Therefore , the solution of the given problem of ratio comes out to be percent change is 50% for the 1/2.
What is ratio?To construct a pair of related variables "a" with "b," whereby "b" may also be bigger than zero, apply the straightforward formula "a / b." Two ratios are combined to form one ratio. The ratio would indeed be 1:1 if there were just one guy and three women. In the group, there are fraction 3/4 girls and 1/4 boys. Parts can be a division between two or more items, a number, or a portion of the volume of a component.
Here,
Given :
Ratio is 1/2
To convert into percentage ,
We multiply it by 100
=> 1/2 * 100
=> 50 %
Thus , percent change is 50%
Therefore , the solution of the given problem of ratio comes out to be percent change is 50% for the 1/2.
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Find the imaginary part of (5 - 12i)²
Daniel invests a lump sum of money in a savings account with a fixed annual interest rate of 5% that is compounded
continuously. After 7 years, the account balance reaches $5,676.27. How much was initially invested?
Using Compound Interest, The initially invested amount was $5400.
What does compound interest mean?The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You'll have $110.25 after the second year is over.
The formula for compound interest is
[tex]C = P(1 + \frac{r}{n})^{nt}[/tex]
Where C is the compound interest value after n years.
P is the principal amount.
I is interest.
n is the number of years.
It is given that percentage of interest is 5% so I=0.05. C=$5676.27.
n=7.
According to the formula of compound interest,
5676.27 = P(1+0.05)7 P = 5676.27 1.051084
P = 5400
Therefore the amount that was invested initially was $5400.
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That ratio of the risk premium to the standard deviation of the excess returns is known as the reward-to-volatility or the _ ratio.
Answer:
Sharpe Ratio?
if you looking for a name for your definition, thats it
good luck!
List all the subsets of the given set. 0
The subsets are ______
( Use a comma to separate answers as needed .)
The subsets are {}, {0}.
What is the subset in mathematics?
In mathematics, a subset is a set consisting of elements that are also elements of another set. A set A is said to be a subset of set B if and only if every element of A is also an element of B. In other words, if you have a set A and another set B, and all the elements of set A are present in set B, then set A is considered a subset of set B.
In mathematics, a subset is a collection of elements that belong to a larger set. The elements in a subset can be any type of mathematical objects, such as numbers, vectors, or functions. A set is a subset of itself, and the empty set is a subset of every set.
The subsets of the given set {0} are the empty set {} and the set itself, {0}. So, the subsets of the given set 0 are {}, {0}.
Hence, the subsets are {}, {0}.
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In triangle FGH, g=8ft, h=13ft, and measure of angle F=72 degree. Find measure of angle G
To find the measure of angle G in triangle FGH, we can use the fact that the sum of angles in a triangle is always 180 degrees.
First, we can find the measure of angle H using the fact that the sum of angles in a triangle is 180 degrees:
H = 180 - F - G
H = 180 - 72 - G
H = 108 - G
Next, we can use the Law of Cosines to find the length of side FG:
FG^2 = GH^2 + FH^2 - 2(GH)(FH)cos(F)
FG^2 = 8^2 + 13^2 - 2(8)(13)cos(72)
FG^2 = 169.21
FG ≈ 13.01 ft
Finally, we can use the Law of Cosines again to find the measure of angle G:
cos(G) = (FG^2 + GH^2 - FH^2) / (2(FG)(GH))
cos(G) = (169.21 + 64 - 169) / (2(8)(13))
cos(G) = 0.7686
G ≈ 40.6 degrees
Therefore, the measure of angle G in triangle FGH is approximately 40.6 degrees.
The temperature decreasesd by 11 degrees enter a integer that represents this situation in the box
Step-by-step explanation:
The answer should be -11
Answer: -11 (negative eleven)
An integer is a real number. Which includes 0, positive numbers, and negative numbers. Since the temperature outside went down by 11 degrees rather than increased, it is negative. Which means our integer is -11.
I hope this helps & Good Luck <3 !
14. JD is selling high quality bats in his baseball supply store. His new shipment of 30 bats arrives, with a wholesale cost of $80 for each bat. He decides to markup the price by 120% in order to make a good profit. After 3 months he has sold 16 of the bats, but needs to make room for more inventory. He decides to discount the remaining bats by 40%. If he sells all of the remaining bats at the new discounted price, how much profit will he make after selling all of the bats?
Answer: JD's markup price is $80 * 120% = $96 per bat.
So, the retail price of each bat is $80 + $96 = $176.
The total revenue from the sale of 16 bats is 16 * $176 = $2,816.
He still has 30 - 16 = 14 bats left.
The discount price of each bat is $176 - ($176 * 40%) = $106.40.
The total revenue from the sale of 14 bats at the discount price is 14 * $106.40 = $1,493.60.
The total revenue from all the bats is $2,816 + $1,493.60 = $4,309.60.
The profit JD makes from selling all the bats is $4,309.60 - ($80 * 30) = $1,039.60.
Step-by-step explanation:
The profit which will he make after selling all of the bats is $1,039.60.
What is Profit?This is referred to as the amount of money that you gain when you are paid more for something than it cost you to make, get, or do it.
JD's markup price = $80 ×120% = $96 per bat.
Retail price = $80 + $96 = $176.
Revenue of 16 bats is 16 * $176 = $2,816.
Since 30 - 16 = 14 bats which is what we have left.
The discount price of each bat is $176 - ($176 * 40%) = $106.40.
The total revenue from the sale of 14 bats at the discount price is 14 * $106.40 = $1,493.60.
Therefore the total revenue from all the bats is $2,816 + $1,493.60 = $4,309.60.
The total profit = $4,309.60 - ($80 * 30) = $1,039.60.
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Mrs. Gomez is buying a triangular table for the corner of her classroom. The
side lengths of the table are 5 feet, 3 feet, and 4 feet.
Is this triangular table a right triangle?
OA. No, because 3+ 4+ 5.
B. No, because 3² +4² #5²
C. Yes, because 32 +4² = 5²
D. Yes, because 3² +4² > 5²
The triangular table that Mrs. Gomez is buying for her classroom is a right triangle table because 3² +4² = 5². That is option C.
What is a right angle triangle?A right angle triangle is the type of triangle that has one side of its angle perpendicular to another and the value of the three sides can be calculated through the use of the Pythagorean formula.
The Pythagorean formula is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.
Since, 5= c
b= 3
a = 4
Therefore, 3² +4² = 5² shows that the table is a right angle triangle.
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A statistics class suspected that students at their school were getting less than 8 hours of sleep. They took a random sample of 42 students and asked them how many hours of sleep they get per night. The students in the sample reported sleep amounts that had a mean of 7.5 hours and a standard deviation of 1.6 hours. These results produced a test statistic of t -2.03 and a P-value of approximately 0.025. Assuming the conditions for inference were met, what is an appropriate conclusion at the a = 0.05 significance level?
Choose 1 answer: A. Fail to reject the null hypothesis. This isn't enough evidence to conclude that the mean amount of sleep is less than 8 hours. B. Fail to reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours. C. Reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours. D. Reject the null hypothesis. This isn't enough evidence to conclude that the mean amount of sleep is less than 8 hours.
The correct answer is to Reject the null hypothesis. This is strong evidence that the mean amount of sleep is less than 8 hours.
The test statistic of t = -2.03 and P-value of approximately 0.025 suggest that the mean amount of sleep for students is significantly less than 8 hours.
The P-value of 0.025 is less than the significance level of 0.05, which means that there is enough evidence to reject the null hypothesis that the mean amount of sleep is 8 hours.
Therefore, the appropriate conclusion at the a = 0.05 significance level is that the mean amount of sleep for students is less than 8 hours.
Hence, the correct answer is C.
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Eric works for a salary of $3,500 per month.
What is Eric’s gross pay for one year?
Eric’s gross pay for one year if he earns a salary of $3,500 per month is $42,000.
What is Eric’s gross pay for one year?The total amount of money an employee receives before taxes is referred to as gross pay.
Given that;
Eric's salary per month = $3,500 Eric’s gross pay for one year = ?Eric’s gross pay for one year = Eric's salary per month × 12 months
Eric’s gross pay for one year = $3,500 × 12
Eric’s gross pay for one year = $42,000
Therefore, the gross pay is $42,000.
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2. Pequot Lakes, Minnesota has a spherical water tower that is known as “the world’s largest fishing bobber.” The water tower holds 6,684 cubic feet of water. The water tower needs to be repainted, and it will have to be painted twice to get two coats of coverage. One gallon of paint can cover 350 square feet. How many gallons of paint will be needed to paint the water tower?
Answer:
28.93 gallons of paint
Step-by-step explanation:
The volume of a sphere can be found using the formula:
V = (4/3)πr^3
We are given that the water tower holds 6,684 cubic feet of water, so we can use this to find the radius:
6684 = (4/3)πr^3
(6684 * 3) / (4 * π) = r^3
r = (6684 * 3 / (4 * π))^(1/3) = 35.73 feet
Next, we need to find the surface area of the sphere. The surface area of a sphere can be found using the formula:
A = 4πr^2
So, the surface area of this water tower can be found as:
A = 4π * 35.73^2 = 4π * 1286.13 = 5071.57 square feet
Finally, we need to find the amount of paint needed to paint the surface area twice. One gallon of paint can cover 350 square feet, so we can divide the surface area by 350 to find the number of gallons of paint needed:
Gallons of paint = (5071.57 * 2) / 350 = (10143.14 / 350) = 28.93 gallons
So, 28.93 gallons of paint are needed to paint the water tower twice.
What is 4x^3+4x^m+8x^5+4 written in polynomial standard form?
The polynomial in standard form is 8x^5 + 4x^4 + 4x^3 + 4
How to determine the standard form of the polynomialFrom the question, we have the following parameters that can be used in our computation:
4x^3+4x^m+8x^5+4
Express properly
So, we have the following representation
4x^3 + 4x^4 + 8x^5 + 4
Order the powers in decreasing order
This gives
8x^5 + 4x^4 + 4x^3 + 4
Hence, the standard form is 8x^5 + 4x^4 + 4x^3 + 4
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q1 and q2 are 24m apart. if q2 is 49 times q1, where between the two charges would the net electric field be equal to 0
The point where the net electric field is equal to zero is located approximately 0.48936m away from q1 and 24m - 0.48936m = 23.51064m away from q2.
Describe charge?Charge is a fundamental property of matter that describes its electrical state. It is a scalar quantity that can be either positive, negative, or neutral, and is measured in Coulombs (C). The concept of charge is used to explain many of the phenomena that occur in electricity and magnetism, such as electric fields, currents, and voltages. Positive and negative charges are thought to be due to the presence or absence of electrons, which are the smallest negatively charged particles in matter. Neutral objects have an equal number of positive and negative charges, resulting in a net charge of zero. The interaction of charges with each other results in many of the electrical and magnetic phenomena observed in the world around us.
The net electric field at a point is equal to zero if the electric field due to one charge is exactly canceled by the electric field due to the other charge.
Since q2 is 49 times greater than q1, the electric field due to q2 will be 49 times greater than the electric field due to q1 at any given point. In order to cancel the electric field due to q1, we need to place q2 at a point that is 49 times closer to q1 than the original separation of 24m.
Let's call the new separation between the charges x. Then, x = 24m / 49, which is approximately equal to 0.48936m.
So, the point where the net electric field is equal to zero is located approximately 0.48936m away from q1 and 24m - 0.48936m = 23.51064m away from q2.
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hello could anyone help me
I think that answer is yes
Ryan is taking a survey to find out how many people prefer soda A over soda B. He surveyed 100 people and forty-nine preferred soda A. Seven percent had no preference for soda A or soda B. What percentage of peoples surveyed preferred soda B?
Answer: 44%
Step-by-step explanation:
100 - 49 - 7 = 44 people who preferred Soda B
44 of a 100 = 44%
Answer: 44%
Step-by-step explanation:
Since we have 100 people, each person is one percent.
49 people preferred A, so we can subtract 49 from 100.
100 - 49 = 51
7 people didn't have an opinion, so we can subtract 7 from 51.
51 - 7 = 44
That means that 44 people preferred B, which is 44%
Luke has a 65-gallon rectangular aquarium with base 48 inches by 18
inches. He centers it on a rectangular tabletop. There a
re 3 inches
between each side of the aquarium and each side of the tabletop as shown
What is the area, in square inches, of the tabletop?
The area of the tabletop in square inches is 1071 square inches.
What is area?An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.
Given that, there are 3 inches between each side of the aquarium and each side of the tabletop.
The length of the tabletop will be:
l = 48 + 3 = 51 inches.
The width of the tabletop will be:
w = 18 + 3 = 21 inches.
The area of the table top will be:
A = (l)(b)
A = (51)(21)
A = 1071 square inches.
The area of the tabletop in square inches is 1071 square inches.
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Please solve this for me, this is all the info presented in the question.
About 0.04% percent of quokkas weigh over 15.5 pounds.
What is normal distribution?Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Given that, the weights of quokkas can be described by the Normal model N(10, 2.7).
Let Y the weights of quokkas
Given that, Y~N(μ= 10, σ²=2.7)
So, σ=1.643
a) The probability, P(Y＞15.5) denotes chances that quokkas weight over 9.3 pounds, and it is,
P(Y>9.3) = P(Z> (15.5-μ)/σ)
= P(Z> (15.5-10)/1.643)
= P(Z>3.347)
= 0.0004
= 0.0004×100 =0.04%
b) The probability, P(Y＜11.9) denotes chances that quokkas weight under 11.9 pounds, and it is,
P(Y>9.3) = P(Z> (11.9-μ)/σ)
= P(Z> (11.9-10)/1.643)
= P(Z>1.156)
= 0.1250
= 0.1250×100 =12.5%
c) The probability, P(11.9≤Y≤15.5) denotes chances that quokkas weight will be between 11.9 and 15.5 pounds, and it is,
P(11.9≤Y≤15.5) = P((15.5-μ)/σ ≤ Z ≤ (11.9-μ)/σ)
= P((15.5-10)/1.643) ≤ Z ≤ (11.9-10)/1.643)
= P(3.347≤ Z ≤1.156)
= P(Z≤3.347)-PZ ≤1.156)
= 0.0004-0.1250
= 0.1246
= 0.1246×100
= 12.46%
Therefore, about 0.04% percent of quokkas weigh over 15.5 pounds.
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SOME ONE HELP! I WILL MAKE BRAINLIST!
Note that the proof related to the above parallelogram is given as follows:
ΔSVX ≅ ΔUTX Given
SV || TU Given
SV ≅ TU Corresponding part of congruent triangle
VUTS parallelogram Definition of parallelogram.
What is a Parallelogram?A quadrilateral having two pairs of parallel sides is known as a parallelogram. It is possible to demonstrate that the opposing sides of a parallelogram are congruent.
A parallelogram is any quadrilateral having two pairs of congruent opposing sides. Parallelograms contain two congruent opposing angles, thus a quadrilateral with two congruent opposite angles must be a parallelogram.
A parallelogram's diagonals intersect each other, therefore a quadrilateral with diagonals that bisect each other must be a parallelogram. Finally, if a quadrilateral contains two parallel and congruent sides, it must be a parallelogram.
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How do you describe a calibration curve?
A calibration curve is a graphical representation of the relationship between the output of a measuring instrument and the actual values of the quantity being measured.
What is the calibration curve?
A calibration curve is typically created by measuring a set of known values of the quantity being measured, and plotting the measured values against the actual values. The curve is used to make adjustments to the measurements obtained with the instrument, so that they more accurately reflect the actual values of the quantity being measured.
A calibration curve can be described as a plot of the relationship between the output of a measuring instrument and the actual values of the quantity being measured. The curve is typically linear, and the slope of the curve represents the sensitivity of the instrument. The y-intercept of the curve represents the offset or bias of the instrument, and any deviations from a straight line represent non-linearity in the measurement.
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Solve the initial value problem
dx/dt−4x=cos(5t)
with x(0)=1.
x(t) = ?
We are given the following differential equation, [tex]\frac{dx}{dt}-4x=cos(5t)[/tex], with the initial condition [tex]x(0)=1[/tex]. This is a linear DE in the form, [tex]\frac{dx}{dt}+P(t)x=Q(t)[/tex], where [tex]\mu(t)=e^{\int\ {P(t)} \, dt }[/tex].
First, finding [tex]\mu(t)[/tex].
[tex]\Longrightarrow\mu(t)=e^{\int\ {P(t)} \, dt }\Longrightarrow\mu(t)=e^{\int\ {-4} \, dt }[/tex]
[tex]\mu(t)=e^{-4t }[/tex]
Multiply the DE by [tex]\mu(t)[/tex].
[tex]\Longrightarrow\frac{dx}{dt}-4x=cos(5t)\Longrightarrow e^{-4t} [\frac{dx}{dt}-4x=cos(5t)][/tex]
[tex]\Longrightarrow (e^{-4t}) \frac{dx}{dt}-(e^{-4t})4x=(e^{-4t})cos(5t)[/tex]
[tex]\Longrightarrow e^{-4t} \frac{dx}{dt}-4e^{-4t}x=e^{-4t}cos(5t)[/tex]
Verify that the L.H.S is a product rule of [tex]e^{-4t}x[/tex].
[tex]\Longrightarrow \frac{d}{dt}[e^{-4t}x ] =(e^{-4t}*-4)x+(e^{-4t})(\frac{dx}{dt} )[/tex]
[tex]\Longrightarrow \frac{d}{dt}[e^{-4t}x ] =-4e^{-4t}x+e^{-4t}\frac{dx}{dt}[/tex]
This matches, so we can move forward by integrating both sides of the DE.
[tex]\int\ {[e^{-4t}x ]'} \, =\int\ {e^{-4t}cos(5t)} \, dt[/tex]
The integral on the R.H.S is pretty nasty to do using integration by parts and u-sub. I will use a table of integrals.
[tex]\int\ {e^{ax}cos(bx) } \, dx=\frac{e^{ax}(acos(bx)+bsin(bx))}{a^2+b^2}[/tex]
Let [tex]a=-4[/tex] and [tex]b=5[/tex]
[tex]\int\ {[e^{-4t}x ]'} \, =\int\ {e^{-4t}cos(5t)} \, dt[/tex]
[tex]\Longrightarrow e^{-4t}x = \frac{e^{-4t}(-4cos(5t)+5sin(5t))}{(-4)^2+(5)^2}+C[/tex]
[tex]\Longrightarrow e^{-4t}x = \frac{e^{-4t}(-4cos(5t)+5sin(5t))}{41} +C[/tex]
Now for the initial condition, [tex]x(0)=1[/tex].
[tex]\Longrightarrow e^{-4(0)}(1) = \frac{e^{-4(0)}(-4cos(5(0))+5sin(5(0)))}{41} +C[/tex]
[tex]\Longrightarrow (1)(1) = \frac{(1)(-4(1)+(0))}{41} +C[/tex]
[tex]\Longrightarrow 1 = -\frac{4}{41} +C[/tex]
[tex]\Longrightarrow 1+\frac{4}{41} = C[/tex]
[tex]\Longrightarrow C=\frac{45}{41}[/tex]
Now we have, [tex]e^{-4t}x = \frac{e^{-4t}(-4cos(5t)+5sin(5t))}{41} +\frac{45}{41}[/tex], solve for x.
[tex]\Longrightarrow x = \frac{\frac{e^{-4t}(-4cos(5t)+5sin(5t))}{41}}{ e^{-4t}} +\frac{\frac{45}{41}}{e^{-4t}}[/tex]
[tex]\Longrightarrow x = \frac{(-4cos(5t)+5sin(5t))}{41}} +\frac{45e^{4t}}{41}[/tex]
Thus, the answer to the given differential equation with an initial condition is, [tex]x = \frac{(-4cos(5t)+5sin(5t))}{41}} +\frac{45e^{4t}}{41}[/tex].
HELP PLEASEEEEEEEEEEEEEEEEEE
AROC formula
(f(b)-f(a))/b-a
f(11)-f(3) / 11 - 3
-623 -(-47) / 8
= -72
Hope this helps,
- Jeron :- )
(25 POINTS) How many solutions does the system of linear equations represented in the graph have?
One solution at (-1, 0)
One solution at (0, -1)
No solution
Infinitely many solutions
The correct option regarding the solution of the system of equations is given as follows:
One solution at (-1, 0).
What is the solution to the system of equations?We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
For this problem, we have a single equation, hence the solution is obtained when the graph crosses the x-axis.
The graph crosses the x-axis when x = -1 and y = 0, hence the solution is given as follows:
(-1,0).
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The drama club is selling tickets to their play to raise money for the show's expenses.
Each student ticket sells for $4 and each adult ticket sells for $9. The auditorium can
hold no more than 110 people. The drama club must make a minimum of $720 from
ticket sales to cover the show's costs. If r represents the number of student tickets
sold and y represents the number of adult tickets sold, write and solve a system of , a
inequalities graphically and determine one possible solution.
Answer: The total number of tickets sold (student and adult) cannot exceed 110, so we can write the first inequality as:
r + y ≤ 110
The minimum amount of money needed from ticket sales is $720, so we can write the second inequality as:
4r + 9y ≥ 720
To graph the system of inequalities, we can start by plotting the two lines corresponding to r + y = 110 and 4r + 9y = 720. The solution to the system of inequalities is the area on the graph that is shared by both of the inequalities (i.e., the area above the line 4r + 9y = 720 and below the line r + y = 110).
One possible solution for the number of student tickets (r) and adult tickets (y) is (30, 80). This means that 30 student tickets and 80 adult tickets can be sold to meet the conditions and raise at least $720.
Step-by-step explanation:
If points F and G are contained in a plane, then is entirely contained in that plane. A. True B. False
It is true that if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.
What is the two-dimensional plane?A two-dimensional plane, also known as a plane in two dimensions, is a flat surface that has length and width, but no thickness. It is an abstract mathematical concept that can be represented graphically.
Here,
In geometry, if two points are contained in a plane, then any line segment connecting those two points is also contained in that plane. So, if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.
Thus, it is true that if points F and G are contained in a plane, then the line segment FG that connects them is entirely contained in that plane.
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Let u =(a,7) and v =(4,4)a.find the value of a such that u is parallel to vb.two nonzero vectors u(u1,u2) and v(v1,v2) are perpendicular to each other if 0. find the value of a such that u is perpendicular to v.
The value of a that makes u parallel to v is a = 4 and the value of a that makes u perpendicular to v is -7.
How to solve vectors using dot and scalar product?a. For two vectors to be parallel, their direction ratios must be equal. In other words, their components must have the same ratio. For vectors u = (a, 7) and v = (4, 4), we have:
u1/u2 = a/7 = v1/v2 = 4/4
So the value of a that makes u parallel to v is a = 4.
b. For two nonzero vectors to be perpendicular, their dot product must be equal to zero. The dot product of u = (a, 7) and v = (4, 4) is given by:
u · v = a * 4 + 7 * 4 = 4a + 28
To make this equal to zero, we can solve for a:
4a + 28 = 0
4a = -28
a = -7
So the value of a that makes u perpendicular to v is -7.
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Need help fast. please
According to the model, the current population of Algeria is 38 million.
How to find the population ?The model for the population in t years from now is given by the model P = 38 ( 1 + r ) ^ t.
This means that when given the model, the current population of Algeria is 38 million because the 38 in the model represents the value of population when no years have elapsed.
We can solve for this to get :
= 38 ( 1 + r ) ^ t
= 38 ( 1 + r ) ⁰
= 38 x 1
= 38
= 38 million
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Find the arc length function for the curve measured from the point P in the direction of increasing t and then reparametrize the curve with respect to arc length starting from P, and (b) find the point 4 units along the curve (in the direction of increasing t) from P. r(f) = (5 - t) i + (4t - 3) j + 3t k. P(4, 1, 3)
The new arc length function for the curve after reparametrization is as follows
[tex]\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k[/tex]
What is meant by the arc length of a curve?
The distance between two places along a segment of a curve is known as the arc length.
The formula for arc length is used to determine how far something is along the curved line that makes up an arc. The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc.
Given,
Vector equation of curve r(t) = (5 - t) i + (4t - 3) j + 3t k
Given P = (4, 1, 3)
5 - t = 4
So, t = 1
Now differentiate r(t)
r'(t) = -i + 4j + 3k
Magnitude of r'(t) = |r'(t)| = √[(-1)² + 4² + 3²] = √26
The arc length function for the curve
[tex]s = \int\limits^t_1 { |r'(t)| } \, dt = \int\limits^t_1 { \sqrt{26} } \, dt = \sqrt{26} (t-1)[/tex]
[tex]t = \frac{s}{\sqrt{26} } + 1[/tex]
Now to reparametrize the curve with respect to arc length, substitute t with (s/√26) + 1 in r(t).
[tex]r(s) = (5 - ( \frac{s}{\sqrt{26} } + 1)) i + (4( \frac{s}{\sqrt{26} } + 1) - 3) j + 3( \frac{s}{\sqrt{26} } + 1) k\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k[/tex]
Therefore the new arc length equation of the curve when [tex]t = \frac{s}{\sqrt{26} } + 1[/tex] is as follows
[tex]\\\\r(s) = ( 4 - \frac{s}{\sqrt{26}})i + (\frac{4s}{\sqrt{26} } + 4)j+(\frac{3s}{\sqrt{26} } + 3)k[/tex].
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PLEASE HELP ASAP!!! FIND THE MULTIPLICITY AND ZEROS FOR THE GRAPH.
The zeros and their multiplicity are:
Zero: -1, Multiplicity: 1
Zero: 0, Multiplicity: 1
Zero: 1, Multiplicity: 1
Zero: 2, Multiplicity: 1
Zero: 2.5, Multiplicity: 1
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given:
A graph of a polynomial is given in the diagram.
A polynomial is intercepting the x-axis five times.
That means, there are five zeros.
The zeros and their multiplicity are:
Zero: -1, Multiplicity: 1
Zero: 0, Multiplicity: 1
Zero: 1, Multiplicity: 1
Zero: 2, Multiplicity: 1
Zero: 2.5, Multiplicity: 1
Hence, all the required values are given above.
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Find the slope of the line
Slope: m=
Answer:
Hi there! The answer is 3/5
Step-by-step explanation:
The rise is 3 and the run is 5.
Brainiest, please? Can you click on the crown on my answer?
Answer: 3/5
Step-by-step explanation:
Looks at the points (0,1) and (5,4).
Formula: y2-y1/x2-x1
Substitute: 4-1/5-0 = 3/5
m = 3/5
3. F(-2) +9
F(x)=-3x-2
Answer:
F(-2) = -3(-2) - 2 = 6 - 2 = 4
F(-2) + 9 = 4 + 9 = 13
Step-by-step explanation:
F(-2) = -3(-2) - 2 = 6 - 2 = 4
F(-2) + 9 = 4 + 9 = 13