Answer:
-1
Step-by-step explanation:
Given that:
r = sin 2θ , θ = ± π/4 , ± 3π/4
Recall that:
x = r cosθ
y = r sinθ
The differential of y with respect to x
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{dy}{d \theta}}{\dfrac{dx}{d \theta}}[/tex]
[tex]\dfrac{dy}{dx} =\dfrac{\dfrac{dy}{d \theta}}{\dfrac{dx}{d \theta}} = \dfrac{ r cos \theta + sin \theta* \dfrac{dr}{d \theta} } {\dfrac{dr}{d \theta} *cos \theta- sin \theta \ r}[/tex]
at θ = π/4 , r = sin π/2
r = 1
[tex]\dfrac{dy}{dx} = \dfrac{ r cos \theta + 2 cos (2 \theta)*sin \ \theta } {2 \ cos (2 \theta) *cos \theta- sin 2 \theta * sin \theta}[/tex]
where;
θ = π/4
[tex]\dfrac{dy}{dx} = \dfrac{ 1 \times cos (\dfrac{\pi}{4}) + 2 cos (\dfrac{\pi}{2})*sin (\dfrac{\pi}{4}) } {2 \ cos (\dfrac{\pi}{2})*cos (\dfrac{\pi}{4})- sin (\dfrac{\pi}{2}) * sin (\dfrac{\pi}{4})}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{1}{\sqrt{2}}+0 }{0-1 * \dfrac{1}{\sqrt{2}}}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{1}{\sqrt{2}} }{- \dfrac{1}{\sqrt{2}}}[/tex]
[tex]\mathbf{\dfrac{dy}{dx} =-1}[/tex]
slope of the curve (dy/dx) at theta(θ) = pi/4 is -1
1) What does the equation x = 4 represent in R^2? a) a circle.b) a plane.c) a line.d) a pointWhat does it represent in R^3? a) a plane.b) a line.c) a circle.d) a point.2) What does the equation y + 3x = 2 represent in R^3? a) a plane.b) a circle.c) a line.d) a point.What does z - 4y = 8 represent? a) a line.b) a circle.c) a point.d) a plane.What does the pair of equations y = 2, z = 8 represent? In other words, describe the set or points (x, y, z) such that y = 2 and z = 8. a) a line.b) a circle.c) a plane.d) a point.
Answer:
The equation [tex]x=4[/tex] represents in R^2 c) a line
The equation [tex]x=4[/tex] represents in R^3 a) a plane
The equation [tex]y+3x=2[/tex] represents in R^3 a) a plane
The equation [tex]z-4y=8[/tex] represents d) a plane
The pair of equations [tex]y=2,z=8[/tex] represents a) a line
Step-by-step explanation:
Let's start by studying each question :
1)
In R^2 , [tex]x=a[/tex] with [tex]a[/tex] ∈ IR is the equation of all vertical lines
In this case, the only free variable is the variable ''y''
R^2 has two dimensions (x and y) so if we set [tex]x=4[/tex] we will have only one free variable in R^2 (which is a line in R^2). Therefore, [tex]x=4[/tex] represents a line in R^2
Now, in R^3 we have three dimensions (x, y and z) so if we set [tex]x=4[/tex] we will have only two free variables (y and z) and [tex]x=4[/tex] will represent a plane (which have two dimensions) in R^3.
2) The equation [tex]y+3x=2[/tex] in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.
The equation [tex]y+3x=2[/tex] in R^3 (given that we have two free variables) represents a plane.
Using the same reasoning, the equation [tex]z-4y=8[/tex] represents a plane (given that it has two free variables : ''y'' and ''x'')
Finally, the pair of equations [tex]y=2,z=8[/tex] set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.
The final answer is a) a line.
Which problem can be solved by division of decimals? How much money does Jon need to buy 10.3 gallons of gas that costs $3.79 a gallon? What grade does Maria need on her next test to achieve a total of at least 400 points if she had 4 previous tests that had grades of 75.3, 92.1, 78.6, and 81.0? Helena saved $45.00 toward a dress that costs $78.00. How much more does she need to save? Mica spent $45.50 on 7 indoor baseball sets. How much does it cost for one set?
Answer:
Mica spent $45.50 on 7 indoor baseball sets. How much does it cost for one set?
Step-by-step explanation:
Answer:
ITS D I TOOK THE TEST
Step-by-step explanation:
Is there a known infinite product for e? What I mean is, it’s similar to an infinite series.
"e" is an irrational number because it cannot be seen as a quotient of two integers. In the bright side, it can be shown as a continued fraction. "e" may also be used as an infinite product, infinite series, and any other limit to any sequence.
Best of Luck!
Mrs. Santiago wants to buy a new dining room table. She is trying to decide between a large table that costs $548.00 and a smaller table that costs $135.00. How much money will Mrs. Santiago save if she buys the smaller table?
Answer:
$413
Step-by-step explanation:
548
- 135
413
Answer:
413.00
Step-by-step explanation:
Subtract.
548.00 minus 135.00 is 413.00.
That is the answer.
For Elizabeth's lemonade recipe, 4 lemons are required to make 2 cups of lemonade. At what rate are lemons being used in cups of lemonade per lemon?
Answer:
2 lemons per cup
Step-by-step explanation:
4/2 is two.
Answer:
2 lemons per cup
Step-by-step explanation:
HELP! WILL GIVE BRAINLIEST IF YOUR ANSWER IS RIGHT Maria lives in Mexico. Both of her parents are Mexican. Maria is a Mexican citizen. She was born in an American hospital when her parents were on a short vacation in San Diego, California. Was Maria an American citizen at birth? Explain your answer.
Yes, Maria was a "citizen" of America.
What is citizenship?A legal status and relation between an individual and a state that entails specific legal rights and duties.
Given that, Maria lives in Mexico. Both of her parents are Mexican. Maria is a Mexican citizen. She was born in an American hospital when her parents were on a short vacation in San Diego, California.
The answer is yes,
A child born in American soil will be an American citizen.
Hence, Maria an American citizen at birth.
For more references on citizenship, click;
https://brainly.com/question/18099945
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Perform the indicated operation. 11(-2), 22, 9, -22, -9 which one us it
Answer:
-22
Step-by-step explanation:
When numbers are placed closed like that, and have a parenthesis, you will multiply.
11(-2) = 11 * -2 = -22
-22 is your answer.
~
Answer:
[tex]\Huge \boxed{-22}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]11(-2)[/tex]
Multiplying,
[tex]\Longrightarrow \ \ 11*-2[/tex]
[tex]\Longrightarrow \ \ -22[/tex]
[tex]\rule[225]{225}{2}[/tex]
write a quadratic equations given the roots 5/2 and 9
Answer:
(x-5/2)(x-9).
x^2-5/2x-5/2x+45/2.
Multiply the number by 2.
which is 2(x^2-5/2x-5/2x+45/2).
2x^2-5x-5x+45.
2x^2-10x+45.
What is (6x10^6)(4x10^-1) ?
Answer:
Step-by-step explanation:
Multiply the 6 and 4 together. 6*4 = 24
The next part is a bit tricky. Add the powers on the base 10. Keep the base 10.
10^(6 - 1) = 10^5
Now put the two parts together. 24 * 10^5
The number in front of the 10 must be between 1 and 10.
So 24 can be written as 24 = 2.4 * 10^1
2.4 * 10^1 * 10^5 = 2.4 * 10^(5 + 1) = 2.4 * 10^6
what exponent will make this true? Enter your naswer in the box 10?=1,000
Answer:
10 to the 2nd power
Step-by-step explanation:
What is the domain of the given function?
Answer:
Domain = 3, 6, -1, 5, -4
Step-by-step explanation:
The Domain is the first coordinate of a coordinate set so it is x
Hope This Helps :)
Which number is a reasonable estimate for 553 +363?
A 1,300
B 1,000
600
D 200
its b because you can round 363 to 400 and 553 to 600 400 + 600 = 1000
Question Given the following functions f(x) and g(x), find (f ° g)(x).
f(x)=-x^2-x+7
g(x)=5x+4
Answer:
Step-by-step explanation:
g(x) = 5x + 4
f(5x + 4) = (5x + 4)^2 - (5x + 4) + 7
25x^2 + 40x + 16 - 5x - 4 + 7
25x^2 + 35x + 19
AWARDING BRAINLIEST!!
Beth is solving this equation: 1/x+3=3/x
She says “I can multiply both sides by x and get the linear equation 1 + 3x = 3, whose solution is x = 2/3.”
Which of the following statements makes this a correct argument, or shows that it is incorrect? Select all that apply.
Question 1 options:
After multiplying both sides by x you need to subtract 1 from both sides
You can assume x ≠ 0 because both sides are undefined if x = 0.
You cannot multiply both sides by x because you do not know what x is.
The equation is not linear, so you cannot use the methods normally used for solving linear equations.
Answer:
1. After multiplying both sides by x you need to subtract 1 from both sides
2. You can assume x ≠ 0 because both sides are undefined if x = 0.
Step-by-step explanation:
Given
[tex]\frac{1}{x} + 3 = \frac{3}{x}[/tex]
Required
Which of the options shows the validity of Beth's action
The first option answers the question and the reason is as follows;
Multiply both sides by x
[tex]x * (\frac{1}{x} + 3) = \frac{3}{x} * x[/tex]
Open the bracket
[tex]1 + 3x = 3[/tex]
As stated in option 1; Subtract 1 from both sides
[tex]1 - 1 + 3x = 3 - 1[/tex]
[tex]3x = 2[/tex]
Divide both sides by 2
[tex]x = \frac{2}{3}[/tex]
Another correct option is the option 2
Because the expression is undefined if x = 0
See Proof by substituting 0 for x
[tex]\frac{1}{0} + 3 = \frac{3}{0}[/tex]
Division by 0 is undefined.
Hence, option 2 is also correct
The other options (3 and 4) are incorrect
Isabella left a 15% tip for a meal. The total cost of the meal, including the tip, was $23. What was the cost of the meal before the tip was added?
Answer:
the meal was $3.45
Step-by-step explanation:
Answer: cost before tip is $20
Step-by-step explanation:
Tip=20(0.15)
= 3
Total = Cost + Tip
= 20 + 3
= 23
Which list shows these numbers in ascending order?
-V6, 2, -23, 2.5
1
What is an equivalent form of the following function?
f(x) = 4(x - 1)2 + 12
O A. f(x) = 4x2 - 8x + 16
O B. f(x) = 4x2 - 8x + 8
OC. f(x) = 4x2 - 2x + 16
OD. f(x) = 4x2 + 8x + 8
Since cos(x) is the derivative of sin(x), then integral 16 sin^2(x) cos(x) dx can be done by substituting u = sin (x) sin (x) and du = cos (x) cos (x)^dx. With the substitution u = sin(x), we get integral 16 sin^2 (x) cos(x) dx = 16 integral u^2 du. which integrates to + C. Substituting back in to get the answer in terms of sin(x), we have integral 16 sin^2 (x) cos (x) dx = + C.
Complete
Find the integral of [tex]f(x) = 16sin^2 (x ) cos(x) dx[/tex]
Answer:
The solution is [tex]\frac{16}{3} sin^{3}x + c[/tex]
Step-by-step explanation:
So
[tex]Let \ u = sin(x)[/tex]
=> [tex]\frac{du}{dx} = cos (x)[/tex]
=> [tex]du = cos(x)dx[/tex]
So
[tex]\int\limits {16sin^2 (x ) cos(x) dx} \, \equiv \int\limits {16u^2 du}[/tex]
=> [tex]\int\limits {16u^2 du} = 16 [\frac{u^3}{3} ] + c[/tex]
Now substituting sin(x) for u
[tex]\frac{16}{3} u^3 + c = \frac{16}{3} sin^{3}x + c[/tex]
So the integral of [tex]f(x) = 16sin^2 (x ) cos(x) dx[/tex] is
[tex]\frac{16}{3} sin^{3}x + c[/tex]
Solve the equation. -10x + 1 + 7x = 37
A. X = -15
B. X =-12
C. X = 12
D. X = 15
Answer:
B. X =-12
Step-by-step explanation:
- 10x + 1 + 7x = 37
-10x + 7x = 37 - 1
-3x = 36
x = 36/-3
x = - 12
Simplify:
(4xy^-6)^-3
[tex](4xy^{-6} )^{-3}[/tex]
Answer:
(4^-3)(x^-3) y^(18)
or
y^18/ (64 x^3)
Step-by-step explanation:
(4xy^-6)^-3
Distribute the exponent to all terms in the parentheses
(4^-3)(x^-3) (y^-6)^-3
a^ b^c = a^ (b*c)
(4^-3)(x^-3) y^(-6*-3)
(4^-3)(x^-3) y^(18)
If we do not want negative exponents
a ^ -b = 1/ a^b
y^18/( 4^3 x^3)
y^18/ (64 x^3)
Oliver reads 28 ½ pages of a book in 1 1/6 hours. Express his speed in pages per hour?
Answer:
Answer: The speed of Oliver is 24\dfrac{1}{3}24
3
1
pages per hour.
Step-by-step explanation: Given that Oliver reads 28\dfrac{1}{2}28
2
1
pages of a book in 1\dfrac{1}{6}1
6
1
hours.
We are to express his speed in pages per hour.
We will be using the UNITARY method to solve the given problem.
Number of pages read by Oliver in 1\dfrac{1}{6}=\dfrac{7}{6}1
6
1
=
6
7
hours is
=28\dfrac{1}{2}=\dfrac{57}{2}.=28
2
1
=
2
57
.
Therefore, the number of pages read by Oliver in 1 hour is given by
\dfrac{57}{2}\times\dfrac{6}{7}=24\dfrac{3}{7}.
2
57
×
7
6
=24
7
3
.
Thus, the speed of Oliver is 24\dfrac{1}{3}24
3
1
pages per hour.
Step-by-step explanation:
Plz Mark me as brainliest
you roll a die what is the probability a prime number will come up?
Answer:
1/2 or 50%
Step-by-step explanation:
Total numbers: 1 to 6
Prime numbers: 2, 3, 5
Possible outcomes= 6Favorable outcomes = 3Probability
3/6 = 1/2 or 50%Help please I don’t understand
Answer:
Answer is -6
Step-by-step explanation:
first do from small bracket -(-6)=+6
and then -6-6=-12
do-12+6=-6
58 POINTS!!! The line contains the point (8,2) and is parallel to a line with a slope of -2/3 The equation of the line is
Answer:
The answer is
[tex]y = - \frac{2}{3} x + \frac{22}{3} [/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
Since the lines are parallel their slope are also the same
So the slope of parallel line = - 2/3
So the equation of the line containing the point (8 , 2) and slope - 2/3 is
[tex]y - 2 = - \frac{2}{3} (x - 8) \\ y - 2 = - \frac{ 2}{3} x + \frac{16}{3} \\ y = - \frac{2}{3} x + \frac{16}{3} + 2[/tex]
We have the final answer as
[tex]y = - \frac{2}{3} x + \frac{22}{3} [/tex]Hope this helps you
Slope intercept form: y = mx + b
Parallel lines have the same slope, so the slope is -2/3.
We can solve using point slope form.
y - 2 = -2/3(x - 8)
y - 2 = -2/3x + 16/3
y = -2/3x + 22/3
Best of Luck!
Solve the equation for a 62=a(25-0)(25-50)
the outdoor temperature was 8 degrees at midnight the. temperature declined 5 degrees during each. of the next 3 hours what was the temperature at 3 A.M.
Which refers to the rate of change in velocity?
Answer:
acceleration refers to the rate of change in velocity
if a dog food costs 0.75 per pound, and dog bones cost 1.75 each, what is the cost of 2 bones and 25 pounds of dog food?
Answer:
2 bones and 25 pounds of dog food would cost $22.25
Step-by-step explanation:
what are all the names that apply to 1/8 Irrational,Integer,Whole,Real, Or irrational
Answer:
Rational NumberReal numbersStep-by-step explanation:
Solve for h : -37+h=-2
Answer:
h = 35
Step-by-step explanation:
Step 1: Write out equation
-37 + h = -2
Step 2: Add 37 to both sides
-37 + 37 + h = -2 + 37
h = 35