the point (8, 7) is; y = x - 1
What are parallel lines in geometry?Parallel lines are lines do not intersect and which while on the same plane, have the same slope.
The given line to which the required line is parallel to is y = x + 6
The point through which the required line passes = (8, 7)
The slope of the given line, y = x + 6, is 1,
The slope of parallel lines are equal, which gives;
The slope of the required line is 1
The equation of the required line in point and slope form is therefore;
y - 7 = 1×(x - 8) = x - 8
y = x - 8 + 7 = x - 1
The equation of the required line in slope–intercept form is; y = x - 1
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Can you help me with this true and false problem?
FALSE.
Explanations:Given the linear relations 2x - 3y = 4 and y = -2/3 x + 5
Both equations are equations of a line. For the lines to be perpendicular, the product of their slope is -1
The standard equation of a line in slope-intercept form is expressed as
[tex]y=mx+b[/tex]m is the slope of the line
For the line 2x - 3y = 4, rewrite in standard form
[tex]\begin{gathered} 2x-3y=4 \\ -3y=-2x+4 \\ y=\frac{-2}{-3}x-\frac{4}{3} \\ y=\frac{2}{3}x-\frac{4}{3} \end{gathered}[/tex]Compare with the general equation
[tex]\begin{gathered} mx=\frac{2}{3}x \\ m=\frac{2}{3} \end{gathered}[/tex]The slope of the line 2x - 3y = 4 is 2/3
For the line y = -2/3 x + 5
[tex]\begin{gathered} mx=-\frac{2}{3}x \\ m=-\frac{2}{3} \end{gathered}[/tex]The slope of the line y = -2/3 x + 5 is -2/3
Take the product of their slope to determine whether they are perpendicular
[tex]\begin{gathered} \text{Product = }\frac{2}{3}\times-\frac{2}{3} \\ \text{Product = -}\frac{4}{9} \end{gathered}[/tex]Since the product of their slope is not -1, hence the linear relations do not represent lines that are perpendicular. Hence the correct answer is FALSE
Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.f(x)=sqrt(x)+2g(x)=x^2+7f(g(x))= ?g(f(x))= ?
Answer:
[tex]\begin{gathered} \begin{equation*} f(g(x))=\sqrt{x^2+7}+2 \end{equation*} \\ \begin{equation*} g(f(x))=x+4\sqrt{x}+11 \end{equation*} \end{gathered}[/tex]Explanation:
Given the functions f(x) and g(x) below:
[tex]\begin{gathered} f(x)=\sqrt{x}+2 \\ g\mleft(x\mright)=x^2+7 \end{gathered}[/tex]Part A
We want to find the simplified form of f(g(x)).
[tex]f(x)=\sqrt{x}+2[/tex]Replace x with g(x):
[tex]f(g(x))=\sqrt{g(x)}+2[/tex]Finally, enter the expression for g(x) and simplify if possible:
[tex]\implies f\mleft(g\mleft(x\mright)\mright)=\sqrt{x^2+7}+2[/tex]Part B
We want to find the simplified form of g(f(x)). To do this, begin with g(x):
[tex]g\mleft(x\mright)=x^2+7[/tex]Replace x with f(x):
[tex]g(f(x))=[f(x)]^2+7[/tex]Finally, enter the expression for f(x) and simplify if possible:
[tex]\begin{gathered} g\mleft(f\mleft(x\mright)\mright)=(\sqrt{x}+2)^2+7 \\ =(\sqrt{x}+2)(\sqrt{x}+2)+7 \\ =x+2\sqrt{x}+2\sqrt{x}+4+7 \\ \implies g(f(x))=x+4\sqrt{x}+11 \end{gathered}[/tex]Therefore:
[tex]\begin{equation*} g(f(x))=x+4\sqrt{x}+11 \end{equation*}[/tex]3. A student solved an order of operations problem asshown.(2 - 4)2 – 5(6 - 3) + 13(-2)2 - 30 - 3 + 134 - 33 + 13-16What error did this student make? Explain in completesentences. What should the correct answer be?
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
Parentheses first
[tex]\begin{gathered} (2-4)=-2 \\ (6-3)=3 \\ \end{gathered}[/tex]substitute
[tex]\begin{gathered} (-2)2-5(3)+13 \\ -4-15+13 \\ -4-2 \\ -6 \\ \end{gathered}[/tex]The student error was misapplication of the comutative property
What is (are) the solution(s) to the system of equations y = -x + 4 and y = -x^2 + 4 ?
Given:
[tex]\begin{gathered} y=-x+4----(1) \\ y=-x^2+4----(2) \end{gathered}[/tex]Required:
To find the solutions to the given equations.
Explanation:
Put equation 1 in 2, we get
[tex]\begin{gathered} -x+4=-x^2+4 \\ \\ -x+4+x^2-4=0 \\ \\ x^2-x=0 \\ \\ x(x-1)=0 \\ \\ x=0,1 \end{gathered}[/tex]When x=0,
[tex]\begin{gathered} y=-0+4 \\ y=4 \end{gathered}[/tex]When x=1,
[tex]\begin{gathered} y=-1+4 \\ =3 \end{gathered}[/tex]Final Answer:
The solution are
[tex]x=0,1[/tex]The solution sets are
[tex]\begin{gathered} (0,4)\text{ and} \\ (1,3) \end{gathered}[/tex]Which of the following describes point D?
Answer:
(0,4)
Step-by-step explanation:
Hi! :)
I am Pretty sure this is what it is, if this is not what you are needing please let me know.
Which of the following numbers are not natural numbers?Select one:a. 1,000,000b. 5,032c. 1/4d. 25
Natural numbers are those who you use to count elements, they are by definition positive integers.
C. is not an integer, so it is not a natural number
b. 5032, a. 1000000 and d.25 are positive integers. These are natural numbers.
the answers to questions 4 & 5 please!!
The height of the cone is (c) 5 cm.
What is a cone?A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.So, the volume of a cone is: V = 1/3πr²h
V is 83.73 and r is 4.Now, calculate the height of the cone as follows:
V = 1/3πr²h83.73 = 1/3π4²h83.73 = 1/3π16h3(83.73) = 3.14(16)h251.19 = 50.24hh = 251.19/50.24h = 4.9999Rounding off: 5 cm
Therefore, the height of the cone is (c) 5 cm.
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what are the equations of the asysyoptes of the rational function
To find the asymptotes, we have to solve the following.
[tex]x^2-4x+3=0[/tex]We have to find two numbers whose product is 3 and whose sum is 4. Those numbers are 3 and 1.
[tex](x-3)(x-1)=0[/tex]So, the solutions are x = 3 and x = 1.
Hence, the asymptotes x = 1 and y = 1/2.The graph below shows the function.
• 5th 3230 [] What would be the slope of a line perpendicular to the line graphed above? -2 2 1/2 -1/2 Zoom in Double Jeop 3:39
When two lines are perpendicular to each other, their slopes would be a negative inverse of each other. This simply means the slope of a line perpendicular to the one in the question should be equal to the negative inverse of the one we have here. Let us begin by calculating the slope of this line.
When you are given two endpoints, the slope is derived as;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]When the coordinates are (0, 3) and (-1.5, 0)
That is, when x = 0 then y = 3 (observe the point where the line touches the vertical axis), and when x = -1.5, then y = 0 (observe the point where the line touches the horizontal axis)
Therefore, the coordinates (0, 3) and (-1.5, 0) are now your (x1, y1) and (x2, y2)
[tex]\begin{gathered} m=\frac{0-3}{-1.5-0} \\ m=\frac{-3}{-1.5} \\ m=2 \end{gathered}[/tex]Therefore the slope of a line perpendicular to the one on the graph is -1/2.
I really need help solving this practice from my prep guide in trigonometry
Given: Different angles in degrees and in terms of pi. The different angles are:
[tex]\begin{gathered} a)714^0 \\ b)\frac{23\pi}{5} \\ c)120^0 \\ d)\frac{31\pi}{6} \end{gathered}[/tex]To Determine: The equivalence of the given angles
The equivalent of degree and pi is given as
[tex]\begin{gathered} 2\pi=360^0 \\ \pi=\frac{360^0}{2} \\ \pi=180^0 \\ 360^0=2\pi \\ 1^0=\frac{2\pi}{360^0} \\ 1^0=\frac{1}{180}\pi \end{gathered}[/tex][tex]\begin{gathered} a)714^0 \\ 1^0=\frac{1}{180}\pi \\ 714^0=\frac{714^0}{180^0}\pi \\ 714^0=3\frac{29}{30}\pi \\ 714^0=\frac{119\pi^{}}{30} \end{gathered}[/tex][tex]\begin{gathered} b)\frac{23\pi}{5} \\ 1\pi=180^0 \\ \frac{23\pi}{5}=\frac{23}{5}\times180^0 \\ \frac{23\pi}{5}=828^0 \end{gathered}[/tex][tex]\begin{gathered} c)120^0 \\ 1^0=\frac{\pi}{180} \\ 120^0=120\times\frac{\pi}{180} \\ 120^0=\frac{2\pi}{3} \end{gathered}[/tex][tex]\begin{gathered} d)\frac{31\pi}{6} \\ 1\pi=180^0 \\ \frac{31\pi}{6}=\frac{31}{6}\times180^0 \\ \frac{31\pi}{6}=930^0 \end{gathered}[/tex]ALTERNATIVELY
A revolution is 360 degree
[tex]\begin{gathered} a)714^0 \\ \text{Multiples of 360 degre}e \\ 2\times360^0=720^0 \\ \text{equivalent of 714 degre}e\text{ would be} \\ 720^0-714^0=6^0 \end{gathered}[/tex][tex]undefined[/tex][tex]\begin{gathered} a)714^0=\frac{119\pi}{30} \\ b)\frac{23\pi}{5}=828^0 \\ c)120^0=\frac{2\pi}{3} \\ d)\frac{31\pi}{6}=930^0 \end{gathered}[/tex]Can't help me??
x/4 - 9 = 7
solve the equation... use transposing method
The Answer Is x = 64.
Explanation.x/4 - 9 = 7
x/4 = 7 + 9
x/4 = 16
x = 16 × 4
x = 64
_________________
Class: High School
Lesson: Equation
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
Answer:
x = 64
Step-by-step explanation:
x/4 - 9 =7
Step 1: Add 9 to both sides
x/4 - 9 + 9 = 7 + 9
x/4 = 16
Step 2: Multiply right side by 4
x/4= 16 x 4
x = 64
Step 3: Prove your x-value
64/4 = 16 - 9 = 7
64/4 - 9 = 7
So x = 64
PS: Please make brainliest.
Nicole wants to use his 18% employee discount to buy a video game that is priced at $69.99. A 6.5% sales tax is applied to the discounted price. What will be the total cost of the video game, including the sales tax?
Given:
The discount rate, D=18%.
The mared price, M=$69.99.
The sales tax percentage on discounted price, s=6.5%.
The discounted price is,
[tex]\begin{gathered} C=\frac{(100-D)}{100}\times M \\ C=\frac{100-18}{100}\times69.99 \\ C=57.39 \end{gathered}[/tex]The sales tax on the discounted price is,
[tex]\begin{gathered} S=\frac{s}{100}\times C \\ S=\frac{6.5}{100}\times57.39 \\ S=3.73 \end{gathered}[/tex]The total cost of the video game including the sales tax is,
[tex]\begin{gathered} T=C+S \\ T=57.39+3.73 \\ T=61.12 \end{gathered}[/tex]Therefore, the total cost of the video game including the sales tax is $61.12.
If 1000 pennies are put into rolls of 50 pennies, how many rolls will be made?
Answer:
12
Step-by-step explanation:
50x2=100
100x10=1000
2+10=12
Task 2: Interest in Finance
Interest is a concept familiar to most people: every credit card in existence has a term called annual percentage rate (APR), which is an interest rate. Suppose you charged $1,000 to a credit card that has a minimum payment each month equal to the interest owed. Can you figure out how much the interest rate is based on this amount?
The formula for simple interest is where I is the amount you will pay in interest, r is the rate at which interest will accrue, P is the principal (amount borrowed), and m is the number of times the interest is applied.
2
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2
To solve for the interest rate of your credit card, you need to understand which variables in the above formula you have. If your minimum monthly payment is $22 on the $1,000 credit card bill, which variables do you know the values of?
Type your response here: rate= interest/$1000
Manipulate the formula so it will calculate the interest rate you are paying instead of the amount of money you are paying.
Type your response here:
Now that you have a formula that will give you the interest rate, plug in the values for the problem and solve for that interest rate. Interest rates are usually represented for a time period: over what time period does this rate apply? What would the interest rate be if it were a yearly rate?
Type your response here:
Now consider a different situation. Payday loans are a type of loan where you can get money for a future paycheck, typically two weeks in advance. A typical payday loan service might charge $15 for a loan against a paycheck you will receive in two weeks. The interest rate is 10% of the paycheck over that two-week period. Given this information, which variables in the interest formula are known? Develop a formula that will solve for the unknown variable.
Type your response here:
Solve for the value of the unknown variable.
Type your response here:
1. One cannot figure out how much the interest rate is based on the amount charged to the credit card unless other variables are supplied.
2. We know the values of the following variables now:
The interest amountThe principal amount.3. The interest rate is 2.2% per month.
4. The period that this interest rate applies is monthly, called the MPR.
5. The annual interest rate (APR) is 26.4%.
6. The known variables about this payday loan are the interest amount, the interest rate, and the period.
7. A formula to solve for the unknown variable, principal/credit amount, is P = I / (RT), where I = interest, R = rate, and T = time period.
8. The solution for the value of the unknown variable, Principal, is $3,900.
Minimum monthly payment = interest amount = $22
Credit card bill = $1,000
Rate = interest/$1,000
Rate = $22/$1,000 = 0.022
= 2.2%
MPR = 2.2%
APR = 26.4% (2.2% x 12)
Payday Loans:The service charge for a 2-week loan = $15
Interest rate = 10%
Principal/Payloan = $3,900 ($15 / (10% x 2/52)
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hello can you help me with this math question and this a homework assignment
We know that two vectors are ortogonal if and only if:
[tex]\vec{v}\cdot\vec{w}=0[/tex]where
[tex]\vec{v}\cdot\vec{w}=v_1w_1+v_2w_2[/tex]is the dot product between the vectors.
In this case we have the vectors:
[tex]\begin{gathered} \vec{a}=\langle-4,-3\rangle \\ \vec{b}=\langle-1,k\rangle \end{gathered}[/tex]the dot product between them is:
[tex]\begin{gathered} \vec{a}\cdot\vec{b}=(-4)(-1)+(-3)(k) \\ =4-3k \end{gathered}[/tex]and we want them to be ortogonal, so we equate the dot product to zero and solve the equation for k:
[tex]\begin{gathered} 4-3k=0 \\ 4=3k \\ k=\frac{4}{3} \end{gathered}[/tex]Therefore, for the two vector to be ortogonal k has to be 4/3.
15. Given f (n)=3( 12), what is the value off (8) ?
We have some function f(x) and want to evaluate the function for some value of x, in this case for x=8.
Evaluate a function means replace the x for the value you want to evaluate, in this case for 8, so:
[tex]\begin{gathered} f(x)=3(1-x) \\ f(8)=f(x=8)=3(1-8) \\ f(8)=3\cdot(-7)=-21 \end{gathered}[/tex]A woman is floating in a
boat that is 175 feet from
the base of a cliff. The cliff
is 250 feet tall. What is the
angle of elevation from
the boat to the top of the
cliff?
The angle of depression between the cliff and the boat is 55.0
What is angle of depression?
The angle of depression is the angle between the horizontal line and the observation of the object of from the horizontal line. It's basically used to get the of distance of the two objects where the angles and an of object's distance from the ground are known to us.
A boat is moving 175 feet from the base and a women is in the boat.the height of the cliff is 259 feet tall. Here we have to find the angle between the cliff and the boat.
As per the given question
We have a right angled traingle where base is 175 ft and height is 250 ft.
Thus,
We know that tan theta =opposite/adjacent
250/175
So theta=tan^-1(250/175)
So theta = 55.0
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reduce the square root of -360
reduce the square root of
[tex]\begin{gathered} \sqrt[]{-360} \\ 360=36\cdot10=6^2\cdot10 \\ \end{gathered}[/tex]There is no square root for the negative number
so, this is represent a complex number
So,
[tex]\begin{gathered} \sqrt[]{-360}=\sqrt[]{-1}\cdot\sqrt[]{360} \\ =i\cdot\sqrt[]{6^2\cdot10} \\ =i\cdot6\sqrt[]{10} \\ =6\sqrt[]{10}\cdot i \end{gathered}[/tex]