What is the measure of ZA in terms of/ and m?АCnBΖΑ
Answers
Cos (alpha) = l/m
mA = Cos^-1(l/m)
Related Questions
a triangle is shown which is similar to Triangle XYZ
Answers
Ok, so you're being show a set of triangles and the only information you have about them are the lengths of their sides. This means that there is a relation between the sides of one of this triangles with the sides of the XYZ.
Now, if you look at triangle C you can see that their sides have exactly the double length of the sides of triangle XYZ. This means that the angles of triangle C are the same that those of triangle XYZ so they are similar.
there are 45 balloons at a birthday party and only 15 of them have prizes inside.if a student is allowed to pop one balloon what is the probability she will not win a price.A. 1/3B. 2/3C. 1/5D. 4/5
Answers
Given:
Total number of balloons = 45
Number of balloons with prizes = 15
Let's find the number of balloons without prizes.
Number of balloons without prizes = Total balloons - Number of balloons with prizes
= 45 - 15 = 30
If a student is allowed to pop one balloon, let's find the probability she will not win a price.
To find the probability she will not win a prize, apply the formula:
[tex]\begin{gathered} x=\frac{\text{Number of balloons without prizes}}{\text{Total ballons}} \\ \\ x=\frac{30}{45} \end{gathered}[/tex]Simplify the fraction.
Divide the numerator and denominator by the greatest common factor.
GCF of 30 and 45 = 15
Divide both the numerator and denominator by 15:
[tex]\begin{gathered} x=\frac{30\div15}{45\div15}=\frac{2}{3} \\ \\ x=\frac{2}{3} \end{gathered}[/tex]Therefore, the probability the student will not win a prize is ⅔
ANSWER:
B. ⅔
Find the volume of this cone.Use 3 for TT.14 ft14 ftV = Tr?h=3V ~ [?]ft
Answers
Given the image find the volume of this cone:
The volume of this cone =
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ where\pi\text{ = 3} \\ d=14 \\ r=\frac{d}{2}=\frac{14}{2}=7ft \\ h=4ft \end{gathered}[/tex]radius = 7ft
height = 4ft
Volume of the cone =
[tex]\begin{gathered} V=\frac{3(7)^2(4)}{3} \\ V=49(4) \\ V=196ft^3 \end{gathered}[/tex]
Therefore the volume of the cone = 196ft³
Given that f(x)= -2 square root x minus 1+3, describe the transformations applied to f(x) from the parent function y=x.
Answers
The graph for the given transformation is attached below
the transformation of graph is stretched
What is transformation in graph ?Graph transformation is the process of modifying an existing graph or graph equation to create variations of the previous graph. This is a common type of problem in algebra, especially in modifying algebraic equations.
Graph may be shifted or moved on the xyxy plane. In some cases, it is stretched, rotated, flipped, or a combination of these transformations. Many problems are ``shift the function f(x)f(x) in one direction by cc units'', ``stretch the function f(x)f(x) by cc units'', or ``function f ( x) Transform f(x) in xx units around the xx, yy, or zz axis." In each case, the transformation affects the underlying function in a specific way that can be understood and calculated.
CalculationTo find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Parent Function:
g(x) =√x
Horizontal Shift: Right 1 Units
Vertical Shift: Up 4Units
Reflection about the x-axis: Reflected
Vertical Stretch: Stretched
learn more about transformation in graph here :
brainly.com/question/21981889
#SPJ9
Identify the phase shift, vertical translation and range for each function.a.
Answers
In sine and cosine functions, we have the following forms:
[tex]\begin{gathered} f\mleft(x\mright)=A\sin\mleft(Bx+C\mright)+D \\ f\mleft(x\mright)=A\cos\mleft(Bx+C\mright)+D \end{gathered}[/tex]Where A is the amplitute, 2π/B is the period, C is the phase shift and D is the vertical shift.
By comparison, we can see that:
[tex]\begin{gathered} f\mleft(x\mright)=A\sin\mleft(Bx+C\mright)+D \\ f\mleft(x\mright)=\sin\mleft(x+45°\mright)+2 \end{gathered}[/tex][tex]\begin{gathered} A=1 \\ B=1 \\ C=45° \\ D=2 \end{gathered}[/tex]Then, the phase shift is 45°, the vertical shift is 2.
The vertical shift is the same as the middle horizontal axis of the function, so we know that the middle of the function is y = 2. The amplitute is how many units the function varies up and down from the middle. Since the Amplitute is 1, the function varies from 2 - 1 to 2 + 1, that is, it varies from 1 to 3. So, the range of the function is:
[tex]R=\left[1,3\right][/tex]16. In the diagram below, the measure of ZW is 6 times as large as the measure of 2XWhat is the measure of angle ZWIA60°12001449D150°
Answers
From the diagram, angles W and X are supplementary, this means the addition of their measures is equal to 180 degrees, that is,
[tex]m\angle W+m\angle X=180\degree[/tex]The measure of angle W is 5 times as large as the measure of angle X, then:
[tex]m\angle W=5m\angle X[/tex]Substituting this second equation into the first one, and solving for the measure of angle X:
[tex]\begin{gathered} 5m\angle X+m\angle X=180\degree \\ 6m\angle X=180\degree \\ m\angle X=\frac{180\degree}{6} \\ m\angle X=30\degree \end{gathered}[/tex]In consequence, the measure of angle W is:
[tex]\begin{gathered} m\angle W=5(30\degree) \\ m\angle W=150\degree \end{gathered}[/tex]1) There are 8,040 primary care doctors in Indiana. The population of Indiana is 6.6 million.Which of the following best represents the primary care doctors per capita for Indiana inScientific Notation? 2 pointsa) 1.22 x 103b) 8.21 x 10-4c) 821d) 1.22 x 10-3
Answers
Problem Statement
The question tells us
7 m l 4 mc What is the area of this parallelogram? 8 m 0 104 m2 88 m2 7 m 56 m2 0 32 m2
Answers
we get that the area is:
[tex]A=7\cdot8+2\cdot\frac{4\cdot8}{2}=56+32=88m^2[/tex]4 friends had a scarf each at 86.4 in long what was total length of all scarfs in feet
Answers
The total length of all 4 scarfs is 345.6 feet.
According to the question,
We have the following information:
4 friends had a scarf each at 86.4 feet in length.
Now, we can easily find the length of all scarfs by following the given steps.
1 scarf = 86.4 feet
Now, in order to find the length of all 4 scarfs, we will multiply the length of 1 scarf by the number of scarfs.
Length of 4 scarfs = 4*86.4 feet
Length of 4 scarfs = 345.6 feet
Hence, the total length of all four scarfs in feet is 345.6 feet.
To know more about length here
https://brainly.com/question/28537063
#SPJ1
The dimensions of a rectangular prism are shown below. What is the lateral surface area of the rectangular prism? (Note: The rectangle prism is not drean to scale)
Answers
Given:
Height of prism, h = 10 in
Width of prism, w = 3 in
Length of prism, L = 7 in
Let's find the lateral surface area of the rectangular prism.
To find the lateral surface area of the rectangular prism, aply the formula below:
[tex]\text{LSA}=Ph[/tex]Where P is the perimeter of the base.
h is the height of the prism.
To find the perimeter of the rectangular base, apply the perimeter of a rectangle formula:
P = 2w + 2L
Thus, we have:
[tex]\begin{gathered} \text{LSA}=(2\ast3+2\ast7)10 \\ \\ \text{LSA}=(6+14)10 \\ \\ \text{LSA}=(20)10 \\ \\ \text{ LSA = 200 inches}^2 \end{gathered}[/tex]Therefore, the lateral surface area of the given rectabgular prism is 200 square inches.
ANSWER:
[tex]\text{ A. 200 inches}^2[/tex]The weight limit at a weigh station for an 18-wheeler is 40 tons, which includes the weight of the truck and all material on-board. Jack is driving an 18-wheeler (with trailer) that weighs about 32,000 pounds without any cargo on board. He is hauling market pigs this week. If the average weight of a market pig is 250 pounds, about how many pigs can Jack carry on the 18-wheeler and stay within the weight regulations? (1T = 2000lbs)
Answers
From the question, we have the following information:
1. The weight limit for an 18-wheeler is 40 tons (weight of the truck + all material on board).
2. The 18-wheeler that Jack is driving weighs about 32,000 pounds (without any cargo onboard).
3. The average weight of a market pig is 250 pounds.
To solve this problem, we have that the conversion factor is 1T = 2000lbs, and we need to convert the given values into Tons to find the number of pigs that Jack can carry on the 18-wheeler.
Case: 18-wheeler ---> 32,000 pounds. We need to make the conversion into Tons. Then, we have:
[tex]32000lbs\cdot\frac{1T}{2000\text{lbs}}=16T[/tex]Case: the weight of the pigs ---> 250 pounds:
[tex]250\text{lbs}\cdot\frac{1T}{2000\text{lbs}}=0.125T[/tex]And now, we have that we have 40T - 16T = 24T (available to have as a cargo).
If we have that each pig weighs 0.125T, then, we can represent this situation as follows:
[tex]0.125x=24[/tex]To solve this equation, we can divide both sides of it by 0.125 (division property of equality):
[tex]\frac{0.125}{0.125}x=\frac{24}{0.125}\Rightarrow x=192[/tex]Then, we have that Jack can carry as many as 192 pigs (if they weigh 250 pounds on average) as cargo, and staying within the weight regulations.
Reduce the ratio to its lowest form. 9:6
Answers
Find the circumference. Leave your answer in terms of n.48.2.4 cmA. 2.47 cmB.3.67 cmC.1.27 cmD. 4.87 cm49.
Answers
Solution
For this case we have the diemater given
D= 2.4 cm
then the radius is:
r= 2.4/2= 1.2cm
And then we can find the circumference with the following formula:
[tex]C=2\pi r=2\pi\cdot1.2\operatorname{cm}=7.54\operatorname{cm}[/tex]Then the answer is:
A. 2.4 pi cm
A kayak can travel 60 miles downstream in 10 hours while it would take 30 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current. Let k represent the speed of the kayak in still water and let c represent the speed of the current.
Answers
A kayak can travel 60 miles downstream in 10 hours while it would take 30 hours to make the same trip upstream. Find the speed of the kayak in still water, as well as the speed of the current. Let k represent the speed of the kayak in still water and let c represent the speed of the current.
we have
k -------> represents the speed of the kayak in still water
c -----> represents the speed of the current
so
downstream
Remember that
the speed is equal to divide the distance by the time
s=d/t
d=s*t
60=(k+c)*10
k+c=6 ------k=6-c -----> equation 1
upstream
60=(k-c)*30
k-c=2 ------> k=2+c -----> equation 2
equate equation 1 and equation 2
6-c=2+c
solve by c
2c=6-2
2c=4
c=2
Find the value of k
k=6-2 -----> k=4
therefore
the speed of the kayak in still water is 4 mph
the speed of the current is 2 mphWhich of the numbers below is less than 2.2? Select all that apply.A) 3.25B)52C)D) – 3.5E) 0.1
Answers
We have a multiple-choice question, about which numbers are less than 2.2
To do this we will go through it number by the number
For 3.25
This number is greater than 2
For 1/4
1/4 is the same as 0.25, this number is less than 2
For -5/2
-5/2 Being a negative number this by the rule will always be less than a positive number, so it is less than 2
For -3.5
-3.5 Being a negative number this by the rule will always be less than a positive number, so it is less than 2
For 0.1
This number is less than 2
In conclusion, all numbers except 3.25, are less than 2.2
Need help with this problem, I need help figuring out the interval notation.
Answers
Given the following inequality:
[tex]x\: <\: 8\: or\: x\: \ge\: \: 9[/tex]Plotting this inequality in a number line graph will be:
Therefore, the solution in interval notation is:
[tex]\mleft(-\infty\: ,\: 8\mright)\cup\: \lbrack9,\: \infty\: )[/tex]The perimeter of parallelogram ABCD is 92 cm. AD is 1 cm more than twice AB. Find the lengths of all four sides of ABCD. (1 point) AB = 15 cm, AD = 15 cm BC = 31 cm, CD = 31 cm O AB = 22.5 cm, AD = 23.5 cm, BC = 23.5 cm, CD = 22.5 cm O AB = 16 cm, AD = 33 cmn BC = 33 cm CD = 16 cm O AB = 15 cm, AD = 31 cm BC = 31 cm CD = 15 cm о
Answers
AB=15 AD=31 BC=31 CD=15
Explanation
Step 1
the perimeter of the parallelogram ABCD is
[tex]\begin{gathered} \text{Perimeter}=AB+BC+CD+AD \\ \text{Also} \\ \text{Perimeter}=92\text{ cm} \\ so \\ 92=AB+BC+CD+AD\text{ Equation(1)} \end{gathered}[/tex]on a parallelogram, 2 length are similear
[tex]\begin{gathered} BC=AD(\text{blue lines)} \\ \text{and} \\ AB=CD(\text{black lines)} \end{gathered}[/tex]now, replace in equation (1)
[tex]\begin{gathered} 92=AB+BC+CD+AD\text{ Equation(1)} \\ 92=AB+AD+AB+AD \\ 92=2AB+2AD \\ 92=2(AB+AD)\text{ Equation (2)} \end{gathered}[/tex]Step 2
now,AD is 1 cm more than twice AB, in other words, you have to add 1 to twice AB to ger AD
[tex]AD=1+2AB\text{ Equation (3)}[/tex]Step 3
solve equation (2) and (3)
replace equation (3) in equation(2)
[tex]\begin{gathered} 92=2(AB+AD)\text{ Equation (2)} \\ 92=2(AB+(1+2AB))\text{ } \\ 92=2(AB+1+2AB) \\ 92=2(1+3AB) \\ 92=2+6AB \\ \text{subtract 2 in both sides} \\ 92-2=2+6AB-2 \\ 90=6AB \\ \text{divide both sides by 6} \\ \frac{90}{6}=\frac{6AB}{6} \\ 15=AB \end{gathered}[/tex]Step 4
replace the value of AB in equation (3) to find AD
[tex]\begin{gathered} AD=1+2AB\text{ Equation (3)} \\ AD=1+2(15) \\ AD=1+30 \\ AD=31 \end{gathered}[/tex]I hope this helps you
Find the surface area of the cylinder. (SHOW ALL WORK)d = 12 m20 m
Answers
To find the surface area of a cylinder, the formula is.
[tex]\text{Surface Area = 2}\pi rh+2\pi r^2[/tex]Where diameter, d, and height, h, is given below as,
[tex]\begin{gathered} d=12m \\ h=20m \end{gathered}[/tex]Where radius, r, is half of the diameter,
[tex]\begin{gathered} r=\frac{d}{2},\text{ where d =12m} \\ r=\frac{12}{2}=6m \end{gathered}[/tex]Substituting for r and h into the surface area formula above,
[tex]\begin{gathered} \text{Surface Area =2}\pi rh+2\pi r^2=2\pi r(h+r) \\ \pi\text{ is taken as 3.14} \\ =2(3.14)(6)\lbrack20+6\rbrack=37.68\times26=979.68m^2 \end{gathered}[/tex]Hence, the surface area of the cylinder is 979.68m²
Find the missing side length of each triangle round to the nearest 10th if necessary
Answers
Answer:
[tex]a=11.2\text{ m}[/tex]Step-by-step explanation:
The Pythagorean theorem states that if the square of a side is equal to the sum of the square of the other two sides, then the triangle must be a right-angle triangle.
[tex]a^2+b^2=c^2[/tex]So, for the given values:
b=5.1, c=12.3, a=?
[tex]\begin{gathered} a^2=c^2-b^2 \\ a=\sqrt[]{12.3^2-5.1^2} \\ a=\sqrt[]{151.29-26.01} \\ a=\sqrt[]{125.28} \\ a=11.19 \\ \text{ Rounding to the nearest tenth:} \\ a=11.2\text{ m} \end{gathered}[/tex]explanation:
took the test:)
Find the x - and y-intercepts of the graph of the linear equation 3x + 6y = 24.
Answers
Let's find:
x-intercept =
y - intercept =
the expected value is $1.71 . If the same bet is made 872 times ,how much would you expect to win or lose? round your answer to two decimal places .Losses must be expressed as negative value
Answers
cardsWe were given the following information:
A standard deck of cards has 52 cards
There are 13 Clubs cards in a standard deck
The probability of drawing a Clubs card is given by:
[tex]P_1=\frac{13}{52}[/tex]In the second draw, there are 51 cards left. The probability of picking a Clubs is given by:
[tex]P_2=\frac{12}{51}[/tex]The total probability is equal to the product of the individual probabilities, this is:
[tex]\begin{gathered} P=P_1\times P_2 \\ P=\frac{13}{52}\times\frac{12}{51} \\ P=0.0588\approx0.059 \\ P=0.059 \end{gathered}[/tex]The Expected Value for 1 game is calculated as shown below:
[tex]\begin{gathered} EV=P_1*X_1+P_2*X_2 \\ X_1=\text{event of }winning\text{ \$}765,P_1=0.059 \\ X_2=\text{event of }losing\text{ \$}46,P_2=1-0.059=0.941 \\ EV=(0.059\times765)-(0.941\times46) \\ EV=45.135-43.286 \\ EV=1.849\approx1.85 \\ \\ \therefore EV=\text{\$}1.85 \end{gathered}[/tex]If the same bet is done 872 times, I would expect to win:
[tex]\begin{gathered} 872\cdot EV=872\times1.85 \\ 872\cdot EV=1613.20 \end{gathered}[/tex]I would expect to win $1,613.20
A ladder leans against a building, making a 63 angle of elevation with the ground.The top of the ladder reaches a point on the building that is 37 feet above theground. To the nearest tenth of a foot, what is the distance between the base of the building and the base of the ladder? Use the correct abbreviation for the units.If the answer does not have a tenths place then include a zero so that it does.
Answers
Solution
- To better understand the problem, we can make a sketch as follows:
- The above figure depicts what was described by the question.
- We are asked to find the distance between the base of the ladder and the base of the building, and we have labeled it as x.
- To find the value of x, we simply apply SOHCAHTOA.
- That is,
[tex]\begin{gathered} \tan\theta=\frac{Opposite}{Adjacent} \\ \\ \tan63\degree=\frac{37}{x} \\ \\ \text{ Rewrite,} \\ \\ x=\frac{37}{\tan63\degree} \\ \\ \therefore x=18.852441...\approx18.9\text{ \lparen TO THE NEAREST TENTH OF A FOOT\rparen} \end{gathered}[/tex]Final Answer
The distance of the base of the building from the base of the ladder is 18.9 feet.
What is the recursive formula for the sequence?8, 6, 4, 2, 0, ...an = an-1 - 2, where a = 8an = an-1 + 2, where a = 8an = 2n-1 - 2, where a = -2an = 2n-1 + 2, where a = -2
Answers
Arithmetic sequences are given by the expression:
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_n=the\text{ term we need to find} \\ a_1=first\text{ term of the sequence} \\ d=\text{ common difference} \end{gathered}[/tex]So, in this case the formula would be:
[tex]a_n=8-2(n-1)[/tex]Can you help me solve this? The second is the practice line of Chloe
Answers
We have that the practice line of Chloe is given by the second figure. Let us find what is the length that Chloe has for practice. We have a right triangle, and we also have the lengths of the legs of the triangle. We can apply here the Pythagorean Theorem to find the hypotenuse (Chloe zip line of practice). Then, we have:
[tex]h^2=20^2+26^2^{}\Rightarrow h=\sqrt[]{20^2+26^2}\Rightarrow h=32.80ft[/tex]Now, let us find the side CD of the triangle ACD. We can apply the Law of Sines to solve for this side of the triangle:
[tex]\frac{CD}{\sin(16)}=\frac{420}{\sin(90)}\Rightarrow CD=\frac{420\cdot\sin(16)}{\sin(90)}\Rightarrow CD=\frac{420\cdot0.2756}{1}[/tex]Then, the side CD is:
[tex]CD=115.752ft[/tex]We can use the same Law of Sines to find the side AD. Since the inner sides of a triangle sum 180, we have that the angle < DCA = 74:
[tex]\frac{AD}{\sin(74)}=\frac{420}{\sin(90)}\Rightarrow AD=\sin (74)\cdot420\Rightarrow AD=403.73ft[/tex]We now can apply the Law of Sines again to find BD:
[tex]\frac{BD}{\sin(36)}=\frac{AB}{\sin(90)}\Rightarrow BD=AB\cdot\sin (36)\Rightarrow BD=500ft\cdot\sin (36)[/tex]Then, we have:
[tex]BD=500ft\cdot0.5878\Rightarrow BD=293.9ft[/tex]We can calculate the angle E from the practice line of Chloe. We can also apply the Law of Sines:
We already calculated the hypotenuse of this triangle before, and the length is equal to 32.80ft, then we have:
[tex]\frac{\sin(90)}{32.80}=\frac{\sin(E)}{20}\Rightarrow\sin (E)=\frac{20}{32.80}=0.6097\Rightarrow\angle E=\arcsin (0.6097)[/tex]Then, we have that:
[tex]\angle E=37.57[/tex]This angle value is near the measure of the angle of Daredevil's zip line.
From the comparison of the triangles, we can see that the Daredevil triangle is almost similar to that of the triangle used by Chloe to practice. We have that they have similar angles and the proportions of the sides are:
[tex]\frac{500}{32.80}\approx\frac{293.9}{20}\approx\frac{403.73}{26}\approx15[/tex]The Beginner's triangle is not a similar triangle to that of the triangle used by Chloe, the angles are not similar, and the sides do not have the same proportion to that of Chloe's practice.
Therefore, Daredevil's line is closest to Chloe's practice zip line because the triangles used in each case present almost the same ratio, and all the sides and angles have a similar proportion. Then, Chloe practices on a similar zip line. The Beginner's zip line is not similar to that of Chloe's zip line practice.
Arrange these functions from the greatest to the least value based on the average rate of change in the specified Interval. Rx) = x² + 3x interval: (-2.3] f(x) = 3x -8 interval: (4,5) f(x) = x² - 2x interval: (-3, 4) f(x) = x²-5 interval: (-1, 1] > > >
Answers
To find the average rate of change of a function within a given interval, we use the following formula;
[tex]\frac{f(b)\text{ - f(a)}}{b-a}[/tex]So for the first equation, we have;
[tex]\begin{gathered} f(x)=x^2\text{ + 3x} \\ a\text{ = -2} \\ b\text{ = 3} \\ f(a)=f(-2)=(-2)^2+3(-2)=4-6=-2 \\ f(b)=f(3)=3^2\text{ + 3(3)=9+9 = 18} \\ \\ So; \\ \frac{f(b)-f(a)}{b-a}\text{ = }\frac{18-(-2)}{3-(-2)}=\frac{18+2}{3+2}=\frac{20}{5}=4 \end{gathered}[/tex]For the second equation, we have;
[tex]\begin{gathered} f(x)\text{ = 3x-8} \\ a=4 \\ b=5 \\ f(a)=f(4)=3(4)-8=12-8=4 \\ f(b)=f(5)=3(5)-8=15-8=7 \\ \frac{f(b)-f(a)}{b-a}=\frac{7-4}{5-4}=\frac{3}{1}=3 \end{gathered}[/tex]For the third equation, we have;
[tex]\begin{gathered} f(x)=x^2-2x \\ a=-3 \\ b=4 \\ f(a)=f(-3)=(-3)^2-2(-3)=9+6=15 \\ f(b)=f(4)=4^2-2(4)=16-8=8 \\ \\ \frac{f(b)-f(a)}{b-a}=\text{ }\frac{15-8}{4-(-3)}=\frac{7}{7}=1 \end{gathered}[/tex]For the last equation, we have;
[tex]\begin{gathered} f(x)\text{ = }x^2-5 \\ a=\text{ -1} \\ b=1 \\ f(a)=f(-1)=(-1)^2-5=1-5=-4 \\ f(b)=f(1)=1^2-5=1-5=-4 \\ \\ \frac{f(b)-f(a)}{b-a}=\text{ }\frac{-4-(-4)}{1-(-1)}=\frac{0}{2}=\text{ 0} \end{gathered}[/tex]So arranging the functions from highest to lowest based on the value obtained, we have;
[tex]x^2+3x,3x-8,x^2-2x,x^2-5[/tex]-Use the dot product to determine whether v and w are orthogonal.v = 2i +2j, w = 2i - 2jSelect the correct choice below and, if necessary, fill in the answer box to complete your chO A. They are orthogonal because the dot product isO B. They are not orthogonal because the dot product is
Answers
Answer:
Concept:
Two vectors a and b are orthogonal if they are perpendicular, i.e., the angle between them is 90° (Fig. ... Condition of vectors orthogonality. Two vectors a and b are orthogonal if their dot product is equal to zero.
The dot product of two vectors will be calculated using the formula below
[tex]\begin{gathered} a=a_1i+a_1j,b=b_1i+b_2j \\ a.b=a_1b_1+a_2b_2 \end{gathered}[/tex]The vectors are given below as
[tex]v=2i+2j,w=2i-2j[/tex]By applying the principle, we will have
[tex]\begin{gathered} vw=(2\times2)+(2\times-2) \\ v\text{.}w=4-4 \\ v.w=0 \end{gathered}[/tex]Hence,
They are orthogonal because the dot product is = 0
The final answer is OPTION A
An accountant invested $5000 at a simple intereste of 8 % for 2 years. What total amount of interest will› have from her investment?
Answers
Given:
Principal, P = $5000
Interest rate, R = 8% = 0.08
Time, T = 2 years
Let's fnd the toatal amount of interest.
To find the interest, apply the simle interest formula:
[tex]I=\text{PRT}[/tex]Hence, we have:
[tex]\begin{gathered} I=5000\times0.08\times2 \\ \\ I=800 \end{gathered}[/tex]Therefore, the total amount of interest is $800.
ANSWER:
$800
Write the equation of the line that passes through the point P(0.0) and is perpendicular to the line y=-4x+5. Ο Α. y=* OB y=-* O C. y=5x D. y=4x o E. y = x+5
Answers
Answer:
The equation of the line is
[tex]y=\frac{1}{4}x[/tex]Explanation:
Given the equation:
y = -4x + 5 ...................................................................(1)
the slope of this line is -4
Two lines are perpendicular if the product of their slopes is -1
Let m be the slope of the line perpendicular to equation (1)
Then
-4 × m = -1
-4m = -1
Divide both sides by -4
m = 1/4
Given:
[tex](x_1,y_1)=(0,0)[/tex]The equation of the line is:
y - 0 = (1/4)(x - 0)
y = (1/4)x
Find the ordered pair that is a member of both 3x + 5y = 4 and x = -3 -6y or indicate if there is no solution or infinite possibilities.
Answers
In this problem the equation system is:
[tex]\begin{gathered} 3x+5y=4 \\ x=-3-6y \end{gathered}[/tex]SO we can replace the second equation into the first equation so:
[tex]3(-3-6y)+5y=4[/tex]and we solve for y so:
[tex]\begin{gathered} -9-18y+5y=4 \\ 13y=-9-4 \\ y=-\frac{13}{13} \\ y=-1 \end{gathered}[/tex]Now we can replace the value of y into the second equation so:
[tex]\begin{gathered} x=-3-6(-1) \\ x=-3+6 \\ x=3 \end{gathered}[/tex]So the ordered pir is:
[tex](3,-1)[/tex]How to solve problem 19. Area of the shaded region
Answers
To find the area of the shaded region, we need to find the area of the hexagon and subtract the area of the circle.
To find the area of the hexagon, we should find the length of the apothem, which is also the radius of the circle.
Since we can divide the hexagon into 6 equilateral triangles, we can use this to find the apothem:
We can take one of those 6 triangles:
The purple line, h is the height of the triangle but also is the apothem of the hexagon. Now, we have two right triangles that we can use to find h (apothem):
And now, we can use the pythagorean theorem to find the length of h:
[tex]2.05^2+h^2=4.1^2[/tex]And solve:
[tex]\begin{gathered} h=\sqrt{4.1^2-2.05^2}=\sqrt{16.81-4.2025}=\sqrt{12.6075} \\ \end{gathered}[/tex]Now. we can find the area of the hexagon and the circle.
The formula for the area of a hexagon is:
[tex]A_{hexagon}=2\sqrt{3}a^2[/tex]Where a is the apothem. Then:
[tex]A_{hexagon}=2\sqrt{3}(\sqrt{12.6075})^2=43.674[/tex]And now, need to calculate the area of the circle:
[tex]A_{circle}=\pi(\sqrt{12.6075})^2=39.608[/tex]And the area of the shaded region is the difference between the area of the hexagon and the area of the circle:
[tex]43.674-39.608=4.066[/tex] The answer, to the nearest tenth, is 4.1 square units