Answers
The rate of oscillation at t = 2 seconds is -0.31 cm/s
How to find the rate at which the spring is oscillating?We know that the spring is oscillating according to the equation:
s(t) = 9*cos(t) (t would be in "radians", not degrees, check that on your calculator)
The rate at which this oscillates is given by the derivate of the above equation, remember that the derivate of cos(t) is -sin(t), then we will get:
s'(t) = -9*sin(t)
The rate of oscillation at t= 2 seconds is:
s'(2) = -9*sin(2) = -0.31
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Related Questions
what is tne solution of 2|2x-1|-8=18?
Answers
The solution of the equation 2|2x - 1| - 8 = 18 is x = 7 or x = -6.
The solution of the equation 2|2x - 1| - 8 = 18 can be obtained as follows:
Step 1: Add 8 to both sides of the equation2|2x - 1| = 26
Step 2: Divide both sides of the equation by 2|2x - 1| / 2 = 26 / 2|2x - 1| = 13
Step 3: The absolute value of a number is always positive, so we can divide the equation into two separate equations.|2x - 1| = 13 or -|2x - 1| = 13
Step 4: Solve for x in each equation.
Solution for the first equation:|2x - 1| = 132x - 1 = 13 or 2x - 1 = -13 2x = 14 or 2x = -12 x = 7 or x = -6
Solution for the second equation:-|2x - 1| = 13|2x - 1| = -13
There is no solution to this equation because the absolute value of a number cannot be negative.
Therefore, the solution of the equation 2|2x - 1| - 8 = 18 is x = 7 or x = -6.
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The radius of the base of a cylinder is expanding at a constant rate of 3 mm/min. If the height of
the cylinder is a constant 20 mm, find the rate at which the VOLUME of the cylinder is changing at the
moment when the radius of the base of the cylinder is 10 mm. Also find the rate at which the SURFACE
AREA of the cylinder is changing at this same moment.
(V = r²h, SA=2лrh+2rr²)
I’m getting 1800pi mm^3/min for volume and 360pi mm^2/min for surface area but I’m not sure if it’s correct
Answers
The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.
To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.
Given:
Radius rate of change: dr/dt = 3 mm/min
Height: h = 20 mm
Radius: r = 10 mm
Volume of the cylinder (V) = \(r^2h\)
Differentiating with respect to time (t), we have:
dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)
Since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dV/dt = 2(10)(20)(3) + (10^2)(0)
dV/dt = 600 + 0
dV/dt = 600 mm^3/min
Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.
Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)
Differentiating with respect to time (t), we have:
dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)
Again, since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)
dSA/dt = 0 + 120π + 120π
dSA/dt = 240π mm^2/min
Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.
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Lấy ngẫu nhiên 25 lọ thuốc Vitamin tổng hợp do một máy tự động đóng chai ta thu được s'2 =0,012(l2).Máyđượcgọilàđạtchuẩnnếuđộphântántheoquyđịnhlà2 =0,005(l2). Với mức ý nghĩa 0,05 hãy kiểm định máy đóng chai có đạt chuẩn không? Biết lượng thuốc trong chai là biến ngẫu nhiên có phân phối chuẩn.
Answers
Answer:
I really can't read this
Step-by-step explanation:
If 3x = 21, find the value of 23 - 4x.
a. -5
b. 5
c. 2
d. -2
Please help!!
Answers
Answer:
A
Step-by-step explanation:
QUESTION IS IN IMAGE! DO NOT NEED TO SHOW WORK UNLESS YOU NEED OR WANT TO!
Answers
Given:
Find-:
The value of "x"
Explanation-:
Use the property of circle:
The angle is always the same, no matter where it is on the same arc between endpoints:
Apply the property,
\(x+14=41\)The value of "x" is:
\(\begin{gathered} x+14=41 \\ \\ x=41-14 \\ \\ x=27 \end{gathered}\)So,
The value of "x" is 27.
x2+10x+=()2
step by step
Answers
The value of the expression x² + 10x, when x = 2 is 24.
In the expression x² + 10x, x represents a variable, which is a placeholder for a value that can change. We are given that x = 2, which means we substitute 2 for x in the expression:
x² + 10x = 2² + 10(2)
Here, 2² means 2 raised to the power of 2, which is 2 multiplied by itself: 2² = 2 x 2 = 4.
10(2) means 10 multiplied by 2, which is 20.
So we can substitute these values in the expression:
x² + 10x = 2² + 10(2)
= 4 + 20
= 24
Therefore, when x is equal to 2, the value of the expression x² + 10x is 24.
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The complete question:
Evaluate the expression x² + 10x, when x = 2.
1
Merko has an 80-1 scale-drawing of the floor plan of her house. On the floor plan, the dimensions of
her rectangular living room are 17 inches by 23 inches
Weat is the area of her real living room in square inches?
Answers
Answer:you need use a scale and the numbers that are provided of the dimensions of the room
Step-by-step explanation:
11. What is the median of this data set?
70, 72, 90, 78, 92, 67, 94,78
67
92
25
Answers
The median of this data set 70, 72, 90, 78, 92, 67, 94,78, 67, 92, 25 when arranged is 78
What is the median of this data set?70, 72, 90, 78, 92, 67, 94,78, 67, 92, 25
Median of a data set refers to the middle value when arranged in ascending(lowest to largest) or descending(largest to lowest) order. The median is the number separating the higher half of a data sample, a population, or a probability distribution, from the lower half.
Arranging in ascending order:
25, 67, 67, 70, 72, 78, 78, 90, 92, 92, 94
Hence, the median is 78
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Which ray is a bisector of angle A B C?
Select one:
A. stack B C with rightwards arrow on top
B. stack B D with rightwards arrow on top
C. stack B A with rightwards arrow on top
D. stack B F with rightwards arrow on top
What is GH?
Select one:
A. 5
B. 10
C. 15
D. 25
What is the value of y?
Select one:
A. 2
B. 4
C. 16
D. 20
What is m angle D B E?
Select one:
A. 20
B. 30
C. 40
D. 50
What is m angle A B E?
Select one:
A. 20
B. 30
C. 40
D. 60
If m angle F B A equals 7 x plus 6 y, what is m angle F B A?
Select one:
A. 40
B. 44
C. 47
D. 60
Answers
Answer:
1). Option B.
2). Option C.
3). Option A.
4). Option C.
5). Option D.
6). Option C.
Step-by-step explanation:
1). Bisector of angle ABC is,
Option (B). stack BD with rightwards arrow on top.
2). Since GH = GI [Given]
3x = 5x - 10
5x - 3x = 10
2x = 10
x = 5
Therefore, GH = 3x
= 3(5)
= 15
Option (C). is the answer.
3). Since m∠ABD ≅ m∠DCB [Given]
and m∠DCB ≅ m∠CBE [Since GH ≅ GI]
Therefore, m∠ABD ≅ m∠CBE
10y = 8y + 4
10y - 8y = 4
2y = 4
y = 2
Option (A). is the answer.
4). m∠DBE = m∠DBC + m∠CBE
= 10y + (8y + 4)
= (18y + 4)°
By putting y = 2,
m∠DBE = 18×2 + 4
= 36 + 4
= 40°
Option (C) will be the answer.
5). m∠ABE = m∠ABD + m∠DBC + m∠CBE
= 10y + 10y + (8y + 4)
= 28y + 4
= 28×2 + 4
= 56 + 4
= 60°
Option (D) will be the answer.
6). If m∠FBA = 7x + 6y
By putting x = 5 and y = 2
m∠FBA = 7(5) + 6(2)
= 35 + 12
= 47°
Option (C) will be the answer.
Answer:
1). Option B.
2). Option C.
3). Option A.
4). Option C.
5). Option D.
6). Option C.
Step-by-step explanation:
Need Help You Can Get 35 point!!!
The width of a rectangular field is represented by x meters. The length of the field is 10 more than twice its width . The area of the field is 5500m^2
Part A
Write an equation that can be used to determine the dimensions, in meters, of the field.
Part B
What is the width, in meters, of the field?
The width is ( ) meters.
Answers
Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x
Part B: width is 50 meters.
How to determine the valueThe formula for calculating the area of a rectangle is expressed with the equation;
A = lw
Such that the variables are expressed as;
A is the areal is the lengthw is the widthWe then have that;
l = 2x + 10
Substitute the values
5500 = (2x + 10)(x)
expand the bracket
5500 = 2x² + 10x
2x² + 10x - 5500
x² + 5x - 2750
x² + 55x - 50x - 2750
x(x + 55) - 50(x + 55)
x = 50 meters
Length = 2(50) + 10
Length = 100 + 10 = 110 meters
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If the simple interest on $2000 for 3 years is $300, then what is the interest rate?
Answers
\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill &\$300\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &3 \end{cases} \\\\\\ 300=(2000)(r)(3)\implies 300=6000r\implies \cfrac{300}{6000}=r \\\\\\ \cfrac{1}{20}=r\implies 0.05=r\implies \stackrel{\textit{converting to percent}}{100\cdot 0.05}\implies \stackrel{\%}{5}=r\)
Using the integers −9 to 9 at most one time each, place a digit in each box ( ___ , ____) and. ( ___ , ____) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3)
Answers
Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).
To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).
In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:
(x₁ + x₂)/2 = 1
(y₁ + y₂)/2 = 3
We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:
(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2
(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6
Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:
x₁ + (2-x₁) = 2 => x₁ = 1
y₁ + (6-y₁) = 6 => y₁ = 3
So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.
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plz help I'll give 10 plz
Answers
Answer:
C. 8
Step-by-step explanation:
xy - 3x
x = 4 and y = 5
(4)*(5) - 3(4)
20 - 12 = 8
Keith has landscaping bricks that are 0.75 feet long.
Keith put 19 bricks
Answers
Feet long bricks - 0.75
No of bricks she added
is 15
So now we will multi plied
0.75× 19
Se solution 0.75
× 15
________
11 . 25
So the Answer is 11 . 25 is the final
answer
hope this Answer will help you
The parabola X= √y-9 opens: right left down up?
Answers
The parabola x = √(y - 9) opens upwards.The given parabolic equation is x = √(y - 9). Let's identify the direction of opening of this parabola.The general form of the equation of a parabola is y = a(x - h)² + k.
Comparing this to the given equation, we can see that h = 0 and k = 9. The vertex is therefore (h, k) = (0, 9). Now, let's determine whether the parabola opens upwards or downwards.
If the coefficient of (x - h)² is positive, the parabola opens upwards, and if it's negative, the parabola opens downwards. In this case, since the coefficient of (x - h)² is 1, which is positive, the parabola opens upwards.
Therefore, the parabola x = √(y - 9) opens upwards.
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Please help!!!!!!!!!!!
Answers
Answer:
h = 1,268 cm
Step-by-step explanation:
V = (π·r²·h)/3, general formula
83 = (π·4²·h)/3, substitute what is given V= 83 cm³ and r = 4 cm
83 ·3 = (π· 16·h)·3/3, multiply both sides by 3 and solve 4² = 16
249 = π·16·h, multiply 83·3 = 249 and 3/3 = 1
249/ π·16 = h , divide both sides by π·16
1,268.146587 = h, solve
1,268 ≈ h , is rounded to the nearest cm
A truck with 30-in.-diameter wheels is traveling at 50 mi/h.
Find the angular speed of the wheels in rad/min, "hint convert miles to inches & hours to minutes:
_________rad/min
How many revolutions per minute do the wheels make?
___________rpm
Answers
Answer:
A. the angular speed is 3771.4 rad/min
b. 5921 rpms
Step-by-step explanation: I just got this same question right on a test.
another fraction problem. Have tried this one a couple of times and cant find fault in what i did
Answers
Answer:
Perimeter = 12 1/2 in
Area = 9.375 in
Step-by-step explanation:
Perimeter:
(3 3/4) + (3 3/4) + (2 1/2) + (2 1/2) = 12 1/2
Area:
(3 3/4) * (2 1/2) = 9.375
Answer:
P = 12 1/2 in
A = 9 3/8 in²
Step-by-step explanation:
L = 3 3/4 in
W = 2 1/2 in
Area:
A = L × W
A = (3 3/4 in)(2 1/2 in)
A = 15/4 in × 5/2 in
A = 75/8 in²
A = 9 3/8 in²
Perimeter:
P = 2(L + W)
P = 2(3 3/4 in + 2 1/2 in)
P = 2(15/4 in + 5/2 in)
P = 2(15/4 in + 10/4 in)
P = 2(25/4 in)
P = 25/2 in
P = 12 1/2 in
write 2/5 as a decimal
Answers
Answer:
.4
Step-by-step explanation:
You divide 2 by 5.
2 ÷ 5 = .4
Answer:
I believe 2/5 as a decimal is 0.4.
Step-by-step explanation:
Make the denominator 10 and then simplify to 4/10 following the answer 0.4.
rogress bar may be uneven because questions can be worth more or less (including zero) depending on your
Which of the following equations has the solution x = all real numbers?
O. 5(3x) + 6x = 3x + 15 + 2x
5(3x).+ 7x = 3x + 15 - x
5(3x) + 7x = 3x + 10 - x
5(3x) + 7x = x + 15 - 3x
Answers
The equations that has the solution x = all real numbers is 5(3x)+ 7x = 3x + 15 - x and 5(3x) + 7x = 3x + 10 - x,
What is meant equation?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Here given equations,
5(3x) + 6x = 3x + 15 + 2x
15x + 6x = 3x + 15 + 2x
15 x + 6x - 3x -2x = 15
16 x = 15
x = 15/16
5(3x).+ 7x = 3x + 15 - x
15 x + 7x = 3x + 15 - x
15 x + 7x - 3x + x = 15
22x - 3x + x = 15
20 x = 15
x = 15/20
x = 3/4
5(3x) + 7x = 3x + 10 - x
15x + 7x - 3x + x = 10
20x = 10
x = 10/20
x = 1/2
5(3x) + 7x = x + 15 - 3x
15x +7x - x + 3x = 15
24x = 15
x = 15/24
x = 5/8
Therefore the equations that has the solution x = all real numbers are :
5(3x).+ 7x = 3x + 15 - x and 5(3x) + 7x = 3x + 10 - x .
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A customer at an electronics store opened a store credit card to purchase a computer for $1,800. The store put the entire purchase on the credit card with an APR of 17.99%. The customer
pays $125 per month until the balance is paid off. Determine the total amount of interest paid.
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
O $188.09
O $295.01
O $243.11
O $182.45
Answers
The last row of the table will show the total interest paid, which is approximately $243.11.
The correct option is C.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
To calculate the total interest paid,
we need to first find out how many months it will take to pay off the entire balance.
We can use the following formula to calculate the number of months:
N = -log(1-(r×b/p))/log(1+r)
where N is the number of months, r is the monthly interest rate (which is the annual percentage rate divided by 12), b is the balance, and p is the payment.
In this case,
r = 0.1799/12 = 0.01499 (monthly interest rate), b = $1,800, and p = $125.
Plugging these values into the formula, we get:
N = -log(1-(0.01499 × 1800/125))/log(1+0.01499) ≈ 16.24
So it will take about 16.24 months to pay off the entire balance.
Using a spreadsheet, we can create a table with the following columns:
Month: 1 to 16
Balance: starting with $1,800 and decreasing by $125 each month
Interest: calculated as the monthly interest rate times the balance
Payment: $125
Total Interest: calculated as the sum of the interest for all previous months
The last row of the table will show the total interest paid, which is approximately $243.11.
Therefore, the value is (C) $243.11.
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Answer: Option C is correct $243.11
Step-by-step explanation: I got it right On the test!!!
Write 45% as a decimal.
Answers
Answer:
0.45
Step-by-step explanation:
Because you have to write 45% has money so 45.00 divide by 100 = 0.45 hope this is right and helpful. Can you mark me brainliest
let be the amount of coffee (in ounces) that an undergraduate student at uiuc drinks per day. suppose we know that has a mean of 10 oz and a standard deviation of 5.2 oz. suppose there are 120 students in stat 107. assuming stat 107 students are a random sample, calculate the standard error of the average amount of coffee a stat 107 student drinks per day . is greater than 12.7 oz.
Answers
0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.
Given that,
Standard deviation (σ) = 5.2 oz
mean (μ) = 10 oz
Number of students (n) = 120
As we know,
P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ\(\sqrt{n}\)}/σ])
= P (z > [{12.7 - 10\(\sqrt{120}\)}/5.2])
= P (z > 1.86)
= 1 - P ( z < 1.86)
= 1 - 0.862394
= 0.137606
Thus, P( z > 12.7 oz.) = 0.137606
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What is amazing about the square of 111, 111, 111?
Answers
Answer:
The square of 111,111,111 is 12,345,678,987,654,321. What's amazing about it is that if you read the digits from left to right, then it's a palindrome. If you read the digits from right to left, it's also a palindrome. This property makes it a doubly-palindromic number, which is quite rare and interesting.
A team is selling discount cards as a fundraiser. The table shows the number of cards sold and the remaining amount of money needed.
A table showing Discount Cards Fundraiser with two columns and six rows. The first column, Cards Sold, has the entries, 10, 20, 30, 40, 50. The second column, Remainder of Goal, has the entries, $875, $795, $715, $635, $555.
Which word describes the slope of the line representing the data in the table?
zero
undefined
negative
positive
5
9
Answers
The word that describes the slope of the line representing the data in the table is "negative."
To determine the slope of the line representing the data in the table, we need to examine the relationship between the number of cards sold and the remaining amount of money needed.
Looking at the given data, we observe that as the number of cards sold increases, the remaining amount of money needed decreases. This indicates an inverse relationship between the two variables.
The slope of a line represents the rate of change between two variables. In this case, the slope is negative because the line decreases as we move from left to right.
Therefore, the word that describes the slope of the line representing the data in the table is "negative."
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3/4 times 7 i need help plz
Answers
Answer:
5.25 or 21/4 or 5 1/4
Step-by-step explanation:
hope this helps
help me please thank youuuu
Answers
Answer:
B. g(x) = -x² - 2
Step-by-step explanation:
f(x) = x²
g(x) = -x²
The graph now has a maximum of (0, 0) and is curving downwards. To make the graph go down by -2 subtract 2 from the equation
g(x) = -x² - 2
I hope this helps!
The rule is X/5-8=Y What does Y equals to when X=20
Answers
Answer:
Y= -4
Step-by-step explanation:
According to the rules of GEMDAS, division precedes subtraction.
Substitute 20 into where X is in the equation, so it would look like:
20/5-8=Y
From here, simplify. 20/5 is 4. 4-8=-4
Here's how work would look like on my paper"
X/5-8=Y
20/5-8=Y
4-8=Y
Y=-4
helpppplpppplllplplp!!!??!
Answers
Answer:
my answer came out to 8.3 repeating
Step-by-step explanation:
A 95% confidence interval for the mean number of television per American household is (1.15, 4.20). For each of the following statements about the above confidence interval, choose true or false.
a. The probability that u is between 1.15 and 4.20 is .95.
b. We are 95% confident that the true mean number of televisions per American household is between 1.15 and 4.20.
c. 95% of all samples should have x-bars between 1.15 and 4.20 televisions.
d. 95% of all American households have between 1.15 and 4.20 televisions
e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the population mean.
f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the sample mean.
Answers
Answer:
a. False
b. True
c. False
d. False
e.True
f. True
Step-by-step explanation:
The 95% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 95% confidence that the number of televisions per American household is between 1.15 to 4.20.