The inital height of the rocket is -3 ft (since the mortar is 3 ft below ground)
To determine the maximum height of the rocket we have to remember the equation
[tex]v^2_f-v^2_0=2a(s-s_0_{})[/tex]where vf is the final velocity, v0 is the initial velocity, a is the acceleration (in this case the gravity), s is the final position and s0 is the initial position.
Since the maximum height is reach when vf=0, then we have
[tex]0^2-(150)^2=2(-32.2)(y-(-3))[/tex]Solving for y we have
[tex]\begin{gathered} -\frac{(150)^2}{2(-32)}=y+3 \\ y=-\frac{(150)^2}{2(-32)}-3 \\ y=348.56 \end{gathered}[/tex]So the maximum height is 348.56 ft.
To determine the time it takes the rocket to reach the maximum height we have to remember the formula
[tex]s=s_0+v_0t+\frac{1}{2}at^2_{}[/tex]plugging the values we have:
[tex]348.56=-3+(150)t+\frac{1}{2}(-32)t^2[/tex]Solving the equation for t, we have
[tex]\begin{gathered} 348.56+3=150t-16t^2 \\ 16t^2-150t+351.56=0 \\ \text{applying the general formula for quadratic equations we have } \\ t=\frac{-(-150)\pm\sqrt[]{(-150)^2-4(16)(351.56)}}{2(16)} \\ =\frac{150\pm\sqrt[]{22500-22500}}{32} \\ =\frac{150\pm\sqrt[]{0}}{32} \\ =\frac{150\pm0}{32} \\ \text{then} \\ t=4.6875 \end{gathered}[/tex]therefore the time to reach the maximum height is 4.6875 s.
To find out how much time does the rocket take to hit the ground we have to use the same formula as before, only in this case s=0. Then
[tex]\begin{gathered} 0=-3+150t-16t^2 \\ \text{solving for t we have} \\ t=\frac{-150\pm\sqrt[]{(150)^2-4(-16)(-3)}}{2(-16)} \\ =\frac{-150\pm\sqrt[]{22308}}{-32} \\ =\frac{-150\pm149.3586}{-32} \\ \text{then} \\ t_1=9.3549 \\ t_2=0.02 \end{gathered}[/tex]therefore the time to reach the ground is 9.3549 s.
A parachutist's speed during a free fall reaches 65 meters per second. What is this speed in feet per second? At this speed, how many feetwill the parachutist fall during 20 seconds of free fall? In your computations, assume that I meter is equal to 3.3 feet. Do not round youranswers.
The speed of a parachutitst in free fall is 65m/s. In order to find this velocity in feet per second you use the following identities:
1 m = 100 cm
2.54 cm = 1 in
12 in = 1 ft
Each of the previous identity is used as a convertion factor. You proceed as follow:
[tex]65\frac{m}{s}\cdot\frac{100\operatorname{cm}}{1m}\cdot\frac{1in}{2.54\operatorname{cm}}\cdot\frac{1ft}{12in}=213.2\frac{ft}{s}[/tex]where you put as the denominator the quantity with the unit that it is necessay to cancel out. For instance, in the first factor (65m/s) you have meters in the numerator, in order to cancel meter, the next factor (100cm/1m) has to have a denominator with units in meter. Then you have a numerator with centimeters, and you use a factor that allows you to cancel centimeter, as the factor 1in/2.54cm makes.
To calculate the height traveled by the parachutist you use the following formula:
[tex]h=vt+\frac{1}{2}gt^2[/tex]v: speed of the parachutist = 213.2 ft/s
t: time = 20 s
g: gravitational acceleration = 32ft/s²
You replace the previous values into the formula for h, the height traveled:
[tex]\begin{gathered} h=(213.2\frac{ft}{s})(20s)+\frac{1}{2}(32\frac{ft}{s^2})(20)^2 \\ h=10664ft \end{gathered}[/tex]Hence, the parachutist falls 10664 ft
Choose the equation of the horizontal line that passes through the point (-5,9)
We are asked to find the equation of the horizontal line that passes through the point (-5, 9)
Recall that point-slope is given by
[tex]y-y_1=m(x_{}-x_1)[/tex]Where m is the slope of the line and x1 and y1 are the coordinates of the given point.
We know that the slope of a horizontal line is 0.
So let us substitute m = 0 and the given point into the above formula
[tex]\begin{gathered} y-9_{}=0\cdot(x_{}-(-5)_{}) \\ y-9=0 \\ y=9 \end{gathered}[/tex]Therefore, the equation of the line is y = 9
what are the ordered pairs of the solutions for this system of equations?f (x)=x^2-2x+3;f (x)=-5x+1
we get:
[tex]\begin{gathered} x^2-2x+3=-5x+1\rightarrow \\ x^2+3x-2=0\rightarrow x=\frac{-3+\sqrt[]{17}}{2},x=\frac{-3-\sqrt[]{17}}{2} \end{gathered}[/tex]so the pairs are,
[tex](\frac{-3+\sqrt[]{17}}{2},\frac{15-5\sqrt[]{17}}{2}+1),(\frac{-3-\sqrt[]{17}}{2},\frac{15+5\sqrt[]{17}}{2}+1)[/tex]Question 134 of 190FINAL- MathematicsIf it takes 4.5 gallons of paint to paint 3 rooms, how many whole gallons of paint will you have to buy to paint 7 rooms?DO NOT
ANSWER:
11 gallons
STEP-BY-STEP EXPLANATION:
We can calculate the amount of gallons to be able to whistle 7 rooms by means of the following proportion:
[tex]\frac{4.5}{3}=\frac{x}{7}[/tex]Let x be the number of gallons needed, we solve for x:
[tex]\begin{gathered} x=\frac{4.5}{3}\cdot7 \\ \\ x=10.5\approx11\text{ gallons} \end{gathered}[/tex]Since they must be whole gallons, it takes 11 gallons to paint 7 rooms.
Evaluate the expression when X = 2X to the second power -8x -3
Evaluate for x = 2:
[tex](2)^2-8(2)-3=4-16-3=4-19=-15[/tex]For the given equation, enter the value of B when x= - 1/5B/x =20
Answer:
[tex]B=4[/tex]Step-by-step explanation:
To solve the following equation.
[tex]\begin{gathered} \frac{B}{x}=20 \\ \end{gathered}[/tex]Substitute x=-1/5, and use inverse operations to solve equations.
*Addition and subtraction are inverse operations, multiplication, and division too.
[tex]\begin{gathered} \frac{B}{\frac{1}{5}}=20 \\ 5B=20 \\ B=\frac{20}{5} \\ B=4 \end{gathered}[/tex]Which of the following graphs shows the solution for the inequality y+3<2/3(x-9)?
Explanation
We are to select the best option that represents the graph of the inequality
[tex]y+3\leq-\frac{2}{3}(x-9)[/tex]From the above, we have the slope as -2/3
Also, we have the x-intercept as 9/2 or 4.5
Then we have the y-intercept as 3
Thus
the graph is
standing 200ft from the base of an antenna, Maria measures the angle of elevation to the top of the antenna to be 38 degrees. If her eye level is 5ft above the ground, what is the height of the antenna to the nearest foot?
Given: The bearing and distance of Maria and an antenna
To Determine: The height of the antenna from the given information
Solution
From the given information, the diagram below can be deduced
From the diagram above, the height of the antenna is TB
Using SOH CAH TOA
[tex]\begin{gathered} tan38^0=\frac{TC}{EC} \\ EC=BG=200ft \\ SO, \\ tan38^0=\frac{TC}{200} \\ TC=200\times tan38^0 \end{gathered}[/tex][tex]\begin{gathered} TC=156.257ft \\ TB=TC+CB \\ EG=CB=5ft \\ TB=156.257+5 \\ TB=161.257ft \\ TB\approx161ft \end{gathered}[/tex]Hence, the height of the antenna is 161ft
Find y given that x = -6: y = -6x - 3Select one:O a. 39O b. -9O c. 33Od. -3
Answer:
c. 33
Explanation:
Given the equation:
[tex]y=-6x-3[/tex]When x=-6:
[tex]\begin{gathered} y=-6(-6)-3 \\ =36-3 \\ =33 \end{gathered}[/tex]The value of y when x=-6 is 33.
Option C is correct.
f(x)=4x^2+7x-18 find f(-9)
To find f(-9) you have to replace x = -9 into f(x) as follows:
f(x)=4x²+7x-18
f(-9) = 4(-9)² + 7(-9) - 18
f(-9) = 4(81) - 63 - 18
f(-9) = 324 - 63 - 18
f(-9) = 243
how do I construct the correct equation needed to solve for x with the options below
The equation therefore can be represented as follows
16x + 4 = 110 + 3x + 11
Given f(x) = Vx+1, which graphs represents | 1(2)?yA.B.cC.D.Select one:O a. AObBОс. СO d. D.
Given:-
[tex]\sqrt[3]{x+1}[/tex]To find:-
The graph of,
[tex]f^{-1}(x)[/tex]To find the required value, first we convert it.
[tex]y=\sqrt[3]{x+1}[/tex]By solving the above equation. we get,
[tex]x=y^3-1[/tex]Now we sketch the graph of,
[tex]x=y^3-1[/tex]By sketching. we get,
So this is the required graph.
So the correct option is A.
Ben and Jerry’s sells 3 times more ice cream cones ($2) than shakes ($9). If last month’s sales totaled $9,600, how many of each were sold?
It is given that the sales of ice cream is three times as shakes.
Let x be the number of ice creams and y be the number of shakes,
So x=3y.
Also the total sales if ice cream is $2 and shake is $9 is $9600 so it follows:
[tex]\begin{gathered} 2x+9y=9600 \\ 2\times3y+9y=9600 \\ 15y=9600 \\ y=640 \end{gathered}[/tex]Since x=3y so it follows that x=1920.
So Number of shakes sold is 640 and number of ice cream cones sold is 1920.
What is the remainder when x^2 + 5x - 24 is divided by x - 6?
Given:
The dividend is,
[tex]x^2+5x-24[/tex]The divisor is,
[tex]x-6[/tex]To find: The remainder
Explanation:
Let us take,
[tex]p(x)=x^2+5x-24[/tex]Using the remainder theorem,
Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number.
If p(x) is divided by the linear polynomial x - a, then the remainder is p(a).
Here,
[tex]a=6[/tex]Substitute the value of a in the above polynomial.
[tex]\begin{gathered} p(6)=6^2+5(6)-24_{} \\ =36+30-24 \\ =42 \end{gathered}[/tex]Hence, the remainder is 42.
Final answer: The remainder is 42.
find the exact length of a circular Arc if the radius is 2 ft, with a angle of π/2 radian.
We get that
[tex]S=r\cdot\theta=2\cdot\frac{\pi}{2}=\pi[/tex]What is the domain and range of the function? 15c
The first thing we have to know is that the Domain are all the values that x can take in the function and that the Range are all the values that the function takes in y
Taking this into account, the best way to see the domain and range is by graphing the function
[tex]\begin{gathered} f^{-1}(x)=3+\log _4(\frac{1-x}{3}) \\ f^{-1}(x)=3+\log _4(1-x)-\log _4(3) \end{gathered}[/tex]If you want to find the Domain we have to guarantee that what is inside the logarithm and have a x is greater than zero:
[tex]\begin{gathered} 1-x>0 \\ 1>x \end{gathered}[/tex]This means that the domain will only be those values less than 1
Find the intervals where the following function is increasing decreasing or constant express your answer in intervalentation
Explanation
The given function represents a constant function defined by
[tex]f(x)=2[/tex]The intervals where the function is constant is
[tex](-\infty,\infty)[/tex]How do I do this math problem I’m kinda lazy
X - y = 0X + y = - 4
We are given the following system of equations:
[tex]\begin{gathered} x-y=0,(1) \\ x+y=-4,(2) \end{gathered}[/tex]We are asked to determine the solution by graphing the system.
To do that we will graph each of the equations. We will solve for "y" in equation (1), to do that we will add "y" to both sides:
[tex]\begin{gathered} x-y+y=y \\ x=y \end{gathered}[/tex]Switching the direction of the equation we get:
[tex]y=x[/tex]Now, we graph the equation. We notice that this is the equation of a line since it has the form:
[tex]y=mx+b[/tex]In this case, m = 1 and b = 0.
To graph a line we need to know two points in the line. We will determine those points by giving values to "x". We will substitute the value x = 0, we get:
[tex]y=0[/tex]Substituting "x = 1" we get:
[tex]y=1[/tex]Therefore, the two points are:
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,1) \end{gathered}[/tex]Now we plot both points and join them with a line. The graph is the following:
Now we solve for "y" in equation (2). To do that we will subtract "x" from both sides:
[tex]y=4-x[/tex]Now, we graph using the same procedure as before. We will graph both lines in the same coordinate system and we will determine their interception point, like this:
The interception point is the solution of the system. Therefore, the solution is:
[tex](x,y)=(-2,-2)[/tex]Serial numbers for a product are to be made using 3 letters followed by 3 digits. The letters are to be taken from the first 8 letters of the alphabet, with norepeats. The digits are taken from the 10 digits (0, 1, 2, ..., 9), with no repeats. How many serial numbers can be generated?
The serial number of the product would look like XXX-### where XXX represents the letters and ### represents the number. The letter part of the serial number will be taken from the first 8 letters of the alphabet. To know how many different arrangements of letters can be done, we will be using permutation. The permutation equation is described as
[tex]P(n,r)=\frac{n!}{(n-r)!_{}}_{}[/tex]For the permutation of 3 letters, r = 3, for n = 8, the number of possible arrangements is
[tex]P=\frac{8!}{(8-3)!}=336[/tex]In a similar manner, we can pick 3 digits out of the 10 digits and arrange them in several manners using the permutation equation. For the digit part, we have r = 3 and n = 10. Computing for the number of possible arrangements for the digit part of the serial number, we have
[tex]P=\frac{10!}{(10-3)!}=720[/tex]Finally, to get the overall number of serial numbers that can be generated, let's just multiply the permutation for both letters and digits. We get
[tex]336\times720=241920[/tex]Therefore, there are 241920 serial numbers that can be generated.
To avoid calculating difficult probabilities by hand, use aA. stimulationOB. simulcastOC. simulationD. stimulusReset SelectionNextto estimate the probability.
When probabilities are tedious, the method of of using hand is likely to produce errors. We can use simulation in this case. Thus, the correct option is
Which is more, 10 tons or 20,004 pounds?
A ton is equivalent to 2000 pounds. Then, 10 tons are 20,000 pounds.
Therefore, 20,004 pounds is more.
2. Rewrite by factoring the GCF from each expression.a) 8r + 12O 8 (r + 3)O 4 (2r + 3)O 4 (2r + 12)O 8 (r + 12)
We are asked to rewrite the given expression by factoring the GCF from the expression.
[tex]8r+12[/tex]GCF is the greatest common factor.
Factors of 8 = 1, 2, 4, 8
Factors of 12 = 1, 2, 3, 4, 6, 12
Notice that the greatest common factor is 4
So, take out 4 from the expression
[tex]8r+12=4(2r+3)[/tex]Therefore, the correct answer is
[tex]4(2r+3)_{}[/tex]can you do the check part too? so i can understand. thank you!
12 is dividing on the left, then it will multiply on the right.
[tex]\begin{gathered} 9+t=(-3)\cdot12 \\ 9+t=-36 \end{gathered}[/tex]9 is adding on the left, then it will subtract on the right
t = -36 - 9
t = -45
To check the answer, replace the value found into the original equation, as follows:
[tex]\frac{9-45}{12}=\frac{-36}{12}=-3[/tex]For each system of linearesuations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, choose thebest description of its solution. If the system has exactly one solution, give its solution.System ASystem BSystem C
A system of equations is independent when it has exactly 1 solution.
A system of consistent equations is independent when it has an infinte number of solutionshen it has an i
Looking at system A, the lines of the two equations are parallel. This means that they will never intersect and this implies that there is no solution. They are inconsistent
Looking at system B, the lines of the two equations are coincide. This means that they are the same lines. Since there is no point of intersection, there is an infinite number of solutions hence, they are dependent. on. They e inconsis and dependent
Looking at system C, the lines of the two equations are coincide. This means that there is only one solution and it's at the point of intersection solution. They are consistent and independent. Looking at the point of intersection, the solution would be the x and y coordinates of this point. Hence, solution = (1, 2)
Tis implies that there is no solution
In Livingston, the use of landlines has been declining at a rate of 20% every year. of there are 23,000 landlines this year, many will there be in 6 years?? if necessary, round your answer to the nearest whole number
In 6 years there are
Apply N1= 230000
N = N1 - N1•20/100 - N1• (20/100)^2 - N1•(20/100/^3 - N1•(20/100)^4 - N1(20/100)^5 - N1•(20/100) ^6
Then replace 20/100= 1/5
N= 23000 - 23000 • ( 1/5 + 1/25 + 1/125/ + 1/625 + 1/3125 + 1/15625 )
N= 23000 - 5750 = 17250
Then answer is
In 6 years there will be 17250 landlines
Does the graph show an increasing or decreasing linear function?A) IncreasingB) Decreasing
The values of the y-variable decrease as the values of the x-variable increase, then the graph shows a decreasing liner function
so I have to make a table for the following equations and then graph them y= 2x+7
we have
y= 2x+7
this is the equation of the line
Make the table
For different values of x, calculate the values of y
so
For x=-1
y=2*(-1)+7
y=5
For x=0
y=2*(0)+7
y=7
For x=1
y=2*(1)+7
y=9
For x=2
y=2*(2)+7
y=11
therefore
we have the points
(-1,5) (0,7) (1,9) (2,11)
Plot the points and join them to graph the line
using a graphing tool
see the attached figure
please wait a minute
Solve for x. Show steps.x + 4 = 2x - 510x + 12 = 8x + 4-6 - 29 = 5x - 7
Part A
Given the equation
[tex]x+4=2x-5[/tex]To solve for x, we first collect like terms
[tex]\begin{gathered} x-2x=-5-4 \\ -x=-9 \\ \text{Divide both sides by -1} \\ x=9 \end{gathered}[/tex]Part B
Given the equation:
[tex]\begin{gathered} 10x+12=8x+4 \\ \end{gathered}[/tex]First, we bring all terms containing x to the left-hand side and the constants to the right-hand side.
[tex]\begin{gathered} 10x-8x=4-12 \\ 2x=-8 \\ \text{Divide both sides by 2} \\ x=-4 \end{gathered}[/tex]Part C
Given the equation:
[tex]-6-29=5x-7[/tex]Collect like terms to obtain:
[tex]\begin{gathered} 5x=-6-29+7 \\ 5x=-28 \end{gathered}[/tex]Divide both sides by 5
[tex]x=-5\frac{3}{5}[/tex]Find the values of each variable using sin, cos or sine
To obtain the value of x, substitute the values of the following.
[tex]\begin{gathered} \theta=70\degree \\ \text{opposite side}=x \\ \text{hypothenuse}=30 \end{gathered}[/tex]Thus, we obtain the following
[tex]\begin{gathered} \sin \theta=\frac{opposite\text{ side}}{hypothenuse} \\ \sin 70\degree=\frac{x}{30} \end{gathered}[/tex]Multiply both sides of the equation by 30 and then simplify.
[tex]\begin{gathered} 30\sin 70\degree=x \\ x\approx28.19 \\ x\approx28 \end{gathered}[/tex]Since the two sides are equal, the base angles must be equal. Thus, we obtain the following.
[tex]\begin{gathered} \theta=70\degree \\ \text{adjacent side}=y \\ \text{hypothenuse}=30 \end{gathered}[/tex]Substitute the values using the following equation.
[tex]\begin{gathered} \cos \theta=\frac{adjacent\text{ side}}{hypothenuse} \\ \cos 70\degree=\frac{y}{30} \end{gathered}[/tex]Multiply both sides of the equation by 30 and then simplify.
[tex]\begin{gathered} 30\cos 70\degree=y \\ y\approx10.26 \\ y\approx10 \end{gathered}[/tex]Therefore, the value of x is approximately 28.19 and the value of y is approximately 10.26.