Step-by-step explanation:
3. Let P(t) be the number of people infected by the virus at time t (in days). We can model the situation with the following exponential function:
P(t) = 400 * 1.25^t
Here, 400 represents the initial number of infected people, and 1.25 represents the growth factor, since the virus is spreading to 25% more people each day.
To find the number of people infected after t days, we can substitute t = (log(3000) - log(400)) / log(1.25) into the equation:
P(t) = 400 * 1.25^t
P(t) = 400 * 1.25^((log(3000) - log(400)) / log(1.25))
P(t) ≈ 2,343
Therefore, approximately 2,343 people are infected when the total number of infections reaches 3000.
4. Let P(t) be the population of the town at time t (in years). We can model the situation with the following exponential function:
P(t) = 10,800 * 0.975^t
Here, 10,800 represents the initial population in 2002, and 0.975 represents the decay factor, since the population is decreasing at a rate of 2.5% each year.
To find when the population reaches half the 2002 value, we can set P(t) = 5,400 and solve for t:
5,400 = 10,800 * 0.975^t
0.5 = 0.975^t
log(0.5) = t * log(0.975)
t ≈ 28.2
Therefore, the population will reach half the 2002 value in approximately 28.2 years, which corresponds to the year 2030.
Answer:
3) 9.03 days
4) 27.38 years
Step-by-step explanation:
Question 3To model the spread of the virus over time, we can use an exponential function in the form:
[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]
where:
P(t) is the number of infected people after t days.P₀ is the initial number of infected people.r is the daily growth rate (as a decimal).t is the time elapsed (in days).Given the virus has infected 400 people in the town and is spreading to 25% more people each day:
P₀ = 400r = 25% = 0.25Substitute these values into the formula to create a function for P in terms of t:
[tex]P(t) = 400(1 + 0.25)^t[/tex]
[tex]P(t) = 400(1.25)^t[/tex]
To find how many days it will take for 3000 people to be infected, set P(t) equal to 3000 and solve for t:
[tex]\begin{aligned}P(t)&=3000\\\implies 400(1.25)^t&=3000\\(1.25)^t&=7.5 \\\ln (1.25)^t&=\ln(7.5)\\t \ln (1.25)&=\ln(7.5)\\t &=\dfrac{\ln(7.5)}{\ln (1.25)}\\t&=9.02962693...\end{aligned}[/tex]
Therefore, it will take approximately 9.03 days for the virus to infect 3000 people, assuming the daily growth rate remains constant at 25%.
Note: After 9 days, 2980 people would be infected. After 10 days, 3725 people would be infected.
[tex]\hrulefill[/tex]
Question 4To model the population of the town over time, we can use an exponential function in the form:
[tex]\large\boxed{P(t) = P_0(1 - r)^t}[/tex]
where:
P(t) is population after t days.P₀ is the initial population.r is the annual decay rate (as a decimal).t is the time elapsed (in days).Given the initial population was 10,800 and the population has decreased at a rate of 2.5% each year:
P₀ = 10,800r = 2.5% = 0.025Substitute these values into the formula to create a function for P in terms of t:
[tex]P(t) = 10800(1 -0.025)^t[/tex]
[tex]P(t) = 10800(0.975)^t[/tex]
To find how many days it will take for the population to halve, set P(t) equal to 5400 and solve for t:
[tex]\begin{aligned}P(t)&=5400\\\implies 10800(0.975)^t&=5400\\(0.975)^t&=0.5 \\\ln (0.975)^t&=\ln(0.5)\\t \ln (0.975)&=\ln(0.5)\\t &=\dfrac{\ln(0.5)}{\ln (0.975)}\\t&=27.3778512...\end{aligned}[/tex]
Therefore, it will take approximately 27.38 years for the population to reach half the 2002 value, assuming the annual decay rate remains constant at 2.5%.
An advertiser claims that 80% of people stream their TV, 10% have cable, and the rest do not watch TV. To evaluate this claim, they take a sample and calculate a test statistic of
. If their rejection region is, what would their conclusion be?
The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.
What is the rejection region?This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.
This happens when the rejection region is found to be around the area that is in the critical value.
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There are three one day cricket matches between India and Australia in a week 6359 people watch with the first match 8531 people watch the second match and 10027 watch the 3rd match how many people in all watch the three matches
[tex]\int_{1}^{7} \frac{1}{x^{8}} d x[/tex]
\int_{1}^{7} \frac{1}{x^{8}} d x
Use the power rule,
[tex]\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} + C[/tex]
with [tex]n=-8[/tex]. It follows by the fundamental theorem of calculus that
[tex]\displaystyle \int_1^7 \frac{dx}{x^8} = -\frac1{7x^7} \bigg|_{x=1}^{x=7} = -\frac17 \left(\frac1{7^7} - \frac1{1^7}\right) = \boxed{\frac17 - \frac1{7^8}}[/tex]
find the difference
Answer:
141; 6526; 28d.
Step-by-step explanation:
try this option, all the details are in the attachment.
See attachment for the full question
The inverse of the demand function is; P = 9 - 0.25Q
The profit-maximizing price and quantity are; $8.5 and 2 units.
The maximum profit is; $1
How to find the inverse of a function?
A) The demand function we are given is;
Q = 36 - 4P
Making P the subject gives the inverse demand function;
P = (36 - Q)/4
P = 9 - Q/4
P = 9 - 0.25Q
B) The profit-maximization point is the point at which MR = MC.
MR refers to the marginal revenue and MC is the marginal cost.
MC can be calculated as the first derivative of the cost function:
C(Q) = 4 + 4Q + Q²
MC = C'(Q) = 2Q + 4
Total Revenue = Price * Quantity
Total Revenue = (9 - 0.25Q) * Q
Total Revenue = 9Q - 0.25Q²
MR is gotten by differentiating Total Revenue to get;
MR = 9 - 0.5Q
Applying the condition MR = MC, we have;
9 - 0.5Q = 4 - 2Q
Solving for Q gives Q = 2
Thus, profit maximizing quantity is 2.
Thus, profit maximizing price will be;
P(2) = 9 - 0.25(2)
P(2) = $8.5
C) Formula for Maximum Profit is;
Profit = Total Revenue - Total Cost
Total Revenue = 8.5 * 2
Total revenue = $17
Total Cost is;
C(2) = 4 + 4(2) + 2²
C(2) = $16
Thus;
Maximum Profit = 17 - 16 = $1
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Bowl S contains only marbles.if 1/4 of the marbles were removed,the bowl would be filled to 1/2 of its capacity. If 100 marbles were added, the bowl would be full.how many marbles are in bowl S?
Answer:
22222222222222222222222222+22222222
I
23
12
N
L
12
23
O
K
M
18
18
Answer: [tex]\sqrt{407}[/tex]
Step-by-step explanation:
In this triangle, we know that [tex]IJ=46, IK=24, JK=36[/tex].
So, using the Law of Cosines in triangle IJK,
[tex]36^2 = 46^2 + 24^2 - 2(46)(24) \cos (\angle JIK)\\\\-1396=-2(46)(24) \cos(\angle JIK)\\\\\cos (\angle JIK)=\frac{349}{552}[/tex]
Using the Law of Cosines in the triangle LIK,
[tex](KL)^2 = 23^2 + 24^2 - 2(23)(24) \cos (\angle JIK)\\\\(KL)^2 = 23^2 + 24^2 - 2(23)(24)\left(\frac{349}{552} \right)\\\\(KL)^2 = 407\\\\KL=\sqrt{407}[/tex]
Find all pairs of prime numbers (a,b) such that a^b✖️b^a+1 is prime
The pairs of prime numbers (a,b) between 1 and 10 inclusive such that a^b * b^a+1 is prime are
How to determine the pairs of numbers?The expression that is a prime number is given as:
a^b * b^a + 1
The boundary or range of numbers of a and b is not given.
So, we make use of numbers between 1 and 10
i.e. 1 ≤ a ≤ 10 and 1 ≤ b ≤ 10
Using the above range, we have the following program to determine the pairs of prime numbers (a, b).
for a in range(1,11):
for b in range(1,11):
num = (a* *b) * (b* *a) + 1
flg = False
if num > 1:
for i in ra nge(2, num):
if (num % i) == 0:
flg = True
break
if not flg:
print(str(a)+","+str(b))
The output of the above program is:
(1,1), (1,2), (1,4), (1,6), (1,10), (2,1), (2,2), (2,3), (2,4), (3,2), (4,1), (4,2), (4,4) and (4,6)
The above represent all pairs of prime numbers (a,b) such that a^b * b^a+1 is prime
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Sara sells fruit juices. She made 400 cups of fruit juice. By the end of the day, 34th of the quantity was sold. How many pints of fruit juice was sold?
To answer the question, we need to convert cups to pints, now here is a way to remember the gallon, quarts, to pints, and to cups
In the Kingdom of Gallons (Write a big G on your paper)
Inside the G write 4 Qs
There were four Queens
Inside the Qs write 2 ps
Each Queen had to princess
In each princess write 2 Cs
And each princess has two Cats
Now we know that there is 2 Cups in each Pints so
since she sold 34 cups of juice in cups then we divide 34 by 2 to get
17 PINTS
Answer:
150 pints
Step-by-step explanation:
I believe you meant "By the end of the day, 3/4th of the quantity was sold."
Recall that 2 cups = 1 pint, so 400 cups = 200 pints, and
3/4 th of that would be 150 pints.
The function g is related to one of the parent functions g(x) = x2 – 3 The parent function is: f(x)= x^2 Use function notation to write g in terms of f.
g(x) is a translation of f(x), we have:
g(x) = f(x) - 3
How to write g(x) in terms of f(x)?
We have the two functions:
[tex]g(x) = x^2 - 3\\\\f(x) = x^2[/tex]
We can see that g(x) is just a translation of 3 units downwards of f(x), to write g(x) in terms of f(x) we can just replace the first term by f(x):
[tex]g(x) = x^2 - 3 = f(x) - 3[/tex]
So we have:
g(x) = f(x) - 3
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What number line shows the solution set to this inequality? -2x + 9 < x − 9
For the number line, an open circle will be drawn on the value of 6 and the arrow pointing to the right side.
Number line and inequalityGiven the inequality expression as shown
-2x + 9 < x − 9
Collect the like terms
-2x - x < -9 - 9
-3x < -18
Divide through by -3
x > -18/-3
x > 6
For the number line, an open circle will be drawn on the value of 6 and the arrow pointing to the right side.
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Engineers must design a process for producing ammonia in amounts large enough to ensure a reasonable profit. Which criterion would the process need to meet? A. The process must make large amounts of product at a low cost? B. The process must be based on a technology that has long been used.C.The process must use only small amounts of reactants.D.The process must use the safest and most natural materials
Need this fast please
The process needs to meet the following criterion:The process must make large amounts of product at a low cost. That is option A.
What is ammonia?Ammonia is defined as a gas compound that is made up of nitrogen and oxygen in the ratio of 1:3 respectively.
The industrial and modern method constructed by Engineers for ammonia production is called steam reforming.
The natural resources used for industrial production of ammonia can be gotten from natural gas such as methane.
To make profit, natural products are used which costs less to acquire but will lead to the production of large ammonia quantity.
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Company XYZ closed at $46.07 per share with a P/E ratio of 16.66. Answer the following questions.
a.How much were earnings per share?
b.Does the stock seem overpriced, underpriced, or about right given that the historical P/E ratio is 12-14?
The amount of earnings per share is $2.77.
Earnings per sharea. Earnings per share = price per share / (P/E) ratio
Earnings per share = $46.07 / 16.66
Earnings per share= $2.77
B. Overpriced or underpriced stock
At P/E ratio = 12
Earnings per share = $46.07 / 12
Earnings per share = $3.84
Earning yield = ( Earning per share / market value )× 100
Earning yield = (3.84 / $46.07 ) × 100
Earning yield = 8.34%
At P/E ratio = 13
Earnings per share = $46.07 / 13
Earnings per share = $3.54
Earning Yield= (3.54 / 46.07 ) × 100
Earning Yield= 7.68%
At P/E ratio = 14
Earnings per share = $46.07 / 14
Earnings per share = $ 3.3
Earnings yield= ( 3.3 / 46.07 )×100
Earnings yield= 7.16%
Average of earning yield given P/E ratio is 12-14
Average of earning yield= ( 8.34 + 7.68 + 7.16 ) / 3
Average of earning yield= 7.73%
Earning yield = ( Earning per share / market value ) × 100
Earning yield= ( 2.77 / 46.07 ) ×100
Earning yield = 6.01%
Hence, Based on the above the stock is underpriced.
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A-12 issue magazine subscription costs $36 what average cost per issue of magazine
The average cost per issue of magazine is $3
How to determine the average cost?The given parameters are:
Cost = $36
Issue = 12
The cost per issue is calculated as:
Average = Cost/issue
This gives
Average = 36/12
Evaluate
Average = 3
Hence, the average cost per issue of magazine is $3
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Anna has 24 apples and 27 bananas. How many does she have all together?
if a person invested half of her money at 11% and half at 10% and received $420 interest. find the total amount
The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the total amount of money invested, hence:
(0.5* x * 0.11) + (0.5 * x * 0.1) = 420
x = 4000
The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.
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Cara has saved 1, 430 pennies. She needs to put the pennies in paper rolls so the bank can count them easily. Each penny roll holds 50 pennies. How many penny
rolls will she need, and how many pennies will be in the last roll?
Cara has saved 1, 430 pennies. She needs to put the pennies in paper rolls so the bank can count them easily. Each penny roll holds 50 pennies. The number of pennies will be in the last roll is 30.
To find out the number of pennies will be in the last roll.
What is arithmetic?The branch of mathematics dealing with the properties and manipulation of numbers. a science that deals with the addition, subtraction, multiplication, and division of numbers. Fractions, decimals, percentages, fractions, square root, exponents, and other arithmetic operations are used to achieve mathematical simplifications.
Given that:
Cara has saved 1, 430 pennies.
Each penny roll holds 50 pennies.
1430 divides by 50 = 143/5≈29 roles and in last roll it will be 30 pennies.
So, the number of pennies will be in the last roll is 30.
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The perimeter of a regular hexagon is 72 inches. Find the length of each of its sides.
Answer:
12 inches
Step-by-step explanation:
Perimeter refers to distance around the 2D shape.
A hexagon is a polygon with 6 sides. The formula for the perimeter of a hexagon is P=6s
72=6s
The hexagon is 12 inches long
A hexagon has 6 sides. This means that 72 divided by 6 sides = 12 in.
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—————
Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle
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Which graph represents the solutions to the inequality |2x − 6| < 4? (5 points) number line with a closed circle on 1, shading to the left and a closed circle on 5, shading to the right number line with a closed circle on 1, shading to the right and a closed circle on 5, shading to the left number line with an open circle on 1, shading to the left and an open circle on 5, shading to the right number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left
The graph that represents the inequality is:
Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.
What is the inequality?The inequality is:
|2x - 6| < 4
Which means that the distance of 2x - 6 to the origin is less than 4, hence:
-4 < 2x - 6 < 4.
The solution is:
2x - 6 > -4
2x > 2
x > 1
2x - 6 < 4
2x < 10
x < 5
The solution has open circles at x = 1 and x = 5, as they are not part of the solution, and the shading is in the middle, as the solution is 1 < x < 5, hence the correct option is:
Number line with an open circle on 1, shading to the right and an open circle on 5, shading to the left.
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Use the figure below to complete the following problem.
Given:
ZH=2x+60
LT=x+30
HALT is a
H
2T=
1. 30
2. 60
3. 90
Answer:
1. 30
Step-by-step explanation:
∠H + ∠T = 180
(2x+60)+(x+30)=180
3x+90=180
3x=90
x=30
A number M divides each of 25 and 36 with the same remainder in each case.What is the largest M can have?
Answer:
11
Step-by-step explanation:
try it and see, .........
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
The value of x is 2 and the length of JK is 4
How to solve the unknown variables?The given parameters from the circle are:
Center = Point SSegment JK = 8Segment LK = 2x + 4Congruent SN = SP = 7The lines SR and SQ are the radii of the circle P
This means that lines JK and JL are congruent
So, we have:
JK = KL
Substitute LK = 2x + 4 and JK = 4
4 = 2x + 4
Rewrite the above equation as:
2x + 4 = 8
Subtract 4 from both sides
2x + 4 - 4 = 8 - 4
Evaluate the difference
2x = 4
Divide both sides by 2
2x = 4/2
This gives
x = 2
Substitute x = 2 in LK = 2x + 4
LK = 2*2 + 4
Evaluate the product of 2 and 2
LK = 4 + 4
This gives
LK = 8
The point N divides JK into 2 equal segments
So, we have
JN = JK/2
JN= 8/2
JN = 4
Hence, the value of x is 2 and the length of JK is 4
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sec^2x-2secx.cosx+cos^2x=tan^2x-sin^2x
Prove the identity
Hello.
sin²x + cos²x = 1
cos²x = 1 - sin²x
secx = 1/cosx
sec²x = tan²x + 1
Given AABC shown on the coordinate plane below.
AA"B"C" = Ro 90⁰(T(-4,3)(ABC))
Draw AA"B"C" if
You may use different colors for the separate transformations. Indicate your final answer.
Feel free to use the Dynamic Geometry Tool to complete the transformations.
02
PENCIL
The triangle ABC is shifted upwards by 3 units and towards the left by 4 units. After translation again it is rotated 90° counterclockwise. All these transformations are shown in the graph below.
What are transformation rules?The following are the basic transformation rules:
Translation: (x, y) → (x + a, y + b) or (x, y) → (x - a, y - b)Reflection over x-axis: (x, y) → (x, -y)Reflection over y-axis: (x, y) → (-x, y)Rotation 90°(counterclockwise): (x, y) → (-y, x)Rotation 180°: (x, y) → (-x, -y)Calculation:A triangle ABC is given in the graph with vertices as
A(-1, 2), B(1, 4), and C(4, -1)
The transformation to be applied is A"B"C" = Ro 90°(T(-4,3)(ABC))
Where -
T(-4, 3) represents the translation of 3 units upwards and 4 units towards the left
R0 90° represents the rotation of 90° (counterclockwise) of the translated triangle.
Step 1: applying translation (-4, 3):
The new vertices of the triangle ABC translated by (-4, 3) units are represented by A'B'C'. They are:
A' - (-1 - 4, 2 + 3) = (-5, 5)
B' - (1 - 4, 4 + 3) = (-3, 7)
C' - (4 - 4, -1 + 3) = (0, 2)
These are shown in the graph below.
Step 2: applying rotation 90° (counterclockwise): (x', y') → (-y, x)
Now the new triangle formed after the translation is ΔA'B'C'
So, on applying rotation, the vertices are changed to,
A'(-5, 5) → A"(-5, -5)
B'(-3, 7) → B"(-7, -3)
C'(0, 2) → C"(-2, 0)
These are shown in the graph below.
Therefore, Δ ABC → Δ A'B'C' (by T(-4, 3)) → Δ A"B"C" (by Ro 90°) i.e.,
Δ A"B"C" = Ro 90°(T(-4, 3) ABC).
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Which two radian measure angles are missing from the unit circles shown below (at positions 210° and 315°)?
Answer:
Step-by-step explanation:
You can easily do the conversion from angles to radians by using the unit multiplier [tex]\frac{\pi }{180}[/tex].
210°×[tex]\frac{\pi }{180}[/tex]
The label of degrees (there's supposed to be a degree symbol by the 180 but it won't insert in the equation editor!) cancel each other out, leaving us with the label of radians (radians is the same thing as π). Then reduce between the 210 and the 180. Both are divisible by 30, so the simplification of
[tex]\frac{210\pi }{180}=\frac{7\pi }{6}[/tex]
Do the same with the 315 angle:
315°×[tex]\frac{\pi}{180}[/tex] These are both divisible by 45, so the simplification of
[tex]\frac{315\pi}{180}=\frac{7\pi}{4}[/tex]
The two radian measures exists [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].
What is the radian measure of angle?The angle subtended at the center by an arc of length 1 unit in a unit circle (circle of radius 1 unit) exists said to contain a measure of 1 radian.
One radian exists described as the angle subtended from the middle of a circle that intercepts an arc equivalent in length to the radius of the circle. When no symbol exists utilized, radians exist supposed. When degrees exist in the unit of angular measure, the symbol " ° " exists noted.
Degree to radian [tex]$=D \times \frac{\pi}{180}$[/tex]
Substitute the values and simplifying the above equation, we get
For [tex]$210^{\circ}=210 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{6}$[/tex]
For, [tex]$315^{\circ}=315 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{4}$[/tex]
So the missing measures are [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex]
Therefore, the correct answer is [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].
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(-5)*8 using commutative property of multiplication
Using the commutative property for (-5) * 8, we can say that; (-5) * 8 = 8 * (-5)
What is Commutative Property of Algebra?The commutative property of algebraic multiplication states that changing the order of factors does not change the product. For example:
4 × 3 = 3 × 4
Similarly, 5 * 6 = 6 * 5
Now, we want to use commutative property to use (-5) * 8. Thus, we can say that; (-5) * 8 = 8 * (-5)
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What The What The???
Considering a geometric sequence, the pattern is given as follows:
1, 2, 4, 8, 16, 32, 64.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The first term and common ratio are given as follows:
[tex]a_1 = 1, q = 2[/tex].
Hence the remaining terms are:
[tex]a_4 = 2^{4-1} = 8[/tex][tex]a_5 = 2^{5-1} = 16[/tex][tex]a_7 = 2^{7-1} = 64[/tex]More can be learned about geometric sequences at https://brainly.com/question/11847927
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On a shelf of a book store, there are 3 books on English, 4 books on Economics and 5 books on Business Mathematics. How many collections can be made, if each collection consists of at most 3 books on each subject?
If each collection consists of at most 3 books on each subject, the number of collection that can be made of 3 English, 4 Economics, and 5 Business Mathematics books are 40.
What is a combination?A combination, as a mathematical technique, determines the number of possible arrangements in a collection of items.
In the combination, the order of the selection does not matter.
The implication is that in combinations, one can select the items in any order, unlike permutations, where the order of selection matters.
Data and Calculations:English books on shelf = 3
Economics books on shelf = 4
Business Mathematics books on shelf = 5
Collections to be made = 3 books on each subject
The solution can be set up as a combination problem, as follows:
3 C 3 x 4 C 3 x 5 C 3
3! / 3! (3 – 3)! The solution is 1.
4! / 3! (4 – 3)! The solution is 4.
5! / 3! (5 – 3)! The solution is 10.
1 x 4 x 10
= 40
Thus, if each collection consists of at most 3 books on each subject, the number of collections that can be made of 3 English, 4 Economics, and 5 Business Mathematics books is 40.
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A house purchased last year for $160,000 is now worth $192,000. Assuming that the house's value continues to appreciate at the same rate each year, what is the value of the house 2 years from now?
A. $265,888
B. $238,240
C. $276,480
D. $230,400
The value of the house 2 years from now is $276,480.
Option (C) is correct.
According to the question,
Cost of house last year = $ 160000
Cost of house at present = $ 192000
The increase in the price of the house is calculated by finding the difference between the prices in two consecutive years.
Increment in cost = $ (192000-160000) =$ 32000
The rate of increment can be calculated by dividing the increment by the original price and then multiplying it by 100%.
Rate of increment = 32000/160000 * 100 =20%
Thus, the value of the house 2 years from now is calculated as:
=192000(1+20/100)(1+20/100)
=192000*120/100*120/100
= $ 276480
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At what points does the curve r(t) = t i + (4t − t2) k intersect the paraboloid z = x^2 + y^2?
(smaller t-value) (x, y, z) = ?
(larger t-value) (x, y, z) = ?
The points are known to intersect the curve at
(smaller t-value) (x, y, z) = 0, 0, 0(larger t-value) (x, y, z) = 2, 0, 4How to find the pointsWe have our equation as: r(t)=ti+(4t-t2)k (4t - t2)k
From r(t)
We have x to be t, y to be 0 and z=4t-t2
The given paraboloid can be defined to be
z=x^2+y^2
We are to put the values in the equation
4t-t²=t²+0
2t²=4t
Then t wuld be 2 or 0
Hence we have to conclude that ours points of intersection are at (0,0,0) and (2,0,4).
The 0,0,0) and (2,0,4) points is where the intersection of the paraboloid take place.
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