Given the equation of a curve is y=5/x²The value of dy/dx= -10/27Hence, estimate the value of 5/(2.98)²
Answers
The given equation is:
[tex]y=\frac{5}{x^2}[/tex]a. Find the value of dy/dx when x=3
Start by finding the derivative:
[tex]\frac{dy}{dx}=\frac{d(\frac{5}{x^2})}{dx}[/tex]You also can express 5/x^2 as 5*x^(-2):
[tex]\frac{5}{x^2}=5x^{-2}[/tex]You know the derivative of a power is:
[tex]\frac{d}{dx}x^n=n\cdot x^{n-1}[/tex]Apply it to your case:
[tex]\frac{d}{dx}5x^{-2}=(-2)\cdot5\cdot x^{-2-1}=-10\cdot x^{-3}[/tex]And finally:
[tex]\begin{gathered} x^{-n}=\frac{1}{x^n} \\ \text{Apply it to your equation} \\ \frac{dy}{dx}=\frac{-10}{x^3} \end{gathered}[/tex][tex]\begin{gathered} \text{When x=3} \\ \frac{dy}{dx}=\frac{-10}{3^3}=\frac{-10}{27} \end{gathered}[/tex]b. Estimate the value of 5/(2.98)^2:
[tex]\begin{gathered} y=\frac{5}{x^2}=\frac{5}{2.98^2}=0.563 \\ \text{Which also means x=2.98} \\ \text{Let's find the derivative when x=2.98} \\ \frac{dy}{dx}=\frac{-10}{2.98^3}=\frac{-10}{26.46}=-0.377 \end{gathered}[/tex]Related Questions
The height of a sand dune (in centimeters) is represented by cm, where is measured in years since . Find and , and determine what each means in terms of the sand dune. Give the values of and below, including units.
Answers
The height of the sand dune after 13 years is 324 cm. The rate of change height of sand dunes is - 8t.
Given the equation is -
f(t)=1000-4t²
f(13) = 1000 - 4 (13)²
= 1000 - 676
= 324 cm
f'(t) = - 8t
f'(13) = - 8(13)
= -104cm
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Complete Question -
The height of a sand dune (in centimeters) is represented by f(t)=1000-4t2 cm, where t is measured in years since 1995. Find f(13) and f'(13), and determine what each means in terms of the sand dune. Give the values of f(13) and f'(13) below, including units.
1. Squares with side lengths 6, 8, and 10 meters?2. Squares with areas 64 in?, 100 in?, 144 in2? 3. Two squares with side length 5 feet and a square with area 50 square feet?4. Explain how you know whether three squares will join at their corners to form a right triangle.
Answers
In order to know if 3 squares will form a right triangle,
a. The sum of the length of two of the squares must be greater than the length of the last square.
b. The lengths of the squares (if they are integers) must form a Pythagorean triple.
Pythagorean triples are:
3, 4, 5
5, 12, 13
8, 15, 17
9, 40, 41
there are more triples but we only need these for this question
c. They must conform to the Pythagoras Theorem.
[tex]\begin{gathered} \text{Pythagoras theorem is:} \\ c^2=a^2+b^2 \\ \text{where c is the largest side of the right angled triangle or hypothenus} \\ \text{while a and b are adjacent and opposite of the right angled triangle} \end{gathered}[/tex]Now we can proceed with these points at hand.
1. Squares with side lengths 6, 8, 10 can be written as:
2(3), 2(4), 2(5).
Ignoring the "2", we can see that this follows the Pythagorean triple.
therefore, 6, 8, 10 can form a right-angled triangle
2. 64, 100, 144 can be written as:
4(16), 4(25), 4(36)
Ignoring the "4", we can see that this does not follow the Pythagorean triple.
If we input the values into the Pythagoras theorem, we shall have:
[tex]\begin{gathered} 64^2+100^2\text{ = 4096 + 10000 = 14096} \\ 144^2=\text{ 20736} \\ \text{Therefore, we can s}ee\text{ that:} \\ 64^2+100^2\text{ }\ne\text{ }144^2 \end{gathered}[/tex]Therefore, 64, 100, 144 cannot form a right-angled triangle
3. Two squares with lengths 5 and a Square with an area of 50 square feet:
We need to find the length of the square with an area of 50 square feet.
[tex]\begin{gathered} \text{Area of square = l}^2 \\ \text{where l is the length of the side} \\ 50=l^2 \\ \text{square root both sides} \\ l\text{ = }\sqrt[]{50\text{ }}\text{ = 5}\sqrt[]{2} \end{gathered}[/tex]Now that we know the length of the 3rd and largest side of this triangle, we can now determine whether it is a right-angled triangle.
This case has a non-integer as part of the sides of the triangle, thus, condition b does not apply.
We must check via Pythagoras theorem:
[tex]\begin{gathered} By\text{ pythagoras:} \\ 5^2+5^2=25+25=50 \\ \text{while,} \\ (5\sqrt[]{2})^2=5^2\times(\sqrt[]{2})^2=25\times2=50 \\ \text{Thus we can s}ee\text{ that:} \\ 5,5,5\sqrt[]{2}\text{ can form a right-angled triangle} \end{gathered}[/tex]Therefore, the final answer: 1 and 3 can form a right-angled triangle but 2 cannot
4. I have given the reasons why they form a right-angled triangle above. But let me restate them:
In order to know if 3 squares will form a right triangle,
a. The sum of the length of two of the squares must be greater than the length of the last square.
b. The lengths of the squares (if they are integers) must form a Pythagorean triple.
Pythagorean triples are:
3, 4, 5
5, 12, 13
8, 15, 17
9, 40, 41
there are more triples but we only need these for this question
c. They must conform to the Pythagoras Theorem.
[tex]\begin{gathered} \text{Pythagoras theorem is:} \\ c^2=a^2+b^2 \\ \text{where c is the largest side of the right angled triangle} \\ \text{while a and b are adjacent and opposite of the right angled triangle} \end{gathered}[/tex]
24. If a ream of paper (500 sheets) is 2.125 inches thick, how thick is one sheet of paper? Give your answer in scientific notation. (1) 1.0625 x 103 (2) 42.5 x 103 (3) 4.25 x 103 (4) 4.25 x 10-3 (5) 4.25 x 10-2
Answers
When Mr. Jackson got in his car yesterday, the odometer read 187,198.9 km. When he got home, the reading was 187,399.4 km. How far did Mr. Jackson drive?
Answers
Answer:
200.5
Step-by-step explanation:
reading of odometer at beginning = 187,198.9 km
reading of odometer after reaching home = 187,399.4
distance travelled = 187,399.4 - 187,198.9 = 200.5 km
Find the distance between the pair of points (-10,-3) and (6,-3)
Answers
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]In this problem we have
(x1,y1)=(-10,-3)
(x2,y2)=(6,-3)
substitute in the formula
[tex]d=\sqrt{(-3+3)^2+(6+10)^2}[/tex][tex]d=\sqrt{(0)^2+(16)^2}[/tex]d=16 units
the distance is 16 units
Enter the answer in the space provided.Consider the functionWhat is the average rate of change of f(z) from z = 6toz=6?
Answers
To find the average rate of ch
Write the correct equation for the following statement and then solve for the given number of
miles.
You decide to rent a limo for prom. The rate is $200 plus $5 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
If you travel 45 miles what will be your total bill at the end
of the evening?
Answers
Answer:
$425
Step-by-step explanation:
You want the cost of a 45 mile trip in a limo that costs $200 plus $5 per mile.
Mileage costThe cost of each mile is $5, so the cost of 45 of them will be ...
45 × $5 = $225
Total costThere is a one-time charge of $200 added to the mileage charge, so the total cost will be ...
total bill = $200 + mileage bill
total bill = $200 +225 = $425
The total bill will be $425.
An object is launched at 18.4 meters per second (m/s) from a 36.8-meter tall platform. The equation for the object's heights at time t seconds after launch is s(t) = -4.912 + 18.4t + 36.8, where s is in meters. • When does the object strike the ground? (Select ] How long did it take the object to get to its maximum height? Select ] What was the height of the object at 3.32 seconds? | Select ]
Answers
1) To find when the object strikes the ground, we need to find the roots of the equation. Using quadratic formula:
[tex]\begin{gathered} t_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t_{1,2}=\frac{-18.4\pm\sqrt[]{18.4^2-4(-4.912)(36.8)}}{2(-4.912)} \\ t_{1,2}=\frac{-18.4\pm\sqrt[]{1061.6064}}{-9.824} \\ \\ t_1=\frac{-18.4+32.582}{-9.824}=-1.44 \\ t_2=\frac{-18.4-32.582}{-9.824}=5.2 \end{gathered}[/tex]t can't be negative, then the object strikes the ground after 5.2 seconds
2) The maximum height is the vertex of the parabola. The t-coordinate is computed as follows:
[tex]t=\frac{-b}{2a}=\frac{-18.4}{2(-4.912)}=1.87[/tex]It takes 1.87 seconds for the object to get to its maximum height
3) To find the height after 3.32 seconds, we have to replace t = 3.32 int the equation:
[tex]\begin{gathered} s(3.32)=-4.192(3.32)^2+18.4(3.32)+36.8 \\ s(3.32)=-54.142+61.088+36.8 \\ s(3.32)=43.746 \end{gathered}[/tex]The height was 43.746 meters
A college believes that 22% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 5 percentage points with 99% confidence?
Answers
Use the following expression for the number of elements of a sample, related to a certain proportion a Z-score:
[tex]n=(\frac{Z}{E})^2\cdot p\cdot q[/tex]where,
p: percentage of applicants in decimal form = 0.22 (28%)
q = 1 - p = 1 - 0.22 = 0.78
E: percentage margin = 0.05 (5%)
Z-score for 99% confidence = 2.576 (found in a Z-score table)
Replace the previous values of the parameters into the formula for n and simplify:
[tex]n=(\frac{2.576}{0.06})^2\cdot0.22\cdot0.78\approx316[/tex]Hence, approximately 316 students are needed for the sample.
You have maxed out your $800 credit card from Utopian One Bank. The interest on the card is 21%. Find the interest and the final cost you pay on this bill. (Hint this problem is computed like sales tax)
Answers
Given the question
$800 dollars
21% interest
Caclulate the question how you would calculate the sales tax.
B1 = 800 dollars
B2 = the final cost
[tex]\frac{21\times800}{100}=168[/tex]Interest rate = 168
800 + 168 = 968
968 is the final cost.
Interest rate = $168
Final cost = $968
graph (-3,2)(1,2)(8,2)(12,4)
Answers
The graph for the given points is as below:
What is graph?
The link between lines and points is described by a graph, which is a mathematical description of a network. A graph is made up of some points and the connecting lines. It doesn't matter how long the lines are or where the points are located. A node is the name for each element in a graph.
The graph for the given points attached below.
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A company sells sneakers and has a revenue that can be represented by the function R(s) = 90s – s2, where s represents the number of pairs of sneakers sold. The sneaker company has a fixed cost of $1,500, and each pair of sneakers costs $30 to manufacture. Which of the following functions represents the profit P(s) of the sneaker company?
P(s) = – s2 + 120s + 1,500
P(s) = – s2 + 60s + 1,500
P(s) = – s2 + 120s – 1,500
P(s) = – s2 + 60s – 1,500
Answers
The function that can represent the profit P(s) of the sneaker company is D. P(s) = – s2 + 60s – 1,500.
What is a function?Mathematically, a function shows a set of inputs that produce one output.
Functions have the domain (independent variable) and the codomain or range (dependent variable).
The domain is always the set of input values, while the range is the output value of the function.
Revenue function R(s) = 90s – s2
Fixed cost = $1,500
Variable cost per unit = $30
Profit = Revenue - Variable and Fixed Costs
Profit function P(s) = 90s – s2 - 30s - 1,500
= 60s - s2 - 1,500
or -s2 + 60s - 1,500
Thus, the correct profit function is Option D.
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What whole number of 2 is 1024?
Answers
Step-by-step explanation:
?????
what are you trying to ask ?
2 × 512 = 1024
2¹⁰ = 1024
what exactly do you need ?
Write the equation of a line in slope intercept form that has a
slope of
2/3 and has a
y-intercept of 10.
Answers
Answer:
y = 2/3 x + 10
Step-by-step explanation:
In the slope-intercept form, the equation for a line is expressed as follows: y = mx + b, where m represents the slope and b the y-intercept.
Hope this helps! \( ﾟヮﾟ)/
What is the slope of the line that goes through the points (1,-5) and (4,1)?OA-4/3OB.-3/4Ос. 1/2OD. 2
Answers
We can calculate the slope using the next formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
(1,-5)=(x1,y1)
(4,1)=(x2,y2)
We substitute the values into the formula above
[tex]m=\frac{1+5}{4-1}=\frac{6}{3}=2[/tex]the slope of the line is m=2, the answer is D
Help Me Please..!
[1st Person That Answer Will Get Brainlyest.]
Answers
List A i.e. |-6(5/7)|, |-6(3/7)|, |5(2/7) shoe the absolute value in order from greatest to the lowest.
What is absolute value?Without taking direction into account, absolute value defines how far away from zero a certain number is on the number line. A number can never have a negative absolute value.
By deducting 1, you may determine the numbers' decreasing order. To write the numbers 10 to 6 in descending order, for instance, we would start with 10, the greatest number in the preceding series, and continue taking away 1 until we reached the lowest number.
There are 4 lists given from which it is obtained only list A is only in which the numbers are in descending order,
|-6(5/7)| = +6.71
|-6(3/4) = +6.42
|-5(2/7)} = +5.28
The numbers are in decreasing order as,
+6.71 > +6.42 > +5.28
Thus, list A i.e. |-6(5/7)|, |-6(3/7)|, |5(2/7) shoe the absolute value in order from greatest to the lowest.
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Find the measure of the missing angle. *Don't worry about the degree symbol
Answers
this is an ange formed by two intersecting chords
then the missing angle is given by
[tex]\theta=\frac{1}{2}(arcCB+arcSD)[/tex][tex]\theta=\frac{1}{2}(191+55)[/tex][tex]\theta=\frac{1}{2}(246)[/tex][tex]\theta=123\degree[/tex]the missing angle is 123°
Given f(x)=cosxf(x)=cosx, which function below doubles the amplitude and has a period of 3π3π?g(x)=3cos2xg of x is equal to 3 cosine 2 xg(x)=12cos2xg of x is equal to 1 half cosine 2 xg(x)=2cos2x3g of x is equal to 2 cosine 2 x over 3g(x)=3cos3x2g of x is equal to 3 cosine 3 x over 2
Answers
Answer:
[tex]g(x)=2\cos \frac{2x}{3}[/tex]Explanation:
A cosine function is generally given as;
[tex]\begin{gathered} y=a\cos (b) \\ \text{where Amplitude }=|a| \\ \text{ Period }=\frac{2\pi}{|b|} \end{gathered}[/tex]Given the below function;
[tex]f(x)=\cos x[/tex]If we compare both functions, we'll see that a = 1 and b = 1.
If we need another function with double the amplitude, then the value of a in that function will be (a = 2 x 1 = 2).
If we're to have another function g(x), with a period of 3 pi, let's go ahead and determine the value of b in the second function;
[tex]\begin{gathered} \frac{2\pi}{b}=3\pi \\ 3\pi\cdot b=2\pi \\ b=\frac{2\pi}{3\pi} \\ b=\frac{2}{3} \end{gathered}[/tex]Since we now have that for the second function g(x), a = 2 and b = 2/3, therefore g(x) can be written as below;
[tex]g(x)=2\cos \frac{2x}{3}[/tex]
Answer:
The derivation that correctly uses the cosine sum identity to prove the cosine double angle identity is A. A 2-column table with 3 rows. Column 1 has entries 1, 2, 3. Column 2 is labeled Step with entries cosine (2 x) = cosine (x + x), = cosine (x) cosine (x) minus sine (x) sine (x), = cosine squared (x) minus sine squared (x)
Step-by-step explanation:
It should be noted that the cosine difference identity is found by simplifying the equation by first squaring both sides.
Therefore, the derivation that correctly uses the cosine sum identity to prove the cosine double angle identity is that a 2-column table with 3 rows. Column 1 has entries 1, 2, 3. Column 2 is labeled Step with entries cosine (2 x) = cosine (x + x), = cosine (x) cosine (x) minus sine (x) sine (x), = cosine squared (x) minus sine squared (x).
In conclusion, the correct option is A.
juans dog Stan's two feet and 3 inches tall Peters dog stands 9 in tall how much taller is juans dog than Peters dog
Answers
To answer this question, we need to transform all the values into one type of measure. In this case, we can work with inches. Then, we have:
[tex]2ft\cdot\frac{12in}{1ft}=24in[/tex]Then, we have that in two feet we have 24 inches. Then, we have:
Juan's dog: 24 inches + 3 inches ---> 27 inches tall.
Peter's dog: 9 inches tall.
Now, how much taller is Juan's dog than Peter's dog is:
[tex]\frac{\text{Juan's dog}}{\text{Peter's dog}}=\frac{27in}{9in}=3[/tex]Therefore, Juan's dog is 3 times taller than Peter's dog.
-10x - 2y = 28
y = -5x - 14
Answers
Answer:
parallel
(0, 0)
Step-by-step explanation:
I have no clue how to answer this so I'll do my best.
-10x - 2y = 28 y = -5x - 14
-2y = 10x = 28
÷-2 ÷-2 ÷-2
--------------------
y = -5x - 14
The lines are parallel
----------------------------------------------------------------------------------------------------------
I hope this helps!
The graph of a function g is shown below.
Find g (-2)
Answers
Is the comparison true
8•1/11>8
Answers
Comparison of the given inequality ( 8.1 /11 ) > 8 is not true.
As given in the question,
Given inequality is :
( 8.1 /11 )> 8
Simplify the given inequality ( 8.1 /11 ) > 8 to check the comparison is true or not.
(8.1 /11)> 8
Multiply both the sides of the given inequality by 11 we get,
( 8.1/11 ) × 11 > 8× 11
⇒ (8 .1) × ( 11/ 11) >88
(8.1 ) × 1 > 88
⇒ ( 8. 1) > 88
For the above inequality, it is not possible as 8 .1 is smaller than 88.
Therefore, comparison of the given inequality ( 8.1 /11 ) > 8 is not true.
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Which ones are considered functions
Answers
Answer:
The answer is be because the x dose not repeat
Step-by-step explanation:
the x dose not repeat just look for the non repeating x
LESSON Sine and Cosine Ratios 13-2 Practice and Problem Solving: A/B After verifying that the triangle to the right is a right triangle, use a calculator to find the given measures. Give ratios to the nearest hundredth and angles to the nearest degree. 1. Use the Pythagorean Theorem to confirm that the triangle is a right triangle. Show your work.
Answers
I saw this
is this correct? to start solving your question?
1.- Pythagorean theorem
6^2 = (5.2)^2 + (3)^2
36 = 27.04 + 9
36 = 36 Yes, it is a right triangle
2.-
[tex]\begin{gathered} \sin \text{ 1 = }\frac{5.2}{6} \\ \sin 2\text{ = }\frac{3}{6}\text{ = }\frac{1}{2} \end{gathered}[/tex]Suppose that the annual rate of return for a common biotechnology stock is normally distributed with a mean of 5% and a standard deviation of 6%. Find the probability that the one-year return of this stock will be negative. Round to four decimal places.
Answers
===================================================
Work Shown:
Compute the z score for x = 0.
z = (x - mu)/sigma
z = (0 - 0.05)/(0.06)
z = -0.83333 approximately
Then use a calculator to find that P(Z < -0.83333) = 0.2023
There's about a 20.23% chance of getting negative returns, i.e. the person will lose money on the investment.
Arc length s. Central Angle 36 feet. π/2 radiansFind the radius r of a circle with an arc length s and a central angle 0.
Answers
The formula for determining the length of an arc is expressed as
length of arc = #/360 * 2 * pi * radius
where
# represents the central angle
From the information given
length of arc = 36
We would convert from radians to degree
1 pi rad = 180 degrees
pi/2 rad = 180/2 = 90 degrees
Thus, # = 90 degrees
The equation becomes
36 = 90/360 * 2 * pi * radius
36 = 0.25 * 2 * 3.14 * radius
36 = 1.57 * radius
radius = 36/1.57
radius = 22.93 feet
A travel agent arranged a payment plan for a client. It required a down payment of $150 and 15 monthly payments of $657. What was the total cost of the plan?
Answers
Answer:
$10,005
Step-by-step explanation:
We need to find the total cost of the plan and we already know that the client need to pay $150 for downpayment and 15 monthly payments of $657.
So all we need to find is the 15 monthly payments of $657. (Which we could found with multiplying $657 with 15)
$657×15 = $9,855
Now we just add it with the downpayment ($150) to find the total cost of the plan.
$9,855+$150 = $10,005
You could write the steps like this:
$150+($657×15)=$10 005
can you help me i have to see if it is a direct variation
Answers
a direct variation is a relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. For instance,
[tex]y=mx[/tex]in which variables x and y are related by a constant m. A numerical examples of a Direct variations are:
[tex]\begin{gathered} y=-5x \\ y=\frac{2}{3}x \\ y=-\frac{7}{6}x \end{gathered}[/tex]etc. In our case, the figure shows a line. The general equation of a line is in the form
[tex]y=mx+b[/tex]This is almost the same a direc variation, however it has the y-intercept b. In our case, form the graph, we can see that
b=4. In other words, b is the point in which the lines cross y-axis.
Hence, our line doesnt represent a Direct variation since there is a y-intercept b=4.
[tex] \rm\int_{0}^{ \frac{\pi}{2} } \frac{1}{ \sqrt{1 - {sin}^{2} ( \frac{1}2) {sin}^{2} \varphi } } d \varphi \\ [/tex]
Answers
This is an another elliptical integral, but of the first kind:
[tex]\displaystyle F(k) = \int_0^{\pi/2} \frac{dx}{\sqrt{1-k^2\sin^2(x)}}[/tex]
[tex]\implies \displaystyle \int_0^{\pi/2} \frac{d\varphi}{\sqrt{1-\sin^2\left(\frac12\right)\sin^2(\varphi)}} = \boxed{F\left(\sin\left(\frac12\right)\right)}[/tex]
Pre calc, easy answer, not the best WiFi sorry if I get disconnected
Answers
So,
First of all, we should remember the following:
In this case, we have the following transformation:
[tex]f(x)=\sqrt[]{x}\to g(x)=3\sqrt[]{x}[/tex]As you can see, we're multiplying the function f by 3. So, this is an example of a vertical stretch of the function f by a factor of 3. So the answer is B.