What are the magnitude and direction of w = ❬–10, –12❭? Round your answer to the thousandths place.
Answers
The direction of a vector is the orientation of the vector, that is, the angle it makes with the x-axis.
The magnitude of a vector is its length.
The formulas to find the magnitude and direction of a vector are:
[tex]\begin{gathered} u=❬x,y❭\Rightarrow\text{ Vector} \\ \mleft\Vert u|\mright|=\sqrt[]{x^2+y^2}\Rightarrow\text{ Magnitude} \\ \theta=\tan ^{-1}(\frac{y}{x})\Rightarrow\text{ Direction} \end{gathered}[/tex]In this case, we have:
• Magnitude
[tex]\begin{gathered} w=❬-10,-12❭ \\ \Vert w||=\sqrt[]{(-10)^2+(-12)^2} \\ \Vert w||=\sqrt[]{100+144} \\ \Vert w||=\sqrt[]{244} \\ \Vert w||\approx15.620\Rightarrow\text{ The symbol }\approx\text{ is read 'approximately'} \end{gathered}[/tex]• Direction
[tex]\begin{gathered} w=❬-10,-12❭ \\ \theta=\tan ^{-1}(\frac{-12}{-10}) \\ \theta=\tan ^{-1}(\frac{12}{10}) \\ \theta\approx50.194\text{\degree} \\ \text{ Add 180\degree} \\ \theta\approx50.194\text{\degree}+180\text{\degree} \\ \theta\approx230.194\text{\degree} \end{gathered}[/tex]Therefore, the magnitude and direction of the vector are:
[tex]\begin{gathered} \Vert w||\approx15.620 \\ \theta\approx230.194\text{\degree} \end{gathered}[/tex]
Related Questions
Describe the vertical asymptote (s) and hole (s) for the graph of y = (x+2) (x+4)/ (x+4) (x+1)
Answers
Given:
[tex]y=\frac{(x+2)(x+4)}{(x+4)(x+1)}[/tex]Required:
We need tofnind the vertical asymptote(s) and hole (s) for the graph of the given function.
Explanation:
Vertical asymptotes can be found when the numerator of the function is equal to zero.
The numerator of the given function is (x+4)(x+1)
[tex](x+4)(x+1)=0[/tex][tex](x+4)=0\text{ or }(x+1)=0[/tex][tex]x=-4\text{ or x=-1}[/tex]The asymptote of the given function is either x =-4 or x =-1.
Recall that a hole exists on the graph of a rational function when both the numerator and denominator of the function are equal to zero.
The common factor of the given rational function
Question 8 of 10Jerry drew AJKL and AMP so that < K =¿N, LL = LP, JK= 6, andMN = 18. Are A JKL and A MNP similar? If so, identify the similarity postulateor theorem that applies.
Answers
Solution.
Given
In triangle JKL and MNP,
Thus, triangle JKL and MNP are equiangular
Hence, we can conclude that both triangles are similar by AA
The answer is option A
Answer:
A
Step-by-step explanation:
QuestionsWhat is the equation of the line?y = 2x - 4y = 1/2x + 2y = 2x + 2y = 1/2x-4
Answers
We have the graph of the equation, and we want to know the equation of the line.
We remember that we need to parts: the slope and the y-intercept. On the graph, we see that when x=0, the graph passes through the point 2, and thus the y-intercept is 2.
[tex]b=2[/tex]Lastly, we will find the slope. For doing so, we will find two values of the line. In this case, we saw that the y-intercept is 2, so a point is (0,2).
Other point is (-4,0), as the x-intercept is -4.
For finding the slope, we remember the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{0-(-4)}=\frac{2}{4}=\frac{1}{2}[/tex]And thus, the slope is 1/2.
This means that the line equation will be:
[tex]\begin{gathered} y=mx+b \\ y=\frac{1}{2}x+2 \end{gathered}[/tex]
Two linear functions are shown below. Compare each fuoction to answer the questions. Function 2: Function 1: -11 8 -7 13 3 Ng -3 18 Part A: What is the rate of change for Function 1? Part B: What is the rate of change for Function 2? Part C: Which function has the greater rate of change?
Answers
The rate of change of a linear functions is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are points through the graph.
Function 1.
From the table we have that the functions passes through the points (-11,8) and (-7,13), pluggin the values in the formula above we have:
[tex]\begin{gathered} m=\frac{13-8}{-7-(-11)} \\ m=\frac{5}{11-7} \\ m=\frac{5}{4} \end{gathered}[/tex]Therefore the rate of change of functions 1 is 5/4
Function 2.
From the graph we notice that the functions passes through the points (-3,-4) and (1,-1), hence:
[tex]\begin{gathered} m=\frac{-1-(-4)}{1-(-3)} \\ m=\frac{-1+4}{1+3} \\ m=\frac{3}{4} \end{gathered}[/tex]Therefore the rate of change of function 2 is 3/4.
Comparing both rates of change we conclude that Function 1 has the greater change of rate.
Yesterday, all three restaurants sold the number of meals that resulted in them earning the maximumprofit.Put the restaurants in order from least to most profit earned.Drag each tile to the correct box.
Answers
For Franco's Hotdogs, the graph shows a parabola. The profit is the y-value of the function, as can be seen, the maximum profit earned is $200 for Franco's Hotdogs.
Now, for Hanna's Barbeque the maximum profit earned is the maximum h(x) value shown in the table, then the maximum profit is $250 for Hanna's Barbeque.
For Rhonda's Burgers, it says the maximum profit is $227.
Then, the restaurant with the least profit earned is Franco's Hotdogs, the next one is Rhonda's Burgers and the restaurant with the most profit earned is Hanna's Barbeque, because:
[tex]200<227<250[/tex]Thus, that is the order.
Answer:
Franco's Hotdogs, Rhonda's Burgers, Hannah's Barbeque
Step-by-step explanation:
I did the tutorial
determine whether the given below each equation represents a direct variation or not if it does find the constant of the variation 3y = 4x
Answers
,y= kx
Where k is the constant of variation.
First solve for y:
3y=4x
y= 4/3 x
So, the constant of variation k= 4/3
It represents a direct variation.
The temperature at 4 p.m. one day was - 6° Celsius. By 11 p.m the temperature had risen 11 degrees. Find thetemperature at 11 pmThe temperature at 11 p.m was 0°c.
Answers
Since the temperature rises by 11 degrees we need to add this to the original temperature, then:
[tex]-6+11=5[/tex]Therefore the temperature at 11 pm is 5° Celsius.
Be sure to fully show the system of equations for each problem and the process used to solve the system.You are starting an office-cleaning service. You decide to charge both large and small offices. You charge $55 for a small office and $85 for a large office. You clean 14 offices and make $920. How many small offices and how many large offices did you clean?
Answers
Given:
The charge for a small office = $55.
The charge for a large office = $ 85.
The total number of offices = 14.
The total amount = $ 920.
Required:
We need to find a number of small offices and large offices.
Explanation:
Let x be the number of the small office and y be the number of the large office.
The equation of the total number of offices.
[tex]x+y=14[/tex][tex]x=14-y[/tex]The equation of the total amount.
[tex]55x+85y=920[/tex]Substitute x =14-y in the equation.
[tex]55(14-y)+85y=920[/tex][tex]55\times14-55y+85y=920[/tex][tex]770+30y=920[/tex]Subtract 770 from both sides of the equation.
[tex]770+30y-770=920-770[/tex][tex]30y=150[/tex]Divide both sides by 30.
[tex]\frac{30y}{30}=\frac{150}{30}[/tex][tex]y=5[/tex][tex]Substitute\text{ y=5 in the equation x=14-y.}[/tex][tex]x=14-5[/tex][tex]x=9[/tex]Final answer:
The equations are
[tex]x+y=14[/tex][tex]55x+85y=920[/tex]The number of small offices are 9.
The number of large offices are 5.
A researcher studying public opinion of proposed social security changes obtains a simple random sample of 50 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases? b. 25% of all adult Americans support the changes. b. The researcher must ask [] more American adults.
Answers
b) We have 25% support the changes, therefore solve:
[tex]np(1-p)=10[/tex]where p =25% = 0.25
So
[tex]\begin{gathered} n(0.25)(1-0.25)=10 \\ n(0.25)(0.75)=10 \\ n(0.1875)=10 \\ \frac{n(0.1875)}{0.1875}=\frac{10}{0.1875} \\ n=53.3\approx54 \end{gathered}[/tex]Need 54 people but already have 50, then:
[tex]54-50=4[/tex]Answer: 4
Choose the correct way to end the sentence.The lines x – 2y = 4 and y = 2x – 2 areA. parallelB. neitherC. perpendicular
Answers
Given the equations of the lines:
[tex]\begin{gathered} x-2y=4\rightarrow(1) \\ y=2x-2\rightarrow(2) \end{gathered}[/tex]We will write both equations in slope-intercept form to find the slope of each line:
The equation of the first line:
[tex]\begin{gathered} x-2y=4 \\ -2y=-x+4\rightarrow(\div-2) \\ \\ y=\frac{1}{2}x-2 \end{gathered}[/tex]so, the slope of the line (1) = 1/2
the equation of the second line:
[tex]y=2x-2[/tex]so, the slope of the second line = 2
Comparing the slopes of the lines:
1) the slopes are not equal, so the lines are not parallel
2) the product of the slopes = 1/2 * 2 = 1
So, the lines are not perpendicular
so, the answer will be option B. neither
State if the three numbers can be the measures of the ustedes of a triangle. 12, 18, 9
Answers
State if the three numbers can be the measures of the ustedes of a triangle.
12, 18, 9
Remember that
The triangle inequality theorem, states that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
so
12+9 > 18
21 > 18 -----> is true
You only need to see that the two smaller sides are greater than the largest side
therefore
the answer is
Yes, the three numbers can be the measures of the ustedes of a trianglemultiply and simplify 2/5 × -7/4
Answers
Answer:
[tex]\frac{2}{5}\times\frac{-7}{4}=\frac{-7}{10}[/tex]Explanation:
Given the expression:
[tex]\frac{2}{5}\times\frac{-7}{4}[/tex]This is the same thing as
[tex]\frac{2\times(-7)}{5\times4}[/tex]evaluating this, we have
[tex]\frac{-14}{20}[/tex]Simplifying this, we have
[tex]\frac{-7}{10}[/tex]Solve the quadratic equation by completing the square.x ^ 2 - 18x + 70 = 0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas.
Answers
Answer:
Form:
[tex]\boxed{(x-9)^2=11}[/tex]Solution:
[tex]x=12.32,5.68[/tex]Explanation:
Step 1. The expression we have is:
[tex]x^2-18x+70=0[/tex]And we are required to find the appropriate form after completing the square, and then the solution or solutions to the equation.
Step 2. Compare the given equation with the general quadratic equation:
[tex]ax^2+bx+c=0[/tex]Our values for a, b, and c are:
[tex]\begin{gathered} a=1 \\ b=-18 \\ c=70 \end{gathered}[/tex]Step 3. Using the value of b, find the following expression:
[tex](\frac{b}{2})^2[/tex]The result is:
[tex](-\frac{18}{2})^2\longrightarrow(-9)^2[/tex]Step 4. Take the original equation
[tex]x^2-18x+70=0[/tex]Move the +70 as a -70 to the right-hand side:
[tex]x^2-18x=-70[/tex]And now add to both sides the expression found in step 3 for (b/2)^2:
[tex]x^2-18x+(-9)^2=-70+(-9)^2[/tex]Step 5. Factor the left-hand side of the equation as a perfect square binominal:
[tex]\begin{gathered} P\operatorname{erf}ect\text{ square binomial formula:} \\ (a\pm b)^2=a^2\pm2ab+b^2 \end{gathered}[/tex]Applying this to our expression:
[tex](x-9)^2=-70+(-9)^2[/tex]Step 6. Solve the operations on the right-hand side:
[tex]\begin{gathered} (x-9)^2=-70+81 \\ \downarrow\downarrow \\ \boxed{\mleft(x-9\mright)^2=11} \end{gathered}[/tex]The form is the equation is:
[tex]\boxed{(x-9)^2=11}[/tex]Step 7. To find the value or values of x, solve for x in the previous equation:
[tex]\begin{gathered} (x-9)^2=11 \\ \downarrow\downarrow \\ x-9^{}=\pm\sqrt[]{11} \\ \downarrow\downarrow \\ x^{}=\pm\sqrt[]{11}+9 \end{gathered}[/tex]Step 8. To find the two solutions we use the '+' and '-' signs separately:
[tex]\begin{gathered} x^{}=\sqrt[]{11}+9\longrightarrow x=3.3166+9=12.3166 \\ x^{}=-\sqrt[]{11}+9\longrightarrow x=-3.3166+9=5.6834 \end{gathered}[/tex]Rounding these values for x to the nearest hundredth (2 decimal places):
[tex]\begin{gathered} x=12.32 \\ x=5.68 \end{gathered}[/tex]Answer:
Form:
[tex]\boxed{(x-9)^2=11}[/tex]Solution:
[tex]x=12.32,5.68[/tex]hich is equivalent to RootIndex 5 StartRoot 1,215 EndRoot Superscript x?
243x
1,215 Superscript one-fifth x
1,215 Superscript StartFraction 1 Over 5 x EndFraction
243 Superscript StartFraction 1 Over x EndFraction
Answers
The given expression is equivalent to [tex]$(1215)^{x/5}[/tex].
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following equation -
[tex]$(\sqrt[5]{1215})^{x}[/tex]
For [tex]$\sqrt[a]{x} = x^{1/a}[/tex]
Using the rule, we can write -
[tex]$(\sqrt[5]{1215})^{x}[/tex] = [tex]$(1215)^{x/5}[/tex]
Therefore, the given expression is equivalent to [tex]$(1215)^{x/5}[/tex].
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on a coordinate plane triangle XYZ is rotated 90 degrees counterclockwise about the origin to form triangle XYZ which conclusion is always true
Answers
Given a 90° rotation of triangle XYZ, every segment will rotate 90°, meaning that each segment will form a right angle with the corresponding transformed segment.
Thereby, the correct answer is:
[tex]\bar{YZ}\perp\bar{Y^{\prime}Z^{\prime}}[/tex]Answer B
The function, fx) = x^2 - 4x + 3, has y-values that increase when x<2. TrueFalse
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} f(x)=x^2-4x+3 \\ f(x)=y \\ \Rightarrow y=x^2-4x+3 \\ y=x^2-4x+3 \end{gathered}[/tex]We will proceed to choose values for x (values of x lesser than 2); x = 1, 0, -1
[tex]\begin{gathered} y=x^2-4x+3 \\ x=1 \\ y=1^2-4(1)+3=1-4+3=4-4=0 \\ y=0 \\ (x,y)=(1,0) \\ \\ x=0 \\ y=0^2-4(0)+3=0-0+3=3 \\ y=3 \\ (x,y)=(0,3) \\ \\ x=-1 \\ y=(-1^2)-4(-1)+3=1+4+3=8 \\ y=8 \\ (x,y)=(-1,8) \end{gathered}[/tex]From the calculation, we see a trend that the y-values increase as the x-value decreases. Hence, it is true
Solve for v-2v-5v-17=25 Simplify your answer as much as possible
Answers
Given:
-2v-5v-17=25
To determine the value of v, we first add similar elements first:
[tex]\begin{gathered} -2v-5v-17=25 \\ -7v-17=25 \end{gathered}[/tex]Next, we add 17 to both sides:
[tex]\begin{gathered} -7v-17+17=25+17 \\ Simplify \\ -7v=42 \\ \frac{-7v}{-7}=\frac{42}{-7} \\ v=-6 \end{gathered}[/tex]Therefore, the value of v is -6.
please help I can't get no more wrong I 5,8 j 9,8 H 5,3
Answers
The coordinates of the points are:
H (5, 3)
I (5, 8)
J (9, 8)
Given that H and I have the same x-coordinate, then the side length of side HI is obtained, subtracting the y-coordinates, as follows:
[tex]HI=y_I-y_H=8-3=5[/tex]Given that I and J have the same y-coordinate, then the side length of side IJ is obtained, subtracting the x-coordinates, as follows:
[tex]IJ=x_J-x_I=9-5=4[/tex]The side length between H and I is 5 units
The side length between I and J is 4 units
What is a multiple root of a polynomial and how do you find it?
Answers
The Solution:
The given polynomial is
[tex]P(x)=2x^4-4x^3-16x^2[/tex]A root of the polynomial P(x) is the value of x for which the polynomial P(x) is equal to zero.
That is, any value of x that makes P(x) = 0, is a root of P(x).
The Multiplicity of a Root: This is the number of times a particular root appears as a root in a polynomial.
To find the root of a polynomial, say P(x), you have to equate P(x) to zero, and then solve for the value of x.
So, we shall follow the above procedures to find the root(s) of P(x), and thereafter determine if there are multiple roots.
[tex]\begin{gathered} P(x)=2x^4-4x^3-16x^2=0 \\ \text{Factoring out 2x}^2,\text{ we have} \\ 2x^2(x^2-2x-8)=0 \end{gathered}[/tex]This means that:
[tex]\begin{gathered} x^2-2x-8=0 \\ or \\ 2x^2=0 \end{gathered}[/tex]Solving quadratic equations above by Tthe Factorization Method, we get
[tex]\begin{gathered} x^2-2x-8=0 \\ x^2-4x+2x-8=0 \\ x(x-4)+2(x-4)=0 \\ (x-4)(x+2)=0 \end{gathered}[/tex]So,
[tex]\begin{gathered} P(x)=2x^2(x-4)(x+2)=0 \\ \text{This means} \\ 2x^2=0\text{ }\Rightarrow x=0 \\ x-4=0\text{ }\Rightarrow x=4 \\ x+2=0\text{ }\Rightarrow x=-2 \\ So,\text{ the roots of P(x) are 0, -2, and 4} \end{gathered}[/tex]Looking at the roots of P(x) above, there is no root that appears more than once, hence, the multiplicity of each of the roots is one.
Instructions: Given the recursive rule, match it to the explicit form.
Answers
Explanation:
If we have a recursive expression with the form
[tex]a_n=a_{n-1}\cdot c[/tex]Then, the explicit formula is
[tex]a_n=a_1\cdot c^{n-1}[/tex]Therefore, for each option, we get:
[tex]\begin{gathered} a_n=a_{n-1}\cdot2\text{ with a}_1=1 \\ \text{ Then} \\ a_n=1\cdot2^{n-1}=2^{n-1} \end{gathered}[/tex][tex]\begin{gathered} a_n=a_{n-1}\cdot-2\text{ with a}_1=2 \\ \text{ Then} \\ a_n=2\cdot(-3)^{n-1} \end{gathered}[/tex][tex]\begin{gathered} a_n=a_{n-1}\cdot4\text{ with a}_1=-1 \\ \text{ Then} \\ a_n=-1\cdot4^{n-1}=-4^{n-1} \end{gathered}[/tex][tex]\begin{gathered} a_n=a_{n-1}\cdot2\text{ with a}_1=-3 \\ \text{ Then} \\ a_n=-3\cdot2^{n-1} \end{gathered}[/tex]Answer:
Therefore, the answer is:
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
Step-by-step explanation:
as this is a right-angled triangle, we use Pythagoras to get also c :
c² = a² + b² = 2² + 7² = 4 + 49 = 53
c = sqrt(53)
we know, sine = opposite/Hypotenuse.
so,
sin(A) = 2/sqrt(53) = 0.274721128...
from the norm circle we know cosine is the other leg of the right-angled triangle :
cos(A) = 7/sqrt(53) = 0.961523948...
tan(A) = sin(A)/cos(A) = 2/7 = 0.285714286...
sec(A) = 1/cos(A) = sqrt(53)/7 = 1.040015698...
csc(A) = 1/sin(A) = sqrt(53)/2 = 3.640054945...
cot(A) = 1/tan(A) = cos(A)/sin(A) = 7/2 = 3.50
oh, and FYI :
A = 15.9453959...°
What is the probability that a family with five children will have at least one boy? Write your answer as a percent rounded to the nearest whole.
Answers
The answer is 0.96875.
Solution;
A family has five children
The probability that at least one of them is a boy = 1-P (all of them are girls)
= 1-(1/2)5
= 1-1/32
= 31/32
= 0.96875
Probability is simply the chance that something will happen. Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome. Analyzing events according to their probabilities is called statistics.
A probability sentence is a declarative sentence in which the term probability or one of its derivatives occurs. The modern mathematical theory of probability has its roots in the gambling experiments of his Gerolamo Cardano in 1654, Blaise Pascal and Pierre de Fermat laid the basic foundations of probability theory, making them the fathers of probability.
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Find the slope of the linear function f with f(2) = 16 and f(4) = -2
Answers
f(2) = 16, Let this be represented as (2, 16)
f(4) = -2, Let this be represented as (4, -2)
[tex]\begin{gathered} \text{slope =}\frac{change\text{ in y}}{\text{change in x}} \\ \\ \text{slope = }\frac{-2-16}{4-2} \\ \text{slope = }\frac{-18}{2} \\ \\ \text{slope}=\text{ -9} \end{gathered}[/tex]Find the solution of the system of equations.5 +2g = 185x-Y=36
Answers
Ok we have the following system of equations:
[tex]\begin{gathered} 5x+2y=18 \\ 5x-y=36 \end{gathered}[/tex]So the first thing to do is take one of the equations above and clear either x or y. I'm going to pick the second equation and clear y:
[tex]\begin{gathered} 5x-y=36 \\ 5x=36+y \\ 5x-36=y \\ y=5x-36 \end{gathered}[/tex]Now we substitute this result in the first equation:
[tex]\begin{gathered} 5x+2y=5x+2\cdot(5x-36)=18 \\ 5x+10x-72=18 \\ 15x=18+72=90 \\ x=\frac{90}{15}=6 \end{gathered}[/tex]Now that we know x we take the result of clearing y from the second equation and find its value:
[tex]\begin{gathered} y=5x-36 \\ y=5\cdot6-36=30-36 \\ y=-6 \end{gathered}[/tex]So in the end x=6 and y=-6.
convert the following fraction to a decimal 3 15/16 a 2,5472 b. 3.156 c. 3.0375 d. 4. 238
Answers
ANSWER:
3.9375
EXPLANATION:
Given:
[tex]3\frac{15}{16}[/tex]To convert this to decimal, first convert the fraction, 15/16 to decimal:
[tex]\frac{15}{16}=\text{ 0.9375}[/tex]Now add the 3 whole number to 0.9375:
[tex]3\text{ + 0.9375 = 3.9375}[/tex]Calculate the area of the circle shown below.10 in Approximate Value_________Exact Value________(round your approximate answers to thehundredths)Circumference of the circle:_________ in?_________ in?
Answers
The radius of the circle is r=10 in.
The circumference of the circle is,
[tex]\begin{gathered} C=2\pi r \\ =2\pi\times10 \\ =20\pi \\ =62.83in \end{gathered}[/tex]Thus, the exact value of circumference is 20pi inches and the approximate value is 62.83 in.
Evaluate the expression b= 3/10c= 2/153c-bwrite in the simplest form
Answers
Evaluate those values into the expression:
[tex]\begin{gathered} 3c-b \\ so\colon \\ 3(-\frac{2}{15})-\frac{3}{10} \\ -\frac{6}{15}-\frac{3}{10}=\frac{-60-45}{150}=-\frac{105}{150}=-\frac{7}{10} \\ \end{gathered}[/tex]Answer:
[tex]-\frac{7}{10}[/tex]Answer:
-7/10
Step-by-step explanation:
3 × -2 / 15 - 3/10
-12/30 - 9/30
-21/30
-7/10
The rate of change of function "f" is the same from x = -2 to x = 1 as it is from x = 1 to x = 4.Function “f” is a ? function
Answers
Linear functions have a constant rate of change for any interval of x-values. Then, function “f” is a linear function
put the following functions in order for smallest maxium to largest maxium
Answers
4) A cannonball is shot out of a cannon at a 459angle with an approximatecannon from which the ball was fired sits on the edge of a cliff, and its he20 meters. The equations given below represent the cannonball's heighand its horizontal distance (x) from the face of the cliff, (E)seconds afterHow many seconds after the ball was fired does its verticat height abovehorizontal distance from the cliff?
Answers
Let t be the amunt of seconds that have passed when the height of the cannonball above the ground is the same as its horizontal fistance from the cliff.
Since the height of the cannonball above the ground is represented using the variable y and the horizontal distance from the cliff is represented using the variable x, then, the condition that the height equals the horizontal distance can be expressed as:
[tex]y=x[/tex]Replace the expressions for y and x in terms of t into the equation:
[tex]-5t^2+2t+20=2t[/tex]We obtained a quadratic equation on the variable t.
Notice that the term 2t appears in both members of the equation. Then, it can be cancelled out:
[tex]-5t^2+20=0[/tex]Solve for t²:
[tex]\begin{gathered} \Rightarrow-5t^2=-20_{} \\ \Rightarrow t^2=\frac{-20}{-5} \\ \Rightarrow t^2=4 \end{gathered}[/tex]Take the square root to solve for t:
[tex]\begin{gathered} \Rightarrow t=\pm\sqrt[]{4} \\ =\pm2 \end{gathered}[/tex]Since t must be greater or equal to 0, then the negative solution should be discarded.
Therefore, the vertical height of the cannonball equals its horizontal distance from the cliff 2 seconds after the ball is fired.
The correct choice is option B) 2