Answer:
c) 8
Step-by-step explanation:
its C. because 17-9=8.
Identify the graph of x^2-5x+y^2=3 for theta π/3 and write and equation of the translated or rotated graph in general form.
Answer:
The answer is circle; 2(x')² + 2(y')² - 5x' - (5√3)y' - 6 = 0 ⇒ answer (b)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
* x² - 5x + y² = 3
∵ A = 1 , B = 0 , C = 1
∴ B² - 4AC = (0) - 4(1)(1) = -4 < 0
∵ B² - 4AC < 0
∴ it will be either a circle or an ellipse
* Lets use this note to chose the correct figure
- If A and C are equal and nonzero and have the same sign,
then the graph is a circle.
- If A and C are nonzero, have the same sign, and are not equal
to each other, then the graph is an ellipse.
∵ A = 1 an d C = 1
∴ The graph is a circle.
* To find its center of the circle lets use
∵ h = -D/2A and k = -E/2A
∵ A = 1 and D = -5 , E = 0
∴ h = -(-5)/2(1) = 2.5 and k = 0
∴ The center of the circle is (2.5 , 0)
* Now lets talk about the equation of the circle and angle Ф
∵ Ф = π/3
- That means the graph of the circle will transformed by angle = π/3
- The point (x , y) will be (x' , y'), where
* x = x'cos(π/3) - y'sin(π/3) , y = x'sin(π/3) + y'cos(π/3)
∵ cos(π/3) = 1/2 and sin(π/3) = √3/2
∴ [tex]y=\frac{\sqrt{3}}{2}x'+\frac{1}{2}y'=(\frac{\sqrt{3}x'+y'}{2})[/tex]
∴ [tex]x=\frac{1}{2}x'-\frac{\sqrt{3}}{2}y'=(\frac{x'-\sqrt{3}y'}{2})[/tex]
* Lets substitute x and y in the equation x² - 5x + y² = 3
∵ [tex](\frac{x'-\sqrt{3}y'}{2})^{2}-5(\frac{x'-\sqrt{3}y'}{2})+(\frac{\sqrt{3}x'-y'}{2})^{2}=3[/tex]
* Lets use the foil method
∴ [tex]\frac{(x'^{2} -2\sqrt{3}x'y'+3y')}{4}-\frac{(5x'-5\sqrt{3}y')}{2}+\frac{(\sqrt{3}x'+2\sqrt{3}x'y'+y'^{2})}{4}[/tex]=3
* Make L.C.M
∴ [tex]\frac{(x'^{2}-2\sqrt{3}x'y'+3y'^{2})}{4}-\frac{(10x'-10\sqrt{3}y')}{4}+\frac{(3x'^{2}+2\sqrt{3}x'y'+y'^{2})}{4} =3[/tex]
* Open the brackets ∴[tex]\frac{x'^{2}-2\sqrt{3}x'y'+3y'^{2}-10x'+10\sqrt{3}y'+3x'^{2}+2\sqrt{3}x'y'+y'^{2}}{4}=3[/tex]
* Collect the like terms
∴ [tex]\frac{4x'^{2}+4y'^{2}-10x'+10\sqrt{3}y'}{4}=3[/tex]
* Multiply both sides by 4
∴ 4(x')² + 4(y')² - 10x' + (10√3)y' = 12
* Divide both sides by 2
∴ 2(x')² + 2(y')² - 5x' + (5√3)y' = 6
∵ h = -D/2A and k = E/2A
∵ A = 2 and D = -5 , E = 5√3
∴ h = -(-5)/2(2) = 5/4 =1.25
∵ k = (5√3)/2(2) = (5√3)/4 = 1.25√3
∴ The center of the circle is (1.25 , 1.25√3)
∵ The center of the first circle is (2.5 , 0)
∵ The center of the second circle is (1.25 , 1.25√3)
∴ The circle translated Left and up
* 2(x')² + 2(y')² - 5x' - (5√3)y' - 6 = 0
∴ The answer is circle; 2(x')² + 2(y')² - 5x' - (5√3)y' - 6 = 0
* Look to the graph
- the purple circle for the equation x² - 5x + y² = 3
- the black circle for the equation (x')² + (y')² - 5x' - 5√3y' - 6 = 0
Answer:
B
Step-by-step explanation:
edge
If you're any good at compound inequalities.
Cindy has $20 to spend at the store. She buys a pack of colored pencils that cost $4 and jelly beans that cost $2 per pound. If she spends more than $8 at the store, write a compound inequality that shows the possible number of pounds of jelly beans she could have purchased.
Answer:
Step-by-step explanation:
Let x be the amount of colored pencils she buys, and let y be the number of jelly beans that she buys. We have the following inequalities..
4x + 2y ≤ 20 (the cost times the amount has to be less than or equal to 20)
4x + 2y > 8 (she spends more than $8)
We can rewrite the inequality like this...
8 < 4x + 2y ≤ 20
Now reduce since all coefficients are even, they can be divided by 2
4 < 2x + y ≤ 10
We want values of x and y that can satisfy the situation.
There are many points,
If x = 1, then you can have y =3 to 8
If x = 2, then you can have y = 1 to 6
If x = 3, then you can have y = 1 to 4
If x = 4, then you can have y = 1 or 2
x = 5, the y = o
Final answer:
To find the possible number of pounds of jelly beans Cindy could purchase, we set up a compound inequality considering the $4 spent on colored pencils and the $2 per pound cost of jelly beans. Solving the inequality 4 < 4 + 2x < 20 gives us the range 0 < x < 8, meaning Cindy could have bought more than 0 pounds but less than 8 pounds of jelly beans.
Explanation:
To solve the problem involving Cindy's shopping at the store, let's create a compound inequality with the following conditions: she has $20 to spend, she has already spent $4 on colored pencils, and the jelly beans cost $2 per pound. Cindy wants to spend more than $8 in total at the store, which includes the cost of the pencils and the jelly beans.
Let's define x as the number of pounds of jelly beans that Cindy can purchase. The cost of the jelly beans is $2 per pound, so the total cost for the jelly beans is $2x.
Since she spent $4 on pencils, adding the cost of the jelly beans needs to be more than $4 (to exceed the $8 total spending) but less than $20 (to stay within her budget). Hence, the compound inequality will be:
4 < 4 + 2x < 20
Now let's solve for x:
First, subtract 4 from all parts of the inequality:
0 < 2x < 16
Next, divide all parts by 2:
0 < x < 8
The solution tells us that Cindy could have purchased more than 0 but less than 8 pounds of jelly beans.
Find the inverse function:
Given F(x)= (8-2x)^2
Final answer:
To find the inverse function of a given function, interchange x and F(x) and solve for x. The steps involve replacing F(x) with y, interchanging x and y, and then solving for y.
Explanation:
To find the inverse function of F(x) = (8 - 2x)², we need to switch the roles of x and F(x) and solve for x. Step by step:
Replace F(x) with y: y = (8 - 2x)²
Interchange x and y: x = (8 - 2y)²
Solve the resulting equation for y: y = 4 - √(x) / 2
The function F(x) = (8 - 2x)² does not have an inverse function because it's not one-to-one. Instead, for all x, the inverse is a constant function [tex]\( F^{-1}(x) = 4 \)[/tex].
To find the inverse function of F(x) = (8 - 2x)², we need to switch the roles of x and y and then solve for y. So, let's start by writing y instead of F(x):
y = (8 - 2x)²
Now, our goal is to solve this equation for x. First, we'll expand the expression:
y = (8 - 2x)(8 - 2x)
y = 64 - 16x - 16x + 4x²
y = 4x² - 32x + 64
Now, to find the inverse, we switch x and y and solve for y :
x = 4y² - 32y + 64
This is a quadratic equation in terms of y, so we need to solve it. To do that, we can use the quadratic formula:
[tex]\[ y = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
where a = 4, b = -32, and c = 64. Plugging in these values:
[tex]\[ y = \frac{{32 \pm \sqrt{{(-32)^2 - 4(4)(64)}}}}{{2(4)}} \][/tex]
[tex]\[ y = \frac{{32 \pm \sqrt{{1024 - 1024}}}}{{8}} \][/tex]
[tex]\[ y = \frac{{32 \pm \sqrt{0}}}{{8}} \][/tex]
[tex]\[ y = \frac{{32 \pm 0}}{{8}} \][/tex]
[tex]\[ y = \frac{{32}}{{8}} \][/tex]
y = 4
So, the inverse function of F(x) is [tex]\( F^{-1}(x) = 4 \)[/tex].
This result suggests that the function F(x) is not one-to-one, meaning it doesn't have an inverse that's a function. Instead, it suggests that for every value of x, the function F(x) produces the same output, which is 4. Therefore, F(x) doesn't have a unique inverse function.
Which of the following number lines models the expression below?
-2.5 + (-1)
Answer:
The first option i.e a
Step-by-step explanation:
- 2.5 + (-1) = - 2.5 -1 = -3.5
and the arrow indicating towards -3.5 is first option
MATH HELP PLEASE I WILL MARK BRAINLIEST 1st and 2nd picture are both for question 1 the 3rd picture is a different question
Kerim bought a $2,000 bicycle. The bicycle's value depreciates, or decreases, by $300 a year. Which graph represents this situation?
Answer:First one is D
Step-by-step explanation:
The graph passses through the pints neccessary for it to decrease by 300
Your company has a plan that matches your retirement contributions up to 2% of your salary. Your annual salary is $22,000. You are paid bi-weekly (26 times per year). How much should you contribute to the retirement account each pay period to take full advantage of the company match
Answer:
The contribution is $ [tex]16.92\\[/tex] per biweekly payment
Step-by-step explanation:
Salary received in each of the [tex]26 \\[/tex] pay is
[tex]\frac{2}{100} * \frac{22000}{26} \\= 16.92\\[/tex]
Final answer:
To take full advantage of your company's retirement match, contribute at least $16.92 from each bi-weekly paycheck to your retirement account, which is 2% of your annual salary divided by 26 pay periods.
Explanation:
To determine how much you should contribute to the retirement account each pay period to take full advantage of the company match, you need to calculate 2% of your annual salary and then divide that number by the number of pay periods in a year. Here's the step-by-step calculation:
Calculate 2% of your annual salary ($22,000): 0.02 × $22,000 = $440.Divide the annual match by the number of pay periods: $440 ÷ 26 = approximately $16.92.To fully utilize the company's matching program, you should contribute at least $16.92 from each bi-weekly paycheck to your retirement account.
PLEASE HELP!! TIMED QUESTION!!
Solve for x.
y=x^2 +23
A. x= +/- sq root y +23
B. x = y - 23
C. x= +/- sq root y = 23
D. x = y + 23
y=×^2+23
Answer letter B
×=y-23
A recent survey by the cancer society has shown that the probability that someone is a smoker is P(S)=0.29. They have also determined that the probability that someone has lung cancer, given that they are a smoker is P(LC|S)=0.552. What is the probability (rounded to the nearest hundredth) that a random person is a smoker and has lung cancer P(S∩LC) ?
0.53
0.04
0.14
0.16
Answer:
The correct answer option is P (S∩LC) = 0.16.
Step-by-step explanation:
It is known that the probability if someone is a smoker is P(S)=0.29 and the probability that someone has lung cancer, given that they are also smoker is P(LC|S)=0.552.
So using the above information, we are to find the probability hat a random person is a smoker and has lung cancer P(S∩LC).
P (LC|S) = P (S∩LC) / P (S)
Substituting the given values to get:
0.552 = P(S∩LC) / 0.29
P (S∩LC) = 0.552 × 0.29 = 0.16
Find the slope of the line
40 Points!
Answer:
-1/2
Step-by-step explanation:
Rise in X / Rise in Y
1 / 2 = 1/2
The answer to ur question is slope =-1/2
Choose the function that represents the graph of the transformation of f(x) = |x| that opens down and has a vertex of (3,2)
f(x) = |x - 3| - 2
f(x) = -|x - 3| + 2
f(x) = |x + 3| + 2
f(x) = -|x + 3| + 2
Answer:
f(x) = -|x - 3| + 2.
Step-by-step explanation:
f(x) = |x| is shaped like a V and the vertex is at (0, 0). f(x) = -|x| is a reflection in the x-axis so will be an inverted V , opening down. f(x) = - |x - 3| will be the -|x| moved 3 units to the right with the vertex at (3, 0). To bring the vertex to (3, 2) it will move upwards 2 units.
So it is f(x) = -|x - 3| + 2.
f(x)=-|x-3|+2
Negative before the abs value inverts the graph and it moves right 3 and up 2
Use the binomial expression (p+q)n
to calculate a binomial distribution with n = 5 and p = 0.3.
Answer:
{0.16807, 0.36015, 0.3087, 0.1323, 0.02835, 0.00243}
Step-by-step explanation:
The expansion of (p+q)^n for n = 5 is ...
(p+q)^5 = p^5 +5·p^4·q +10·p^3·q^2 +10·p^2·q^3 +5·p·q^4 +q^5
When the probability p=0.3 and q = 1-p = 0.7 the terms of this series correspond to the probabilities of 5, 4, 3, 2, 1, and 0 favorable outcomes out of 5 trials.
For example, p^5 = 0.3^5 = 0.00243 is the probability of 5 favorable outcomes in 5 trials where the probability of each favorable outcome is 0.3.
___
The attachment shows the calculation of these numbers using a graphing calculator. It lists them in reverse order of the expansion of (p+q)^5 shown above, so that they are the probabilities of 0–5 favorable outcomes in the order 0–5.
Graph the function. Describe its position relative to the graph of the indicated basic function.
f(x)= 4^x-3 ; relative to f(x)= 4^x
Answer:
The answer is (b) moved right 3 units and moved down 3 units
Step-by-step explanation:
∵ f(x) = 4^x ⇒ red in the graph
∵ f(x) = 4^(x-3) - 3 ⇒ blue in the graph
∵ x becomes x - 3 ⇒ means:
The graph moved right 3 units
∵ f(x) = 4^x becomes 4^(x-3) - 3 ⇒ means:
The graph moved down 3 units
∴ The answer is (b)
The graph of f(x) = 4ˣ - 3 is shifted down 3 units compared to the graph of f(x) = 4ˣ
What is an exponential function?An exponential function is in the form:
y = abˣ
Where y,x are variables, a is the initial value of y and b is the multiplication factor.
The graph of f(x) = 4ˣ - 3 and f(x) = 4ˣ is attached.
The graph of f(x) = 4ˣ - 3 is shifted down 3 units compared to the graph of f(x) = 4ˣ
Find out more on exponential function at: https://brainly.com/question/12940982
If (x, y) is a solution to the system of equations, what is the value of x? 2x + 1 2 y = 2 1 2 x + 2y = 6 A) 4 17
Answer:
(1.5, 1.5)
Step-by-step explanation:
To solve the system of equations, use elimination, substitution, or graphing to find the solution. The solution is the point (x,y) where they intersect.
Graph 2x + 12y = 21 and 2x + 2y = 6.
See attached picture.
The solution is (1.5, 1.5).
(Q9) How does the value of c affect the graph of f(x) = ex+c?
What's the answers to this? I'm not sure if I am correct. HELPPPPPPP
[tex] ln( \sqrt{ex {y}^{2} {z}^{5} } ) \\ = ln{(ex {y}^{2} {z}^{5} ) }^{ \frac{1}{2} } \\ = \frac{1}{2} ln(ex {y}^{2} {z}^{5} ) \\ = \frac{1}{2} ln(e) + \frac{1}{2} ln(x {y}^{2} {z}^{5} ) \\ = \frac{1}{2} + \frac{1}{2} ln(x {y}^{2} {z}^{5} ) [/tex]
Answer:
Answer A B and D
Step-by-step explanation:
This one requires and eagle eye. You have to be a bit careful with it.
The one you checked (D) is correct. There are a couple more and one is really tricky.
The first one is actually correct.
So is the second one, which I'll show first. Only C is incorrect.
======
B]
ln(e^(1/2) + ln(x^(1/2)) + ln(y^(2/2) + ln(z^(5/2))
1/2 + ln(x^(1/2)) + ln(y) + (5/2) ln(z)
1/2 + 1/2 ln(x) + ln(y) + 5/2 ln(z)
A]
(1/2) * Ln(ex*z) + ln(yz^2)
(1/2)ln(e) + (1/2)ln(x) + (1/2)ln(z) + ln(y) + lnz^2
ln(e) = 1; ln(z^2) = 2 ln(z)
1/2 + 1/2 ln(x) + 1/2 ln(z) + ln(y) + 2ln(z)
1/2 ln(z) + 2ln(z) = 5/2 ln(z)
So put all this together
1/2 + 1/2 ln(x) + 5/2 ln(z) + ln(y) which is Exactly like B
The perimeter of the rectangle is 30 inches. What is the formula that shows the length of side c?
Final answer:
To find the length (c) of a rectangle when the perimeter is 30 inches, we use the formula c = (P - 2w) / 2, with P representing the perimeter and w the width.
Explanation:
The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given that the perimeter (P) is 30 inches, and we are looking to find the formula that shows the length of side c assuming c represents either the length or the width of the rectangle. Let's say c represents the length for this context. Therefore, the formula rearranges to c = (P - 2w) / 2. We use this formula when we know the perimeter and the width (w), and we want to find the length (c).
The graph represents the ways Janelle can win the beanbag toss game. Which describes a way Janelle can win the game? land on round 7 times; land on square 1 time land on round 6 times; land on square 2 times land on round 5 times; land on square 3 times land on round 4 times; land on square 4 times
Answer:
Land on round 4 times; land on square 4 times
Step-by-step explanation:
Answer:
The correct option is 4.
Step-by-step explanation:
In the graph orange region represents the ways Janelle can win the beanbag toss game.
From the given graph it is clear that the related line passes through the points (2,5) and (10,0).
If a line passes through two points, then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The equation of related line is
[tex]y-5=\frac{0-5}{10-2}(x-2)[/tex]
[tex]y-5=-\frac{5}{8}(x-2)[/tex]
Add 5 on both the sides.
[tex]y-5+5=-\frac{5}{8}(x)+\frac{5}{4}+5[/tex]
[tex]y=-\frac{5}{8}(x)+\frac{25}{4}[/tex]
The shaded region is above the line, so the sign of inequality is ≥.
The required inequality is
[tex]y\geq -\frac{5}{8}(x)+\frac{25}{4}[/tex]
Check the each point whether it satisfy the inequality of not.
In option (1), the given point is (7,1).
[tex]1\geq -\frac{5}{8}(7)+\frac{25}{4}[/tex]
[tex]1\geq 1.875[/tex]
This statement is false.
In option (2), the given point is (6,2).
[tex]2\geq -\frac{5}{8}(6)+\frac{25}{4}[/tex]
[tex]2\geq 2.5[/tex]
This statement is false.
In option (3), the given point is (5,3).
[tex]3\geq -\frac{5}{8}(5)+\frac{25}{4}[/tex]
[tex]3\geq 3.125[/tex]
This statement is false.
In option (4), the given point is (4,4).
[tex]4\geq -\frac{5}{8}(4)+\frac{25}{4}[/tex]
[tex]3\geq 3.75[/tex]
This statement is true. It means the point (4,4) describes a way Janelle can win the game. Therefore the correct option is 4.
WILL GIVE BRAINLIEST! PLEASE HELP!
What is measure of angle R?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
[tex] R = 28.07^\circ [/tex]
Step-by-step explanation:
Since you have the lengths of all the sides, you can use sine, cosine, or tangent to find the answer. Let's use the tangent ratio.
For angle R, PQ is the opposite leg, and QR is the adjacent leg.
[tex] \tan R = \dfrac{opp}{adj} [/tex]
[tex] \tan R = \dfrac{8}{15} [/tex]
[tex] R = \tan^{-1} \dfrac{8}{15} [/tex]
[tex] R = 28.07^\circ [/tex]
Answer:
were are the answer selection
Step-by-step explanation:
The diagonal of a square is 6 meters long. How long is a side of the square? What is the area of the square?
Answer:
4.24
Step-by-step explanation:
You can use the formula d=sqrt(2a to calculate this with ease.
Help!!!!!!!!!!!!!!!!!! Look at the picture.
Answer:
[tex]f(a^{2})=7(a^{4})-8[/tex]
Step-by-step explanation:
we have
[tex]f(x)=7x^{2}-8[/tex]
we know that
[tex]f(a^{2})[/tex]
Is the value of f(x) for [tex]x=a^{2}[/tex]
so
substitute the value of x in the function
[tex]f(a^{2})=7(a^{2})^{2}-8[/tex]
[tex]f(a^{2})=7(a^{4})-8[/tex]
Use green's theorem to compute the area inside the ellipse x252+y2172=1. use the fact that the area can be written as ∬ddxdy=12∫∂d−y dx+x dy . hint: x(t)=5cos(t). the area is 85pi .
b.find a parametrization of the curve x2/3+y2/3=42/3 and use it to compute the area of the interior. hint: x(t)=4cos3(t).
The area of the ellipse [tex]E[/tex] is given by
[tex]\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy[/tex]
To use Green's theorem, which says
[tex]\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
([tex]\partial E[/tex] denotes the boundary of [tex]E[/tex]), we want to find [tex]M(x,y)[/tex] and [tex]L(x,y)[/tex] such that
[tex]\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1[/tex]
and then we would simply compute the line integral. As the hint suggests, we can pick
[tex]\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1[/tex]
The line integral is then
[tex]\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy[/tex]
We parameterize the boundary by
[tex]\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}[/tex]
with [tex]0\le t\le2\pi[/tex]. Then the integral is
[tex]\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt[/tex]
[tex]=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi[/tex]
###
Notice that [tex]x^{2/3}+y^{2/3}=4^{2/3}[/tex] kind of resembles the equation for a circle with radius 4, [tex]x^2+y^2=4^2[/tex]. We can change coordinates to what you might call "pseudo-polar":
[tex]\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}[/tex]
which gives
[tex]x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}[/tex]
as needed. Then with [tex]0\le t\le2\pi[/tex], we compute the area via Green's theorem using the same setup as before:
[tex]\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt[/tex]
[tex]=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt[/tex]
[tex]=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt[/tex]
[tex]=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt[/tex]
[tex]=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt[/tex]
[tex]=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi[/tex]
The areas of the ellipse and curve interior can be calculated using Green's Theorem and the respective parametrizations, x(t) = 5cos(t) and x(t) = 4cos3(t), followed by integrating.
Explanation:To compute the area inside the ellipse using Green's Theorem, we use the fact that the area can be written as ∬ dxdy = 1/2 ∫ d(−y dx+x dy). Using the hint, x(t) = 5cos(t), we parametrize the ellipse and integrate over the boundary to compute the area.
Similarly, for the parametrization of the curve x2/3 + y2/3 = 42/3, we could use the hint x(t) = 4cos3(t), which is a cube root form representation. After this, compute the area of the interior using the proper integration methods.
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It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear .
Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear:
1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et
2. t2(d2y/dt2)+t(dy/dt)+2y=sin t
3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t3
4. y''-y+y2=0
You have 10 choices to choose for each problem:
a. 1st. order linear differential equation
b. 2nd. order linear differential equation
c. 3rd. order linear differential equation
d. 4th. order linear differential equation
e. 5th. order linear differential equation
f. 1st. order non-linear differential equation
g. 2nd. order non-linear differential equation
h. 3rd. order non-linear differential equation
i. 4th. order non-linear differential equation
f. 5th. order non-linear differential equation
The equations are classified as follows: 1. 2nd order non-linear differential equation, 2. 2nd order linear differential equation, 3. 3rd order non-linear differential equation, 4. 1st order non-linear differential equation.
Explanation:The task given is to classify each differential equation into one of several categories: whether the order of the equation is first, second, third, fourth or fifth, and whether or not it is a linear differential equation.
(1+y2)(d2y/dt2)+t(dy/dt)+y=et is a g. 2nd. order non-linear differential equation because it involves the second derivative and y2 makes it non-linear. t2(d2y/dt2)+t(dy/dt)+2y=sin t is a b. 2nd. order linear differential equation because it involves the second derivative and all terms are linear in y. (d3y/dt3)+t(dy/dt)+cos2(t)y=t3 is an h. 3rd. order non-linear differential equation due to the cos2(t)y term. y''-y+y2=0 is a f. 1st. order non-linear differential equation because it involves only the first derivative and the y2 term makes it non-linear.Learn more about Classifying Differential Equations here:https://brainly.com/question/39328181
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Part A: The product of (n2 – 6n + 3) and -4n is
A. -4n^3+24n^2+12n
B. -4n^3+24n^2-12n
C. 4n^3+24n^2-12n
Part B: When this product is multiplied by -n, the result is
A. 4n^4-24n^3+12n^2
B. -4n^4+24n^3+12n^2
C. 4n^4+24n^3+12n^2
Answer:
Part A) Option B. [tex]-4n^{3}+24n^{2}-12n[/tex]
Part B) Option A. [tex]4n^{4}-24n^{3}+12n^{2}[/tex]
Step-by-step explanation:
Part A) we have
[tex](n^{2}-6n+3)(-4n)[/tex]
the product is equal to
[tex]=(n^{2})(-4n)-6n(-4n)+3(-4n)\\=-4n^{3}+24n^{2}-12n[/tex]
Part B) When this product is multiplied by -n, the result is
we have
[tex](-4n^{3}+24n^{2}-12n)(-n)[/tex]
[tex]=(-4n^{3})(-n)+24n^{2}(-n)-12n(-n)\\=4n^{4}-24n^{3}+12n^{2}[/tex]
What is the correct answer to the equation below? Round to the nearest whole number.
Answer:
89
Step-by-step explanation:
86+78+80+99+99+92+86 = 620
620/7 = 88.57142857
And since you requested the nearest whole number the 88 turns into an 89 due to the fact that the tenth place is a 5 (or greater).
2.5 gallons of water are poured into 5 equally sized bottles. How much water is in each bottle?
Answer:
3.7 liters
Step-by-step explanation:
The required amount of water in each bottle is 0.5 gallon.
Given that,
2.5 gallons of water are poured into 5 equally sized bottles, how much water is in each bottle is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Total volume = 2.5 gallon,
Number of bottle = 5,
Gallon per bottle = 2.5 / 5 = 0.5 gallon per bottle
Thus, the required amount of water in each bottle is 0.5 gallons.
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A lifeguard earns $320 per week for working 40 hours plus $12 per hour worked over 40 hours. A lifeguard can work a maximum of 60 hours per week.
Which graph above best represents the lifeguard’s weekly earnings in dollars for working h hours over 40?
A) Answer choice F
B) Answer choice G
C) Answer choice H
D) Answer choice J
Answer:
Step-by-step explanation:
Answer is G
Graph [G] will be the correct graph representing the lifeguard’s weekly earnings in dollars for working [h] hours over 40.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is A lifeguard earns $320 per week for working 40 hours plus $12 per hour worked over 40 hours. A lifeguard can work a maximum of 60 hours per week.
For over 40 hours of work, the graph on the y - axis will start from the point (0, 320). Of the two possible graphs, we have to find the find whose slope will be 12 since, the lifeguard receives $12 per hour.
Slope of graph [F] = (400 - 320)/(10 - 0) = 80/10 = 8
Now, slope of graph [G] = (500 - 320)/(15 - 0) = 180/15 = 12
Graph [G] is the correct choice.
Therefore, Graph [G] will be the correct graph representing the lifeguard’s weekly earnings in dollars for working [h] hours over 40.
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Jason has 2 pizzas that he cuts into fourths how many 1/4-size pizzas does he have
Since he has four cuts for each pizza, jason has 8 pizzas
The cost of three tickets to a movie is at least $20. Select an inequality that represents the cost x (in dollars) of each ticket. Then solve the inequality. Write your solution in decimal form rounded to the nearest cent.
Answer:
3x=$20
Step-by-step explanation:
well first you divide 3x/3=$20/3
3 can go into 20 6 times that would 18 and then u would have a remainder of 2 dollars and 3 cant go into 2 so it would be .67 so x=6.67
2x + y = 3
x - 2y = -1
If equation one is multiplied by 2 and then the equations are added, the result is _____.
3x = 2
3x = 5
5x = 5
multiply 2x+y = 3 by 2
4x + 2y = 6
x - 2y = -1
add terms (be careful about signs!)
5x + 0 = 2
5x = 5Answer:
5x=5
Step-by-step explanation:
A printer prints 75 pages in 5 minutes at the same rate, how many pages does the printer print in 7 minutes
Why this is so easy
Ok so, 75/5=15
15*7 =105 so the answer is 105 pages