Answers
Answer:
s(8) = 1162
Step-by-step explanation:
We are told that the acceleration is;
a(t) = 18t + 16
Now, acceleration is the first derivative of velocity. Thus, we will integrate the acceleration function to get the velocity function.
v(t) = ∫a(t) = ∫(18t + 16)
v(t) = 9t² + 16t + c
We are told that at t = 0, v(0) = 16
Thus;
9(0)² + 16(0) + c = 16
c = 16
Thus;
v(t) = 9t² + 16t + 16
Also, the velocity is the first derivative of distance. Thus;
S = ∫v(t) = ∫9t² + 16t + 16
S = 3t³ + 8t² + 16t + c
At t = 0, s(t) = 10. Thus;
10 = 3(0³) + 8(0²) + 16(0) + c
c = 10
Thus;
s(t) = 3t³ + 8t² + 16t + 10
At t = 8;
s(8) = 3(8³) + 8(8²) + 16(8) + 10
s(8) = 1162
Related Questions
What are the roots of the quadratic equation below?
2x2 + 8x + 7 = 0
ANSWER ASAP!
Answers
Answer:
x = 2 ± [tex]\frac{\sqrt{2} }{2}[/tex]
Step-by-step explanation:
what is the highest common multiple of 120 and 150
Answers
Answer:
30 I suppose
Step-by-step explanation:
Study the work shown to find the exact solutions of
this trigonometric equation.
Select all that are solutions of the equation over
the specified domain.
Answers
Answer:
first and fourth options
x = pi/6
x= 11pi/6
Step-by-step explanation:
cos(30 degrees) = sqrt(3)/2
as pi stands for a half circle of 180 degrees
30 degrees = pi/6
cos(30) = cos(-30) = cos (330) =
cos(pi/6) = cos(-pi/6) = cos(11×pi/6)
Answer:
A and d
Step-by-step explanation:
Edge:)
I have to pack 296 apples into 8 boxes. How many apples will there be in a box if each box contains the same number of apples
Answers
Answer:
37
Step-by-step explanation:
296÷8=37
Hope this helps! :)
Answer:
37 apples will be in 9 boxes
Step-by-step explanation:
296 ÷ 8 = 37
What's 90cm as a fraction of 2.4m in its simplest form
Answers
Answer:
3/8
Step-by-step explanation:
Both measurements should be in same measure.So convert m to cm
2.4m = 2.4 * 100 = 240.0 = 240 cm
[tex]\frac{90}{240}=\frac{9}{24}=\frac{3}{8}[/tex]
A and B are independent events. P(A) = 0.80 and P(B) = 0.10.
What is P(A and B)?
Answers
Answer:
C 0.90
Step-by-step explanation:
Add 0.10 and 0.80=0.90
Answer:
D
Step-by-step explanation:
P(A and B)=P(A)×P(B)=0.80×0.10=0.08
7. Find the length of X (in the picture) plssss I need help. (GIVING PPINTS AND BRAINLY)
Answers
Answer:
[tex] \frac{8}{5} = \frac{4}{x} \\ 8x = 20 \\ x = 2.5[/tex]
Answer:
here the resize factor is 5/8
so we need to calculate
x = 4 *5/8
= 20/8
= 2.5
I assume you get the basic idea from the other question you posted.
What is the probability of rolling a number less than or equal to 8 with the
sum of two dice, given that at least one of the dice must show a 6?
Answers
Answer:
I hope this helps
the outcomes are the compulsory 6, and 1 or 2
Step-by-step explanation:
[tex] \frac{3}{6} \\ \frac{1}{2} or \: 0.5[/tex]
Consider the following data representing the price of plasma televisions (in dollars).
1325, 1266, 1123, 1233, 1387, 1249, 1120, 1140, 1347, 1337, 1402, 1259, 1421, 1351, 1452, 1277, 1309, 1232, 1112, 1243, 1429
Copy Data Price of Plasma Televisions (in Dollars) Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency
1067–1126 1127–1186 1187–1246 1247–1306 1307–1366 1367–1426
Determine the class width of the classes listed in the frequency table.
Answers
Answer:
[tex]Width = 59[/tex]
Step-by-step explanation:
Given
The above data
Required
The class width
To do this, we simply calculate the difference between the class limits of any one of the classes.
Taking 1187–1246 as a point of reference, the class width is:
[tex]Width = 1246 - 1187[/tex]
[tex]Width = 59[/tex]
How is the graph of y= square root x+3 translated from the graph of y = √x
Answers
9514 1404 393
Answer:
3 units left
Step-by-step explanation:
Replacing x in a function with (x-h) translates the graph to the right by h units. Here, you have h = -3, so the graph is translated left 3 units.
Please help me understand
Answers
Answer:
A is is correct since the interquatile or a is 15 since 15 plus 15 equals 30 and 20 plus 20 equals 40
B is incorrect since the interquare are not both 30
C is incorrect since both interquatiles are wrong
D is incorrect since the standrard devations are off
Help please!!! Will mark brainliest!!
A student was asked to solve for √x = -1. Is the student correct?
√x = -1
(√x)² = (-1)²
x = 1
(a) Yes, because x = 1 is the only real solution.
(b) Yes, because x has infinitely many solutions.
(c) No, because x is a complex number.
(d) No, because there is no solution for x.
Write a conclusion based on your answer.
Answers
Answer:
D
Step-by-step explanation:
the end result of a radical can never be negative unless the negative sign shows outside of the radical
Please help I don't understand
Answers
Answer:
Angle a is not the same as angle y
Step-by-step explanation:
I think
Based on a regression analysis, a researcher concluded that 45% of the variance in minutes of activity per day can be explained by age, hours of sleep, and minutes spent on social media. What does the value 45% represent
Answers
Answer:
Coefficient of determination, R²
Step-by-step explanation:
The proportion of variation of the dependent variable that can be explained by the regression line is defined by the coefficient of determination, R².
In the scenario described above, the proportion of variation in the number of minutes of activity per day(dependent variable) that can be explained by age, hours of sleep and minutes spent on social media (independent variables) which forms the regression line is 0.45 (45%) is the coefficient of determination while (1 - 0.45) = 0.55 is due to other factors.
please help me steps by steps
Answers
Answer:
question 19 = no solution because not enough information
question 20 = 18 for volume
Step-by-step explanation:
question 19:
cylinder formula
surface A =2πrh+2πr2
2π times 9 times 7 + 2π times 9 times 2
SA = 508.938009882
volume equals 395.840674352
question 20:
biggest one,
4h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4
V=18 IS the volume
Answer:
The last formulas are called
square based pyramid formula
cone formula
sphere formula
Can help with the first two as im short of time
Hope this helps.
Always remember to check the units^3
Step-by-step explanation:
19) V = π r 2 h = 1781.28303 ft3 = 1781.3ft^3
20) V = 1/2 b h l = 180m^3
A drapery store manager was interested in determining whether a new employee can install vertical blinds faster than an employee who has been with the company for two years. The manager takes independent samples of 10 records of installations times of vertical blinds of each of the two employees and computes the following information. Test whether the new employee installs vertical blinds faster, on the average, than the veteran employee, at the level of significance 0.05.
New Employee Veteran Employee
Sample Size 10 10
Sample Mean 22.2 min 24.8 min
Standard Deviation 0.90 min 0.75 min
Required:
What is the appropriate conclusion for this test?
Answers
Answer:
we arrive at the conclusion that the new employee installs the vertical blinds faster on average.
Step-by-step explanation:
null hypothesis; m₁-m₂ =0
alternative hypothesis; m₁-m₂<0
Given the information in this question, we first have to solve for the t statistic
[tex]t=\frac{22-24.8}{\sqrt{\frac{0.90^{2} }{10}+\frac{0.75^{2} }{10} } }[/tex]
[tex]t=\frac{-2.6}{\sqrt{o.081+0.05625} }[/tex]
[tex]t=\frac{-2.6}{0.37047}[/tex]
t = -7.018
the degree of freedom = n₁+n₂-2
= 10+10-2
= 18
Alpha α = 0.05
from these results the t critical value = -1.734
because the test statistic -7.018 < -1.734,
at 0.05 level of testing, we arrive at the conclusion that the new employee installs the vertical blinds faster on average than the veteran.
GIVING OUT BRAINLIEST PLUS 10 PTS
Answers
Answer:
Letter B
Step-by-step explanation:
I used a graphing calculator,
Hope this helps
Given m||n, find the value of x and y
Answers
Hope this might help you (•.•) :)
Chase thought only 23 people would come to banquet but 48 showed up. What is percent error?
Answers
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
(b) Use Formula 9 to find the curvature.
r(1) = (t , 1/2t2, t2)
Answers
Answer:
a. i. (i + tj + 2tk)/√(1 + 5t²)
ii. (-5ti + j + 2k)/√[25t² + 5]
b. √5/[√(1 + 5t²)]³
Step-by-step explanation:
a. The unit tangent
The unit tangent T(t) = r'(t)/|r'(t)| where |r'(t)| = magnitude of r'(t)
r(t) = (t, t²/2, t²)
r'(t) = dr(t)/dt = d(t, t²/2, t²)/dt = (1, t, 2t)
|r'(t)| = √[1² + t² + (2t)²] = √[1² + t² + 4t²] = √(1 + 5t²)
So, T(t) = r'(t)/|r'(t)| = (1, t, 2t)/√(1 + 5t²) = (i + tj + 2tk)/√(1 + 5t²)
ii. The unit normal
The unit normal N(t) = T'(t)/|T'(t)|
T'(t) = dT(t)/dt = d[ (i + tj + 2tk)/√(1 + 5t²)]/dt
= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + [-10tk/√(1 + 5t²)⁻³]
= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + j/√(1 + 5t²)+ [-10t²k/√(1 + 5t²)⁻³] + 2k/√(1 + 5t²)
= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) - 10t²k/[√(1 + 5t²)]⁻³ + 2k/√(1 + 5t²)
= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ - 10t²k/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) + 2k/√(1 + 5t²)
= -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + (j + 2k)/√(1 + 5t²)
We multiply by the L.C.M [√(1 + 5t²)]³ to simplify it further
= [√(1 + 5t²)]³ × -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + [√(1 + 5t²)]³ × (j + 2k)/√(1 + 5t²)
= -(i + tj + 2tk)5t + (j + 2k)(1 + 5t²)
= -5ti - 5²tj - 10t²k + j + 5t²j + 2k + 10t²k
= -5ti + j + 2k
So, the magnitude of T'(t) = |T'(t)| = √[(-5t)² + 1² + 2²] = √[25t² + 1 + 4] = √[25t² + 5]
So, the normal vector N(t) = T'(t)/|T'(t)| = (-5ti + j + 2k)/√[25t² + 5]
(b) Use Formula 9 to find the curvature.
The curvature κ = |r'(t) × r"(t)|/|r'(t)|³
since r'(t) = (1, t, 2t), r"(t) = dr'/dt = d(1, t, 2t)/dt = (0, 1, 2)
r'(t) = i + tj + 2tk and r"(t) = j + 2k
r'(t) × r"(t) = (i + tj + 2tk) × (j + 2k)
= i × j + i × 2k + tj × j + tj × 2k + 2tk × j + 2tk × k
= k - 2j + 0 + 2ti - 2ti + 0
= -2j + k
So magnitude r'(t) × r"(t) = |r'(t) × r"(t)| = √[(-2)² + 1²] = √(4 + 1) = √5
magnitude of r'(t) = |r'(t)| = √(1 + 5t²)
|r'(t)|³ = [√(1 + 5t²)]³
κ = |r'(t) × r"(t)|/|r'(t)|³ = √5/[√(1 + 5t²)]³
Use a calculator to find the mean of the data. {217, 253, 214, 247, 217, 253, 232, 246, 223, 227, 229, 247, 206, 241, 239, 223, 222, 216, 252, 209, 236, 256}
Answers
Answer:
[tex]\frac{5105}{22}[/tex]
Step-by-step explanation:
Used Python function to get all the numbers and add them, then I divided it by 22, which is the number of numbers in the array.
The mean of the data is 232.045.
To find the mean of the data.
What is mean?Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Mean = (Sum of all the observations/Total number of observations). Mean is the most commonly used measure of central tendency. There are different types of mean, viz. arithmetic mean, weighted mean, geometric mean (GM) and harmonic mean (HM).
Given that:
The data are:
217 + 253 + 214 + 247 + 217 + 253 + 232 + 246 + 223 + 227 + 229 + 247 + 206 + 241 + 239 + 223 + 222 + 216 + 252 + 209 + 236 + 256 = 5105
=5105 / 22 = 232.045
So, the mean of the data is 232.045.
Learn more about mean here:
https://brainly.com/question/24072290
#SPJ2
The option is missing:
A. 230.811
B. 231.045
C. 232.045
D. 232.811
Evaluate: 11c+5a-8 for a=4 and c=-6
Answers
Answer:
- 54
Step-by-step explanation:
11 c + 5 a - 8
11 × -6 + 5 × 4 - 8 (given :- a = 4 and b = -6)
- 66 + 20 - 8
- 54
Which list of numbers is in order from least to greatest?
A: −6, |4|, 2, |−3|
B: 2, |−3|, |4|, −6
C: −6, |−3|, 2, |4|
D −6, 2, |−3|, |4|
Answers
If using the method of completing the square to solve the quadratic equation x^2+15x+21=0, which number would have to be added to "complete the square"?
Answers
Step-by-step explanation:
the answer is in the above image
Answer:
my answer is 225/5 sorry comments for wrong
In this figure below, lines m and n are parallel: image above ^
HELPP PLS ASAP
Answers
Answer:
83 or a
Step-by-step explanation:
if angle 6 is 97 then the total would be 180 meaning that 83 would be the answer to 5s angle
"83 degrees" is correct.
On a line, it can be assumed that all the angles must add up to 180 degrees. If you have two angle on a line and don't know the value of one of them, you can subtract that angle from 180 to find the missing angle. Considering this, 180 - 97 = 83.
What number is 18% more than 1257 Round your answer to two decimal places needed,
Answers
What is the area of each semicircle of the following composite figure?
12 ft x 4 ft rectangle and a 4 ft circle
12.56 ft 2
6.28 ft 2
50.24 ft 2
25.12 ft 2
Answers
Drag each step and justification to the correct location on the table. Each step and justification can be used more than once, but not all steps and justifications will be used.
Order each step and justification that is needed to solve the equation below.
-2x=28-6x
Answers
Answer:
Step-by-step explanation:
Steps Justifications
1). -2x = 28 - 6x 1). Given
2). -2x + 6x = 28 - 6x + 6x 2). Addition property of equality
3). 4x = 28 3). Simplification
4). [tex]\frac{4x}{4}=\frac{28}{4}[/tex] 4). Division property of equality
5). x = 7 5). Simplification
Obiwan is standing at a distance of 1.5m from the base of a tree. From where he is standing, he can see the top of the tree. If the tree is 15m high and Obiwan is 1m tall, what is the angle of elevation of the top of the tree?
Answers
Answer:
∅ = 83.9º
Step-by-step explanation:
tan = opp/adj
opp = 15 - 1 = 14
tan∅ = 14/1.5
∅ = arctan 14/1.5
use calculator
∅ = 83.884496433714593º
Rounded
∅ = 83.9º
The graph below does not represent a function. Explain why.
Answers
Notice how points T and Z are vertically aligned, or vertically lined up. This is where the graph fails the vertical line test.
The input x = 2 leads to the outputs y = 3 and y = 5 (which are the y coordinates of points Z and T in that order).
A function is only possible when any given input leads to exactly one output only. It would be like saying "the conversion function from Celsius to Fahrenheit has 0 degrees C convert to both 32 degrees F and 50 degrees F at the same time". But such a statement makes no sense and it's not useful. So this is one example of why having one output makes sense for a function.
In short, we need one output for any given input. But the input x = 2 leads to more than one output. That's why we don't have a function.