Based on the AED 40,000 net loss that the SoftNet line brings to Hava Racquets company, the incremental effect if the Softnet line is eliminated is that the company would save AED 10,000.
What is the incremental effect?If Hava Racquets Company decides to scrap the Softnet line, then it means that they will no longer be incurring the AED 40,000 net loss that the line had brought to them.
They would instead incur a fixed cost of AED 30,000 which they can apply to their other operations.
This means that in exchange for a AED 40,000 loss, they would instead get a AED 30,000 loss.
The savings on these losses is:
= 40,000 - 30,000
= AED 10,000
This means that Hava Racquets Company will make a saving of AED 10,000 if they eliminate the line.
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Z^4-5(1+2i)z^2+24-10i=0
Find the value of z.
Can someone please help me with this one?
Using the quadratic formula, we solve for [tex]z^2[/tex].
[tex]z^4 - 5(1+2i) z^2 + 24 - 10i = 0 \implies z^2 = \dfrac{5+10i \pm \sqrt{-171+140i}}2[/tex]
Taking square roots on both sides, we end up with
[tex]z = \pm \sqrt{\dfrac{5+10i \pm \sqrt{-171+140i}}2}[/tex]
Compute the square roots of -171 + 140i.
[tex]|-171+140i| = \sqrt{(-171)^2 + 140^2} = 221[/tex]
[tex]\arg(-171+140i) = \pi - \tan^{-1}\left(\dfrac{140}{171}\right)[/tex]
By de Moivre's theorem,
[tex]\sqrt{-171 + 140i} = \sqrt{221} \exp\left(i \left(\dfrac\pi2 - \dfrac12 \tan^{-1}\left(\dfrac{140}{171}\right)\right)\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= \sqrt{221} i \left(\dfrac{14}{\sqrt{221}} + \dfrac5{\sqrt{221}}i\right) \\\\ ~~~~~~~~~~~~~~~~~~~~= 5+14i[/tex]
and the other root is its negative, -5 - 14i. We use the fact that (140, 171, 221) is a Pythagorean triple to quickly find
[tex]t = \tan^{-1}\left(\dfrac{140}{171}\right) \implies \cos(t) = \dfrac{171}{221}[/tex]
as well as the fact that
[tex]0<\tan(t)<1 \implies 0along with the half-angle identities to find
[tex]\cos\left(\dfrac t2\right) = \sqrt{\dfrac{1+\cos(t)}2} = \dfrac{14}{\sqrt{221}}[/tex]
[tex]\sin\left(\dfrac t2\right) = \sqrt{\dfrac{1-\cos(t)}2} = \dfrac5{\sqrt{221}}[/tex]
(whose signs are positive because of the domain of [tex]\frac t2[/tex]).
This leaves us with
[tex]z = \pm \sqrt{\dfrac{5+10i \pm (5 + 14i)}2} \implies z = \pm \sqrt{5 + 12i} \text{ or } z = \pm \sqrt{-2i}[/tex]
Compute the square roots of 5 + 12i.
[tex]|5 + 12i| = \sqrt{5^2 + 12^2} = 13[/tex]
[tex]\arg(5+12i) = \tan^{-1}\left(\dfrac{12}5\right)[/tex]
By de Moivre,
[tex]\sqrt{5 + 12i} = \sqrt{13} \exp\left(i \dfrac12 \tan^{-1}\left(\dfrac{12}5\right)\right) \\\\ ~~~~~~~~~~~~~= \sqrt{13} \left(\dfrac3{\sqrt{13}} + \dfrac2{\sqrt{13}}i\right) \\\\ ~~~~~~~~~~~~~= 3+2i[/tex]
and its negative, -3 - 2i. We use similar reasoning as before:
[tex]t = \tan^{-1}\left(\dfrac{12}5\right) \implies \cos(t) = \dfrac5{13}[/tex]
[tex]1 < \tan(t) < \infty \implies \dfrac\pi4 < t < \dfrac\pi2 \implies \dfrac\pi8 < \dfrac t2 < \dfrac\pi4[/tex]
[tex]\cos\left(\dfrac t2\right) = \dfrac3{\sqrt{13}}[/tex]
[tex]\sin\left(\dfrac t2\right) = \dfrac2{\sqrt{13}}[/tex]
Lastly, compute the roots of -2i.
[tex]|-2i| = 2[/tex]
[tex]\arg(-2i) = -\dfrac\pi2[/tex]
[tex]\implies \sqrt{-2i} = \sqrt2 \, \exp\left(-i\dfrac\pi4\right) = \sqrt2 \left(\dfrac1{\sqrt2} - \dfrac1{\sqrt2}i\right) = 1 - i[/tex]
as well as -1 + i.
So our simplified solutions to the quartic are
[tex]\boxed{z = 3+2i} \text{ or } \boxed{z = -3-2i} \text{ or } \boxed{z = 1-i} \text{ or } \boxed{z = -1+i}[/tex]
Live fund are selling their holdings at $5000 per share. How much would live fun receive if they sold half their holdings in Marx brothers?
Answer:
2500
Step-by-step explanation:
5000 ÷ 2 = 2500
IF THE PROBABILITY THAT A FOOTBALL TEAM WILL WIN THEIR NEXT GAME IS 80%,
WHAT ARE THE ODDS IN FAVOR OF THEM WINNING?
The odds in favor of them winning is 20%
How to determine the probability
From the information given, we have that the probability of them winning the next game is 80%
P( winning) = 80% = 0. 8
The odds against them winning is given as;
1 - probability of winning
We have;
= 1 - 0. 8
= 0. 2
The odds in favor of them winning is simply the probability of them losing;
= 0. 2 × 100
= 20%
Thus, the odds in favor of them winning is 20%
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Divide the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of x. (27x 4 - 18x 3 + 9x 2) ÷ 3x
Answer:
9x3 - 6x2 + 3x
Step-by-step explanation:
(27x 4 - 18x 3 + 9x 2) ÷ 3x
Dividing each term between 3x we have:
9x3 - 6x2 + 3x
We can check the result:
(9x3 - 6x2 + 3x) * (3x)
= (27x4 - 18x3 + 9x2)
A psychologist wants to estimate the proportion of people in a population with IQ scores between 80 and 140. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use the Empirical Rule to estimate the proportion.
Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Considering the mean of 110 and the standard deviation of 15, we have that:
80 = 110 - 2 x 15.140 = 110 + 2 x 15.These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.
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I am so confused on this because I am so sure that it’s -2
Answer:
Yes, it should be -2.Step-by-step explanation:
To solve this, you have to divide this fraction from left to right.
What is a fraction?Fraction is a division or part of a whole number.
First, do apply the fraction rule.
[tex]\rightarrow: \sf{\dfrac{A}{B}\div \dfrac{C}{D}=\dfrac{A}{B}\times \dfrac{D}{C}}[/tex]
[tex]\sf{-\dfrac{1}{50}\times \dfrac{100}{1}}[/tex]
Cancel the common factor of 50.
[tex]\sf{-\dfrac{2}{1} }[/tex]
Divide.
-2/1=-2
[tex]\rightarrow: \boxed{\sf{-2}}[/tex]
So, the final answer is -2.
I hope this helps, let me know if you have any questions.
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Assume that a sample is used to estimate a population proportion p. Find the 95% confidence for a sample of size 246 with 52% successes. Enter your answer as an open -interval using decimals
Using the z-distribution, the 95% confidence interval for the proportion is given as follows:
(0.4576, 0.5824).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The other parameters for the interval are given as follows:
[tex]n = 246, \pi = 0.52[/tex].
The lower and upper bound of the interval, respectively, are given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.4576[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.5824[/tex]
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The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013. What was the cost of hiring a car for 2 days in 2013?
The cost of hiring a car for 2 days in 2013 is Rs. 316.8
How to find the cost of hiring in 2013 ?The cost for hiring a car for 2 days in 2018 was Rs. 264 which was 20% more than in 2013.
Therefore,
cost of hiring for 2018 = Rs. 264
Therefore,
let
cost of hiring in 2013 = 20%(264) + 264
cost of hiring in 2013 = 20 / 100 × 264 + 264
cost of hiring in 2013 = 1 / 5 × 264 + 264
cost of hiring in 2013 = 264 / 5 + 264
cost of hiring in 2013 = 52.8 + 264
cost of hiring in 2013 = 316.8
Therefore, the cost of hiring a car for 2 days in 2013 is Rs. 316.8.
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posite
A rectangle, a triangle, and a hexagon are drawn on the
same plane, as shown. How many points of
intersection are there between the rectangle and
hexagon?
The number of points of intersection between the rectangle and hexagon is = 4
What is point of intersection?The point of intersection between two or more lines is where the lines met at a particular plane. The point of intersection an equally be referred to as the vertex.
A rectangle is a quadrilateral because it's made up of four sides of which the two sides which are opposite, are equal and parallel.
A triangle is a polygon that is made up of three lines that meet to form edges and angles.
A hexagon is a polygon that is made up of six sides and six angles.
From the attached image, the rectangle which has four sides, made an intersection with the hexagon at four points which are marked with an asterisk.
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Answer:
2
Step-by-step explanation:
Janet plans to save $22.50 each week until she has enough to buy a $180 bicycle. After how many weeks will she have enough money for a bicycle.
Answer:
Step-by-step explanation:
8weeeks bc 22.50*8=180
Create a linear equation based on an experience in your everyday life. In this experience, a variable should depend on at least one other variable (the independent variable(s)). If your equation has 2 variables, graph it on the coordinate plane.
The equation that represent the total salary that I earn for working x hours in a week is y = 10x
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
Let y represent the total salary earned by working x hours, hence, if I earn $10 per hour:
y = 10x
The equation that represent the total salary that I earn for working x hours in a week is y = 10x
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Find the perimeter of the rectangle 2A+ 4
a
B
Given: ∠1=∠2
If AC3, BC = 5, and AB=7, find AD.
020
04
040
2/3
Answer:
Option 3
Step-by-step explanation:
[tex]\frac{5}{3}=\frac{AD}{7-AD} \\ \\ 35-5AD=3AD \\ \\ 35=8AD \\ \\ AD=4 \frac{3}{8}[/tex]
Coach Kirby is forming dodgeball teams from students in her physical education class.
She wants teams that each have 6 students. There are fewer than 48 students in the class,
so Coach Kirby can't form as many full teams as she wants.
1)) Let x represent how many full teams Coach Kirby can form. Which inequality describes
the problem?
6x < 48
6x > 48
Solve the inequality. Then, complete the sentence to describe the solution.
1) Coach Kirby can form fewer than 8|
full teams.
Please hurry
Answer:
6x<48
Step-by-step explanation:
ik its this one because theres 48 players and 6 teams both are even numbers so if you did 48÷6x you would get 8 but theres fewer than 48 kids
A new outlet is being planned with an allocated budget of $50,000 per month for advertising and planned average price of $10.00 per pizza. Estimate the monthly sales (number of pizzas) of this outlet.
Answer:
5,000
[tex]50000 \div 10 = 5000[/tex]
The graph shows a system of inequalities. Graph of two inequalities. One is a solid line increasing from left to right passing through negative 3 comma 0 and 0 comma 3, and it has shading below the line. The second is a solid upward opening parabola with a vertex at 1 comma negative 4 and x-intercepts at negative 1 comma 0 and 3 comma 0. This parabola is shaded inside the curve. Which system is represented in the graph? y > x2 –2x – 3 y > x + 3 y < x2 – 2x – 3 y < x + 3 y ≥ x2 – 2x – 3 y ≤ x + 3 y > x2 – 2x – 3 y < x + 3
The inequalities in the system of inequalities are y > x² – 2x – 3 and y > 3x + 4
How to determine the system of inequalities?The graph that completes the question is added as an attachment
The parabola
It has a vertex of (1, -4)
So, we have:
y = a(x - 1)^2 - 4
It passes through (3, 0).
So, we have:
0 = a(3 - 1)^2 - 4
This gives
4a - 4 = 0
Solve for a
a = 1
Substitute a = 1 in y = a(x - 1)^2 - 4
y = (x - 1)^2 - 4
Expand
y = x^2 - 2x + 1 - 4
y = x^2 - 2x - 3
The inner part is shaded.
So, we have:
y > x^2 - 2x - 3
The linear equation
It passes through (0, 4).
So, we have:
y = mx + 4
It passes through (1, 7).
So, we have:
7 = m + 4
Solve for m
m = 3
Substitute m = 3 in y = mx + 4
y = 3x + 4
The upper part is shaded.
So, we have:
y > 3x + 4
Hence, the inequalities in the system of inequalities are y > x² – 2x – 3 and y > 3x + 4
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0
100
200
300
400 500 600 700
Quantity Supplied
nstructions: Refer to the graph and answer the questions below.
Suppose the price is $6. What is the Quantity Supplied?
Suppose the Quantity Supplied is 200. What must the price be?
Suppose the price is $5 resulting in a Quantity Supplied of 300. Then the pric
Answer:
a. 400
b. 4$
Step-by-step explanation:
2$ equals 0 Quantity
3$ equals 100 Quantity
4$ equals 200 Quantity
We can see that starting from 2$, a dollar will increase the Quantity by 100
a fisherman travels 9mi downstream with the current in the same time he travels 3 mi upstream against the current. if the speed of the current is 5mph what is the speed at which the fisherman travels in still water
Answer:
10 mph
Step-by-step explanation:
speed of boat in still water = x
speed of current = 5
speed of boat with current (downstream) = x + 5
speed of boat against current (upstream) = x - 5
distance downstream = 9
distance upstream = 3
time = t
speed = distance/time
distance = speed × time
downstream:
9 = (x + 5)t
upstream:
3 = (x - 5)t
9 = xt + 5t
3 = xt - 5t
9 = xt + 5t
-3 = -xt + 5t
-----------------
6 = 10t
t = 0.6
9 = (x + 5)0.6
15 = x + 5
x = 10
22. Kim earns x dollars per hour for the first 40 hour she works in a week
and 1-
1¹/1/12 times as much for each hour over 40. If she worked 52 hours
last week, how much, in dollars, did she earn?
(A) 52X
0+1=1/x
(C) 52x+1-¹-x
(B) 40+1
(D) 52x-1-x
(E) 58x
40+1 in dollars per hour
Kelsey is looking for a job cutting hair. One option is self-employment at The Oakland Salon, where she would pay $400 per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $4 for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How much would Kelsey pay?
she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.
How to find the amount paid to either salon that is equal?she would pay $400 per month to rent a station and keep all of her earnings.
Another option is to work at a franchise, where she would just have to pay the salon $4 for every haircut.
Therefore,
let
x = number of haircut
Hence,
4x = 400
divide both sides by 4
4x / 4 = 400 / 4
x = 100
Therefore, she will have 100 hair cuts to work at a franchise to have the same amount paid for rent.
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need heeeelp please
Answer:9[tex]a^{10}[/tex][tex]b^{-6}[/tex]=[tex]\frac{9a^{10} }{b^6}[/tex]
Step-by-step explanation:
Answer:
9*a^10*(1/(b^6))
Step-by-step explanation:
(-3a^5*b^-3)^2
(-3)^2 * (a^5)^2 * (b^-3)^2
9a^10*b^-6
9*a^10*(1/(b^6))
can someone help me with all these questions?
1a. 98 cm ^2
1b. 76. 98 cm^2
2a. 42cm
2b. 7. 19 cm
3. a + b/2 (h)
4. 24 cm ^2
5. πr + 2r
6. 13. 2m
7. 45cm^2
8. 252 cm ^ 2
9. 450 cm^ 2
How to solve the area1a. The shape given is a rectangle
The formula for area of a rectangle is given as;
Area = length × width
Area = 7 × 14
Area = 98 cm ^2
1b The shape given is a semi circle
The formula for area of a semicircle is given as;
Area = 1/2 π r^2
radius = diameter/2 = 14/2 = 7cm
Area = 1/2 × 3.142 × 7 × 7
Area = 76. 98 cm^2
2a. The shape given is a rectangle
The formula for perimeter of a rectangle is given as;
Perimeter = 2 ( length + width)
Perimeter = 2 ( 14 + 7) = 2( 21)
Perimeter = 42cm
2b. The shape is a semicircle
Perimeter = π r + 2r
r= 1.4cm; diameter divided by 2
Perimeter = 3. 142(1.4) + 2(1.4)
Perimeter = 7. 19 cm
3. The formula for area of a trapezium is given as
Area = a + b/2 (h)
4. The area of the trapezium is given as;
Area = 9 + 7/2 (3)
Area = 16/2 (3)
Area = 8 × 3
Area = 24 cm ^2
5. Area of semicircle = 1/2 πr^2
Perimeter of a semicircle = πr + 2r
6. From the information given, we have the following
Area = 480 m^2
a = 20m
b = unknown
h = 13. 2m
Area = a+b/2 (h)
Substitute the values
480 = 20+b/2 (13. 2)
480 = 10+ b (13. 2)
480/13. 2 = 10 + b
10+ b = 480/ 13. 2
10 + b = 36. 36
b = 36.36 - 10
b = 26. 36m
7. The formula for area of a rhombus is given as
Area = p × q/2
Where p and q are the diagonals
Area = 7. 5 × 12/2
Area = 90/2
Area = 45cm^2
8. The formula for area for a quadrilateral is given as;
Area of quadrilateral = (½) × diagonal length × sum of the length of the perpendiculars
sum of the length = 13 + 8 = 21cm
Diagonal A= 24cm
Area = 1/2 × 24 × 21
Area = 252 cm ^ 2
9. Area of a pentagonal park = 1/2 × sum of parallel sides × height
Sum of parallel sides = 15 + 15 = 30 cm
height = 30cm
Area = 1/2 × 30 × 30
Area = 450 cm^ 2
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Please help! I am trying to do my homework but I am have trouble with these problems
The interpretation based on the confidence interval given is that the population mean will fall within the interval.
How to illustrate the information?Number of observations = 10
Sample mean = 2.60
Standard deviation = 1.07
The degree of freedom will be:
= n - 1
= 10 - 1 = 9
Confidence level = 95% = 0.95
Level of significance = 1 - 0.95 = 0.05
The value of the t critical from the t table will be 2.262.
The margin of error will be:
= 2.262 × 1.07/✓10
= 0.765
We get the 95% confidence interval for the population mean. This will be:
(2.60 - 0.765( <= U =(2.60 + 0.765)
1.83 <= 3.37
Therefore, the interpretation is that the population mean will fall within the interval.
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Find the area of the kite. 9 2 3
Answer:
33 units²
Refer to the attached page
I've shown the complete calculation over there.
Answer: 33
Step-by-step explanation:
one easy way to do it is by finding the area of the 4 triangles.
because the top two and the bottom two are the same that helps a lot. The first triangle is 9 times three and then cut your answer in half. Do the same thing for the other 9 times three triangle you will end up with 27. for the top two you would multiply 3 times two to get 6 cut 6 in half to get 3. do the same or the other triangle and now you just have to add.
3 plus 3 plus 13.5 plus 13.5
to get 33
Help me pleas I’m stuck
The measures of the angles are
The measure of angle ∠JPK is 50°The measure of angle ∠LPM is 84°The measure of angle ∠NPM is 50°The measure of angle ∠JPI is 84°The measure of angle ∠HPI is 46°How to determine the measure of the angles?Angle JPK
The given parameters are:
∠KPL = 46°
∠NPH = 25°
∠MPN = ∠NPH
By vertical angle theorem, we have:
∠JPK = ∠MPH
Where
∠MPH = ∠MPN + ∠NPH
This gives
∠MPH = ∠NPH + ∠NPH
So, we have:
∠MPH = 25° + 25°
Evaluate
∠MPH = 50°
Recall that:
∠JPK = ∠MPH
So, we have:
∠JPK = 50°
Hence, the measure of angle ∠JPK is 50°
Angle LPM
The angle on a straight line is 180°.
So, we have:
∠LPM + ∠KPL + ∠MPH = 180°
This gives
∠LPM + 46° + 50° = 180°
Evaluate
∠LPM = 84°
Hence, the measure of angle ∠LPM is 84°
Angle NPM
In (a), we have:
∠NPM = ∠NPH
This gives
∠NPM = 50°
Hence, the measure of angle ∠NPM is 50°
Angle JPI
By vertical angle theorem, we have:
∠JPI = ∠LPM
So, we have:
∠JPI = 84°
Hence, the measure of angle ∠JPI is 84°
Angle HPI
By vertical angle theorem, we have:
∠HPI = ∠KPK
So, we have:
∠HPI = 46°
Hence, the measure of angle ∠HPI is 46°
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George cuts a rectangular piece of glass down one of the diagonals as shown below. What is the length of the diagonal that he cut to the nearest whole inch? Enter only the number. An image shows a rectangle with length = 18 inches and width = 36 inches. A red dotted line crosses the rectangle from the upper left corner to the lower right corner.
The length of the diagonal that he cut to the nearest whole inch is 36 inches
TriangleA rectangle with length = 18 inchesWidth = 36 inchesA red dotted line crosses the rectangle from the upper left corner to the lower right corner to form a triangle.
Length of the diagonal of a rectangle;
Hypotenuse² = adjacent² + opposite²
= 18² + 36²
= 324 + 1296
hyp² = 1620
Take the square root of both sideshyp = √1620
hyp = 35.4964786985976
Approximately,
hypotenuse = 36 inches
Therefore, the length of the diagonal that he cut to the nearest whole inch is 36 inches.
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What’s an Inequality?
Answer:
mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Answer:
The quality of being unequal or uneven is known as the inequality.If X and Y are distinct digits such that the eight-digit number 7448X24Y is divisible by both 8 and 9, then find X - Y.
The value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7
How to determine the distinct digits X and Y?The eight-digit number is given as:
7448X24Y
Also, from the question
The number is divisible by 8 and 9
When a number is divisible by 8, then the last three digits of that number would be divisible by 8.
When a number is divisible by 9, the sum of the digits of the number would be divisible by 9.
So, we have:
24Y is divisible by 8
The possible value of Y from the above statement is 0
This is so because 240 is divisible by 8
The sum of the digits of the number would be divisible by 9.
This means that:
7 + 4 + 4 + 8 + X + 2 + 4 + Y = 29 + X + Y
Substitute 0 for Y
29 + X + Y = 29 + X + 0
Evaluate the sum
29 + X + Y = 29 + X
36 is divided by 9
So, we have
29 + X = 36
Subtract 29 from both sides of the equation
X = 7
So, we have
X = 7 and Y = 0
X - Y is calculated as:
X - Y = 7 - 0
Evaluate the difference in the above equation
X - Y = 7
Hence, the value of X - Y such that the eight-digit number 7448X24Y is divisible by both 8 and 9 is 7
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please help this is affecting my grade pls help i beg of you <3
Answer:
C - On the number line, move 3 units to the left. End at -7. The dolphin was 7 feet below sea level.
Step-by-step explanation:
The dolphin's starting point was -4 (4 feet below sea level). If the dolphin if diving down by 3 feet, you add -3 to its starting point.
-4 + -3 = -7.
how to find h’(3)
base on the graph
By the quotient rule for differentiation,
[tex]\displaystyle h'(x) = \dfrac{g(x)f'(x) - f(x)g'(x)}{g(x)^2}[/tex]
According to the plots of [tex]f[/tex] and [tex]g[/tex], we have [tex]f(3)=2[/tex] and [tex]g(3)=3[/tex].
On the interval [2, 4], [tex]f[/tex] is a line through the points (2, 5) and (4, -1), and hence has slope (-1 - 5)/(4 - 2) = -3, so [tex]f'(3)=-3[/tex]. We can similarly find [tex]g'(3)=2[/tex].
Then
[tex]h'(3) = \dfrac{3\cdot(-3)-2\cdot2}{3^2} = \boxed{-\dfrac{13}9}[/tex]
