The vector parametric equation for the line segment CC is <4,0> + t<-4,5>. The line integral of F⃗ along CC is 20. The line integral of F⃗ around the clockwise-oriented triangle with corners at the origin, P, and Q cannot be determined without additional information.
Explanation:(a) To find a vector parametric equation for the line segment CC, we can use the points P=(4,0) and Q=(0,5). We can represent the line segment CC as r(t) = <4,0> + t<-4,5>, where t is the parameter. This equation represents the line segment from P to Q, with t=0 corresponding to P and t=1 corresponding to Q.
(b) Using the parametrization in part (a), we can evaluate the line integral of F⃗ along CC. The line integral is given by ∫CF⃗ ⋅ dr⃗ = ∫baF⃗ (r⃗ (t))⋅r⃗ ′(t)dt. In this case, the line integral is ∫01-5yi⃗ +4xj⃗⋅-4i⃗ +5j⃗ dt
(c) Evaluating the line integral from part (b), we get 20.
(d) The line integral of F⃗ around the clockwise-oriented triangle with corners at the origin, P, and Q can be found using the Green's theorem. We can calculate it by subtracting the line integral along CP from the line integral along CQ. However, we would need more information to determine the path from C to the origin.
Katie works as a waitress and records her monthly tips in the table shown below. If Katie decided not to work the month of November, how would her five month average compare to her six month average for monthly tips? June July August Septemper October November $133.45 $235.31 $239.45 $258.87 $298.45 $115.67 a. Her monthly average would have decreased by $19.57. b. Her monthly average would have increased by $19.57. c. Her monthly average would have increased by $2.07. d. Her monthly average would have decreased by $2.07.
Answer:
Correct answer is B.) Her monthly average would have increased by $19.57.
Step-by-step explanation:
The true statement about her average monthly tip is (b) Her monthly average would have increased by $19.57.
What is average?The average of a dataset is simply the mean value or the expected value of the dataset
The table is given as:
June July August September October November
$133.45 $235.31 $239.45 $258.87 $298.45 $115.67
For the 6 months, the average is:
Average = (133.45+235.31+239.45+258.87+298.45+115.67)/6
Average = 213.53
For the 5 months (i.e. exclusive of December), the average is:
Average = (133.45+235.31+239.45+258.87+298.45)/5
Average = 233.10
The 5 months average is greater than the 6 months average.
And the difference (d) is:
d = 233.10 - 213.53
Evaluate
d = 19.57
Hence, Her monthly average would have increased by $19.57.
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Please answer this multiple choice question, will give brainliest!
Answer:
A angle V and angle Z
Step-by-step explanation:
Using the equilateral triangle's definition of all sides and angles are equal, we can determine that V, Z, and U are congruent.
Estimate the fractional part of the shaded portions below. Explain how you decided
Answer:
do you have a picture?
I can't tell you how I decided it because there's not a picture
If 1 4 of a gallon of milk is shared equally between 6 friends, how much milk will each friend have?
1 Gallon = 4 quarts of milk
1/4 = 1 quart of milk
4 quarts of milk = 8 pints of milk
8/6 = 1.33 pints of milk
Each friend has 1.33 pints of milk
Each friend will get 1/24 of a gallon of milk.
To find out how much milk each friend will have, we need to divide 1/4 of a gallon by 6.
how much milk each friend gets,
(1/4) ÷ 6
(1/4) × (1/6)
= 1/24
Therefore, each friend gets 1/24 of a gallon of milk.
In conclusion, if 1/4 of a gallon of milk is shared equally among 6 friends, each friend will have 1/24 of a gallon of milk.
A game company makes a board game that comes with 2 dice and a card game that comes with 3 dice. Which expression shows the total number of dice in b boxes for the board game and the card game?
Answer:
5
Step-by-step explanation:
3 + 2 = 5
The expression for the total number of dice in b boxes for both a board game, which comes with 2 dice, and a card game, which comes with 3 dice, is 5b. This is calculated by adding the number of dice in each box (2b for the board game and 3b for the card game).
Explanation:The question is asking for an expression that shows the total number of dice in b boxes of the board game and the card game. The board game comes with 2 dice and the card game comes with 3 dice.
To get the total number of dice, one needs to multiply the number of dice in each type of game by the number of boxes, b, and then add the results together.
The total number of dice in the board game is 2b and the total number of dice in the card game is 3b. The sum of these two amounts gives the total number of dice. So the expression for the total number of dice in b boxes of both games is 2b + 3b, which simplifies to 5b.
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Use a proportion or the Pythagorean Theorem to find y. If needed, estimate your answer to two decimal places.
Answer:
y ≈ 17.32
Step-by-step explanation:
The triangles are all similar, so you have ...
long-side/hypotenuse = y/(5+15) = 15/y
Cross-multiplying gives ...
y^2 = 15·20 = 300 . . . . . . . . take the square root to find y
y = √300 = 10√3 ≈ 17.32
Explain the difference between an absolute minimum and a local minimum. a function f has an absolute minimum at x = c if f(c) is the smallest function value on the entire domain of f, whereas f has a local minimum at c if f(c) is the smallest function value when x is near
c.
Answer:
Step-by-step explanation:
Absolute minimum is where, in the infinite domain of f(x), the least value the function is the absolute minimum.
However, the local minimum is only a specific interval on the domain of f(x) where the lowest value is, but only in that interval.
So, usually, this comes up when you're dealing with 1st and 2nd derivatives. The first derivative tells you where local max and mins are, where the 2nd derivative tells you if the concavity is up or down.
An absolute minimum is the lowest point on the entire domain of a function, while a local minimum is the lowest point in a specific interval or neighborhood around a point on the graph.
Explanation:
An absolute minimum and a local minimum are both points on a graph where the function reaches its lowest value, but there are key differences between them.
An absolute minimum is the lowest point on the entire domain of the function. In other words, it is the smallest function value among all the points.
On the other hand, a local minimum is the lowest point in a specific interval or neighborhood around a particular point on the graph. It is possible for a function to have multiple local minima.
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Eric practice piano and guitar for 8 hrs. He practiced piano for 1 fourth of 8 hrs. How many hours did Eric practice the piano this week?
➷ Multiply the total value by 1/4:
1/4 x 8 = 2
He practiced it for 2 hours.
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Answer:
2 hours.
Step-by-step explanation:
The time he practiced the piano = 1/4 * 8 = 2 hours.
The shapes of the horizontal cross-sections of the cone below are all congruent. True or false
Answer:
the answer is false
Step-by-step explanation:
False, The shapes of the horizontal cross-sections of the cone below are not all congruent.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We are given the statement,
'The shapes of the horizontal cross-sections of the cone are all congruent'.
Now, if we cut the cone horizontally, the cross-sectional shape is a 'circle'.
Further, the radius of the circle vary depending on the position form where the cone is cut i.e.
If cut from the top, the circle is approximately equal to a point.
If cut from the middle, the radius of the circle is less than the radius of the cone.
If cut from the bottom, the radius of the circle is equal to the radius of the cone.
Now, 'two figures are congruent if they overlap each other'.
Since, the circles have different radius, they will not overlap each other.
Thus, all the cross-sections of the cone would not be congruent.
Hence, the given statement is false.
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An engineering professor acquires a new computer once every 2 years. the professor can choose from three models: m1, m1, and m3. if the present model is m1, the next model can be m2 with probability .2, or m3 with probability .15. if the present model is m2, the probabilities of switching to m1 and m3 are .6 and .25, respectively. and, if the present model is m3, then the probabilities of purchasing m1 and m2 are .5 and .1, respectively. represent the situation as a markov chain.
Final answer:
The engineering professor's choice of new computer models over time can be modeled using a Markov chain, with specific transition probabilities for moving between models M1, M2, and M3. These probabilities are used to construct a transition matrix that allows us to analyze the selection pattern.
Explanation:
The scenario described can be represented as a Markov chain, which is a mathematical system that undergoes transitions from one state to another, with probabilities that are dependent on the current state only. Here, we have three models, M1, M2, and M3, which represent the states of the Markov chain. The transition probabilities define how likely it is to move from one state to another.
To construct this Markov chain, we set up a probability matrix P where the rows represent the current state, and the columns represent the next state. For the given model:
If the current model is M1, we have transition probabilities of 0.2 to M2 and 0.15 to M3.
If the current model is M2, we have transition probabilities of 0.6 to M1 and 0.25 to M3.
If the current model is M3, we have transition probabilities of 0.5 to M1 and 0.1 to M2.
Since the probabilities must add up to 1, the probability of remaining in the same state is 1 minus the sum of transition probabilities to other states. With these probabilities, we can fill in the transition matrix P:
P(M2|M1) = 0.2, P(M3|M1) = 0.15, P(M1|M1) = 0.65.
P(M1|M2) = 0.6, P(M3|M2) = 0.25, P(M2|M2) = 0.15.
P(M1|M3) = 0.5, P(M2|M3) = 0.1, P(M3|M3) = 0.4.
By using this transition matrix, we can analyze the professor's behavior in selecting new computer models over time.
PLEASE HELP!!!! WILL MARK BRAINLIEST!!!
A science museum has a spherical model of the earth with a diameter of 8.5 m. What is the volume of the
model? Use 3.14 for
and round your answer to the nearest whole number. Show your work.
Answer:
The volume of the model is [tex]321\ m^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the sphere (model of the earth) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
In this problem we have
[tex]r=8.5/2=4.25\ m[/tex] ----> the radius is half the diameter
substitute the values
[tex]V=\frac{4}{3}(3.14)(4.25)^{3}=321\ m^{3}[/tex]
Please help! C is highlighted, but I’m not sure if it is correct. I give brainliest!
Answer:
yes its c
Step-by-step explanation:
cuz its shaded and i have the line under the greater sign and it lines up
What is the slant height x of the square pyramid?
Express your answer in radical form.
Answer:
x = [tex] 4 \sqrt { 3 } [/tex]
Step-by-step explanation:
We are given a diagram of a pyramid with a right angled triangle which has [tex]30[/tex]°, [tex]60[/tex]° and [tex]90[/tex]° angles an the hypotenuse is [tex]8cm[/tex].
Since we have a right angled triangle, we can apply sin here:
We know that [tex]sin 60 = \frac{\sqrt{3} }{2}[/tex] so we can write it as
[tex]\frac{\sqrt{3} }{2} = \frac{x}{8}[/tex]
So we get the slant height of x = [tex]4\sqrt{3}[/tex].
Answer:
The slant height of square pyramid = 4√3 m
Step-by-step explanation:
From the figure we can see a square pyramid with lateral edge 8 m
Also the one angle of face triangle is 60° , therefore the face triangle is an equilateral triangle.
Therefore the base is 8 m
To find the slant height
slant height² = Lateral edge² - (base/2)²
= 8² - (8/2)² = 8² - 4²
= 64 - 16 = 48
Slant height = √48 = 4√3 m
Therefore slant height of square pyramid = 4√3 m
HELP
What is the value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x) ?
A)1/3
B)1/2
C)2
D)13
Answer:
[tex]\large\boxed{C)\ 2}[/tex]
Step-by-step explanation:
[tex]2.5(6x-4)=10+4(1.5+0.5x)\qquad\text{use the distributive property}\\\\(2.5)(6x)+(2.5)(-4)=10+(4)(1.5)+(4)(0.5x)\\\\15x-10=10+6+2x\qquad\text{subtract 2x from both sides}\\\\13x-10=16\qquad\text{add 10 to both sides}\\\\13x=26\qquad\text{divide both sides by 13}\\\\x=2[/tex]
Answer:
C)2
Step-by-step explanation:
Trust me here boyzz
Estimate the limit
A
B
C
D
Answer:
C. [tex]\lim_{x\rightarrow f(x)=2[/tex]
Step-by-step explanation:
Given problem is [tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex].
Now we need to evaluate the given limit.
If we plug [tex]\x=\frac{\pi}{4}[/tex], into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule
take derivative of numerator and denominator
[tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex]
[tex]=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}[/tex]
[tex]=\frac{sec^2(\frac{\pi}{4})-0}{1-0}[/tex]
[tex]=\frac{(\sqrt{2})^2}{1}[/tex]
[tex]=\frac{2}{1}[/tex]
=2
Hence choice C is correct.
I will give brainliest to whoever is right and provides an explanation
Answer:
1024π
Step-by-step explanation:
The formula for the surface area of a sphere is 4πr².
Since the radius is 16 cm, the surface area is:
SA = 4×π×16²= 1024π.
A=4πr^2
A = 4π(16)^2
A = 3216.99
which is the same as 1024π cm^2
(5CQ) Use the comparison test to determine whether the series 25/3+125/9+625/27+... is convergent or divergent.
The terms in the sum are given by the sequence
[tex]\left\{\dfrac{5^{n+1}}{3^n}\right\}_{n\ge1}[/tex]
We have
[tex]\dfrac{5^{n+1}}{3^n}>\dfrac{5^n}{3^n}=\left(\dfrac53\right)^n>1[/tex]
for all [tex]n[/tex], and the series [tex]1+1+1+\cdots[/tex] clearly diverges, so [tex]\dfrac{25}3+\dfrac{125}9+\cdots[/tex] must also diverge.
Answer:
B. Divergent
Step-by-step explanation:
Did test
50 POINTS!! HURRYY
Kari, a biologist, is getting ready for a new study of tropical fish. She needs to fill the tank with precisely 5 gallons of water. She uses a quart container. Division Rules How many times will Kari have to fill the container to make 5 gallons? 10 times 15 times 20 times 25 times
Answer:
20
Step-by-step explanation:
ONE QUART IS 0.25 OF A GALLON. SORRY CAPS LOCK IS STUCK TURNED ON!
Answer:
Step-by-step explanation:
She needs to fill the quart container
20 times.
4 quarts make a gallon, so 20 quarts = 5 gallons.
Select the favorable outcomes for rolling a five on the first roll.
Please help.
A 1/6% chance because there are six sides and 5 is one of them
Answer:
(1-6) (2-5) (3-4) (4-3) (5-2) (6-1)
Step-by-step explanation:
I was just doing this lesson
Plot the points (-1,3), (4,-2), and (1,-5) in a coordinate plane. Are the points the vertices of a right triangle?
Final answer:
To determine if the points (-1,3), (4,-2), and (1,-5) form a right triangle, plot them on a coordinate plane, use the distance formula to calculate the lengths of the sides, and then apply the Pythagorean theorem.
Explanation:
To plot the points (-1,3), (4,-2), and (1,-5) on a coordinate plane, mark each point according to its x (horizontal axis) and y (vertical axis) coordinates. Connect these points to form a triangle. To determine if they are the vertices of a right triangle, you can calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem.
The distance formula is √((x₂-x₁)² + (y₂-y₁)²), and the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
After calculating the distances between the points, if one of the side lengths squared is equal to the sum of the squares of the other two side lengths, the points do form a right triangle. If not, they do not form a right triangle.
Maria buys a sweater at a department store. The sweater costs $40. The store is having a 35% off sale on everything in the store. Enter the amount of money, in dollars, Maria saves from the sale. Do not consider the sales tax.
Answer:
Maria gets $14 off of the original price of $40
Step-by-step explanation:
Megan' pencil is shorter than Tasha's pencil.Tasha's pencil is shorter than Kim's pencil.Is Megan's pencil shorter or longer than Kim's pencil?Draw or write to explain
Answer:
Meghan's pencil is shorter than Kim's pencil.
Step-by-step explanation:
Let's denote Meghan's pencil height with M, Tasha's with T and Kim's with K
Now, we know that
M < T
and T < K
So, by transitive property,
M < K
PLEASE HELP ME ASAAP 1 ANSWER EQUALS ONE SAVE FROM MY MOM WHOPPING MY A 2/4 + 4/6
Answer:
5/6 I think
Step-by-step explanation:
Add 2/4 + 2/6 =
2*3/4*3 + 2*2/6*2 =
6/12 + 4/12 =
6+4/12 =
10/12 =
5/6
[tex] \frac{5}{6} \\ hope \: it \: helps \: \\ :)[/tex]
Can someone help me with this problem
Answer:
A = 20P = 6√10Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
A(-3, 0) , B(3, 2)
[tex]AB=\sqrt{(3-(-3))^2+(2-0)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=\sqrt{4\cdot10}=\sqrt4\cdot\sqrt{10}=2\sqrt{10}[/tex]
A(-3, 0), D(-2, -3)
[tex]AD=\sqrt{(-2-(-3))^2+(-3-0)^2}=\sqrt{1^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}[/tex]
AB = CD and AD = BC
The area of a rectangle:
[tex]A=(AB)(AD)[/tex]
Substitute:
[tex]A=(2\sqrt{10})(\sqrt{10})=(2)(10)=20[/tex]
The perimeter of a rectangle:
[tex]P=2(AB+AD)[/tex]
Substitute:
[tex]P=2(2\sqrt{10}+\sqrt{10})=2(3\sqrt{10})=6\sqrt{10}[/tex]
Given that line EH is a median of triangle EFG find FG
Answer:
12.2
Step-by-step explanation:
We can say that FG = FH + HG
Since EH is the median, FH and HG is equal. Thus we can find x.
[tex]FH=HG\\6x-1.1=4x+1.3\\6x-4x=1.3+1.1\\2x=2.4\\x=\frac{2.4}{2}\\x=1.2[/tex]
Now we can find FH = 6x - 1.1 = 6(1.2) - 1.1 = 6.1, and
HG = 4x + 1.3 = 4(1.2) + 1.3 = 6.1
Hence, FG = 6.1 + 6.1 = 12.2
Plz help meh on this
WIL GIVE BRAINLIEST
the answer is (a-4)^2
Answer:
Let's factor a2−8a+16
a2−8a+16
The middle number is -8 and the last number is 16.
Factoring means we want something like
(a+_)(a+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -8 Multiply together to get 16 Can you think of the two numbers?
Try -4 and -4:
-4+-4 = -8
-4*-4 = 16
Fill in the blanks in
(a+_)(a+_)
with -4 and -4 to get...
(a-4)(a-4)
Answer:
(a−4)(a−4)
Identify the domain of the function shown in the graph.
Answer:
B
Step-by-step explanation:
Domain of a function (Graph) is the set of ALLOWED x-values. Or, the x-values for which the function is defined.
Now, looking at the graph, we can see the line is defined in the region from x = 1 till x = 4, so the domain would be 1 ≤ x ≤ 4.
Answer choice B is right.
Big Smiles Toy Company needs to pack marbles into a box. The company has two boxes they can use. Box A is 9 inches wide, 13 inches long, and 11.5 inches high. Box B is 14 inches wide, 8.5 inches long, and 12 inches high. Big Smiles Toy Company wants to use the larger box. Which box should the company choose and how much larger is it?
Answer:
The answer is Box B by 82.5 inches, let me know if it helped.
Step-by-step explanation
The company should choose Box B as it is larger than Box A. The volume of Box A is 1,497.75 cubic inches and the volume of Box B is 1,428 cubic inches, making Box A 69.75 cubic inches larger than Box B.
Explanation:The company should choose Box B as it is larger than Box A. To calculate the size difference, we need to find the volume of each box, which is calculated by multiplying the length, width, and height of the box. For Box A, the volume is 9 inches * 13 inches * 11.5 inches = 1,497.75 cubic inches. For Box B, the volume is 14 inches * 8.5 inches * 12 inches = 1,428 cubic inches. Therefore, Box A is 69.75 cubic inches larger than Box B.
Write the equation of a line in slope intercept form that has a slope of 4/5 and has a y- intercept of 0
Answer: y = 4\5*x
We can get this through slope intercept form.
Slope intercept form is y=mx +b where m is the slope and b is the y intercept.
We plug in 4.5 for the slope and 0 for the y-intercept.
The length of a rectangle is 3 m longer than its width.
The area of the rectangle is 154 m².
What is the width of the rectangle?
Enter your answer in the box.
Answer:
The width is 51.333
Step-by-step explanation:
l * w = area of rectangle
3 * w = 154
w= 154/3
w=51.333
Answer:
11
Step-by-step explanation:
It right