To find the length of the curve c parameterized by given equations, we differentiate these equations with respect to t, find the magnitude of the derivative vector, and integrate this magnitude from t = 0 to t = 2.
Explanation:Finding the Length of Parametrized CurveTo find the length L of a curve c parametrized by x = et sin(10t) and y = et cos(10t) for 0 ≤ t ≤ 2, we use the formula for the arc length of a curve given in parametric form. The formula is L = ∫ |c'(t)| dt, where |c'(t)| represents the magnitude of the derivative of the parametric equations. The integral is evaluated over the given interval of t.
Step-by-step ExplanationFirst, compute the derivatives of the parametric equations: dx/dt and dy/dt.Next, find the magnitude of the velocity vector |c'(t)| = sqrt((dx/dt)^2 + (dy/dt)^2).Finally, integrate |c'(t)| from t = 0 to t = 2.Using this approach, we find that the length L of the curve c over the interval from 0 to 2 is indeed 2, as verified by the calculus of parametric functions.
Write four decimals with the digit four in a different place in each ones, tenths , hundredths, and thousandths .Then write a statement that compares the value of the digit 4 in the different decimals
the change in the x-coordinates of any two points on a line in the xy-plane is the
Answer
D the run. AP3X
write 91.4 million in both standard form and in scientific notation
91.4 million in standard form is 91400,000.
To express 91.4 million in standard form,
We simply write the number as it is: 91,400,000.
In this form, each place value is clearly represented by its corresponding digit.
In scientific notation, we express the number as a product of a decimal number between 1 and 10, multiplied by a power of 10. For 91.4 million,
It can be written as 9.14 x 10⁷.
In this notation, the decimal point is placed after the first digit, and the power of 10 represents the number of places the decimal point should be moved to the right to obtain the original value.
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What is 1/5 + 2/3 plz answer this
solve 3x=12? 5,36,4,or 3
The ratio of red poms to yellow poms on a float is 5 to 7. If there are 392 yellow poms on the float, how many red poms are there? *
In the fiscal year of 1991-1992, a total of 109,782 child labor permits were issued, 2/3 of which were males. The monthly average for males is?
Final answer:
The monthly average for males who received child labor permits in the fiscal year of 1991-1992 is approximately 6,099, calculated by multiplying the total permits (109,782) by 2/3 and then dividing by 12 months.
Explanation:
To calculate the monthly average for males who received child labor permits in the fiscal year of 1991-1992, we first determine the total number of permits issued to males. Since 2/3 of the total permits were issued to males, we multiply the total number of permits, 109,782, by 2/3:
Total permits for males = 109,782 * (2/3) = 73,188
There are 12 months in a fiscal year, so to find the monthly average, we divide the total permits for males by 12:
Monthly average for males = 73,188 / 12 ≈ 6,099
Therefore, the monthly average number of child labor permits issued to males was approximately 6,099.
the back of a moving truck is 4 feet above the ground. A ramp extending from the back of the truck meets the ground 10 feet from the truck. What is the slope of the ramp?
Answer:
20 feet
Step-by-step explanation:
A construction crew needs to build a road that will be 20 miles long. The crew already completed a stretch that is 6.44 miles long and another that is 8.62 miles long.
How much more road does the construction crew need to build?
(A) 2.18 miles
(B) 4.94 miles
(C)11.38 miles
(D)13.56 miles
Ava's heart rate is 65 beats per minute. If this is her average heart rate, how many times will her heart beat in 10 years.
Answer:
Ava's heart will beat for 341640000 beats in 10 years.
Step-by-step explanation:
Heart rate of Ava is = 65 beats per minute
We have to calculate the heart beat in 10 years.
Since Ava's heart beats in 1 minute = 65 times
Heart beat in 1 hour = 65 × 60
= 3900 beats
Heart beats in 24 hours or one day = 3900 × 24
= 93600 beats
Heart beats in 365 days or 1 year = 93600 × 365
= 34164000 beats
Heart beats in 10 years = 34164000×10
= 341640000 beats
Therefore, Ava's heart will beat for 341640000 beats in 10 years.
A person's blood glucose level and diabetes are closely related. let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean m 85 and standard deviation s 25 (diagnostic tests with nursing implications, edited by s. loeb, springhouse press). note: after 50 years of age, both the mean and standard deviation tend to increase. what is the probability that, for an adult (under 50 years old) after a 12-hour fast,
What is the constant of proportionality for the ratios 2 to 3 and 4 to 6?
Answer:2/3
Step-by-step explanation:
How do you find the corresponding ordered pair of f(23)=2?
The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting
Answer:
the rate is equal to [tex]3.2\frac{inches}{week}[/tex]
Step-by-step explanation:
we have
[tex]h-15=3.2t[/tex]
where
h is the height of a plant
t is the number of weeks after planting
so
Find the rate at which the plant's height is increasing
we know that
The given formula is a linear equation
The rate is equal to the slope of the linear equation
Isolate the variable h
[tex]h=3.2t+15[/tex]
the slope is equal to [tex]m=3.2\frac{inches}{week}[/tex]
therefore
the rate is equal to [tex]3.2\frac{inches}{week}[/tex]
The height was 31 inches in (D) Some time between 3 and 7 weeks.
To find out when the height of the plant was 31 inches using the formula given, we start with the equation:
h - 15 = 3.2t
We want to find the value of ( t ) when the height ( h ) is 31 inches. First, substitute ( h ) with 31 in the equation:
31 - 15 = 3.2t
Now, simplify the left side:
16 = 3.2t
Next, divide both sides by 3.2 to isolate ( t ):
t = [tex]\frac{16}{3.2}[/tex]
Calculating this gives:
t = 5
Therefore, the height of 31 inches was reached at 5 weeks.
So, the answer is: D. Some time between 3 and 7 weeks.
The full question is:
The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting
When was the height 31 inches?
A. Some time between 11 and 18 weeks
B. Some time between 7 and 12 weeks
C. Some time between 6 and 10 weeks
D. Some time between 3 and 7 weeks
Help!!!!!!
A sporting goods store marks up the cost s of soccer balls by 250%. Write an expression that represents the retail cost of the soccer balls. The store buys soccer balls for $5.00 each. What is the retail price of the soccer balls?
(you have to do a expression)
Spring stretches by 21.0 cm when a 135 n object is attached. what is the weight of a fish that would stretch the spring by 62.1
Answer:
399.21 newtons or 40.73 kg
Step-by-step explanation:
In order to solve this you first have to do a rule of threes to calculate how much would the fish will weight compared with the stretching of the spring:
[tex]\frac{21}{162} =\frac{62.1}{weight} \\weight=\frac{62.1*162}{21}=399.21 Newtons[/tex]
So the weight would be 399.21 newtons and it would have 40.73 kilograms in mass.
Two well-known aviation training schools are being compared using random samples of their graduates. it is found that 70 of 140 graduates of fly-more academy passed their faa exams on the first try, compared with 104 of 260 graduates of blue yonder institute. in a two-tailed test, the p-value is .0275, so at = .025 we should:
Final answer:
With a p-value of .0275 being greater than the significance level of .025, the decision in a two-tailed test would be to not reject the null hypothesis, indicating insufficient evidence to show a significant difference between the two schools' FAA exam pass rates.
Explanation:
The student is given information about the performance of the graduates from two aviation training schools regarding FAA exam pass rates on the first try. The pass rates are compared using a statistical hypothesis test, and the p-value from this test is .0275. When the level of significance (α) is set at .025, and we are conducting a two-tailed test, we should make a decision about whether to reject or not reject the null hypothesis.
Since the p-value (.0275) is greater than the level of significance (α = .025), the correct decision would be not to reject the null hypothesis. It means that there's not enough statistical evidence to show a significant difference between the FAA exam pass rates of the two schools at the .025 level of significance. This matches the general hypothesis testing rule: if the p-value is less than α, reject the null hypothesis; otherwise, do not reject it.
In the marching band at Hometown High, there are 77 woodwinds and 88 brass. If there is an equal number of woodwind and brass musicians in each row, what is the greatest number of rows in a performance? A) 9 rows B) 11 rows C) 13 rows D) 15 rows
An integer is 1 less than twice that of another. If their sum is 20, find the integers
Answer:7,13
Step-by-step explanation:
Order the fractions from least to greatest 5/8, 3/4, 1/2, 9/16
In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. Three of the 8 are in one family, and want to sit together. How many ways can this happen?
Since 3 members want to sit together, we'll calculate total ways for it and then for remaining seats in each of its case, we'll see in how many ways can those rest of 5 people wants to sit.
The total number of ways those 8 people can sit is 3,991,680 ways.
Given that:Total 14 seats are there in a row in a doctor's waiting room.8 people are waiting to be seated.3 people are of same family and want to sit together.To find:In how many ways can those people sit?
Number of ways in which 3 family members can sit:Since 3 people wants to sit together, then suppose seats are numbered 1,2,3,...,14.
Then those 3 people can choose seats as:
1,2,3
2,3,4
...
...
12,13,14
Total 12 ways.
In each way, those three can sit on those 3 chairs in any order. The number of ways 3 people will arrange themselves is 3! = 6 ways.
Thus:
Total ways those 3 people can sit in = 12 times 6 = 72 ways.
( i did multiplication since for each of 3 seat chosen they were sitting in 6 ways, and this repeated 12 times would end up on 12 times 6 = 72 ways).
Number of ways those remaining 5 people can sit on remaining 11 seats:On remaining seats (14-3 = 11), we have 5 people to sit.
Those people can choose any seat they want to sit on.
Total ways(combinations) they together choose 5 seats is given by: [tex]^11C_5 = 462 [/tex]
For each of those choice of seats, they can arrange themselves in 5! = 120 ways.
Thus, those 5 people can sit in 120 times 464 = 55440 ways.
Since on each choice of those 3 family members , we have 55440 ways of 5 people sitting on remaining 11 seats, thus in total we have:
55440 times 72 = 3,991,680 ways.
Thus, in total, those 8 people can sit in 3,991,680 number of ways in that row of the doctor's waiting room.
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The Museum of Science in Boston has an exhibit in which metal balls drop down a chute, bounce around, and wind up in one of 21 bins. After 1000 balls have dropped, the heights within the bins clearly follow a bell-shaped curve. The standard deviation is 3 bins.
About how many balls are in bins 1 through 17?
Using the Empirical Rule, we can estimate that about 95% of the balls (950 balls) will fall within the first 17 bins of the bell-shaped distribution, with a standard deviation of 3 bins.
To determine how many balls are in bins 1 through 17 at the Museum of Science in Boston, we can apply the Empirical Rule to the bell-shaped distribution of balls in bins.
Since we have a standard deviation of 3 bins, and a bell-shaped curve approximates a normal distribution, about 95% of the data (balls) will be within two standard deviations of the mean.
Assuming approximately equal distribution across the bins and a large number of trials, bins 1 through 17 would contain slightly less than 95% of the balls, as they represent less than two standard deviations from the mean.
Here is a rough estimate:
Total balls: 1000
Two standard deviations: 95% of 1000 balls = 950 balls
Bins 1 through 17 contain slightly less than 950 balls.
Without the exact mean, we cannot provide a precise number, but we can conclude that about 950 balls will be distributed in bins 1 through 17, give or take, based on the data provided and properties of the normal distribution.
How would you Evaluate. 5⋅4 ^0
1.all real numbers that are less than -3 or greater than or equal to 5
A.x < -3 or x≥5
B.x < 5 or x ≥-3
C.x ≤ -3 or x >5
D.x ≤-3 or x ≤ 5
2.The time a cake must bake is between 25 minutes and 30 minutes, inclusive.
A.25 < x < 30
B.25 ≤ x ≤ 30
C.25 ≤x ≥ 30
D.25 < x > 30
3. Solve. 5 < x -2 <11
A.5 < x < 11
B.7 < x < 13
C.7 < x < 11
D.5 < x < 16
4. Which graph shows the solution of 9 - c < 2 or -3c > 15?
1 is a
2 is b
3 is b
hope it helped
1.5 4.5 13.5 40.5.... what is the seventh term in the sequence?
The seventh term in the sequence is 1093.5.
What is Sequence?A sequence in mathematics is a ordered set od objects or numbers which are related with something.
For example, 1, 3, 5, ..... is a sequence of odd numbers.
Given sequence is,
1.5, 4.5, 13.5, 40.5....
There must be a predictable relation between the numbers in order for them to form in a sequence.
It is clear that,
First term = 1.5
Second term = 3 × 1.5
Third term = 3 × 3 × 1.5 = 1.5 (3)²
............
nth term = 1.5 (3)ⁿ⁻¹
seventh term = 1.5 (3)⁷⁻¹ = 1.5 (3)⁶ = 1093.5
Hence the seventh term is 1093.5.
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Suppose w=xy+yzw=xy+yz, where x=e2t, y=2+sin(4t)x=e2t, y=2+sin(4t), and z=2+cos(5t)z=2+cos(5t).
a. use the chain rule to find dwdtdwdt as a function of x, y, z, and t. do not rewrite x, y, and z in terms of t, and do not rewrite e2te2t as x.
To find dw/dt for w = xy + yzw, we use the chain rule, yielding dw/dt = y(dx/dt) + x(dy/dt) + z(dz/dt) + y(dy/dt) + z(dy/dt). The derivatives dx/dt, dy/dt, dz/dt are calculated using derivative rules. The question-specific parameters are then substituted back into these functions.
Explanation:Let's denote w as a function of x, y, and z, where x, y, and z are functions of t. We will use the chain rule to find dw/dt as a function of x, y, z, and t.
Given the function: w = xy + yzw, using the chain rule, we get the derivative dw/dt as:
dw/dt = x * dy/dt + y * dx/dt + y * dz/dt + z*dy/dt + z * dy/dt = y(dx/dt) + x(dy/dt) + z(dz/dt) + y(dy/dt) + z(dy/dt)
To particularize this expression for our given parameter values, we need to find dx/dt, dy/dt, and dz/dt. Each derivative can be calculated using the derivative rules. In this case we are to leave the equations x=e^2t, y=2+sin(4t), z=2+cos(5t) as they are, not rewriting them in terms of t, and also not rewriting e^2t as x. This results in dw/dt as a function of x, y, z, and t.
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What's the circumference of a circle with a diameter of 30 cm
A grocer has two kinds of tea, one selling for 80 cents per pound and the other selling for 60 cents per pound. How many pounds of each kind must he use to make 50 pounds of tea that will sell for 74 cents per pound?
Answer, There is need to use 35 pounds of 80 cents tea and 15 pounds of the 60 cents tea.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
here, we have,
Imagine what x is tea grocer selling for 80 cents per pound
y is tea grocer selling for 60 cents per pound
{80x+60y
=50*74
=3700
{x+y=50 //*60
{80x+60y=3700
-{60x+60y=3000
20x=700
x=35
y=50-35=15
hence, Answer, There is need to use 35 pounds of 80 cents tea and 15 pounds of the 60 cents tea.
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If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 36 inches, what diameter pizza will reward you with the largest slice? in
We start by expressing the circumference and the size of the slice in terms of the pizza's radius. By setting the pizza slice to be the largest (having an angle of 2π at the centre), we find the radius and hence the diameter of the pizza.
Explanation:The question falls into the area of Circle Geometry. Let's say the radius of the pizza is r inches, the length of the crust is a, and the length of the two straight edges of the pizza slice (each of which is a radius of the circle) are both r.
According to the problem, the perimeter of the pizza slice is given as 36 inches. This sums up the two radii and the length of the crust (a). Therefore, 2r + a = 36.
We know that the crust's length is a fraction of the total circumference of the circle. The whole circle's perimeter is 2πr.
Assuming the angle at the center of the pizza slice is θ (in radians), we have a = θr. θ will be a fraction of 2π depending on the size of the slice.
Substituting θr for a in the equation 2r + a = 36, we get 2r + θr = 36. To get the largest slice, θ has to be as large as possible, 2π.
Replace θ with 2π, we have 2r + 2πr = 36. Solve for r and we find that r = 36/(2+2π). That gives the radius of the pizza. Multiply r by 2 will give us the diameter of the pizza.
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Pizza planet is running a special: 3 pizzas for $16.50. What is the unit rate for one pizza?
Answer:
$5.5
Step-by-step explanation:
16.5 ÷ 3= 5.5