Answers
Answer:
a) 112 ft.
b) 256 ft. and 3 seconds
c) 7 seconds
Step-by-step explanation:
a) The model rocket is lauched from a platform. To find the height of the platform, we need to find h when t = 0, because the rocket starts from the platform when no time has elapsed:
[tex]h=-16t^2+96t+112[/tex]
[tex]h=-16*0+96+0+112\\\\h=112[/tex]
Therefore, the height of the platform is [tex]\fbox{112}[/tex] ft.
b) If you learned calculus before, we can find the maximum height easily. We take the derivative of h and set it equal to 0. Remember, the derivative of a function is simply the slope of it at an instantaneous point. At the maximum point of a function, it's slope equals to 0.
[tex]h=-16t^2+96t+112\\h'=-32t+96+0\\h'=-32t+96[/tex]
Ok! Let's set the derivative of h to 0!
[tex]0=-32t+96\\-96=-32t\\t=3[/tex]
We now know how long it takes for the rocket to reach maximum point (t represents seconds), but we also need to find the maximum height. We can simply plug our t=3 into the function of h, because t=3 is the point where the rocket reaches maximum height:
[tex]h(3)=-16(3)^2+96*3+112\\h(3)=-144+288+112\\h(3)=256[/tex]
The maximum height of the rocket is [tex]\fbox{256}[/tex] ft and the rocket takes [tex]\fbox{3}[/tex] seconds to reach the height.
c) The rocket reaches the ground when h equals 0. We can set up the equation to solve for it:
[tex]h=-16t^2+96t+112\\0=-16t^2+96t+112\\0=-16(t+1)(t-7)\\0=(t+1)(t-7)\\t=-1, t=7[/tex]
However, time can never be negative.
Therefore, it takes the rocket [tex]\fbox{7}[/tex] seconds to reach the ground.
I hope this helps! Let me know if you have any questions :)
Related Questions
16. Using divisibility tests, check whether the number 240720 is divisible by
2, 3, 4, 5, 6, 8, 9, 10 and 11. (Give reason)
Answers
3: it is, because the sum of the digit, 2+4+7+2=15, is divisible by 3
4. it is, because the last 2 digits, 20, is divisible by 4
5. it is, because last digit is 0
6. it is, because it is divisible by 2 and 3
8. it is, because the last 3 digits, 720, is divisible by 8
9. It is not, because the sum of the digits, which is 15, is not divisible by 9
10. It is, because the last digit is 0
11. It is not, because the difference of alternating digits, which is 2+0+2-4-7-0, is not divisible by 11
There are twelve empty rooms in the office of Acme Softwares, inc. Alif and Laila joins the company. How many ways can they be assigned a room each from these twelve
Answers
Answer:
132.
Step-by-step explanation:
That would be the number of permutations of 2 from 12.
12P2 = 12! / (12-2)!
= 132.
Gỉaỉ pt
2x^2×(2x^2+3)=2-x^2 ai giải giúp vs
Answers
2x²×(2x²+3)=2-x²
[tex]x = \frac{1}{2} , - \frac{1}{2} ,i \sqrt{2} , - i \sqrt{2} [/tex]
The sum of three numbers is fourteen. The first number minus three times the third number is the second number. The second number is six more than the first number. Find the three numbers.
Answers
Answer:
1st number (x) = 5
2nd number (y) = 11
3rd number (z) = -2
Step-by-step explanation:
Let the generic solution for this problem be x + y + z = 14.
The first number minus three times the third number equals the second number, so x - 3z = y. The second number is 6 more than the first number, so y = 6 + x.
x - 3z = y, we know that y = 6 + x, so the equation becomes x - 3z = 6 + x.
After some arithmetic, we find that z = -2.
Plugging our knowns back into the generic solution becomes:
x + x - 3z + z = 14
2x - 3(-2) - 2 = 14
2x + 6 - 2 = 14
2x + 4 = 14
2x = 10
x = 5
So we know that z = -2, and x = 5, it's just simple substitution from there.
5 + y + (-2) = 14
5 + y = 16
y = 11
A trinomial is a perfect square when two terms are
a. Positive
b.negative
c. Neither positve
d. Either negative
Answers
Answer:
a trinomial is a perfect square trinomial if it can be factorized into a binomial multiplies to itself. In a perfect square trinomial, two of your terms will be perfect squares.
1/6 of ______ equals 9
What is the blank?
Answers
Answer:
54
Step-by-step explanation:
1/6 × y = 9
y ÷ 6 = 9
y ÷ 6 × 6 = 9 × 6
y = 54
A muffin recipe calls for 3 times as much flour as sugar.
Use this information for
Write an expression that can be used to
find the amount of flour needed for a given
amount of sugar. Tell what the variable in
your expression represents
use the variable ( s ) to represent the amount of sugar
Answers
f=3s
f = the amount of flour
Hope this helps! :)
Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard from, given that the point-slope form is y+1=2/3(x-8)
____x+____y=____
Answers
Answer: 2/3x-y=19/3
Step-by-step explanation:
Points are useless since we already know the point slope form and we can just simply that
y+1=2/3(x-8)
y+1=2/3x-16/3
y=2/3x-19/3
2/3x-y=19/3
Solve for y.
r/3-2/y=s/5
Answers
Answer:
y = 2 / (r/3 - s/5)
Step-by-step explanation:
r/3 - 2/y = s/5
add 2/y to both sides
r/3 = s/5 + 2/y
Subtract s/5 from both sides
r/3 - s/5 = 2/y
multiply both sides by y
y(r/3 - s/5) = 2
Divide both sides by r/3 - s/5
y = 2 / (r/3 - s/5)
mong moi nguoi giup do
Answers
Answer fast please and thanks!
Answers
Answer:
tan 30 = x / 15
General Formulas and Concepts:
Trigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 30°
Opposite Leg = x
Adjacent Leg = 15
Step 2: Solve for x
Substitute in variables [tangent]: tan 30 = x / 15Answer:
3rd one
Step-by-step explanation:
Recall that
Sin = opposite over hypotenuse
Cos = adjacent over hypotenuse
Tan = opposite over adjacent
For the angle with a measure of 30 degrees we are given it's adjacent side length and need to find it's opposite side length
When dealing with opposite and adjacent we use tangent
If tan = opposite over adjacent
Then tan30 = x / 15 and the correct answer choice is the third one
Simplify the expression
Answers
Answer:
6
Step-by-step explanation:
3 sqrt(20) / sqrt(5)
We know that sqrt(a) /sqrt(b) = sqrt(a/b)
3 sqrt(20/5)
3 sqrt(4)
3 *2
6
using the digits 0-9 at most one time each fill in the boxes so that the fraction equals the decimal
Answers
Step-by-step explanation:
Z 00m
336"083"2553
(wZE2XQ) are
The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.
Atmospheric Pressure (mb) Wind Speed (knots) Atmospheric Pressure (mb) Wind Speed (knots)
993 50 1006 40
995 60 942 120
994 60 1002 40
Required:
a. Find the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
b. Find the slope of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
c. Is it reasonable to interpret the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable? Why or why not?
Answers
Answer:
Step-by-step explanation:
X Y X² Y² XY
993 50 986049 2500 49650
995 60 990025 3600 59700
994 60 988036 3600 59640
1006 40 1012036 1600 40240
942 120 887364 14400 113040
1002 40 1004004 1600 40080
[tex]\sum X: 5932[/tex] [tex]\sum Y : 370[/tex] [tex]\sum X^2 : 5867514[/tex] [tex]\sum Y^2 = 27300[/tex] [tex]\sum XY : 362350[/tex]
To determine the regression:
[tex]Mean \ (X) = \dfrac{\sum X }{n} \\ \\ = \dfrac{5932}{6} \\ \\ = 988.67[/tex]
[tex]Mean \ (Y) = \dfrac{\sum Y}{n} \\ \\ = \dfrac{370}{6} \\ \\ = 61.67[/tex]
Intercept [tex]b_o = \dfrac{\sum YX *\sum X^2 - \sum X \sum Y}{n(\sum X^2) - (\sum X)^2}[/tex]
[tex]=\dfrac{370(5867514) -(5932)(370)}{6(5867514) - (5932)^2}[/tex]
= 131760.9563
Slope [tex]b_1 = \dfrac{n(\sum XY) -(\sum X *\sum Y) }{n(\sum X^2)-(\sum X)^2}[/tex]
[tex]b_1 = \dfrac{6(362350) -(5932*370) }{6(5867514)-(5932)^2}[/tex]
[tex]b_1 = -1.2600[/tex]
The regression line equation [tex]Y = b_o +b_1X[/tex]
[tex]Y = 131760.96 -1.2600 X[/tex]
We then make a comparison of the slope of the equation to y = mx+c
slope of the equation = -1.2600
the y-intercept corresponds to when X = 0, thus:
y-intercept = 131760.9563
Yes, it is reasonable to interpret the y-intercept of the regression line, Using atmospheric pressure as an explanatory variable due to the fact that:
X is the independent variable and Y exists as the dependent variable.
Rewrite the equation by completing the square.
x^2 + 7x + 12 = 0
Answers
Answer:
x^2 + 7x + 12 = 0
x^2 + 7x = -12
(+3)(+4)=0
=−3
=−4
I also love r o blox
Hope This Helps!!!
Answer:
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
Step-by-step explanation:
Given
x² + 7x + 12 = 0
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 7x
x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] + 12 = 0
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] + [tex]\frac{48}{4}[/tex] = 0 , that is
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
Factor completely, then place the factors in the proper location on the grid. 25a2 +9b2 + 30ab
Answers
Answer:
(5a+3b)(5a+3b) or SQ(5a+3b)
Step-by-step explanation:
Now you can plot by referring to the above factors
pls help asap!!
For the following geometric sequence, find the recursive formula.
(-80,20,-5...)
Answers
Answer:
For the geometric sequence, it has two forms of formula
We are interested in the recursive formula now
{-80, 20, -5, ...}
The common ratio is (20/-80)=(-5/20)=-1/4=-0.25
So our recursive formula would bea_n=a_{n-1}*(-0.25)=a_{n-1}*(- \frac{1}{4} )an=an−1∗(−0.25)=an−1∗(−41)
Step-by-step explanation:
For the geometric sequence, it has two forms of formula
{-80, 20, -5, ...}
The common ratio is (20/-80)=(-5/20)=-1/4=-0.25
So our recursive formula would be a n=a {n-1}*(-0.25)=a_{n-1}*(- \frac{1}{4} )an=an−1∗(−0.25)=an−1∗(−41)
The diagram below is divided into equal parts. Which shows the ratio of unshaded section to shaded sections
Answers
Answer:
its D
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
there is 5 unshaded and one shaded
What is a demand schedule?
А.
a chart that shows the demand for a type of product at various prices
B.
a graph that shows the demand for a product at a single price point
C.
a chart that shows the demand for a product at various prices
Answers
Answer:
Answer is C
Step-by-step explanation:
In demand when the price goes up the quantity goes up and when the price goes down the quantity also goes down
In Supply when the price goes up the quantity goes down and when the price goes down the quantity goes up
Demand Schedule is a Chart
Demand Curve is a graph
Supply Schedule is a Chart
Supply Curve is a graph
Hope this helps
Step-by-step explanation:
[tex]hope \: it \: helps[/tex]
Do you guys know this
Answers
Answer:
Kindly check attached picture
Step-by-step explanation:
The expected graph is attached in the picture below :
Since additional fee is charged on only luggage exceeding 50 pound weight :
The inequality is :
Additional fee applied to :
Weight > 50
Hence x our arrows starts from 50 to the right of the number line
Evan wants to make an array of 32 miniature cars What are all the different ways Evan can place the cars?
Answers
Answer:
1 × 32, 2 × 16, 4 × 8, 8 × 4, 16 × 2, 32 × 1
Step-by-step explanation:
There are 6 different ways for Evan to create a array of 32 miniature cars.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
An array would constitute the shape of a parallelogram, in which you are essentially solving for s₁ and s₂.
Since there are 32 miniature cars in all, in which both sides, when multiplied, must result in said number:
32 x 1 = 32
2 x 16 = 32
4 x 8 = 32
8 x 4 = 32
16 x 2 = 32
1 x 32 = 32
Hence, There are 6 different ways for Evan to create a array of 32 miniature cars.
Learn more about multiplications;
https://brainly.com/question/14059007
#SPJ2
The sides of a square field are 24 meters. A sprinkler in the center of the field sprays a circular area with a diameter that corresponds to a side of the field. How much of the field is not reached by the sprinkler? Round your answer to the nearest hundredth. Use 3.14 for π.
Answers
Answer:
A
Step-by-step explanation:
i took the test
A right rectangular container is 10 cm wide and 24 cm long and contains water to a depth of 7cm. A stone is placed in the water and the water rises 2.7 cm. Find the volume of the stone.
Answers
Answer:
The volume of the rock is 648 cm^3
Step-by-step explanation:
Likely the only dimension that is free to move is the depth of 7 cm.
Volume of the Rock = L * W * h1
L = 24
W = 10
h1 = 2.7
V = 24 * 10 * 2.7
V = 648 cm^3
emma can read 4 pages of a book in 8 minutes how many pages can she read per minute if she still had it 24 pages how many pages are there in the book
Answers
Answer:
Emma can read 30 pages per minute
Number of book pages 28
Step-by-step explanation:
The student council has 30 male members and 25 female members. What is the ratio of male student council members to female?
Answers
divide each to 5 and that’s 6 : 5
Write the word sentence as an equation.
The quotient of a number n and 5 is 18.
Answers
Answer:
n/5 = 18
Step-by-step explanation:
Quotient means division.
n/5 = 18
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3
C:3
D:8
are the possible answers
Answers
Answer:
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3( true
C:3
D:8
are the possible answers
4. Steven drove from place A to place B at an average speed of 50 km/h. At the same
time, Joseph drove from place B to place A at an average speed of 60 km/h using
the same route. If the distance between A and B were 300 km, what is the distance
between Steven and Joseph after one and one half hours?
5.An owner jeep traveling at an average speed of 70 km/h left the town at 2:00 pm
If it arrived in another town at 6:00 p.m., how far are the two towns?
Answers
Answer:
1. 10 km
2.280 km
please mark my answer as brainliest answer.
the answer is surely correct
5. Two towns are 280km away
At the beginning of a population study, a city had 320,000 people. Each year since, the population has grown by 2.1%. Lett be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t.
Answers
Answer:
y = 320,000(2.1)^t
Step-by-step explanation:
uhm, im not very good at explaining, but everytime the year increases, the population will exponentially increase, that's why 't' is an exponent
Answer:
[tex]y=320000(1.021)^t[/tex]
Step-by-step explanation:
To increase something by x% mulitply it by (1+x)
in other words, to increase sometihng by 2.1% mulitply it by
(1+.021) or 1.021
because we are mulitplying 320000 by 1.021 each year we can write the equation as
y=320000(1.021)^t
If f(x)=2x²-x find f(-3)
Answers
Answer:
21
Step-by-step explanation:
f(x) = 2x^2 - x
f(-3) = 2*(-3)^2 - (-3)
=2*9 +3
=18 +3
=21
Answer: 21
Step-by-step explanation: To find f(-3) or the value of the function when x = -3, we plug in a -3 for the x in our function and we have 2(-3)² - (-3).
Start by simplifying the exponent to get 9.
So we have 2(9) - (-3) or 18 + 3 which is 21.
