Answers
Assuming a is constant and you want the derivatives with respect to t, we have by the chain rule
[tex](a\cos^3t)'=3a\cos^2t(\cos t)'=-3a\cos^2t\sin t[/tex]
[tex](a\sin^3t)'=3a\sin^2t(\sin t)'=3a\sin^2t\cos t[/tex]
Then for the second derivatives, we use the chain and product rules together:
[tex](a\cos^3t)''=(-3a\cos^2t\sin t)'=-6a\cos t\sin t(\cos t)'-3a\cos^3t[/tex]
[tex](a\cos^3t)''=3a\cos t(2\sin^2t-\cos^2t)[/tex]
[tex](a\sin^3t)''=(3a\sin^2t\cos t)'=6a\sin t\cos t(\sin t)'-3a\sin^3t[/tex]
[tex](a\sin^3t)''=3a\sin t(2\cos^2t-\sin^2t)[/tex]
Related Questions
0.4x - 2.5 = 1.3x + 4.7
Answers
0.4x + -2.5 = 1.3x + 4.7
Reorder the terms:
-2.5 + 0.4x = 1.3x + 4.7
Reorder the terms:
-2.5 + 0.4x = 4.7 + 1.3x
Solving
-2.5 + 0.4x = 4.7 + 1.3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1.3x' to each side of the equation.
-2.5 + 0.4x + -1.3x = 4.7 + 1.3x + -1.3x
Combine like terms: 0.4x + -1.3x = -0.9x
-2.5 + -0.9x = 4.7 + 1.3x + -1.3x
Combine like terms: 1.3x + -1.3x = 0.0
-2.5 + -0.9x = 4.7 + 0.0
-2.5 + -0.9x = 4.7
Add '2.5' to each side of the equation.
-2.5 + 2.5 + -0.9x = 4.7 + 2.5
Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.9x = 4.7 + 2.5
-0.9x = 4.7 + 2.5
Combine like terms: 4.7 + 2.5 = 7.2
-0.9x = 7.2
Divide each side by '-0.9'.
x = -8
Simplifying
x = -8
Answer:
x=-8
Step-by-step explanation:
Step 1.) 0.4x-2.5=1.3x+4.7
Step 2.) -2.5=1.3x-0.4x+4.7
Step 3.) -2.5=0.9x+4.7
Step 4.) -2.5-4.7=0.9x
Step 5.) -7.2=0.9x
Step 6.) -7.2/0.9=x
Step 7.) -8=x
10x - 5y = -25
l0x+8y=14
Answers
Greetings,
I hope you and your family are staying safe and healthy!
Answer: x = -1 and y = 3
Step-by-step explanation:
[tex]10x - 5y = -25 \\10x + 8y = 14[/tex]
Let's start by solving [tex]10x - 5y = -25[/tex] for [tex]x[/tex]
[tex]10x - 5y=-25[/tex]
Add 5y to both sides
[tex]10x - 5y + 5y = -25+5y \\10x = 5y - 25[/tex]
Now we need to divide both sides by 10
[tex]\frac{10x}{10} = \frac{5y-25}{10}[/tex]
[tex]x = \frac{1}{2} y + \frac{-5}{2}[/tex]
That's not the answer for x. We are not done yet :)
Now we need to substitute [tex]\frac{1}{2} y + \frac{-5}{2}[/tex] for [tex]x[/tex]
[tex]10x + 8y = 14\\10(\frac{1}{2} y + \frac{-5}{2} + 8y = 14[/tex]
Now we need to simply both sides
[tex]13y - 25 = 14[/tex]
Now we need to add 25 to both sides
[tex]13y - 25 + 25 = 14 + 25 \\13y = 39 \\y = \frac{39}{13} \\y=3[/tex]
We have the valuee for y! Now we need to find the value for x
To find the value of x, we need to substitute 3 for y in:
[tex]x = \frac{1}{2} y + \frac{-5}{2} \\x = \frac{1}{2} 3 + \frac{-5}{} \\x = -1[/tex]
Therefore,
The answer is x = -1 and y = 3
---------------------
Please kindly give me 5 stars and leave a thanks if you find my answer to be helpful. Thanks!
pls help i’m very confused
Answers
Answer:
m<EBD = 130 degrees
Step-by-step explanation:
We can say that Line EC is bisected by Line AD at point B. The angle CBD = 50 degrees is a supplement of the bisected line EC. With this in mind we can say:
EBD + CBD = 180
And we can solve for EBD:
EBD + CBD = 180
EBD + 50 = 180
EBD = 130
So the measure of angle EBD is 130 degrees.
Cheers.
Answer:
130°
Step-by-step explanation:
You need the remaining angle. 50° and the missing angle make up 180°. Therefore, you need to subtract 50 from 180. 180 - 50 = 130. Hence, the missing angle is 130°.
I hope it's ok if I used your photo!
find the area if each figure. round the nearest hundredth where neccessary.
Answers
Answer:
351.48cm²
Step-by-step explanation:
Heron’s Formula
Find half the perimeter (30+30+26)/2=43
It’s the square root of each side subtracted from 43, multiplied together, times 43.
√(43-30)*(43-30)*(43-26)*43=√13*13*17*43=√=123539=351.481cm²
Area of triangle is, 351. 39 cm²
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
All the sides of triangles are,
⇒ 30 cm, 30 cm, and 26 cm
We know that;
⇒ Area of triangle = √ s (s - a) (s - b) (s - c)
Where, 's' is the semi perimeter of the triangle, and a, b and c are three sides of triangle.
Here, Sides are,
⇒ a = 30
⇒ b = 30
⇒ c = 26
Hence, We get;
⇒ s = (a + b + c) / 2
⇒ s = (30 + 30 + 26) / 2
⇒ s = 86 / 2
⇒ s = 43 cm
So, The area of triangle is,
⇒ Area of triangle = √ s (s - a) (s - b) (s - c)
⇒ Area of triangle = √ 43 (43 - 30) (43 - 30) (43 - 26)
⇒ Area of triangle = √ 43 × 13 × 13 × 17
⇒ Area of triangle = 13 √ 731
⇒ Area of triangle = 13 × 27.03
⇒ Area of triangle = 351. 39 cm²
Learn more about the triangle visit;
brainly.com/question/1058720
#SPJ2
Ali is making pottery. He uses 38 of a 2-pound bag of clay to make a set of bowls. Each set has 4 bowls. Drag one expression next to each question. The correct expression for each row is a way to answer that question.
Answers
Answer:
[tex]\frac{3}{8}[/tex]
[tex]2\times \frac{3}{8} = \frac{3}{4}[/tex]
Step-by-step explanation:
According to the given scenario given that
if Ali uses [tex]\frac{3}{8}[/tex] of 2 pounds of clay for a game of 4 bowls
[tex]\frac{3}{8} (2) = \frac{6}{8} = \frac{3}{4}[/tex]
here Ali will use the number of pounds of clay to create a game
[tex]2\times \frac{3}{8} = \frac{3}{4}[/tex]
Now, we need to compute the number of pounds of clay that should be used in every bowl, we need to divide the prior outcome by 4 which is
[tex]\frac{2\times \frac{3}{8}}{4}[/tex]
It takes a bus 6 hours to take a trip. The train takes only 4 hours to make the same trip. The train travels at a rate of speed that is 25 mph more than the speed of the bus. What is the rate of the bus and the rate of the train?
Answers
Answer:
See answer is Explanation
Step-by-step explanation:
4 divided by 25 is 0.16
6 divided by 25 is 0.24
6 x 4 = 24
4 x 25 = 100
6 x 25 = 150
Solve the following equations by factorisation method.Only factorisation not dharacharya.
Answers
Hello, please consider the following.
When [tex]x_1[/tex] and [tex]x_2[/tex] are two roots, we can factorise as
[tex]ax^2+bx+c=a(x-x_1)(x-x_2)=a(x^2-(x_1+x_2)x+x_1x_2)=0[/tex]
So for the first equation, we can say that the sum of the zeros is
[tex]\dfrac{a^2+b^2}{2}=\dfrac{a^2}{2}+\dfrac{b^2}{2}[/tex]
and the product is
[tex]\dfrac{a^2b^2}{4}=\dfrac{a^2}{2}\dfrac{b^2}{2}[/tex]
So we can factorise as below.
[tex]4x^2-2(a^2+b^2)x+a^2b^2=(2x-a^2)(2x-b^2)=0[/tex]
And the solutions are
[tex]\boxed{\sf \n\bf \ \dfrac{a^2}{2} \ \ and \ \ \dfrac{b^2}{2}}[/tex]
For the second equation, we will complete the square and put the constant on the right side and take the root.
Let's do it!
[tex]9x^2-9(a+b)x+2a^2+5ab+2b^2=0\\\\9(x-\dfrac{a+b}{2})^2-9\dfrac{(a+b)^2}{4}+2a^2+5ab+2b^2=0\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{9(a+b)^2-8a^2-20ab-8b^2}{4}\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{9a^2+18ab+9b^2-8a^2-20ab-8b^2}{4}\\\\9(x-\dfrac{a+b}{2})^2=\dfrac{a^2+b^2-2ab}{4}=\dfrac{(a-b)^2}{4}\\\\(x-\dfrac{a+b}{2})^2=\dfrac{(a-b)^2}{2^2\cdot 3^2}[/tex]
We take the root, and we find the two solutions
[tex]\begin{aligned}x_1&=\dfrac{a+b}{2}-\dfrac{a-b}{6}\\\\&=\dfrac{3a+3b-a+b}{6}\\\\&=\dfrac{2a+4b}{6}\\\\&\boxed{=\dfrac{a+2b}{3}}\end{aligned}[/tex]
[tex]\begin{aligned}x_1&=\dfrac{a+b}{2}+\dfrac{a-b}{6}\\\\&=\dfrac{3a+3b+a-b}{6}\\\\&=\dfrac{4a+2b}{6}\\\\&\boxed{=\dfrac{2a+b}{3}}\end{aligned}[/tex]
Thank you.
Molly and Norachai are selling pies for a school fundraiser. Customers can buy blueberry pies and pumpkin pies. Molly sold 5 blueberry pies and 12 pumpkin pies for a total of $143. Norachai sold 10 blueberry pies and 8 pumpkin pies for a total of $142. Find the cost each of one blueberry pie and one pumpkin pie.
Answers
Answer:
Blueberry costs 9 dollars
Pumpkin costs 7 dollars
Step-by-step explanation:
Let "b" represent the price of a blueberry pie
Let "p" represent the price of a pumpkin pie
Step 1: Set equation
5b + 12p = 143 ----- 1
10b + 8p = 142 ----- 2
Step 2: Isolate 1 for "b"
5b = 143 - 12p
[tex]b = \frac{143}{5}-\frac{12}{5}p[/tex] ------- 3
Step 3: Substitute 3 into 2
[tex]10(\frac{143}{5}-\frac{12}{5} p )+8p=142\\286 - 24p + 8p = 142\\-24p + 8p = 142 - 286\\-16p = -144\\p = -\frac{144}{-16}\\ p = 9[/tex]
Step 4: Subsitute p = 9 into 1 for b
[tex]5p + 12(9) = 143\\5p + 108 = 143\\5p = 143 - 108\\5p = 35\\\frac{5p}{5}=\frac{35}{5}\\p = 7[/tex]
Therefore a pumpkin pie costs 7 dollars while a blueberry pie costs 9 dollars
Help with the question below pls, will mark Brainiest
Answers
Answer:
original price = $270 new price = $306.99
Step-by-step explanation:
To solve this we first have to find the original price.
13.7 % of the original price is $36.99 from the question.
We multiply 100 /13.7 * 13.7 /100 to get the 100% value or the original price.
We also multiply 100 /13.7 * 36.99 = $270 to get the original value.
So the original price is $270.
We add $36.99 to the original price to get the new price.
$270 + $36.99 = $306.99
Use the equation below to find v, if u = 20, a= 12, and t= 3.
v=u+at
Answers
Answer:
V is 56
Step-by-step explanation:
V= 20+12(3)
V= 20 + 36
V = 56
slope of (6,7) (9,8)
Answers
Answer:
1/3
Step-by-step explanation:
We can find the slope using the slope formula
m = (y2-y1)/(x2-x1)
= ( 8-7)/(9-6)
= 1/3
Answer:
[tex] \frac{1}{3} [/tex]
Step-by-step explanation:
Step 1: Use slope formula
[tex]m= \frac{y2 - y1}{x2 - 1} [/tex]
[tex]m = \frac{8 - 7}{9 - 6} [/tex]
[tex]m = \frac{1}{3} [/tex]
Therefore the slip of the equation is 1/3
What is the measure of ZABD?
A. 329
B. 589
C. 640
D. 1489
E. 180
Answers
Answer:
148
Step-by-step explanation:
a straight line is always 180 degrees. therefore if you subtract 32 from 180 you are left with 148 degrees.
hope this helps
Answer:
D
Step-by-step explanation:
∠ ABD and ∠ ABC are adjacent angles and are supplementary, thus
∠ ABD + 32° = 180° ( subtract 32° from both sides )
∠ ABD = 148° → D
Parallel lines m and n are cut by a transversal t. Which two angles are NOT corresponding angles?
Answers
Answer:
Hey there!
Corresponding angles are in the same position, so 1 and 6 are not corresponding angles.
Let me know if this helps :)
Answer:
A
step by step explanation
1 and 6
I need help with this plz.
Answers
========================================================
Explanation:
T = (0,0) moves to T ' = (3,0) since we shift 3 units to the right. We add 3 to the x coordinate. The y coordinate does not change since we're not shifting up or down.
Q = (-2,0) moves to Q ' = (1,0) after applying the same rule we did to point T.
M = (-3,2) moves to M ' = (0,2)
Y = (-3,3) moves to Y ' = (0,3)
See the diagram below
Write a verbal sentence to represent the equation.
x+3/4=5
Answers
Answer:
[tex]\Large \boxed{\mathrm{The \ sum \ of \ a \ number \ and \ three \ quarters \ is \ five.}}[/tex]
Step-by-step explanation:
x + 3/4 = 5
x is the unknown number.
3/4 is added to the number.
The result is 5.
The verbal sentence to represent the equation would be:
The sum of a number and three quarters is five.
What is the first derivative of p with respect to q (i.e., differentiate P with respect to q)?P = 6q2 + 3
Answers
Answer:
12qStep-by-step explanation:
Given P = 6q² + 3, we are to find the derivative of the function with respect to q. Generally if y = axⁿ;
dy/dx = naxⁿ⁻¹
Rewriting the given equation as P = 6q² + 3q⁰
Using the formula to find the derivative;
dP/dq = 2(6)q²⁻¹ + 0(3)q⁰⁻¹
dP/dq = 12q¹ + 0
dP/dq = 12q
Hence the derivative of the function P with respect to q is 12q
I need help I have to indicate how many terms it contains then copy and simplify each expression by combining like terms
Answers
Answer:
b) −3y2−2x+1
d) −4xy+4y2−y−10
Step-by-step explanation:
b) -4x + y2 - 9 + 10 - x + 3x - 4y2
(i have just underlined, italic and made it bold to show the like terms)
-4x - x + 3x = -2x
y2 - 4y2 = -3y2
-9 + 10 = 1
-2x - 3y2 + 1
d) 0 - 20 - 5xy + 4y2 + 10 - y + xy
(i have just underlined, italic and made it bold to show the like terms, however the '-y' and '4y2' have no like terms)
0 - 20 + 10 = - 10
-5xy + xy = - 4xy
-10-4xy+4y2-y
Which situation can be represented by -35 + 35? Choose all that apply.
Last night Jenny read 35 fewer pages than the night before. She reads 35 pages tonight.
A diver is 35 feet below the surface of the water and then comes up to the surface.
Eric adds 35 milliliters of water to a test tube containing 35 milliliters.
Manuel owes the electric company $35 and he pays them $35.
Answers
Answer: B & D
Step-by-step explanation:
In this scenario we want to come out with a situation where both sides are in an even playing field, as the equation solves to zero.
If a diver is 35 feet below water (-35) and he comes up to breathe, he goes up 35ft (35) meaning he is at the surface (0).
If Manuel is in debt for 35$ (-35) and then he pays off the 35$ (+35) then he is even (at 0).
Answer:
A diver is 35 feet below the surface of the water and then comes up to the surface.
For the real valued functions f(x) = x-4/x-5 and g(x) = 4x+17, find the composition fog and specify its domain using interval notation.
(F o g)(x)=
Domain of f o g:
Answers
Answer:
(f o g)(x) = [tex]\frac{4x+13}{4x+12}[/tex]
Domain : (-∞, -3) ∪ (-3, ∞)
Step-by-step explanation:
Given : f(x) = [tex]\frac{x-4}{x-5}[/tex]
g(x) = 4x + 17
We have to find the value of (f o g)(x).
Since (f o g)(x) = f[g(x)]
= [tex]\frac{(4x+17)-4}{(4x+17)-5}[/tex]
= [tex]\frac{4x+13}{4x+12}[/tex]
For the Domain of the function (f o g)(x),
Given function is defined for (4x + 12) ≠ 0
4x ≠ -12
x ≠ -3
Therefore, Domain of the function will be : (-∞, -3) ∪ (-3, ∞)
Order the following from LEAST to GREATEST: 26, 6.25, 4.7, 16
Answers
Answer:
4.7 , 6.25 , 16 , 26
Answer:
From least to greatest
4.7
6.25
16
26
4. Find the domain I've got no clue, the lesson made no sense to me either.
Answers
Answer:
x is greater than or equal to -4 but less than or equal to 4
Step-by-step explanation:
The "domain" is all of the x values on the line. But there are an infinite amount of x-values there, so it must be written as that.
Answer:
See below.
Step-by-step explanation:
The domain is simply the range of x-values the graph encompasses. From the given graph, we can see that the graph stretches from x=-4 to x=+4.
However, note that the graph does not include -4 since the point is an open circle. However, it does include +4 since the point is a closed circle. Therefore, the domain of this graph is:
In interval notation:
[tex](-4,4][/tex]
(Parenthesis on the left because -4 is not included. Brackets on the right because +4 is included.)
Simplyfy the expression 4x+(15x+y) -11y
Answers
Answer:
(64x -11)/y
Step-by-step explanation:
Multiply 4x into the parenthesis.
60x + 4xy -11y
Divide by y.
(60x + 4x -11)/y
(64x -11)/y
Steps to solve:
4x + (15x + y) - 11y
~Remove parenthesis and combine like terms
4x + 15x + y - 11y
19x - 10y
Best of Luck!
Divide 36x3 − 96x2 + 48x by 12x.
Answers
Answer:
3x^2-8x+4
Step-by-step explanation:
5.The ratio of the age of a mother and her son is 5:2. If the
age of the son is 16 years, find the age of mother.
Answers
Answer:
The age of mother is:
40 years
Step-by-step explanation:
2a = 5b
b = 16
a = age of a mother
b = age of her son
2a = 5*16
2a = 80
a = 80/2
a = 40
probe:
2*40 = 5*16 = 80
A rectangular flour canister has dimensions of 512 inches by 4 inches by 10 inches. A smaller sugar canister has dimensions of 312 inches by 3 inches by 8 inches. How much smaller is the volume of the sugar canister than the flour canister?
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Which diagram BEST represents the relationship among integers, rational numbers, and whole numbers?
Answers
Answer:
The correct option is;
A)
Step-by-step explanation:
By the representation of numbers in a figurative for, we have;
1) Th rational numbers that can be expressed in the form a/b, where a and b are real numbers
2) The integers are the direct subset of the set of rational numbers and are displayed in he next larger ellipse in the figure
3) The whole numbers are the direct subset of the set of integers.
Answer:
the correct option is A
Step-by-step explanation:
please mark as brainliest
this is the diagram that is right
I need help with Q11 ASAP!!!
Answers
Answer:
Hey there!
When z=48, y=6.
z is 8 times as much as y.
11 part 1: z=8y
11 part 2: I'm going to attach a graph I created at the bottom of this answer :)
Let me know if this helps :)
What is the value of the expression below when y=8y and z=8z? 10y-3z
Answers
Answer:
80y-24z
Step-by-step explanation:
Help 14x^2 + 10 - 3x^2- 3
a) 11x^2 + 2x + 7 ,b) 11x^2 + 10 ,c) 11x^2 + 13 ,d) 11x^2 + 7
Answers
Answer:
D) 11x² + 7
Step-by-step explanation:
combine "like" terms
How many different lines can a plane contain?
Answers
Answer:
For example if the three points are A, B and C in your diagram then there are infinitely many planes that contain the points. The final point is that if the three points do not lie on a line then there is exactly one plane that contains the points.
Step-by-step explanation: