The y-coordinate of the position vector at time t=3 is approximately 1.446.
For the y-coordinate of the position vector at time t=3, we first need to integrate the given velocity components with respect to time to obtain the position components:
x(t) = ∫(dx/dt) dt = ∫sin(t²) dt
= (1/2)∫sin(u)/√(u) du
(where u = t²)
y(t) = ∫(dy/dt) dt
= ∫[tex]e^{cos t}[/tex] dt = [tex]e^{cos t}[/tex] + C
We can then use the given initial condition at time t=4 to determine the constant value C for the y-component:
x(4) = 2, y(4) = 1
Plugging in t=4 to the position equations, we get:
x(4) = (1/2)∫sin(u)/√(u) du = 2
y(4) = [tex]e^{cos 4}[/tex] + C = 1
Solving for C, we get:
C = 1 - [tex]e^{cos 4}[/tex]
Now we can plug in t=3 to find the y-coordinate of the position vector:
y(3) = [tex]e^{cos 3}[/tex] + C
y(3) = [tex]e^{cos 3}[/tex] + 1 - [tex]e^{cos 4}[/tex]
y(3) ≈ 1.446 (rounded to three decimal places)
Therefore, the y-coordinate of the position vector at time t=3 is , 1.446.
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i need help on these 2 questions
ONLY ANSWER IF U KNOW!
Find the limit of the function algebraically.
Answer:
lim [(x(2) + 3) × 1/ x(4) ] = 3 × ( + ○○) = + ○○
B
39 m
Use the inverse trigonometric keys
on a calculator to find the measure
of angle A.
А
21 m
с
A=
(Round the answer to the nearest whole number.)
Answer:
the answer is 20 because you round of 21
PLZ HELP ASAP WILL MARK BRAINLIEST
Answer:
72[tex]\sqrt{3}[/tex]
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ (d₁ and d₂ are the diagonals )
The diagonals bisect each other at right angles
d₁ = 2 × 6 = 12
Use the tangent ration in the upper left right triangle and the exact value
tan60° = [tex]\sqrt{3}[/tex]
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{opp}{6}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 6 )
opp = 6[tex]\sqrt{3}[/tex] , then
d₂ = 2 × 6[tex]\sqrt{3}[/tex] = 12[tex]\sqrt{3}[/tex]
Thus
A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex]
Please help asap thank you
Answer:
1.
Mean:22
Median: 19.5
Mode:12
Range:26
2.
Mean: 21.143
Median: 16
Mode: 5
Range: 43
3.
Mean: 38.5
Median: 37.5
Mode: 13 , 34, 41
Range: 56
4.
Mean: 73.167
Median: 78.5
Mode: 85
Range : 47
5.
Mean: 58.75
Median: 63
Mode: 63
Range : 70
6.
Mean: 68.714
Median: 74
Mode: 74
Range: 57
7.
Mean: 48
47.5
72
66
8.
59.625
61
90
79
9.
31.571
32
46
34
10.
42.111
40
51
51
Prehistoric cave paintings were discovered in a cave in France. the paint contain 25% of the original Carbon-14. Use the exponential decay model for carbon-14, A=A0e^-0.000121t to estimate the age of the paintings
Answer:
The age of paintings is - 26,601 years .
Step-by-step explanation:
Lets calculate-
A= [tex]0.25 A[/tex]o
Therefore ,
[tex]A= A[/tex]o [tex]e^-^0^.^0^0^0^1^2^1^t[/tex]
[tex]ln0.25=-0.000121t[/tex]
[tex]-3.2188=-0.000121t[/tex]
[tex]t=\frac{-3.2188}{-0.000121}[/tex]
t= 26,601.65
Therefore , the age of paintings is 26,601 years old.
Given a ≠ ± b and (a^2-b^2) / (a+b)=12 find a-b.
(I will give brainliest for helpful answers. Please don't put a link in the answer box.)
Answer:
[tex] \sqrt{12a \: + \: 12b \: - \: 2ab \: + \: 2b {}^{2} } [/tex]
Step-by-step explanation:
(a²-b²) / (a+b) = 12
a² - b² = 12(a+b)
(a-b)² + 2ab - 2b² = 12a + 12b
(a-b)² = 12a + 12b - 2ab + 2b²
a - b =
[tex] \sqrt{12a \: + 12b \: - 2ab \: + \: 2b {}^{2} } [/tex]
can u help pls like pls
Answer:
E. 16
Step-by-step explanation:
Easy:
Formula: P=2(l+w)
Plug in and solve:
P=2(3+5)
P = 16 (Option E is correct)
Find the area of the trapezoid
Answer:
42 square units
Step-by-step explanation:
Each square on the grid is 2 units by 2 units.
Bases: OC = 10; SK = 4
Height: OS = 6
area = (b1 + b2)h/2
area = (10 + 4)(6)/2
area = 42
Answer: 42 square units
Answer:
The area of trapezoid is 42 square unit.
Step-by-step explanation:
According to the question
A trapezoid which is consist of many square shapes and each grid square equals 2 units . We need to find the area of trapezoid.
To calculate the area of trapezoid we have given :-
Base ; SK = 4 and OC = 10Height ; OS = 6Formula for finding area of trapezoid is ½ × (Base 1 + Base 2) × Height .Finding the area of trapezoid :-
Area of trapezoid = ½ × ( 4 + 10 ) × 6
Add 4 and 10.Area of trapezoid = ½ × 14 × 6
Multiply 14 by 10.Area of trapezoid = ½ × 84
Divide by 2.Area of trapezoid = 42
Hence,
The area of trapezoid is 42 square unit.
For each j = N, define the functions fj : [0, 2] → R as ri+1 x = [0, 1], fj(x) = min{1, x³+¹} {2 x = (1,2]. (1) Sketch the graph of the functions fo, f1, and f2.
The graph of the functions fo, f1, and f2 can be sketched as follows: fo(x) is a constant function equal to 1 on the interval [0, 2]. f1(x) is a piecewise function that equals x³ + 1 on [0, 1] and 1 on (1, 2]. f2(x) is a piecewise function that equals 1 on [0, 1] and 2 on (1, 2].
To sketch the graph of the functions fo, f1, and f2, we consider their definitions and the given intervals.
The function fo(x) is a constant function that equals 1 on the entire interval [0, 2]. Therefore, its graph will be a horizontal line at y = 1 throughout the interval.
The function f1(x) is a piecewise function. On the interval [0, 1], it equals x³ + 1, which means it starts at y = 1 when x = 0 and increases as x moves towards 1. At x = 1, there is a jump discontinuity, and the function becomes a constant 1 for x in (1, 2]. Therefore, the graph of f1 will be a curve increasing from y = 1 to some maximum point between x = 0 and x = 1, and then it remains constant at y = 1 for x in (1, 2].
The function f2(x) is also a piecewise function. On the interval [0, 1], it equals 1, so its graph will be a horizontal line at y = 1. At x = 1, there is another jump discontinuity, and the function becomes a constant 2 for x in (1, 2]. Therefore, the graph of f2 will have a horizontal line at y = 1 on [0, 1] and a horizontal line at y = 2 on (1, 2].
By considering the definitions and intervals, we can sketch the graphs of fo, f1, and f2 as described above.
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Pamela rides her bike to the park. If she rides at a speed of 12 miles per hour, it
takes her 45 minutes to get to the park. How long will it take her to get to the
park if she rides at a speed of 8 miles per hour? *
Answer:
well to tell you its easy 4 me
A genetic experiment involving peas yielded one sample offspring consisting of 412 green peas and 125 yellow peas. Use a 0.05 significance level to test the most under the same circumstances, 20% of offspring peas will be yellow. Identify the hypothesis, alternative hypothesis et statistics, P-value, conclusion about the null hypothesis and final conclusion that adds the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.
What are the null and alternative hypotheses?
A H_o: p≠0.26 H_1:p=0.26
B H_o: p≠0.26 H_1:p>0.26
C H_o: p=0.20 H_1:p<0.26
D H_o: p=0.26 H_1:p>0.26
E H_o: p=0.26 H_1:p≠0.26
F H_o: p≠0.20 H_1:p<0.26
What is the test statistic?
z = _______
(Round local places as needed)
What is the P-value?
P-value = _________
1) the null and alterative hypotheses are - H_o: p=0.20 H_1:p<0.26 (option C)
2)
The test statistic is -2.17.The p -value is 0.0306.What is the explanation for these?
1) The null hypothesis is that the population proportion of yellow peas is equal to 20%. The alternative hypothesis is that the population proportion of yellow peas is less than 20%.
hence, H_o: p=0.20 H_1:p<0.26
2) The test statistic is calculated as follows -
z = (pa - p₀) / √(p₀(1-p₀)/ n)
Where -
pa is the sample proportion of yellow peas (0.25)
p₀ is the hypothesized proportion of yellow peas (0.20)
n is the sample size (537)
The test statistic is -2.17
p- value =P(Z < -2.17)
The p -value is 0.0306.
Since the p-value is less than the significance level of 0.05,we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population proportion of yellow peas is less than 20%.
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The volume ſin cubic feet) of a black cherry tree can be modeled by the equation ý = -51.7+03x_1 + 4.8x_2, where X_1, is the tree's height (in feet) and X_2, is the tree's dameter (in inches). Use the multiple regression equation to predict the y values for the values of the independent variables
(a) x_1 = 72, X_2 = 8.9
(b) x_1 = 65, x_2 = 10.6
(c) x_1 =81, x_2=16.4
(d) x_1 = 88, X_2 = 19.4
By using the multiple regression equation, the predicted y-values for the values of the given independent variables include the following:
(a) ý = 207.02.
(b) ý = 194.18.
(c) ý = 270.02.
(d) ý = 305.42.
What is a regression line?In Statistics and Mathematics, a regression line simply refers to a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line refers to a line which best fits a set of data.
Next, we would determine the predicted y-values for the values of the given independent variables as follows;
ý = -51.7+03x₁ + 4.8x₂
(a) x₁ = 72 and x₂ = 8.9
ý = -51.7+03(72) + 4.8(8.9)
ý = 207.02.
(b) x₁ = 65 and x₂ = 10.6
ý = -51.7+03(65) + 4.8(8.9)
ý = 194.18.
(c) x₁ = 81 and x₂ = 16.4
ý = -51.7+03(81) + 4.8(16.4)
ý = 270.02.
(d) x₁ = 88 and x₂ = 19.4
ý = -51.7+03(88) + 4.8(19.4)
ý = 305.42.
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What Is The Difference Between Apparent Capacity And Actual Capacity Of A Glass Vessel? IN SURFACE AREA AND VOLUME!!?
The apparent capacity of a glass vessel refers to its perceived size or volume based on external dimensions, while the actual capacity represents the true volume of the vessel, taking into account both interior and exterior dimensions.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
PLEASE HELP ME, I HAVE BEEN WAITING FOR A DAAYY!! How old am i if 400 reduced by 3 times my age is 244?
Answer:
52 years
Step-by-step explanation:
Let
Your age = x
3 times your age = 3 * x
= 3x
The equation can be written as:
400 - 3x = 244
400 - 244 = 3x
156 = 3x
Divide both sides by 3
x = 156/3
x = 52
Therefore,
Your age is 52 years
In a lab, Andrew is studying the growth of a particular species of bacteria. The bacteria in the petri dish started at 300. After 2 days he realizes that the number of bacteria is about 480. After another 2 days he realizes that the number of bacteria in the dish is 288 more than what it was two days ago. a.) Give an equation to estimate the amount of bacteria in the dish after every day. b.) At what rate would the bacteria be growing c.) How many days would it take for the bacteria to reach almost 1229. d.) Find the average rate of change between 6 days and the first day
a) The equation to estimate the amount of bacteria in the dish after every day is N = 90t + 210.
b) The coefficient is 90, indicating that the bacteria is growing at a rate of 90 per day.
c) It would take approximately 11.32 days for the bacteria to reach almost 1229.
d) Average rate of change = (N₂ - 300) / (6 - 1)
a) Let's denote the number of bacteria in the dish after a certain number of days as N. We can create an equation to estimate the amount of bacteria in the dish after every day based on the given information.
On the first day, the initial number of bacteria is 300. After 2 days, the number of bacteria is approximately 480. This gives us two data points: (1, 300) and (3, 480).
To find the equation for estimating the number of bacteria, we can use the two-point form of the linear equation:
N - 300 = ((480 - 300) / (3 - 1))(t - 1)
Simplifying the equation, we get:
N = 90t + 210
Therefore, the equation to estimate the amount of bacteria in the dish after every day is N = 90t + 210.
b) The rate at which the bacteria is growing can be determined from the coefficient of t in the equation. In this case, the coefficient is 90, indicating that the bacteria is growing at a rate of 90 per day.
c) We can use the equation N = 90t + 210 to find the number of days it would take for the bacteria to reach almost 1229. We substitute N = 1229 into the equation and solve for t:
1229 = 90t + 210
1019 = 90t
t ≈ 11.32
Therefore, it would take approximately 11.32 days for the bacteria to reach almost 1229.
d) To find the average rate of change between 6 days and the first day, we need to calculate the change in the number of bacteria divided by the change in time:
Average rate of change = (N₂ - N₁) / (t₂ - t₁)
Here, N₁ is the number of bacteria on the first day (300), t₁ is the first day (1), N₂ is the number of bacteria on the sixth day, and t₂ is the sixth day.
Substituting the values into the formula, we get:
Average rate of change = (N₂ - 300) / (6 - 1)
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please help me yall, Godbless.
Answer:
The rate of change or slope is 2
Step-by-step explanation:
Rise over run 2/1
Someone please help really need it.
Write an equation of the line parallel to y = 5x + 7 that passes through the point (-3,2)
Answer:
y=5x-13
Step-by-step explanation:
Pls help me I’m failing :(
consider the equation below. (if an answer does not exist, enter dne.) f(x) = x3 − 3x2 − 9x 3
Interval of increase: (-∞, -1) ∪ (3, +∞)
Interval of decrease: (-1, 3)
Given function is f(x) = x³ - 3x² - 9x + 4
Differentiating with respect to x,
f'(x) = 3x² - 6x - 9
f'(x) = 3 (x² - 2x - 3)
f'(x) = 3 (x² - 3x + x - 3)
f'(x) = 3 (x(x - 3) + (x - 3))
f'(x) = 3 (x - 3) (x + 1)
For increasing or decreasing,
f'(x) = 0
3 (x - 3) (x + 1) = 0
x = - 1, 3
In interval (-∞, -1 ), f'(x) = positive,
⇒ f(x) is increasing on (-∞, -1 ),
In interval (-1, 3), f'(x) = negative,
⇒ f(x) is decreasing on (-1, 3),
In interval (3, ∞), f'(x) = positive,
⇒ f(x) is increasing on (3, ∞),
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Given question is incomplete, the complete question is below
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x³ - 3x² - 9x + 4 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.)
Gavin is subdividing land into two plots, where one plot is in the shape of a square and the other plot is in the shape of a rectangle. The square plot of land has a side length of 6x3 feet, and the rectangular plot of land has a length of 3x5 feet and a width of 7x2 feet. Use the properties of exponents to determine the expression that represents the area for each plot of land. Then analyze which plot of land has a larger area if x is 3.
Independent random samples of 10 released prisoners in the fraud and 10 released prisoners in the firearms offense categories yielded the given information on time served, in months. At the 1% significance level, do the data
provide sufficient evidence to conclude that the mean time served for fraud is less than that for firearms offenses? Assume the population standard deviations are equal.
Let, be the mean time served for fraud μ_2 the mean time served for firearms offenses. What are the correct hypotheses to test?
A. H_o: μ_1=μ_2
H_a: μ_1>μ_2
B. H_o: μ_1≠μ_2
H_a: μ_1=μ_2
C. H_o: μ_1>μ_2
H_a: μ_1=μ_2
D. H_o: μ_1=μ_2
H_a: μ_1≠μ_2
E. H_o: μ_1<μ_2
H_a: μ_1=μ_2
F. H_o: μ_1=μ_2
H_a: μ_1<μ_2
Compute the test statistic,
t = _______(Round to three decimal places as needed.)
Determine the critical value or values. ______
(Round to three decimal places as needed. Use a comma to separate answers as needed.)
The correct hypotheses to test is (f) H₀ : μ₁ = μ₂; H₁ : μ₁ < μ₂
The test statistic is undefined
The critical value at α = 0.01 is 2.58
What are the correct hypotheses to test?From the question, we have the following parameters that can be used in our computation:
Mean time served for fraud is less than that for firearms offenses
This means that the hypotheses to test are
H₀ : μ₁ = μ₂
H₁ : μ₁ < μ₂
This is represented with option (f)
Computing the test statisticThe test statistic can be calculated using
z = (x₁/n₁ - x₂/n₂)/√[p(1 - p)/n₁ + p(1 - p)/n₂)
Where p = pooled sample proportion
and p = (x₁ + x₂)/(n₁ + n₂)
The required values are not given
So, the test statistic is undefined
Finding the critical valueGiven that
α = 1%
This means that
α = 0.01
The critical value at α = 0.01 is 2.58
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A rectangle field is 3 times as long as it is wide. If the perimeter of the field is 280 yards, what are the fields dimensions
carter has 37 coins, all nickels and dimes in his piggy bank. The value of the coins is $3.17. How many dimes does carter have?
HELP!!! 100 POINTS!!! Find the total surface area of a cylinder with a height of 7 cm and radius of 3 cm. Leave your answer in terms of π.
140π cm2
91π cm2
60π cm2
51π cm2
Answer:
60π cm2
Step-by-step explanation:
Question 2 (1 point)
Which graph shows the solutions to 2x<6?
the lenght of an arc in a circle with diameter 10 inches is 1.25π inches. determine the measure of the arc.
Answer:
[tex]the \: angle \: is \: 0.25\pi[/tex]
Step-by-step explanation:
the arc length is equal to the radius x angle (in radians)
[tex]s=ra[/tex]
s= arc length, r= radius and a= the angle
solve for a ; a= s/r; a=
[tex]1.25\pi/5[/tex]
The measure of the arc is 0.25π.
Important information:
Diameter of a circle = 10 inches.Length of arc = 1.25πMeasure of arc:The formula for arc length is:
[tex]s=r\theta[/tex]
where s is the arc length, r is the radius and [tex]\theta [/tex] is the measure of arc in radian.
The diameter of a circle is 10 inches. So, the radius is 5 inches.
[tex]1.25\pi=5\theta[/tex]
[tex]\dfrac{1.25\pi}{5}=\theta[/tex]
[tex]0.25\pi=\theta[/tex]
Therefore, the measure of the arc is 0.25π.
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what ratio is equivalent to 2/1
Answer:12 : 6 22 : 11 32 : 16
Step-by-step explanation:
Answer:
4:2
Step-by-step explanation:
A trinomial with a leading coefficient of 333 and a constant term of -5−5 what is an equation
Given:
Leading coefficient of a trinomial = 3
Constant term = [tex]-5[/tex]
To find:
The equation of trinomial.
Solution:
If an expression contains three terms, then it is known as trinomial.
The general form of a trinomial which contains leading term and a constant is:
[tex]ax^2+bx+c[/tex]
Where, a,b,c are real non-zero numbers. Here, a is the leading coefficient and c is the constant.
Putting a=3 and c=-5, we get
[tex]3x^2+bx+(-5)[/tex]
[tex]3x^2+bx-5[/tex]
Therefore, the required trinomial is [tex]3x^2+bx-5[/tex], where b is a non zero real number.
y = -9x Proportional or Non Proportional