Parameterize the line segment (call it [tex]C[/tex]) by
[tex]\vec r(t)=(1-t)(4,4,2)+t(5,8,-4)=(4+t,4+4t,2-6t)[/tex]
with [tex]0\le t\le1[/tex]. Then the line integral of [tex]\vec f(x,y)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k[/tex] is
[tex]\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^1(4+4t,4+t,3)\cdot(1,4,-6)\,\mathrm dt=\int_0^1(2+8t)\,\mathrm dt=6[/tex]
Final answer:
To evaluate the line integral of the given vector field along the line segment, parametric equations are established, and the integral is simplified to a single-variable integral, resulting in a value of 12.
Explanation:
To evaluate the line integral of f=yi+xj+3k along the segment from (4,4,2) to (5,8,-4), first we find parametric equations for the line segment. The parametric equations are x=4+t, y=4+4t, z=2-6t, where t varies from 0 to 1. We then express the vector field in terms of t, yielding f(t) = (4+4t)i + (4+t)j + 3k. The derivative of the vector position is dr/dt = i + 4j - 6k. The line integral becomes an integral with respect to t, from 0 to 1, of the dot product of f(t) and dr/dt, which simplifies to ∫(8 + 52t - 18)dt = ∫(44t - 10)dt.
Integrating from 0 to 1 gives the final answer as 22 - 10 = 12. This approach demonstrates how converting a line integral into a single-variable integral simplifies the calculation.
Which of the following best describe a parabola
Answer:
Option B
Step-by-step explanation:
We know that a parabola is a set of points that are equidistant from a given line, which is the directrix, and a given fixed point called the focus.
So the correct option is option B.
Answer: Option 'B' is correct.
Step-by-step explanation:
Parabola is a curve in which any given point is at equal distance from focus i.e. a fixed point and directrix i.e. a fixed line.
So, it is the set of all points forming the curve that is equidistant from a single point and a single line.
Hence , option 'B' is correct.
3. For the following geometric sequence, determine a1 and r and find an explicit formula for the sequence: 2, -6, 18, -54…
a. What is a1?
b. What is the common ratio r?
c. Write an explicit formula for an using the formula for geometric sequences an = a1*(r)n – 1.
Step-by-step explanation:
a1 is the first term. In this case, 2.
r is the common ratio. Each term is multiplied by -3 to get the next term, so r = -3.
an = 2 (-3)ⁿ⁻¹
The table shows values for functions f(x) and g(x). What are the known solutions to f(x) and g(x)? Select each correct answer. 1, 3, 7, 9, 11
Answer:
3, 7
Step-by-step explanation:
Since we are asked for the known solutions to f(x) = g(x), we need to consider the values of the functions where x's are the same.
If you look at the table, you will see that f(-9) = g(-9) = 3 and f(2) = g(2) = 7.
The value of x where f(x) = g(x) is 3
Functions and valuesAccording to the given question, we are to find the value of x for which the function f(x) is equal to g(x)
From the given table, we need to find the point where the values of f(x) = g(x). The value of x at this point is the solution.
Therefore from the table, the value of x where f(x) = g(x) is 3
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what is the percent increase from 25 to 500
Answer:
200
Step-by-step explanation:
25 is 1/4 of 100. 25 x 4 = 100. 100 x 5 = 500
If a diameter of a cylinder is 5 yd and the height is 8 yd what is the volume?
Answer:
[tex]\large\boxed{V=50\pi\ yd^3\approx157\ yd^3}[/tex]
Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have the diameter d = 2r = 5yd → r = 2.5yd and the height H = 8yd.
Substitute:
[tex]V=\pi(2.5)^2(8)=\pi(6.25)(8)=50\pi\ yd^3\\\\\pi\approx3.14\to V\approx(50)(3.14)=157\ yd^3[/tex]
Need help on these four and then I am done, please help, I'm slowly getting the hang of it, I've already done all the other ones!
For #11, the answer is C, I’m pretty sure.
For #12, KM = LN, and LM = KN.
I can’t help with the others though, sorry :/
Correlation Coefficients. If the formula _____ were used to find the r-value of the following data, what would be the value of y?
A. 5
B. 9.
C. 7
D. 3
Answer: 0.9839
Step-by-step explanation:
X Values
∑ = 15
Mean = 3
∑(X - Mx)2 = SSx = 10
Y Values
∑ = 35
Mean = 7
∑(Y - My)2 = SSy = 50
X and Y Combined
N = 5
∑(X - Mx)(Y - My) = 22
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 22 / √((10)(50)) = 0.9839
Meta Numerics (cross-check)
r = 0.9839
Answer:
C. 7Step-by-step explanation:
According to the problem, we have to find [tex]y[/tex] which refers to the mean of y-values.
So, we just have to find the mean:
[tex]y=\frac{3+5+6+9+12}{5}=\frac{35}{5}=7[/tex]
Therefore, the right answer is C.
Remember that the mean is defined as the quotient betwene the sum of all values, and the total number of them. In this case, the sum is 35 and the total number is 5.
Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1?
a. f(x) = (x + 7)(x – i)(x + 5)(x + i)
b. f(x) = (x – 7)(x – i)(x – 5)(x + i)
c. f(x) = (x – (7 – i))(x – (5 + i))(x – (7 + i))(x – (5 – i))
d. f(x) = (x + (7 – i))(x + (5 + i))(x + (7 + i))(x + (5 – i))
Answer:
C. [tex]f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))[/tex]
Step-by-step explanation:
We want to find the equation of a polynomial the following properties;
i. Leading coefficient is 1
ii. roots (7 + i) and (5 – i) with multiplicity 1
Recall the complex conjugate properties of the roots of a polynomial.
According to this property, if
[tex]a+bi[/tex] is a root of a polynomial, then the complex conjugate, [tex]a-bi[/tex] is also a root.
This means that:
(7 - i) and (5 + i) with multiplicity 1 are also roots of this polynomial.
The complete set of roots are:
[tex]x=(7+i),x=(7-i),x=(5-i),x=(5+i)[/tex]
Therefore the polynomial is:
[tex]f(x)=(x-(7-i))(x-(5+i))(x-(7+i))(x-(5-i))[/tex]
The correct choice is C.
Final answer:
The correct polynomial function with roots (7 + i) and (5 – i), each with multiplicity 1 and a leading coefficient of 1, is given by (c) f(x) = (x – (7 + i))(x – (5 – i))(x – (7 - i))(x – (5 + i)).
Explanation:
The question asks which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1. For a polynomial to have these roots, its conjugates, (7 - i) and (5 + i), must also be roots because complex roots always come in conjugate pairs if the polynomial has real coefficients.
This leads us to option (c) as the correct answer. To form a polynomial with these roots, we take each root, turn it into a binomial by subtracting it from x, and then multiply these binomials together.
Doing so for the given roots, we get:
f(x) = (x – (7 + i))(x – (5 – i))(x – (7 - i))(x – (5 + i))
This polynomial matches option (c), confirming it as the correct answer.
Two forces act on an object. The first Force has a magnitude of 400 Newtons and acts at an angle of 30 degrees as measured from the horizontal. Second Force has a magnitude of 280 Newtons in accident angle of 135 degrees is measured from the horizontal. Determine the vector v that represents the resultant Force.
a. v=(200-140rtsq2)i+(200rtsq3+140rtsq2)j
b. v=(200+140rtsq2)i+(200rtsq3+140rtsq2)j
c. v=(200rtsq3+140rtsq2)i+(200+140rtsq2)j
d. v=(200rtsq3-140rtsq2)i+(200+140rtsq2)j
ANSWER
Option D is correct
EXPLANATION
We resolve the forces into component forms.
[tex]F_1 = 400 \cos(30) i + 400 \sin(30) j[/tex]
[tex]F_1 = 200 \sqrt{3} i +200j[/tex]
Also the second is resolved to obtain,
[tex]F_2= 280 \cos(135) i + 280 \sin(135) j.[/tex]
[tex]F_2= - 140 \sqrt{2} i + 140 \sqrt{2} j[/tex]
To find the resultant vector, V, We add the corresponding components of the two forces to get:
[tex]V=F_1+F_2 [/tex]
[tex] \implies \: V = (200 \sqrt{3} - 140 \sqrt{2} )i + (200 + 140 \sqrt{2})j[/tex]
The correct answer is D.
The sum of two numbers is 57, and their difference is 27. What are the two numbers?
Answer:
Answer: x = 32, y = 25
Step-by-step explanation:
You can write 2 equations that meet the criteria:
The sum of two numbers is 57
x + y = 57
The difference is 7
x - y = 7
Solve the second equation for x, and substitute in the first equation to solve for y
- solve the second equation for x.
Add y to both sides of the equation
x - y + y = 7 + y
x = 7 + y
- substitute x = 7 + y into the first equation
x + y = 57
(7 + y) + y = 57
7 + 2y = 57
Subtract 7 from both sides of the equation
7 - 7 + 2y = 57 - 7
2y = 50
Divide both sides of the equation by 2 to solve for y
y=25
Insert y = 25 into either equation and solve for x
x - y = 7
x - 25 = 7
Add 25 to both sides of the equation
x - 25 + 25 = 7 + 25
x = 32
Answer: x = 32, y = 25
As a check, plug these values into both equations to make sure that it works
One card is selected at random from a deck of cards. Determine the probability that card selected is a 5 or a 10?
Answer:
0.5
Step-by-step explanation:
because while solving a probability question you divide it by thee full number
A farmer has a square field that measures 100 yards on side. The field had a watering system that sweeps a large circle from the center of the field. The arm of the watering system is 50 yards long. What percentage of the field is watered?
Answer:
hdndhehhe
Step-by-step explanation:
shshheheuesuusuausshhshshshshshhehshshsgshshshshsh I just do it for points lol hahahdjejejdbjejdjrjdjdjfjfkskdkdnfnjjjjdhdhdhdhjdjdjjdjfjfdjsjdjfjdjfjfjjfjfisndjfbsisbiabsiwhwiwu2828akbdidbsjdiebeieheieb POINTS HAHA LOLPlease answer fast!!! Will give brainliest!!!
Given: m HL =40°, m EV =130°, m VL =110°. Find: m∠EYH.
Answer:
The measure of angle EYH is [tex]25\°[/tex]
Step-by-step explanation:
step 1
Find the measure of arc EH
we know that
[tex]arc\ EV+arc\ VL+arc\ HL+arc\ EH=360\°[/tex] ----> by complete circle
substitute the given values
[tex]130\°+110\°+40\°+arc\ EH=360\°[/tex]
[tex]280\°+arc\ EH=360\°[/tex]
[tex]arc\ EH=360\°-280\°=80\°[/tex]
step 2
Find the measure of angle EYH
we know that
The measurement of the outer angle is the semi-difference of the arcs which comprises
[tex]m<EYH=\frac{1}{2}(arc\ EV-arc\ EH)[/tex]
substitute the values
[tex]m<EYH=\frac{1}{2}(130\°-80\°)=25\°[/tex]
The Mitchells are renting a boat for the day. It costs $100, plus $20 for each hour. They have to pay for a whole hour even if they are not out there for a whole hour. For example if they boat for 3 and a half hours, they have to pay for 4 hours. They don't want to spend more than $250 for the day. How many hours can they boat? Write an inequality and solve. A)100 + 20x ? 250. They can boat for 7 hours. B)100 + 20x ? 250. They can boat for 8 hours. C)100 + 20x ? 250. They can boat for 8 hours. D)100 + 20x ? 250. They can boat for 7 hours.
Your answer would be C.
Step-by-step explanation:
250 dollars. 250-100= 150. 150/20 equls 7.5. 7.5 will round to 8. It iwll be 8 hours hey will have to pay for.
the number line shows the record low temperatures for four states Hawaii 12 degrees Fahrenheit North Carolina -38 degrees Fahrenheit South Dakota -58 degrees Fahrenheit and Montana -70 degrees farenhight enter the difference in degrees between the record low temperatures in Hawwaii and South Dakota
Answer: -70 degrees difference
Step-by-step explanation:
Answer:
-70!!
Step-by-step explanation:hope this helped!
Please help me out please
Answer:
98
Step-by-step explanation:
If half the diagonal is 7 yd, then the full diagonal is 14 yd.
If we call the side length s, then using Pythagorean theorem:
c² = a² + b²
(14)² = s² + s²
196 = 2s²
s² = 98
The area of a square is s², so:
A = s²
A = 98
The area is 98 yd².
which of the following is a point on the plane curved defined by the parametric equations?
x=4t
y=12t^2+4t-1
a. (4,7)
b. (4,207)
c.(-2,4)
d.(-2,0)
Answer:
d.(-2,0)
Step-by-step explanation:
The given parametric equation is:
[tex]x=4t[/tex]
[tex]y=12t^2+4t-1[/tex]
We make t the subject in the first equation;
[tex]t=\frac{x}{4}[/tex]
We substitute into the second equation to get:
[tex]y=12(\frac{x}{4})^2+4(\frac{x}{4})-1[/tex]
[tex]y=\frac{3}{4}x^2+x-1[/tex]
When x=4 , [tex]y=\frac{3}{4}(4)^2+4-1=15[/tex]
When x=-2 , [tex]y=\frac{3}{4}(-2)^2+-2-1=0[/tex]
Therefore the point (-2,0) lies on the given parametric curve.
Please answer I’ll rate brainlyest
Answer:
Marginal distribution of political party. Choice B
Step-by-step explanation:
The Democrat is a political party. The voters are registered as either, Democrats, Republicans or Others. This implies that a voter selected at random regardless of gender will either be a Democrat a Republican or affiliated to Other political parties.
Therefore, the percent of all voters that are registered Democrats is part of the marginal distribution of political party
What are the outputs of the following function?
{-3, 0, 1, 9}
{-3, -2, 0, 1, 9}
{-2}
{-3, -2}
Answer:
-2
Step-by-step explanation:
The output of the function shown is -2 for each of the four inputs.
Answer:
-2
Step-by-step explanation:
-2
please show me how to do this, I need to show work
Answer:
x ≈ 11.68 ( to 2 dec. places )
Step-by-step explanation:
Given
[tex]6^{(x-8)}[/tex] = 730 ( take log of both sides )
log [tex]6^{(x-8)}[/tex] = log730
(x - 8)log6 = log730 ( divide both sides by log6 )
x - 8 = [tex]\frac{log730}{log6}[/tex] ≈ 3.68 ( add 8 to both sides )
x ≈ 11.68 ( to 2 dec. places )
Answer:
6^ 3.679648309
Step-by-step explanation:
Don't really have one. Went with trial and error. Set calculator to 2 d.p by the way
5(y+1)-7 = 3(y-1)+2y
y = ?
Answer:
no solutionStep-by-step explanation:
[tex]5(y+1)-7=3(y-1)+2y\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\5y+5-7=3y-3+2y\qquad\text{combine like terms}\\\\5y+(5-7)=(3y+2y)-3\\\\5y-2=5y-3\qquad\text{subtract}\ 5y\ \text{from both sides}\\\\-2=-3\qquad\bold{FALSE}[/tex]
4. About 30% of the U.S. population is under 20 years old. About 17% of the population is over 60, which of the following is the probability that a person chosen at random is under 20 or over 60?
-17%
-53%
-47%
-30%
A = person is under 20
B = person is over 60
P(A or B) = P(A) + P(B) ... works because A and B are mutually exclusive
P(A or B) = 0.30 + 0.17
P(A or B) = 0.47 = 47%
The probability that a person chosen at random is under 20 or over 60 is 47% , option C is the correct answer.
What is Probability ?Probability is a topic in mathematics where the likeliness of an event is studied.
The range of probability is 0 to 1 .
0 indicates uncertainty to 1 indicating certainty.
It is given in the question that
30% of the U.S. population is under 20 years old
About 17% of the population is over 60
probability that a person chosen at random is under 20 or over 60 = ?
Let P(A) represents person under 20
Let P(B) represents person over 60
As a person is chosen at random and the events cannot happen together so they are mutually exclusive events.
The probability for mutually exclusive event is given by
P(A or B) = P(A) + P(B)
P(A) = 17% = 0.17
P(B) = 30% = 0.3
P(A or B) = 0.30 + 0.17
P(A or B) = 0.47 = 47%
Therefore , the probability that a person chosen at random is under 20 or over 60 is 47% , option C is the correct answer.
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Mary and her sister mona decide to rent a paddleboat for 2 hours at a total cost of $25 which statement describes the relationship
No hay relaion porque su hermana "mona", es su mascota
Which of the following correctly shows the length of each radius, the point where the circles intersect, and the equation of the tangent line at this point?
actually box 3 is correct.
because their radiuses are easy to find
but the tangent line is x=-4 or x=4
The option third radius for circle A is 4, the radius for circle B is 3 and the point of intersection is (4,3) and the tangent equation is x = 4 is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have two circles in the graph plot:
From the graph plot:
For the circle:A the radius is 4
For the circle:B the radius is 3
The point of intersection point (4, 3)
The tangent line will be:
x = 4
Thus, the option third radius for circle A is 4, the radius for circle B is 3 and the point of intersection is (4,3) and the tangent equation is x = 4 is correct.
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Write
3919
in expanded form.
Answer:
Expanded form means to write the standard form as an equation with addition
so, 3919 would be 3000 + 900 + 10 + 9
Step-by-step explanation:
[tex]\text{Hey there!}[/tex]
[tex]\text{Write 3,919}[/tex]
[tex]\text{Expanded form is where you basically when you write the numbers in a}[/tex] [tex]\text{individual formation (e.g. a + a + a + a)}[/tex]
[tex]\text{3 = 3,000 since it's in the THOUSANDS place}[/tex]
[tex]\text{9 = 900 since it's in the HUNDREDS place}[/tex]
[tex]\text{1 = 10 because it is in the TENS place}[/tex]
[tex]\text{9 = 9 because it is in the ONES place}[/tex]
[tex]\boxed{\boxed{\text{Answer: 3,000 + 900 + 10 + 9}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Write an equation for a cosine function with an amplitude of 3, a period of 2, a phase shift of -2, and a vertical displacement of 5.
y=3cos2π(x+2)+5
y=3cos2π(x−5)+2
y=5cos3π(x−2)+2
y=3cos2π(x+2) / 2+5
Answer:
Last option
[tex]y = 3cos(\pi(x+2)) + 5[/tex]
Step-by-step explanation:
The general cosine function has the following form
[tex]y = Acos(b(x-\phi)) + k[/tex]
Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.
[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.
k is the vertical displacement.
[tex]\phi[/tex] is the shift phase
In this problem :
[tex]A = 3[/tex]
[tex]\frac{2\pi}{b}=2\\\\ b=\frac{2\pi}{2}\\\\ b=\pi[/tex]
[tex]\phi =-2\\\\k = 5[/tex]
So The function is:
[tex]y = 3cos(\pi(x+2)) + 5[/tex]
Which of the following square root of -80
You can factor -80 as
[tex]-80 = (-1)\cdot 16 \cdot 5[/tex]
So, we have
[tex]\sqrt{-80} = \sqrt{(-1)\cdot 16 \cdot 5}[/tex]
The square root of a product is the product of the square roots:
[tex]\sqrt{-80} = \sqrt{(-1)}\sqrt{16}\sqrt{5}[/tex]
Since [tex]i^2=-1[/tex] and [tex]4^2=16[/tex], we have
[tex]\sqrt{-80} = 4i\sqrt{5}[/tex]
The equivalent expression of the complex expression √(-80) will be 4i√5. Then the correct option is C.
What is a complex number?A complex number is a number that is made up of both real and imaginary numbers. The complex number can be given as a + ib where a is the real part and ib is the imaginary part.
The expression is given below.
⇒ √(-80)
And we know that √(-1) = i
Then the expression can be written as
⇒ √(-1 x 16 x 5)
⇒ 4i√5
More about the complex number link is given below.
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use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
Answer:
Second Option
671 m²; 725 m²
Step-by-step explanation:
The lateral area of a triangular prism is:
[tex]A_L = Ph[/tex]
Where P is the perimeter of the triangular base and h is the height of the prism.
In this case, the perimeter of the triangular base is:
[tex]P = 9 + 6+ 10.82\\\\P = 25.82\ m[/tex]
Then the height is 26 m
Then the lateral area of the prism is:
[tex]A_L = 25.82 * (26)\\\\A_L = 671\ m ^ 2[/tex]
Therefore the surface area of the triangular prism is:
[tex]A = 2A_B + A_L[/tex]
Where [tex]A_B[/tex] is the area of the base.
[tex]A_B = \frac{bh}{2}[/tex]
Where b is the base of the triangle and h is the height
In this case:
[tex]b = 9\ m\\\\h = 6\ m\\\\A_B = \frac{9 * 6}{2}\\\\A_B = 27\ m ^ 2[/tex]
Finally
[tex]A = 2 * 27 + 671\\\\A = 54 + 671\\\\A = 725\ m ^ 2[/tex]
The answer is 671 m² and 725 m²
Answer:
[tex]671m^{2};725m^{2}[/tex]
Step-by-step explanation:
Sienna wants to set up a special fund so she can save to buy presents for her friends and family throughout the year. If her gift purchases last year totalled $580, estimate how much she should save each month to have approximately the same amount available for gifts next year? a. Approximately $480 b. Approximately $58 c. Approximately $48 . d. Approximately $96
Answer:
c. $48
Step-by-step explanation:
Answer:
C. Approximately $48
Step-by-step explanation:
Given,
Total amount she have to save this year = $ 580,
The number of months in a year = 12,
So, the amount saved by her in each month
[tex]=\frac{\text{Total amount}}{\text{Number of months}}[/tex]
[tex]=\frac{580}{12}[/tex]
= $ 48.333333..
≈ $ 48
Hence, OPTION C is correct.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Choose the correct formula for the function g.
Answer: C) g(x) = 2ˣ⁻³ + 2
Step-by-step explanation:
The general form of an exponential equation is: g(x) = 2ˣ⁻ᵃ + b where
"a" is a horizontal shift to the left if positive (or right if negative)"b" is a vertical shift up if positive (or down if negative)The new function is shifted UP 2 units and RIGHT 3 units
a = 3b = 2--> g(x) = 2ˣ⁻³ + 2