The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Now, According to the question:
600 [tex]u^2[/tex] of land to be enclosed by fence
Area inside plot should be maximized, amount of fence should be minimized
If we draw a quick sketch, we get something like this:
_____ _____
| | |
| | |
| | |
| | |
The two rectangles could be different sizes but if one rectangle size maximizes area then it would make sense to use that some rectangle for both sides.
Let's put some variables into our picture so we can define our constraints.
y y
| | |
x | x | x |
| | |
| | |
Now we just need an equation to connect our unknowns (how much fence to use) to our constraint (it has to have an exact area of 600 u^2.
A = x × 2y = area = 600
P = 3x + 4y = perimeter = a minimum
First we solve the area equation for y:
y = [tex]\frac{600}{2x}[/tex] = [tex]\frac{300}{x}[/tex]
and then we substitute that result into our perimeter equation:
P = 3x + 4 (300/x)
P = 3x + 1200/x
Our perimeter equation is: P(x) = 3x + 1200/x OR P(x) = 3x +1200[tex]x^-^1[/tex]
We can find what value of x makes our perimeter as small as possible (a minimum) by graphing or by using Calculus.
In Calculus we know that maximums and minimums always occur when the derivative is zero. This is because the slope (rate of change) at these points in a graph are always flat or zero. Our derivative is
P'(x) = 3 - 1200[tex]x^-^2[/tex]
When set equal to zero, we can solve for x:
3 - 1200[tex]x^-^2[/tex]= 0
1 - 400[tex]x^-^2[/tex] = 0
1 = 400/[tex]x^{2}[/tex]
[tex]x^{2}[/tex] = 400
x = ± 20
Our fence length can't be a negative number so our answer must be 20u.
If our x length is 20, then our y length must be 300/x to ensure our area is 600 u^2.
The y length is 300/(20) = 15
Let's put all of our numbers into our picture to see if it make sense.
15 15
| | |
20 | 20 | 20 |
| | |
| | |
15 15
Sure enough our area is 600.
Here's what we have right now:
A(20, 15) = 600
P(20, 15) = 120
How about we try something a little bigger like 20.5 for x and 14.63 for y?
A(20.5, 14.63) = 600
P(20.5, 14.63) = 120.02
How about we try something a little smaller like 19.5 for x and 15.38 for y?
A(19.5, 15.38) = 600
P(19.5, 15.38) = 120.02
It looks like if we try to change x, even a little, to make it bigger or smaller the perimeter only gets bigger.
You might have guessed at the beginning that a square is the best shape to use to maximize area, so let's try that as well.
Each rectangle is 300 u^2. We want a square so each side would be √(300) = 17.32
17.32 17.32
| | |
17.32 | 17.32 | 17.32 |
| | |
17.32 17.32
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Hence, The dimensions of the rectangular plot that require the least amount of fencing is :
A(17.32, 17.32) = 600
P(17.32, 17.32) = 121.24
Learn more about Rectangular plot at:
https://brainly.com/question/29173029
#SPJ4
If N sweaters can be made from x balls of wool, and the function N(x) = 20x - (10x + n) models the number of sweaters produced where n is a constant. If 500 balls of wool were used to produce 4000 sweaters, what is the value of n?
1)500
2) 1,000
3) 4,000
4) 5,000
15) 10,000
The value of n in the function is 1000
How to determine the value of n in the model function?
A model function is a way of describing a real-life system or situation using mathematical concepts and language
We have the function N(x) = 20x - (10x + n) models the number of sweaters produced where n is a constant.
Since 500 balls of wool were used to produce 4000 sweaters. To find the value of n, substitute x = 500 and N = 4000 into the function. That is:
N(x) = 20x - (10x + n)
4000 = 20(500) - (10(500) + n)
4000 = 10000 - 5000 - n
4000 = 5000 - n
n = 5000 - 4000
n = 1000
Learn more about model function on:
brainly.com/question/1415456
#SPJ1
Write an equation in point-slope form of the line that passes through the point (-9, 1) and has a slope of
2/3
Answer:
y-1=2/3(x+9)
Step-by-step explanation:
Sorry cant really explain well but I am positive this is the right answer.
a council has 6 men and 3 women. if we randomly choose two of them to co chair a committee, what is the probability these chairpersons are the same gender
There are a total of 9 women and 6 men on the council, for a total of 15 council members.
If we randomly choose 2 of them to co-chair a committee, the number of ways to choose 2 people of the same gender is:
The number of ways to choose 2 women out of the 3 women on the council is 3 choose 2 = 3.The number of ways to choose 2 men out of the 6 men on the council is 6 choose 2 = 15.
So the total number of ways to choose 2 people of the same gender is 3+15 = 18.
The total number of ways to choose 2 people without considering their gender is 15 choose 2 = 105
So the probability of choosing 2 people of the same gender is 18/105 = 6/35
So, the probability that these chairpersons are the same gender is 6/35.
Austin's brother loaned him $20 and asked him to pay him back in 3 months. He's going to charge 4% interest. Austin is excited about all extra money he will make in interest. Is is correct to be excited?
Answer:
Step-by-step explanation:
Yes, it is correct for Austin to be excited about the extra money he will make in interest. Interest is a common form of compensation for loaning money to another person, and it is generally expected to be paid back along with the principal amount. In this case, Austin will earn 4% interest on the $20 loan over the course of 3 months, which works out to be a total of $0.80. This is a relatively small amount, but it is still money that Austin would not have had if not for the loan. Therefore, it is reasonable for Austin to be excited about the opportunity to make a little extra money.
according to westgard and clia, how many specimens should be run by each method on the same day for 8 to 20 days to compare a test method with a comparative method?
According to Westgard and CLIA , 40-100 specimens should be run by each method on the same day for 8 to 20 days to compare a test method with a comparative method.
CLIA stands for Clinical Laboratory Improvement Amendments . The regulations under CLIA includes, the federal standards which is applicable to all U.S. facilities or sites which are test human specimens for health assessment or it is used to diagnose, prevent, or treat disease.
The Federal Register is the official daily publication for federal agencies and the organization's notices, proposed regulations, and final rules, as well as executive orders and other presidential papers. The regulations published in the Code of Federal Regulations and enforced by federal agencies are known as final rules.
To learn more about CLIA
brainly.com/question/29342147
#SPJ4
Can you guys help me to figure out the area and explain to me pls
Answer:
123.2
Step-by-step explanation:
First find area of the square ABCD, then the triangle AMN.
Find CD:
sin30 = CD/20
CD = 20(sin30) = 10
CD = AD = 10
Find MD:
cos30 = MD/20
MD = 20(cos30) = 17.32
AM = MD - AD = 17.32 - 10 = 7.32
Area of ABCD = (10)(10) = 100
Find height of triangle AMN: AN
cos30 = AN/7.32
AN = cos30(7.32) = 6.34
Area of triangle ANM = 1/2(7.32(6.34) = 23.2
Total Area of the shape = 100 + 23.2 = 123.2
A torch and a battery cost 2. 50 altogether. The torch costs 1. 50 more than the battery. What fraction of the total price is the torch?Give your answer in its simplest form
The fraction of the total price that the torch is is 4/5.
Let x be the cost of the battery.
We know that the torch cost is 1.50 more than the battery cost. So, the cost of the torch is
x + 1.50
The total cost is the sum of the cost of the battery and the torch, so:
x + (x + 1.50) = 2.50
2x + 1.50 = 2.50
Solving this equation we get,
x = 0.50
Therefore the cost of the battery is 0.50 and the cost of the torch is 2.00.
To find the fraction of the total price that the torch is, we divide the cost of the torch by the total cost:
= (2.00) / (2.50)
= 4/5
To know more on fraction
https://brainly.com/question/10354322
#SPJ4
A survey asked stamp collectors how many stamps they have in their collection. The box-and-whisker plot summarizes the responses. Between what 2 numbers do the middle half of the responses fall
Therefore , the solution of plotting data comes out to be each whisker has a crossbar at the very end that is optional and has no significance in terms of length.
What is data plotting?A graph illustrating the correlation between two extra variables is the most common way to present data using a chart. It is also permitted to use diagrams that were manually or digitally drawn. starting at the origin, go 3 units up, then 2 units to the right. It is necessary to display the numbers for the positions 2, 3, and 4 on the reference system. Make your points really clear. 2.3 is represented by the pinkish dot with letter P. For each value in a data collection, you must first create a number line before you can create a line chart.
Here,
The boxplot, in its most basic version, visualizes five sample statistics: the minimum, the smallest value, the mean, the upper quartile, and the maximum.
The plot's box is a rectangle with ends at each quartile that encloses the sample's middle half. Therefore, the box's length represents the sample's interquartile range.
Nothing specific is represented by the box's other dimension. At the sample median, a line is drawn from across box.
Up until they hit the sampling maximum and minimum, whiskers extend from the box's two ends.
Each whisker has a crossbar at the very end that is optional and has no significance in terms of length.
Therefore , the solution of plotting data comes out to be each whisker has a crossbar at the very end that is optional and has no significance in terms of length.
To know more about plotting data visit:
https://brainly.com/question/29096917
#SPJ4
which of the following statements is Incorrect.
Answer:
b
Step-by-step explanation:
de=40
Answer:
DE = 58 is the incorrect statement
please help.......................??
x axis described as the independent variable
What is horizontal line?
A horizontal line is a straight line that goes from left to right or right to left. In coordinate geometry, a line is said to be horizontal if two points on the line have the same Y- coordinate points. It comes from the term “horizon”. It means that the horizontal lines are always parallel to the horizon or the x-axis.A horizontal line is a line extending from left to right. When you look at the sunrise over the horizon you are seeing the sunrise over a horizontal line. The x-axis is an example of a horizontal lineA horizontal line is one that goes from left to right across the page. This is because horizontal lines are parallel to the horizon. This fact can help children to remember the meaning of horizontal lines. It comes from the word “horizon”, which refers to the visible line that separates the earth from the sky.To learn more about horizontal plane refers to:
https://brainly.com/question/17616298
#SPJ1
x-axis is the horizontal line dividing the plane into parts. The x-axis is also described as the abscissa and it used for independent variable.
Tell us about the horizontal line.A horizontal line is any straight path that runs from left to right or from right to left. In coordinate geometry, a line is said to be horizontal if two points on it have the same Y-coordinates. Its origins are in the term "horizon." In other words, the horizontal lines and the horizon, or x-axis, are always parallel.
A line that moves from left to right is said to be horizontally oriented. When you look beyond the horizon, you are seeing the dawn over a horizontal line. The x-axis serves as a representation of a horizontal line.
A horizontal line is one that extends from left to right across the full page. This is explained by the fact that horizontal lines are parallel to the horizon. By considering this fact, children can maintain the meaning of horizontal lines. Its root word, "horizon," refers to the line that may be seen separating the earth from the sky.
To learn more about horizontal plane refers to:
brainly.com/question/17616298
#SPJ1
How do I solve this?
The evaluation of the piecewise function gives:
when x = -3, f(x) = -4; when x = 2, f(x) = 0; and when x = 4, f(x) = 2.
when x = -3, w(x) = 2; when x = 2, f(x) = 5; and when x = 4, f(x) = 5
How to evaluate a piecewise function?A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.
We want to evaluate the piecewise function when x = -3, x =2 and x = 4:
{ -4, x < 2
f(x) = { x-2, -2 ≤ x≤ 4
{0 x > 4
when x = -3:
f(x) = -4 because x < 2 (i.e. -3 < 2)
when x = 2:
f(x) = x-2
f(2) = 2-2 = 0
when x = 4:
f(x) = x-2
f(2) = 4-2 = 2
{ -x - 1, x ≤ -3
w(x) = { 2x + 2, -3 < x < 2
{5, x ≥ 2
when x = -3:
w(x) = -x - 1
w(-3) = -(-3) - 1 = 2
when x = 2:
f(x) = 5
when x = 4:
f(x) = 5
Learn more about piecewise function on:
brainly.com/question/18499561
#SPJ1
For the function f(x) = 9/x-4, find f^(-1)(x).
Answer:
f
(
x
)
=
9
x
−
4
.
Step-by-step explanation:
The inverse of
f
(
x
)
=
9
x
−
4
is a function
g
(
x
)
such that
f
(
g
(
x
)
)
=
(
f
∘
g
)
(
x
)
=
x
but
f
(
g
(
x
)
)
=
9
g
(
x
)
−
4
=
x
The scatter plot above shows the average rent (in dollars) for a 111-bedroom apartment in New York City each year between 200020002000 and 201320132013. Which of the following is the best estimate of the average change in rent each year
The best estimate of the average change in rent each year include the following: C. $40.
How to determine the average change in rent each year?Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;
Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, m = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x on the scatter plot, which represents a line that is passing through the points (0, 800) and (10, 1200):
Rate of change, m = (1200 - 800)/(10 - 0)
Rate of change, m = 400/10
Rate of change, m = 40.
Based on the scatter plot, we can reasonably infer and logically deduce that the average rate of change in rent each year is equal to 40 dollars.
Read more on scatterplot here: brainly.com/question/28605735
#SPJ1
Complete Question:
The scatter plot below shows the average rent (in dollars per month) for a 1-bedroom apartment in New York City each year between 2000 and 2013.
Which of the following is the best estimate of the average change in rent each year?
answer choices
$0.5
$1
$40
$400
The area of a triangle is 2. Two of the side lengths are 6.6 and 1.1 and the
included angle is acute. Find the measure of the included angle, to the nearest
tenth of a degree.
Answer: 51.5 degrees
Step-by-step explanation:
The measure of the included angle is about 51.5 degrees. To find this, we can use the law of sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. So, we can set up an equation using the information given: (area)/(0.5*(1.1)(6.6)) = (sin(x)) where x is the included angle. We know that area is 2, so we can put it in the equation: (2)/(0.5(1.1)(6.6)) = (sin(x)) .
Then using sin(x) = 2/(0.5(1.1)*(6.6)) , we can use a calculator to find the sin(x) = 0.094.
and then using a calculator, we can find that x = sin^-1 (0.094) ≈ 5.2 radians. To convert it to degrees, we can multiply it by 180/π ≈ 57.3. So the measure of the included angle is about 57.3 degrees. To the nearest tenth of a degree, it is 57.3, but it can also be rounded off to 51.5 degrees.
How many right triangles have integer leg lengths a and b and a hypotenuse of length b 1, where b < 100
The possible number of the right triangle is 6. Hence option A is the correct option.
What is the right triangle?
A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
Given that △ABC is a right triangle.
The legs of the △ABC are a and b which are integers. The hypotenuse is b+1. Since b is an integer thus b+1 is an integer.
Pythagorean theorem:
The sum of the square of the legs of a right triangle is the square of the hypotenuse.
According to Pythagorean theorem,
a² + b² = (b+1)²
Applying the algebraic formula (a+b)² = a² + b² + 2ab
a² + b² = b² + 2b +1
Cancel out b² from both sides:
a² = 2b + 1
2b is always a positive number since 2 is multiplied with b. Thus 2b+1 is an odd number.
Since a² = 2b + 1, thus a² is an odd number.
The square of an odd number is an odd number. Thus a is an odd number.
Again given that,
b<100
2b < 200
2b + 1< 201
Putting 2b + 1 = a²:
a² < 201
Now putting a=1 in a² < 201:
1² < 201 (true)
Now putting a=3 in a² < 201:
3² < 201 (true)
Now putting a=5 in a² < 201:
5² < 201 (true)
Now putting a=7 in a² < 201:
7² < 201 (true)
Now putting a=9 in a² < 201:
9² < 201 (true)
Now putting a=11 in a² < 201:
11² < 201 (true)
Now putting a=13 in a² < 201:
13² < 201 (true)
Now putting a=15 in a² < 201:
15² < 201 (false)
If a = 1, 2b+1 = 1 which implies b = 0. The length of a side of a triangle is never zero. Therefore a ≠ 1.
Thus the possible values of a are 3,5,7,9,11,13.
To learn more about the sides of a right triangle, click on the below link:
https://brainly.com/question/9446948
#SPJ1
chord of a circle is 13.2 cm long and circles radius is 9.4 find the angle subtended by the chord at the centre of the circle
Answer:
To find the angle subtended by a chord at the center of a circle, we can use the formula:
θ = 2 * arcsin (c / 2r)
where θ is the angle subtended by the chord, c is the length of the chord, and r is the radius of the circle.
Step 1: Substitute the given values into the formula
θ = 2 * arcsin (13.2 / (2 * 9.4))
Step 2: Simplify the equation
θ = 2 * arcsin (13.2 / 18.8)
Step 3: Use a calculator or a math table to find the value of arcsin
arcsin (13.2 / 18.8) = 0.636 radians
Step 4: Multiply the value obtained by 2
0.636 * 2 = 1.27 radians
Final Answer: The angle subtended by the chord at the centre of the circle is 1.27 radians or 72.8 degrees
Answer:
ForTheTriangleABOtofindthelengthr
Wehave
sin(
2
α
)=
hypotenuse
opposite
=
OA
AB
=
9.4
6.6
=0.70212
whereAB=
2
13.2
=6.6cm
2
α
=sin
−1
(0.70212)
thenweoptain=
α=44.6°×2
=89.2°
The sum of the present ages of two teachers is 54 years. If the age of one teacher is 4 years more than the other, find their present ages. Algebra. please give full answer .
The present ages of the teachers are 25 and 29 years old.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
Given that sum of the present ages of two teachers is 54 years. If the age of one teacher is 4 years more than the other, then;
Let the ages of teachers are x and y
x + y = 54
x = 4 + y
So, 4 + y + y = 54
4 + 2y = 54
y = 25
x = 29
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ1
i have 18 distinguishable socks in my drawer: 8 white, 6 brown, and 4 blue. in how many ways can i choose a pair of socks, provided that i get two socks of the same color?
The required number of ways to choose a pair of socks, provided that i get two socks of the same color are 50.
What is combination?Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.
According to question:We have,
8 white, 6 brown, and 4 blue
So, We need to choose a pair of socks, provided that i get two socks of the same color.
The number of ways are;
Ways to choose 2 white = C(8,2) = 28
Ways to choose 2 brown = C(6,2) = 16
Ways to choose 2 blue = C(4,2) = 6
So
28 + 16 + 6 =
50 ways
Thus, required total number of ways are 50.
To know more about Combination visit:
brainly.com/question/20211959
#SPJ4
8. Two fair (balanced) coins are tossed. What is the probability (in lowest fractional
terms) of two heads?
F. 0
G.1/4
H. ½
J. 2
K. 1
Answer:
G.1/4
Step-by-step explanation:
The probability of getting two heads when two fair coins are tossed is 1/4 or 0.25. This is because for each coin there are two possible outcomes, heads or tails, and the probability of getting heads is 1/2. Therefore, the probability of getting two heads when both coins are tossed is (1/2) * (1/2) = 1/4. So the correct answer is G. 1/4
a rectangle has a length of 9 inches and a width of 5 inches whose sides are changing. the length is increasing by 3 in/sec and the width is shrinking at 5 in/sec. what is the rate of change of the perimeter?
If the length of the given rectangle is increasing by 3 in/sec and the width is shrinking at 5 in/sec then the rate of change of its perimeter is 4 in/sec.
Length, L = 9 inches
Width, W = 5 inches
The perimeter of the rectangle is
P = 2L + 2W.
By Differentiating both sides with respect to time t, we get
dP ⁄ dt = 2 × dL ⁄ dt + 2 × dW ⁄ dt
From the given conditions,
dL ⁄ dt = 3 and dW ⁄ dt = -5
So at the moment when L = 9 and W = 5,
dP ⁄ dt = (2)(3) + 2(−5 )
= 6 - 10
= -4
Therefore, The perimeter of the rectangle is decreasing at a rate of 4 in ⁄ sec.
To know more about perimeter, here
https://brainly.com/question/6465134
#SPJ4
a researcher plans to use a random sample of families to estimate the mean monthly family income for a large population. the researcher is deciding between a 95% confidence level and a 99% confidence level. compared to a 95% confidence interval, a 99% confidence interval will be...
Compared to a 95% confidence interval, a 99% confidence interval will be wider.
A confidence interval is a range of values that is likely to contain the true population mean, with a certain level of confidence.
The level of confidence is usually represented as a percentage, such as 95% or 99%. The higher the level of confidence, the wider the confidence interval will be. This is because a higher level of confidence means that the researcher wants to be more certain that the true population mean falls within the interval, so they will make the interval wider to increase the chances of this happening.
To know more on confidence interval
https://brainly.com/question/29680703
#SPJ4
If $m$ is a real number and $2x^2 mx 8$ has two distinct real roots, then what are the possible values of $m$
The possible values of [tex]$m$[/tex] are all real numbers greater than [tex]$\frac{2}{x^2}$[/tex]
A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. It is called a quadratic equation because the highest degree of its unknown variable (x) is two. The solutions of a quadratic equation can be found by solving the equation using the quadratic formula, factoring, or graphing. Quadratic equations are used in many areas of mathematics, from basic algebra to differential equations.
Let [tex]$y = 2x^2mx8$[/tex]
The two distinct real roots of the equation imply that y is a quadratic equation with two distinct real roots.
So,[tex]$y = 0 = 2x^2mx8 \implies 2x^2mx - 8 = 0$[/tex]
Using the quadratic formula , [tex]$m = \frac{8}{2x^2x}$[/tex]
The two distinct real roots of the equation imply that the discriminant of the quadratic equation, [tex]$\Delta = b^2-4ac$[/tex] is greater than 0.
So, [tex]$\Delta = (2x^2)^2-4(2)(-8) > 0 \implies 4x^4 + 64 > 0$[/tex]
[tex]$4x^4 > -64 \implies x^4 > -16$[/tex]
So, [tex]$m > \frac{8}{2x^2x} \implies m > \frac{8}{2x^2(-4)} = \frac{2}{x^2}$[/tex]
Hence, the possible values of m are all real numbers greater than [tex]$\frac{2}{x^2}$[/tex]
Learn more about quadratic equation here:
https://brainly.com/question/17177510
#SPJ4
Suppose an and bn are series with positive terms and bn is known to be convergent. (a) If an > bn for all n, what can you say about an? Why? O a n converges if and only if an < 2bn. Oman converges by the Comparison Test. O an diverges by the Comparison Test. We cannot say anything about an. o a n converges if and only if an 5 4bn. (b) If an
Nothing that we can say regarding an we are unsure of whether the terms of an are rising or falling, a passes the Comparison Test and sequence, Since bn, an also converges.
what is a sequence?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence.
We are unable to comment on an.
This is due to the fact that bn converges, causing a to exceed bn, and as a result, we are unable to determine whether the terms of an are increasing or decreasing.
What can you say about an if a bn for all n? a passes the Comparison Test and converges.
This is due to the fact that since bn converges and a converges since bn, we may infer that the terms of an are likewise decreasing and that an also sequence since bn based on the comparison test.
To know more about sequence visit:
https://brainly.com/question/21961097
#SPJ4
If −n Please answer fast!!!
hi
Step-by-step explanation:
Answer: If you are bored, try Khan Academy, or answer questions on brainly.
Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter your answer using interval notation.)r(t)=8t^2i+7t^3j
The curve is smooth for [tex]t\neq 0[/tex] on the intervals (-∞, 0), (0, ∞)
We have to consider the curve
[tex]r(t) = 8t^{2}i + 7t^{3}j[/tex]
Now, the objective is to find the open intervals when on which the curve given by the vector valued function is smooth, using the result.
The parametrization of the curve represented by the vector valued function
[tex]r(t) = f(t)i + g(t)j + h(t)k[/tex]
This equation is smooth on an open interval when f'(t), g'(t), and h'(t) are continuous on [tex]l[/tex] and r'(t) [tex]\neq[/tex] 0 for any value of t in the interval.
Now, we know the vector equation:
[tex]r(t) = 8t^{2}i + 7t^{3}j[/tex]
Differentiating r(t) with respect to r,
[tex]r'(t) = 16t i + 21t^{2} j[/tex]
At t = 0, equate r'(t) = 0.
[tex]r'(0) = 16(0) + 21(0)^{2}[/tex]
Therefore, the curve is smooth for all values except 0, as we can see above.
Hence, the curve is smooth for [tex]t\neq 0[/tex] on the intervals (-∞, 0), (0, ∞).
To learn more about smoothness of curves, visit the link:
brainly.com/question/28977975
#SPJ4
Can you help me with this
Step-by-step explanation:
what we see on the left side is that both terms contain (y + 6).
so, the left side is actually
(y + 6) × (x - 5)
therefore,
(x - 5)
is the missing factor on the right side.
he angles of a triangle haves measures of 80°, 75°, and (x-12)°. What is the value of x?
Using the triangle sum theorem, the value of x = 37.
How to Apply the Triangle Sum Theorem?The triangle sum theorem states that the sum of the three angles of a triangle is always 180 degrees.
The sum of the angles in a triangle is always 180 degrees, so we can use the triangle sum theorem to find the value of x.
So we can set up the following equation:
80 + 75 + (x - 12) = 180
80 + 75 + x - 12 = 180
Combine like terms:
x + 143 = 180
x = 180 - 143
x = 37
Solving for x, the value of x = 37
Learn more about the triangle sum theorem on:
https://brainly.com/question/25387605
#SPJ1
If h(x) = -x(1 - x), find h(-3).
Answer:
12
Step-by-step explanation:
h(-3)= -(-3)(1-(-3))=
3(4)=12
The value of a ring ($1000) increases exponentially so that it has a value of $3,000 after 5 years. Find the rate.
Answer: [tex]\sqrt[5]{3}-1[/tex]
Step-by-step explanation:
Let the annual rate of increase be [tex]r[/tex].
[tex]3000=1000(1+r)^5\\\\3=(1+r)^5\\\\\sqrt[5]{3}=1+r\\\\r=\sqrt[5]{3}-1[/tex]
the sum of twice a number, x, and 6 is equal to 4 more than the number, x. what is the vaule of x.
Answer:
2x+6=x+4
2x-x = 4-6
x= -2
Answer:
x=-2
Step-by-step explanation:
cuz , if u added them together the sum would be -2+6=4 , is that ur question? or I've answered smth that has nothing to do?
