Consider the following functions.Sx) = x + 4 and g(x) = x - 7Step 4 of 4: Find(3)).x). Simplify your answerAnswerKeyboards(2)) =Submit Ang
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Given:
[tex]f(x)=x+4\text{ and }g(x)=x-7[/tex]Required:
[tex]\text{We need to find }(\frac{f}{g})(x).[/tex]Explanation:
[tex]\text{We know that }(\frac{f}{g})(x)=\frac{f(x)}{g(x)}.[/tex][tex]Substitute\text{ }f(x)=x+4\text{ and }g(x)=x-7\text{ in the equation.}[/tex][tex](\frac{f}{g})(x)=\frac{x+4}{x-7}[/tex]Final answer:
[tex](\frac{f}{g})(x)=\frac{x+4}{x-7}[/tex]Related Questions
Solve for p in the equation 7p = -63.
Answers
Use the following property of equations to solve the given equation.
Let a, b and c be real numbers, such that c is different from 0. Then:
[tex]a=b\Leftrightarrow\frac{a}{c}=\frac{b}{c}[/tex]On the given equation:
[tex]7p=-63[/tex]Divide both sides of the equation by 7 (as the property says):
[tex]7p=-63\Leftrightarrow\frac{7p}{7}=\frac{-63}{7}[/tex]Simplify the fraction 7p/7:
[tex]\begin{gathered} \frac{7p}{7}=p \\ \Rightarrow p=\frac{-63}{7} \end{gathered}[/tex]Divide -63 by 7. Since -63 is negative and 7 is positive, the result should be negative. Additionally, 63/7 = 9, so:
[tex]\begin{gathered} \frac{-63}{7}=-9 \\ \therefore p=-9 \end{gathered}[/tex]Therefore, the solution for the equation 7p=-63 is p=-9.
The rectangle has an area of 144 square centimeters. which is the perimeter?
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The formula to find the area of a rectangle is:
[tex]\begin{gathered} A=L\cdot W \\ \text{ Where} \\ A\text{ is the area} \\ L\text{ is the length} \\ W\text{ is the width} \end{gathered}[/tex]Then, let it be:
• L: The length of the rectangle.
,• W: The width of the rectangle.
So, we have:
[tex]\begin{gathered} A=144cm^2 \\ L=? \\ W=8cm \end{gathered}[/tex]Now, we can write and solve for L the following equation:
[tex]\begin{gathered} A=L\cdot W \\ 144cm^2=L\cdot8cm \\ \text{ Divide by 8}cm\text{ from both sides} \\ \frac{144cm^2}{8cm}=\frac{L\cdot8cm}{8cm} \\ 18cm=L \end{gathered}[/tex]The following is the procedure for dividing 144 by 8.
On the other hand, the perimeter is the sum of the measures of all sides of a polygon. Then, we have:
[tex]\begin{gathered} \text{Perimter}=L+W+L+W \\ \text{Perimter}=18cm+8cm+18cm+8cm \\ \text{Perimter}=52cm \end{gathered}[/tex]Therefore, the perimeter of the rectangle is 52 cm.
36. If the interest rate on a 30-year mortgage for $325,000 were changed from 2.9% to 2.6%, how much would you save over the life of the loan?
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The formula to calculate the mortgage payment is as follows:
[tex]M=P\frac{\lbrack i(1+i)^n\rbrack}{\lbrack(1+i)^n-1\rbrack}[/tex]Where P is the principal loan amount $325,000
i is the monthly interest rate, divide the annual interest rate by 12 to find the monthly interest rate.
n is the number of payments over the lifetime of the loan (months) then as you have a 30-year mortgage n=30 years x 12 months per year=360 payment months.
a. For 2.9% interest rate:
i=2.9%/12=0.029/12=0.002417
Replace the known values:
[tex]\begin{gathered} M1=325,000\frac{\lbrack0.002417(1+0.002417)^{360}\rbrack}{\lbrack(1+0.002417)^{360}-1\rbrack} \\ M1=325,000\frac{\lbrack0.002417\cdot2.38441\rbrack}{\lbrack2.38441-1\rbrack} \\ M1=325,000\frac{0.005762}{1.38441} \\ M1=1352.75 \end{gathered}[/tex]This would be the monthly payment when interest rate is 2.9%
b. For 2.6% interest rate:
i=2.6%/12=0.026/12=0.002167.
[tex]\begin{gathered} M2=325,000\frac{\lbrack0.002167(1+0.002167)^{360}\rbrack}{\lbrack(1+0.002167)^{360}-1\rbrack} \\ M2=325,000\frac{\lbrack0.002167\cdot2.17963\rbrack}{\lbrack2.17963-1\rbrack} \\ M2=325,000\frac{0.004723}{1.17963} \\ M2=1301.1 \end{gathered}[/tex]Thus, to calculate how much would you save over the life of the loan, multiply each monthly payment by 360 payments, and the difference would be the money you save:
[tex]\begin{gathered} At\text{ 2.9\% interest rate:} \\ 1352.75\times360=486989.1 \\ At\text{ 2.6\% interest rate:} \\ 1301.1\times360=468397.5 \\ \text{Money saved: }486989.1-468397.5=18591.6 \end{gathered}[/tex]Answer: You save $18591.6 over the life of the loan if the interest changed from 2.9% to 2.6%
suppose that the heights of adult men in th united states are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What proportion of the adult men in the united states are less than 6 feet tall?
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Proportion of the adult men less than 6 feet tall = 74.857%
Explanations:The mean height, μ = 70 inches
The standard deviation in height, σ = 3 inches
Proportion of the adult men less than 6 feet
1 foot = 12 inches
6 feet = 12 x 6 = 72 inches
x = 72 inches
Calculate the z-value using the formula below:
[tex]\begin{gathered} z\text{ = }\frac{\text{x -}\mu\text{ }}{\sigma} \\ z\text{ = }\frac{72-70}{3} \\ \text{z = }\frac{2}{3} \\ \text{z = }0.67 \end{gathered}[/tex]Probability that an adult men will be less than 72 inches (6 feet) tall
P(x < 72) = P(z < 0.67) = 0.74857
Therefore, proportion of adult men less than 72 inches (6 feet) tall = 0.74857 x 100% = 74.857%
1) A ball is thrown downward from a window in a tall building. Its position at time t in seconds iss(t) = -16t2 + 32t + 55, where s(t) is in feet. How long (to the nearest tenth) will it take the ball to hit the ground?A)-1.2 secB) 1.2 secC) 2.9 secD) 3 sec
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The equation for the position is,
[tex]s(t)=-16t^2+32t+55[/tex]When the ball hit the ground then value of height is 0 feet. So value of s(t)=0,
The equation for the time is,
[tex]-16t^2+32t+55=0[/tex]Determine the roots of the equation by using the quadratic formula.
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-32\pm\sqrt[]{(32)^2-4(-16)(55)}}{2(-16)} \\ =\frac{-32\pm\sqrt[]{4544}}{-32} \\ =\frac{-32\pm67.41}{-32} \\ =\frac{-99.41}{-32},\text{ }\frac{35.41}{-32} \\ =3.10,-1.10 \end{gathered}[/tex]The value of time can never be less than 0. so approximate value of time is 3 seconds. Correct option is D part.
A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function S=0.50M+1\$.75 , where is the number of miles driven The company also offers an option to insure the car against damage. The insurance charge (in dollars) is given by the function I = 0.25M + 5.80 Let C be the total charge (in dollars) for a rental that includes insuranceWrite an equation relating C to M. Simplify your answer as much as possible.
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Okay, here we have this:
Considering the provided information, we are going to find the requested equation, so we obtain the following:
Then we can see that we must find the function that represents the total cost, therefore we have
Total cost=Standard charge+ Insurance charge
Replacing:
C=0.50M+15.75+0.25M+5.80
C=(0.50M+0.25M)+(15.75+5.80)
C=0.75M+21.55
Finally we obtain that the equation for the total charge is C=0.75M+21.55
Ron runs a computer repair company out of his home. He usually gets 4 salescalls and 7 tech support calls each weekday. How many calls does he get in aweek?
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Given:
There are given that they get 4 sales calls and 7 tech support calls each weekday.
Explanation:
According to the concept:
The total number of days in a week is 7.
Then,
From the question:
They get a total number of calls are:
[tex]4\text{ sales + 7 tech = 11}[/tex]Now,
The number of calls in a week will be:
[tex]7\times11=77[/tex]Final answer:
Hence, the total numbers of calls he gets in a week are 77.
going to send you pictures
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Answer: We have to find the probablity that a registered voter votted in the election
[tex]\begin{gathered} \text{Voters = 3072757} \\ \text{Not-Voted = 3481030 } \\ \text{Total registered=3,072,757+3,481,030=}6,553,787 \end{gathered}[/tex]Therefore, the probability that a registered voter voted is:
[tex]P_r=\frac{3072757}{6553787}=46.56\text{ percent}[/tex]Likewise, the probablity that a registered voter did not vote is:
[tex]53.11\text{ percent }[/tex]
A truck driver is allowed to drive amaximum of 7.5 hours each day. If thedriver’s average speed is 58 miles per hour,how many miles does the driver travel eachday
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The speed can be described as:
[tex]speed=\frac{distance}{time}[/tex]then, if want to find the distance we can say that,
[tex]speed\times time=distance[/tex]if the driver has an average speed and a time limit,
[tex]\frac{58miles}{hour}\times7.5hour=435miles[/tex]Answer:
we can say that the driver can travel a maximum of 435 miles per day at an average speed of 58 miles per hour.
How to write, Twice the difference of 3 and a
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Answer:
2*(3 - x)
Step-by-step explanation:
We don't know what the number is, so i am going to call it x.
Difference of 3 and a number.
The number is x.
Difference of 3 and x is 3 - x.
Twice
We multiply 2. So
2*(3 - x)
Ms. Juhal was making t-shirts. One of the designs had these coordinate points: A (-5, 5), B (-5, 3), C (-5, 1), and D (2, 1). Plot the points on graph paper in the order they are given and connect them. What shape is made?
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Given data:
The given coordinates are A (-5, 5), B (-5, 3), C (-5, 1), and D (2, 1).
The below figure shown the graph of the above coordinate.
Thus, the above figure represents the right angle triangle.
I will send a picture of the equation because it won't make sense if I type it here.
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To find the answer, we will need to replace the population P by 50,000 and solve the initial equation for t because t is the number of years after 2012.
So, we get:
[tex]50,000=25,000e^{0.03t}[/tex]Now, we need to remember some properties of the logarithms:
[tex]\ln e^a=a[/tex]Then, we can solve for t as:
[tex]\begin{gathered} 50,000=25,000e^{0.03t} \\ \frac{50,000}{25,000}=\frac{25,000e^{0.03t}}{25,000} \\ \\ 2=e^{0.03t} \end{gathered}[/tex]So, using the property, we get:
[tex]\begin{gathered} \ln 2=\ln e^{0.03t} \\ \ln 2=0.03t \end{gathered}[/tex]Finally, dividing by 0.03 into both sides, we get that the number of years after 2012 that the population will be 50,000 is:
[tex]\begin{gathered} \frac{\ln 2}{0.03}=\frac{0.03t}{0.03} \\ \frac{\ln 2}{0.03}=t \end{gathered}[/tex]Answer: t = ln2/0.03
Help. I need to be freed from the curse of math homework.
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ANSWER ; On average, Bailey reads 5/7 books per week
EXPLANATION;
Here, we want to get the average number of books per week Bailey reads
To get this, we simply have to divide the number of books she read by the number of weeks it took her to read them
Mathematically, we proceed as follows;
[tex]2\frac{1}{2}\text{ }\div\text{ 3}\frac{1}{2}[/tex]Now, to proceed with the division, we have to turn each of the mixed fractions to improper fraction ( a fraction that has its numerator greater than its denoinator)
To do this, we multiply the denominator by the stand alone number, then add the numerator; after which we place the sum over the denominator
We have an example as follows;
[tex]a\text{ }\frac{b}{c}\text{ = }\frac{(a\times c)+b}{c}[/tex]Applying this to the fractions, we have;
[tex]2\frac{1}{2}\text{ = }\frac{5}{2}\text{ and 3}\frac{1}{2}\text{ = }\frac{7}{2}[/tex]Finally, we proceed with the division;
[tex]\frac{5}{2}\text{ }\div\text{ }\frac{7}{2}\text{ = }\frac{5}{2}\times\frac{2}{7}\text{ = }\frac{5}{7}[/tex]You know 3 angles, angle one at the top has an equation of (y+x)° angle two has the equation (y-x)° angle three at the bottom is blank and angle 4 at the left has the equation 2x° you need to figure out what each angle measures to. angle one at the top and angle four to the left are a linear pair, same with angle 1 and 2 at the right, and 2 and 4 are vertical angles and angles 1 and 3 are vertical angles angle 1 and 3 are obtuse while angle 2 and 4 are acute.
Answers
2x° = 2(30) = 60°
(y+x)° = 90° + 30° = 120°
(y-x)° = 90 - 30 = 60°
Explanation:
2x° and (y-x)° are vertical angles.
Vertical angles are equal.
equating both:
2x = y - x
2x+x = y
3x = y
Also 2x° + (y+x)° = 180° (angles on a straight line)
2x + x + y = 180
3x + y = 180°
recall, 3x = y
Insert the value of y in the equation: 3x + y = 180°
y + y = 180
2y = 180
y = 180/2
y = 90°
y = 3x
x = y/3 = 90/3
x = 30°
One of the angle: 2x° = 2(30) = 60°
(y+x)° = 90° + 30° = 120°
(y-x)° = 90 - 30 = 60°
Any help finding the 0th term? I have a guess but want to know if its correct.
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Given series is:
100,50,25....
so the first term is a=100
and the common ration is: r=1/2
So the nth term of GP is calculated as:
[tex]T_n=ar^{n-1}[/tex]So for 0th term:
[tex]\begin{gathered} T_0=(100)(\frac{1}{2})^{0-1} \\ T_0=100\times(\frac{1}{2})^{-1} \\ T_0=100\times2 \\ T_0=200 \end{gathered}[/tex]So the oth term of given GP is 200.
88,826.564 The 6 in the ones place is ___ the value of the 6 in the hundredth place
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Given the question:
88,826.564
The 6 in the ones place is 100 times (greater than) the value of the 6 in the hundredth place, since:
6/0.06 = 100.
The base of a 14 foot ladder is 6 feet from a building if the ladder reaches the flat roof how tall is the building? The height of the building is_ ftThe height of the building is approximately_ft
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Step 1. Gather the information that we have and make a diagram.
The length of the ladder is 14 ft, the distance from the base of the ladder to the building is 6 ft and the height of the building is unknown.
We will call this unknown height ''a''.
The following diagram represents the situation:
Step 2. The triangle formed between the floor, the building, and the ladder is a right triangle (it has a 90° angle), this means that we can use the Pythagorean theorem to solve this and find ''a''.
The Pythagorean theorem is represented by the equation:
[tex]a^2+b^2=c^2[/tex]where a and b are the legs of the triangle, and c is the hypotenuse of the triangle (the side opposite to the 90° angle)
In our case,
[tex]\begin{gathered} c=14ft \\ b=6ft \end{gathered}[/tex]And we need to find a.
Step 3. Substituting the known values into the Pythagorean theorem:
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2+(6ft)^2=(14ft)^2 \end{gathered}[/tex]Solving the exponential terms:
[tex]a^2+36ft^2=196ft^2[/tex]And solving for a^2 by subtracting 36ft^2 to both sides of the equation:
[tex]\begin{gathered} a^2=196ft^2-36ft^2 \\ a^2=160ft^2 \end{gathered}[/tex]Taking the square root of both sides and simplifying:
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{160ft^2} \\ \\ a=\sqrt[]{16\cdot10}ft \\ \\ a=4\sqrt[]{10}ft \end{gathered}[/tex]This result can also be represented as a decimal number:
[tex]a=4\sqrt[]{10}ft\approx12.65ft[/tex]Answer:
The height of the building is
[tex]4\sqrt[]{10}ft[/tex]The height of the building is approximately
[tex]12.65ft[/tex]The formula for simple interest is I = Prt where I is the interest earned, P is the Principal, r is the interest, and t is the number of years. Solve the formula for "t" in terms of P, i, and r. t = ?
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To solve "t", simply divide both sides by Pr.
[tex]\begin{gathered} \frac{I}{Pr}=\frac{Prt\text{ }}{Pr} \\ \frac{I}{Pr}=t \\ t=\frac{I}{Pr} \end{gathered}[/tex]Therefore, the formula for t is t = I/Pr as shown above.
Jade this information to answer the questions below. If not enough information is given to answer a question, write not enough information
Answers
Answer
• a) 3
,• b) 21
,• c) Not enough information
Explanation
Given
• 28 seniors
,• 24 students went to the trip, where 7/8 were seniors.
Procedure
• a)
We are given the proportion of seniors, if we want to know the proportion of juniors we have to subtract it from 8/8 (whole):
[tex]\frac{8}{8}-\frac{7}{8}=\frac{1}{8}[/tex]Next, we have to multiply the students that went times the proportion:
[tex]24\cdot\frac{1}{8}=3[/tex]3 juniors went on the trip.
• b)
Now we have to multiply the proportion given times the students that went:
[tex]24\cdot\frac{7}{8}=21[/tex]Thus, 21 seniors went on the trip.
• c)
As we are not given the juniors that are in the class, we cannot answer this one.
sarah is putting her sweaters in boxes to organize her closet.seven sweaters can fit in each box. sarah will fill as many boxes as possible, and the remaining sweaters will stack on the shelf in the closet. if sarah has 38 sweaters, how many sweaters will go in her closet? Solve the problem. draw a tape diagram to represent the problem.
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Given: Sarah can fit 7 sweaters in a box
She has 38 sweaters
the remaining sweaters will stack on the shelf in the closet.
By dividing 38 by 7 we will get:
[tex]\frac{38}{7}=\frac{35+3}{7}=\frac{5\cdot7+3}{7}=5\frac{3}{7}[/tex]So, she will need 5 boxes, she will put 35 sweaters in 5 boxes
The remaining sweaters = 38 - 35 = 3 sweaters
So, the answer is: 3 sweaters will go in her closet
can someone help me please
Answers
In this problem we have the price of many utilities, and the quantity consumed of each one. We must compute the total bill of a month.
The cost of each service is:
• Electricity: $0.15/kWh * 2,000 kWh = $300,
,• Gas: $1/(100 ft³) * 4,300 ft³ = $43,
,• Water: $0.03/(10 gal) * 8,000 gal = $24,
,• Phone: $30/line * $10 lines = $300,
,• Phone: $0.10/int min * 500 int min = $50,
,• Internet: $200.
The total bill of the services, is the sum of each individual cost:
• Total bill = $300 + $4,300 + $24 + $300 + $50 + $200 = $917
Answer: A. $917.00
what is the slope of the line?
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You can find the slope using the following formula:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ where\colon \\ (x1,y1)=(0,2) \\ (x2,y2)=(1,0) \\ m=\frac{0-2}{1-0}=\frac{-2}{1}=-2 \end{gathered}[/tex]Teresa made $252 for 12 hours of work. At the same rate, how much would she make for 17 hours of work?
Answers
Given:
Amount earned, A=$252.
The number of hours of work, T=12.
The amount earned for one hour work is,
[tex]E=\frac{A}{T}=\frac{252}{12}=21[/tex]Now, the amount earned for t=17 hour work is,
[tex]A^{\prime}^{^{\prime}}=E\times t=21\times17=357[/tex]Therefore, Teresa would make $357 for 17 hour work.
One exploratory mapping session for a 1m by 1m can last 5 minutes. This new mapping system should be able to handle absolute coordinates in space, but the compass directions might not be available. Given: This mapping system uses cartesian system using as origin (0,0,0) the landing site. The robot starts the exploration at the point (1, 2, -3) and ends the exploration at the point (2, 0, 1). Find: Describe the trajectory of the move using the equation of line between the starting and the final location of the robot.
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We have to find the line between the starting and the final location. We have that the parametrics equations of the line are
[tex]\begin{gathered} x=1+t \\ y=2−2t \\ \begin{equation*} z=−3+4t \end{equation*} \end{gathered}[/tex]The symmetric equations are
[tex]x−1=\frac{y−2}{-2}=\frac{z+3}{4}[/tex]which value of k makes the inequality 11+2k>19 true?
Answers
Answer:
k>4
Explanation:
Given the inequality
[tex]11+2k>19[/tex]First, subtract 11 from both sides.
[tex]\begin{gathered} 11-11+2k>19-11 \\ 2k>8 \end{gathered}[/tex]Next, divide both sides by 2
[tex]\begin{gathered} \frac{2k}{2}>\frac{8}{2} \\ k>4 \end{gathered}[/tex]The value of k that makes the inequality true is any value of k greater than 4.
We can write this in interval notation as:
[tex](4,\infty)[/tex]Which expression is equivalent to 3V 45 – 7V20? -20-630 – 20/5-5/5
Answers
Answer:
[tex]-5\sqrt{5}[/tex]Explanation:
Here, we want to simplify the given expression
We have that as follows:
[tex]\begin{gathered} 3\sqrt{45}\text{ = 3}\times\sqrt{45}\text{ = 3}\times\sqrt{9\times5}\text{ = 9}\sqrt{5} \\ 7\sqrt{20}\text{ = 7}\times\sqrt{20}\text{ = 7}\times\text{ }\sqrt{4\text{ }}\text{ }\times\sqrt{5\text{ }}\text{ = 14}\sqrt{5} \end{gathered}[/tex]Thus, we have the difference as:
[tex]9\sqrt{5}\text{ - 14}\sqrt{5}\text{ = -5}\sqrt{5}[/tex]Find the values of the variables. Then find the side lengths. square LMNO X + 7 M 3x + 1 N
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We have the following:
A square has equal sides, therefore we make the following equality
[tex]\begin{gathered} x+7=3x+1 \\ 3x-x=7-1 \\ 2x=6 \\ x=3 \end{gathered}[/tex]now, replacing:
[tex]\begin{gathered} LM=3+7=10 \\ MN=3\cdot3+1=9+1=10 \end{gathered}[/tex]Therefore, the answer is option b
Explain with definition and example of Cross Product of Vectors.
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Given:
Cross product of vectors.
Required:
To define and explain the cross product of vectors.
Explanation:
Cross product is the binary operation on two vectors in three dimensional space. It again results in a vector which is perpendicular to both the vectors. Cross product of two vectors is calculated by right hand rule.
Right hand rule is nothing but the resultant of any two vectors is perpendicular to the other two vectors. Using cross product, we can also find the magnitude of the resulting vector.
Let
Vector A and Vector B is denoted by
[tex]\vec{A}\times\vec{B}[/tex]and its resultant vector is perpendicular to the vectors A and B.
Cross Product Formula :
[tex]\vec{A}\times\vec{B}=ab\sin\hat{\theta n}[/tex]where n is the unit vector.
Example:
Let
[tex]\begin{gathered} \vec{a}=2i+k \\ \vec{b}=i+j+k \end{gathered}[/tex]So,
[tex]\vec{a}\times\vec{b}=\begin{bmatrix}{i} & {j} & {k} \\ {2} & {0} & {1} \\ {1} & {1} & {1}\end{bmatrix}[/tex][tex]\begin{gathered} =i(-1)-j(2-1)+k(2-0) \\ =-i-j+2k \end{gathered}[/tex]Final Answer:
Cross product is the binary operation on two vectors in three dimensional space.
is 0.6 reduction, enlargement or isometric
Answers
Since the scale factor is less than 1 this means that this is a reduction.
What is the value of log4 16?
Answers
Answer:
[tex]\log_416=2[/tex]
Step-by-step explanation:
Given expression:
[tex]\log_416[/tex]
Rewrite 16 as 4²:
[tex]\implies \log_44^2[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies 2 \log_44[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies 2 \cdot 1[/tex]
Simplify
[tex]\implies 2[/tex]
Therefore:
[tex]\implies \log_416=2[/tex]