Answers
I'm guessing the second derivative is for y with respect to x, i.e.
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}[/tex]
Compute the first derivative. By the chain rule,
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}[/tex]
We have
[tex]y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta[/tex]
[tex]x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta[/tex]
and so
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta[/tex]
Now compute the second derivative. Notice that [tex]\frac{\mathrm dy}{\mathrm dx}[/tex] is a function of [tex]\theta[/tex]; so denote it by [tex]f(\theta)[/tex]. Then
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}[/tex]
By the chain rule,
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}[/tex]
We have
[tex]f=-\dfrac ba\cot\theta\implies\dfrac{\mathrm df}{\mathrm d\theta}=\dfrac ba\csc^2\theta[/tex]
and so the second derivative is
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\frac ba\csc^2\theta}{-a\sin\theta}=-\dfrac b{a^2}\csc^3\theta[/tex]
Related Questions
When solving p2+5=8p-7, kate wrote p2+12=8p. The property she used is
Answers
Answer:
She used the addition property of equality:
p2 + 5 = 8p - 7
+7 +7
p2 + 12 = 8p
A table has an area of 12 and a perimeter of 16 ft. What are the dimensions of the table?
A.2 ft by 6 ft
B.2 ft by 8 ft
C.4 ft by 3 ft
D.4 ft by 4 ft
PLEASE HELP
Answers
Answer:
A
Step-by-step explanation:
You can check to see if it is A is you do A = Bh
The base in this question is 6 while the height is 2. To vcheck area you can multiply these to get 12 units squared. To check the perimeter, you can draw a picture. Label each side, you know that there are going to be two 2's and 2 6's so you can add those for the perimeter:
2 + 2 + 6 +6 = 16 units for the perimeter
Bobby makes trail mix for his hiking group. He mixes 1 and one eighth pounds of peanuts, 12 ounces of raisins, 11 ounces of walnuts, and 7 ounces of pretzels. If Bobby divides the trail mix equally among the 8 hikers in the group, how many ounces of trail mix does each hiker receive?
Answers
Answer:
If he divide the trail mix among 8 hikers equally each will get 48/8 = 6 ounces.
Step-by-step explanation:
He makes a trail mix . He mixed 1 1/8 pounds of peanuts , 12 ounces of raisins, 11 ounces of walnuts and 7 ounces of pretzels. Notice the weight units are not equal to we have to convert the pounds to ounces so all the weight will be in ounces.
1 pound = 16 ounces
1 1/8 pounds = ? ounces
cross multiply
1 1/8 × 16
9/8 × 16 = 18 ounces
Therefore,
His trail mix are
18 ounces of peanuts
12 ounces of raisins
11 ounces of walnuts
7 ounces of pretzels
The total weight = 18 + 12 + 11 + 7 = 48 ounces
Weight of the trail mix = 48 ounces
If he divide the trail mix among 8 hikers equally each will get 48/8 = 6 ounces.
Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!
Answers
Answer:
ishaan is 21
chris is 7
Step-by-step explanation:
Subs 3C from (1) for I in(2):
3C = C + 14 —> C = 7, I = 21
Erin built a wooden box to hold hay on her farm. Hay costs $14dollar sign, 14 per cubic meter. How much will it cost to completely fill the box with hay?
Answers
Here is the complete question.
Erin built a wooden box to hold hay on her farm.The box is 3 \text { m}3 m3, start text, space, m, end text long, 1 \text { m}1 m1, start text, space, m, end text wide, and 1 \text { m}1 m1, start text, space, m, end text high.Hay costs $14dollar sign, 14 per cubic meter. How much will it cost to completely fill the box with hay?
Answer:
it cost $42 to completely fill the box with hay
Step-by-step explanation:
Given that :
The length of the wooden box = 3m ; the width of the box = 1m and the height of the box = 1 m; we can easily determine the volume of the rectangular wooden box;
We all know it would assume the shape of a rectangular prism and it's volume = L × W × H
Thus; the volume of the box = . 3 m × 1 m × 1 m = 3 m³
However, the question proceeds by stating it that the wooden box cost $14 per cubic meter;
So , if 1 cubic meter = $14;
three cubic meters = $14 × 3 = $42
Hence; it cost $42 to completely fill the box with hay
what is the remainder when 22,714 is divided by 886?
Answers
22714-886*25=564
564 is the remainder.
The remainder of the equation A = 22,714 / 886 is given by R = 564
What do you mean by an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It displays the similarity of the connections between the phrases on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.
Given data ,
Let the remainder be represented as R
Let the equation be represented as A
Now , the value of A is
Let the first number be p = 22,714
Let the second number be q = 886
Now , A = p/q
On simplifying , we get
A = 22,714 / 886
886 x 25 = 22150
So , the difference between 22714 - 22150 = 564
Therefore , the value of R is 564
Hence , the remainder is 564
To learn more about equations click :
https://brainly.com/question/19297665
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Plz answer fast with steps
The product of two consecutive odd numbers is 10 more than the square of the smaller number.Find the smaller number.
If you answer i will give you 50 points
Answers
Answer: 5 and 7
Step-by-step explanation:
(x)*(x+2)-10=(x)^2
x^(2)+2x-10=x^2
x^(2)+2x=x^2+10
2x=10
x=5
x+2=5+2=7
Which table represents an exponential function?
Answers
Answer:
C
Step-by-step explanation:
The expression in C is actually defined as y = 5^(x) which is an exponential function.
Answer:
Table C
Step-by-step explanation:
Table C expression is defined as y = 5^(x) which makes it a exponential function.
I need help with this can someone please please help me
Answers
Answer:
SAS
Step-by-step explanation:
A carpenter must pick up a wooden beam from the Home Depot. The wooden beam is 12 feet long. The bed of his truck is 5.5 ft by 8 ft by 2 ft. If he puts the beam in the bed diagonally, how much will the beam stick out the back of the truck
Answers
Answer:
Beam stick out = 2.09 ft
Step-by-step explanation:
Given:
Length of wooden beam = 12 ft
Side of bed = 5.5 ft by 8 ft by 2 ft
Find:
Length of wooden beam needed.
Computation:
[tex]Length\ of \ diagonal = \sqrt{a^2+ b^+ c^} \\\\\\ Length\ of\ diagonal = \sqrt{5.5^2+ 8^2+ 2^2}\\\\ Length\ of\ diagonal = \sqrt{30.25+64+4}\\\\Length\ of\ diagonal = \sqrt{98.25}\\\\Length\ of\ diagonal = \sqrt{30.25+64+4}\\\\Length\ of\ diagonal = 9.91[/tex]
Length of wooden beam needed = 9.91 ft
Beam stick out = 12 ft - 9.91 ft
Beam stick out = 2.09 ft
Find the volume of a right circular cone that has a height of 17.7 cm and a base with a diameter of 15.8 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answers
Answer:
[tex]1156.8cm^3[/tex]
Step-by-step explanation:
The volume of a cone is given as:
[tex]V =\frac{1}{3} \pi r^2h[/tex]
where r = radius
h = height of cone
The height of the cone is 17.7 cm and its base radius is 7.9 cm (diameter is 15.8 cm).
Its volume is:
[tex]V = \frac{1}{3} * \pi = 7.9^2 * 17.7\\ \\V = 1156.8cm^3[/tex]
Answer:
1157.3cm^3
Step-by-step explanation:
voume of a cone =V=πr^2h^3
Diameter = 15.8cm
Height = 17.7cm
Radius = diameter/2
= 15.8/2 = 7.9cm
Pi = 22/7
V = 22/7 ×7.9×7.9×17.7/3
= 22/7×62.41×5.9
V = 1157.25cm^3
Hence the volume of the cone is 1157.3cm^3
to the nearest 10th
At Baskin Robbins, you can choose between the flavors (vanilla, chocolate, cookies 'n cream, strawberry, mango sorbet and mint chocolate chip), the number of scoops (1, 2 or 3), and if you want it in a cone or a cup. What is the probability of someone choosing cookies 'n cream ice cream with 2 scoops?
Answers
Answer:
[tex]\frac{1}{18}[/tex]
Step-by-step explanation:
Given:
Flavors of ice cream are vanilla, chocolate, cookies 'n cream, strawberry, mango sorbet and mint chocolate chip.
Number of scoops can be 1, 2 or 3.
To find: probability of someone choosing cookies 'n cream ice cream with 2 scoops
Solution:
Probability refers to chances of occurrence of some event. Two events A and B are said to be independent if probability of one event does not depend on the probability of the other event.
For such events,
P(A and B)= P(A)×P(B)
Probability = number of favourable outcomes/Total number of outcomes
In the given question, cookies 'n cream ice cream with 2 scoops can be in a cone or a cup.
Therefore,
probability of someone choosing cookies 'n cream ice cream with 2 scoops =( probability of choosing cookies 'n cream ice cream × probability of having two scoops of ice-cream × probability of having ice-cream in a cup )+ (probability of choosing cookies 'n cream ice cream × probability of having two scoops of ice-cream × probability of having ice-cream in a cone )
= [tex]\left ( \frac{1}{6} \right )\left ( \frac{1}{3} \right )\left ( \frac{1}{2} \right )+\left ( \frac{1}{6} \right )\left ( \frac{1}{3} \right )\left ( \frac{1}{2} \right )[/tex]
=[tex]=\frac{1}{36}+\frac{1}{36}\\=\frac{2}{36}\\=\frac{1}{18}[/tex]
A similar right triangle would be created by a rise of 8 and a run of
Answers
Answer:
It would be a run of 3
Step-by-step explanation:
Answer:
The slope is 4/3, so if the rise is increased by 8, then the run must increase by 6.
Step-by-step explanation:
Evaluate m^0-n^2 form=2 and n=-1
Answers
the terms in the sequence increase by the same amount each time ? ? 17 ? ? 29 a)work out the missing terms b)work out in terms of n the nth term of the sequence
Answers
Answer:
The missing terms are 9,13,21 and 25
The nth term is 4n + 5
Step-by-step explanation:
From the arrangement, we can see that 17 is the third term while 29 is the 6th term
Now is this sequence arithmetic or geometric?
Since it increases by the same amount each time, then it is an arithmetic sequence.
Mathematically the third term in an arithmetic sequence with first term a and common difference d is ;
a + 2d = 17 •••••(i)
While for the sixth term, we have
a + 5d = 29 ••••••(ii)
The equations are obtainable for the nth term of an arithmetic sequence which can be written as;
Tn = a + (n-1)d
where a is the first term, n is the term number and d is the common difference
Now solving both equations simultaneously;
We can subtract equation i from ii
Thus;
5d-2d = 29-17
3d= 12
d = 12/3 = 4
we can substitute the value of d in any of the equations to get a
let’s use 1
That would be;
a + 2d= 17
a + 2(4) = 17
a + 8 = 17
a = 17-8
a = 9
Now the first term is 9
Second would be 9 + 4 = 13
Fourth would be 3rd + d = 17 + 4 = 21
Fifth would be 4th + d = 21 + 4 = 25
So the sequence now correctly arranged would be;
9,13,17,21,25,29
where 9,13,21 and 25 are the missing terms
b. Mathematically the nth term of the sequence is
a + (n-1)d
let’s substitute the values of a and d , we have
9 +(n-1)4
9 + 4n-4
4n + 5
for what value of x would the quotient (2x^2+3x-4÷(×+4) not make sense
Answers
Answer:
-4
Step-by-step explanation:
No quotient is defined when the denominator is zero. Here, the denominator will be zero for x = -4.
The value -4 does not make sense for x in this quotient.
How many grams of water would require 4000 joules of heat to raise its temperature from
65°C to 100°C? The specific heat of water is 4.181?
Answers
Answer: 27.33 g water
Step-by-step explanation:
For this problem, we will need to use the equation for heat: q=mCΔT. Since we are given heat, change in temperature, and specific heat, all we have to do is plug them in to find grams.
4000J=m(4.181J/g°C)(100-65°C) [find change in temperature]
4000J=m(4.181J/g°C)(35°C) [divide both sides by specific heat and change in temperature]
m=27.33 g
I’m lazy to do this XD But I’m kinda confused
Answers
Answer:
1) 20 Students 2) 5 Students 3) 11 Students
Step-by-step explanation:
1) Count how many numbers are there (not digits)
2) Count the number of 3's and 4's found
3) Count the number of times a number equal to or greater than 6 appears in the data range.
Solve for x.
[tex] \frac{x}{2} = - 7[/tex]
Answers
Answer:
x = -14
Step-by-step explanation:
[tex]\frac{x}{2}[/tex] = -7
multiply 2 on both sides
the 2's cancel out on the fraction side, leaving x = -7(2)
multiply -7 and 2 to get -14
x = -14
Answer:
-14
Step-by-step explanation:
We must find out what divided by 2 equals -7
So we work backwards
2(-7)
2(-7)=-14
When multiplying negative and positive you get negative
Plug in -14 in x
-14/2=-7
If you can't solve it put it in calculator
Hope this helps plz mark brainliest!
A rectangle has length 9 cm and with 7 cm. The rectangle is to be enlarged by scale factor of 4. Calculate the length of the enlargement.
13cm
28cm
36cm
64cm
Answers
Answer:
i think 28cm is the answer.
the distance between the points (-3,0) and (4,0) is
Answers
Answer:
[tex] \sqrt{7} [/tex]
Step-by-step explanation:
[tex] \sqrt{(4 - ( - 3) + (0 - 0)} [/tex]
[tex] \sqrt{(4 + 3) + 0} [/tex]
[tex] \sqrt{7 + 0} [/tex]
[tex] \sqrt{7} [/tex]
Answer:
7
Step-by-step explanation:
Two points P1 (x1,y1) and P2(x2,y2)
d=SQRT((x2-x1)^2+(y2-y1)^2))
choose your points
let (-3,0) be (x1,y1)
let (4,0) be (x2,y2)
Substitute the values into the equation
SQRT((4-(-3))^2+(0-0)^2))
Simplify
SQRT(7^2+0)
Square root of 7 squared is 7 or -7, however distance cannot be negative so the answer is 7
This applies to all two points however there is a faster solution for these two points as they have the same y value meaning you could've just drawn a line between these two points on a Cartesian plane and counted 7.
what is 7.17+25.8≈ equal to?
Answers
Answer:
7.17 + 25.8 = 32.97
Answer:
7.17+25.8= 32.97
the answer is above
I WILL MARK BRAINLIEST
If a tuna can has a diameter of 6.5 cm , and a height of 3 cm , determine the area of the label. (I'm only asking for the label, not the whole thing :))
Answers
Answer:
61.27cm^2Step-by-step explanation:
The tuna can has a shape of a cylinder, and the area of the tuna lablel is the lateral surface area of the can
[tex]A=2\pi rh[/tex]
Data
diameter d= 6.5cm
radius r = [tex]\frac{diameter}{2}[/tex]= [tex]\frac{6.5}{2} = 3.25cm[/tex]
height h= 3cm
leteral surface area
[tex]A=2*3.142*3.25*3\\= 61.269\\=61.27cm^2[/tex]
Can someone help me please
Answers
Answer:
Can't properly see the question mate
Step-by-step explanation:
Answer:
165
Step-by-step explanation:
A whole line equals to 180 degrees.
180-15=165
Hope this helps plz mark brainliest!
Find the length of side b to two decimal places
Answers
Answer:
b = 14.34
Step-by-step explanation:
sin(Θ) = (Opposite/Hypotenuse)
sin(35)= (b/25)
25 x sin(35) = 14.33941091
Work out 97.974436 + 14 give your answer to 2 decimal places
Answers
Answer:
111.97
Step-by-step explanation:
97+14=111
to 2dp =.97
•°•=111.97
✨Could y'all help me pls cuz im dumb soooo imma give BRAINLIEST and don't jus pick a random answer (-_-")✨
The vertices of a triangle are located at the points A(-1, 0), B(-2, 2), and C(3, 3). A'B'C' is the result of rotating ABC 180° about the origin. Which statement can be used to find the coordinates of the vertices of A'B'C'??
A. multiply each x-value by -1 and keep each y-value the same
B .multiply each x-value by -1 and multiply each y-value by -1
C. multiply each x-value by -1, keep each y-value the same and switch their places
D. keep each x-value the same, multiply each y-value by -1 and switch their places
Answers
Answer:
multiply both the x value and y value by -1
Find the sticker price for a vehicle with the following features and costs: suggested retail price of $15,250, destination charge of $359, equipped with AC, tinted window, and a custom sound system for $800, $210, and $490, respectively.
$16,260
$17,109
$16,050
$16,850
Answers
Answer: The correct answer would be $17,109.
Step-by-step explanation:
The reasoning behind this answer is quite simple and easy to approach.
The suggested retail price is the base price for the vehicle and any other prices presented in the problem would be in addition to the base price.
So, with this information, we know that the base price is $15,250 and that the additional options would be $359 + $800 + $210 + $490.
Therefore, after completing the math for the additional options and adding them to the base price, you will receive the final cost of $17,109.
A bag of 60 skittles has an equal amount of red, orange, yellow, green, and purple what is the probability of choosing a green
Answers
Answer:
1/5
Step-by-step explanation:
60 /5 = 12
So there are 12 red, 12 orange, 12 yellow, 12 green, 12 purple
P(green) = green/ total = 12/60 = 1/5
Answer:
If a bag of skittles has and equal amount of red,orange,yellow,green and purple there are 60 colors and 5 colors so 60 skittles and 5 colors divided give u 12 so that means that there are 12 skittles of each color so the probability would be 12 out 60 skittles
Step-by-step explanation:
On a coordinate plane, a line goes through points (negative 2, 0) and (0, 2). Study the graph of the line. Use the drop-down menu to find its equation. The equation of the line is .
Answers
Answer:
[tex]y=x+2[/tex]
Step-by-step explanation:
Finding Slope:We are given the points (-2,0) and (0,2).
Slope is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{2-0}{0-(-2)}=\frac{2}{2} = 1[/tex]
The slope is one.
Finding the Y-intercept:So far we have [tex]y=x+b[/tex].
We can use a point to find 'b', the y-intercept.
I will use (0,2):
[tex]2=0+b\\2-0=0-0+b\leftarrow \text {Subtraction Property of Equality} \\\boxed {2=b}[/tex]
The y-intercept is 2.
Final Equation:The equation of the line is [tex]y=x+2[/tex].
In slope equations, the 'one' is commonly hidden.
Answer:
y = x + 2
Step-by-step explanation:
