Answer:
[tex]\begin{aligned} \frac{dy}{dx} &= \frac{\cos(t) + \sin(t)}{\cos(t) - \sin(t)} \end{aligned}[/tex] given that [tex]a \ne 0[/tex] and that [tex]\cos(t) - \sin(t) \ne 0[/tex].
Step-by-step explanation:
The relation between the [tex]y[/tex] and the [tex]x[/tex] in this question is given by parametric equations (with [tex]t[/tex] as the parameter.)
Make use of the fact that:
[tex]\begin{aligned} \frac{dy}{dx} = \quad \text{$\frac{dy/dt}{dx/dt}$ given that $\frac{dx}{dt} \ne 0$} \end{aligned}[/tex].
Find [tex]\begin{aligned} \frac{dx}{dt} \end{aligned}[/tex] and [tex]\begin{aligned} \frac{dy}{dt} \end{aligned}[/tex] as follows:
[tex]\begin{aligned} \frac{dx}{dt} &= \frac{d}{dt} [a\, (\cos(t) + \sin(t))] \\ &= a\, (-\sin(t) + \cos(t)) \\ &= a\, (\cos(t) - \sin(t))\end{aligned}[/tex].
[tex]\begin{aligned} \frac{dx}{dt} \ne 0 \end{aligned}[/tex] as long as [tex]a \ne 0[/tex] and [tex]\cos(t) - \sin(t) \ne 0[/tex].
[tex]\begin{aligned} \frac{dy}{dt} &= \frac{d}{dt} [a\, (\sin(t) - \cos(t))] \\ &= a\, (\cos(t) - (-\sin(t))) \\ &= a\, (\cos(t) + \sin(t))\end{aligned}[/tex].
Calculate [tex]\begin{aligned} \frac{dy}{dx} \end{aligned}[/tex] using the fact that [tex]\begin{aligned} \frac{dy}{dx} = \text{$\frac{dy/dt}{dx/dt}$ given that $\frac{dx}{dt} \ne 0$} \end{aligned}[/tex]. Assume that [tex]a \ne 0[/tex] and [tex]\cos(t) - \sin(t) \ne 0[/tex]:
[tex]\begin{aligned} \frac{dy}{dx} &= \frac{dy/dt}{dx/dt} \\ &= \frac{a\, (\cos(t) + \sin(t))}{a\, (\cos(t) - \sin(t))} \\ &= \frac{\cos(t) + \sin(t)}{\cos(t) - \sin(t)}\end{aligned}[/tex].
ANSWER FAST 50 POINTS PLEASE !!!
Identify the property that justifies each step asked about in the answer area below.
Line 1: (9+x)x
Line 2: x(9+x)
Line 3: x(x+9)
Line 1-Line 2-Associative property .
Line 2-Line 3- Distributive property
Solution:-
[tex]\\ \rm\longmapsto (9+x)x[/tex]
[tex]\\ \rm\longmapsto x(x+9)[/tex]
[tex]\\ \rm\longmapsto x(9+x)[/tex]
[tex]\\ \rm\longmapsto x^2+9[/tex]
what is the solution of linear equation of cosx(e^2y-y)=e^y sin2x
This is college? Woah I'm not advanced. Middle school!
Hello! Can someone please answer the photo? I honestly forgot about Prime Factorization... No links please and thank you!
Answer:
D
Step-by-step explanation:
im thinking its d, because prime factorisation is a way of expressing a number as a product of its prime factors.
a isn't correct since 9 isn't is a prime number.
b isn't correct because you wouldn't use decimals typically.
c isn't correct because 1 is not a prime number.
d is the only correct solution since all the numbers listed are prime numbers.
Find the place value of 7 in 374596
Answer:
It is tens
Step-by-step explanation:
3 » ones
[tex]{ \boxed{ \sf{7 \: » \: tens}}}[/tex]
4 » hundreds
5 » thousands
9 » ten thousands
6 » hundred thousands
Can someone help me with an idea please? I need something like this for math and science week but i think my idea is really lame. It has to be a photograph and it can be physics, chemistry or math! Pls lmk your ideas cuz im running out of them
Answer:
take a light bulb and a potato and some wires connect together will give light
Answer:
i have attached a pic of an idea that might help you
:)
Suppose a right triangle has a
hypotenuse length of 12. If one of
the legs has length 5, what would
the length of the last leg be?
Answer:
See the last two lines below. I don't know which one you want.
Step-by-step explanation:
hypotenuse = 12
One leg = 5
other leg = x Substitute into a^2 + b^2 = c^2
x ^2 + 5^2 = 12^2
x^2 + 25 = 144 Subtract 25 from both sides
x^2 = 144 - 25 Combine
x^2 = 119 Take the square root of both sides
x = sqrt(119)
x = 10.91
How do I do this, is the equation 40=ksqrt(65)?
Answer:
Step-by-step explanation:
Start a little more generally. Carefully find k
distance = k * speed ^2
112 = k*40^2
112 = k * 1600 Divide by 1600
112/1600 = k
k = 0.07
Now do the question you are asked to do.
distance = k * speed^2
distance = 0.07 * 65^2
distance = 295.75
Now having done that, you can set up a proportion.
d1 / d2 = k speed1^2/kspeed2^2 Cancel the ks
112/d2 = 40^2 / 65^2 Cross multiply
112 * 65^2 = 40^2 * d2 Divide by 40^2
112 * 65^2/40^2 = d2 Expand the squares
112 * 4225 / 1600 = d2
295.75 = d2
The second way is shorter, but I suggest the long way until you get comfortable with it.
Given directed line segment JL below, find the coordinates of K such
that the ratio of JK to JL is 7:8. Plot point K.
The coordinate of JK is (-1.7, -0.3)
The coordinate of the points that divides the line segment in the given ratio is calculated as:
[tex](x, y) = (\frac{ax_1 +bx_2}{a+b} , \frac{ay_1 +by_2}{a + b} )[/tex]
where;
a:b = 7:8
From the image;
(x₁, y₁) = (-6, 5) and,
(x₂, y₂) = (2, -5)
Substitute the given points in the equation above to calculate the coordinates of JK.
[tex](x, y) = (\frac{7(-6)+8(2)}{7+8} , \frac{7(5) +8(-5)}{7+8} )\\\\(x, y) = (\frac{-26}{15} , \frac{-5}{15} )\\\\(x,y) = (-1.7, -0.3)[/tex]
Thus, the coordinate of JK = (-1.7, -0.3)
Check the image uploaded for the plot of point K
Learn more here:https://brainly.com/question/12547932
Find the length of the third side. If necessary, round to the nearest tenth.
Answer:
a = 6
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
a^2 + 8^2 = 10 ^2
a^2 +64 = 100
a^2 = 100 -64
a^2 = 36
Take the square root of each side
sqrt(a^2) = sqrt(36)
a = 6
the ratio of two number is 4:7 and their hcf is 6 .find their lcm
168
this is the full process
Find the midpoint of the line segment with the given endpoints.
(-1, 5), (6,6)
A) (-3.5, -0.5)
C) (13,7)
B) (2.5, 5.5)
D) (2,6)
can someone help me with this one again bc I didn't show the decimal Decimal: 0.44
Step-by-step explanation:
The answer is 10 times
=> 4 hundredths x 10 = 4 tenths
=> 0.04 x 10 = 0.4, which is correct
Hope that helps
Point C is in the interior of
Answer:
Point C is in the interior of angle ABD.
create 5 problems using all operations that has a solution of 5
Answer:
((5*5) + (10-5) * (50/100)) ÷ 3 = 5
((4*4)+(17-8 *(1.378/2)) ÷ 3.445 = 5
Step-by-step explanation:
Solve equation by completing the square.
Answer:
x=3 and x=5
Step-by-step explanation:
x2−8x+15=0
To solve the equation, factor x2−8x+15 using formula x2+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.
a+b=−8ab=15
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 15.
−1,−15−3,−5
Calculate the sum for each pair.
−1−15=−16−3−5=−8
The solution is the pair that gives sum −8.
a=−5b=−3
Rewrite factored expression (x+a)(x+b) using the obtained values.
(x−5)(x−3)
To find equation solutions, solve x−5=0 and x−3=0.
x=5x=3
hope it helps :)
Build a function whose domain is all real numbers other than -4, and whose range is all real numbers other than 5.
Answer:
An example is the rational function [tex]y=\frac{5x}{x+4}[/tex].
Step-by-step explanation:
The graph of the rational function [tex]y=\frac{5x}{x+4}[/tex] has a vertical asymptote at x = -4 where the denominator is equal to zero. The function is undefined there, so the domain is all real numbers except -4.
The graph has a horizontal asymptote y = 5 so the domain is all real numbers except 5.
See the attached image for the graph of the function (purple) and it's vertical asymptote (black).
-1 and 3 tenths plus 4 tenths
The answer you are looking for is -9/10, or -0.9.
Solution:
-1 3/10+4/10
-13/10+4/10
-9/10, or -0.9
Answer:
-0.9
Step-by-step explanation:
Adnan earns $48,000 per year. His employer offers him a 4 % raise if he stays with the company What would his new salary be ?
A. 49,929
B. 1,920
C.46,080
D. 192,000
Answer:
A. 49,920
Step-by-step explanation:
Multiply the beginning value by 1 plus the percentage in decimal form.
In a survey of small business owners, a response to which of the following questions would be qualitative?
a. How much did your business have in profits last year?
b. How long have you owned a business?
c. What type of business do you own?
d. How many businesses do you own?
For the considered survey, the questions whose response is going to be qualitative is given by: Option C: "What type of business do you own?"
What is qualitative data?
Qualitative data tells about the quality or characteristic. It is tough to express it numerically or not at all expressible numerically. They are usually catagorical.
In contrast, there is quantitative data which can be expressed numerically.
Option A, Option B and Option D will get answers which would be in numbers. Thus, their responses would be quantitative.
Option C's question will get response as type of business that the business owners own. So its not in numbers and tells about the characteristic of businesses.
Thus, for the considered survey, the questions whose response is going to be qualitative is given by: Option C: "What type of business do you own?"
Learn more about qualitative and quantitative data here:
https://brainly.com/question/12929865
Renaldo can rollerblade 9.7 miles per hour. at this rate, how far will he rollerblade in 0.75 hours?
Answer: 1.125 miles
Step-by-step explanation:
A sofa is on sale for $442, which is 85% of the regular price.
[tex]\frac{442}{x} = \frac{85}{100} \\85x = 44200\\x = \frac{44200}{85} = 520[/tex]
Original price is 520
If four times a certain number, increased by 6 is equal to 94, what is the number?
If x represents the number, then which of the following equations could be used to solve the problem?
4x + 6 = 94
x + 6 = 4(94)
4(x + 6) = 94
Answer:
4x + 6 = 94 could be used to solve the problem
I NEED HELP ON THIS!!!
Look at the triangle below.
Which equation is equivalent to the law of cosines?
A
a2=c2−2cx+h2
B
a2=c2−2cx+x2+h2
C
a2=c−x2+h2
D
a2=c2−x2+h2
Answer:
I believe the answer is B. a^2 = c^2 - 2cx + x^2 + h^2
Step-by-step explanation:
The law of cosines states: c^2 = a^2 + b^2 - 2bc * cos(C). If we plug in the values from the diagram, we'll have (c-x)^2 = a^2 + h^2 -2ah * cos(90)
cos(90) = 0, so now we have just (c-x)^2 = a^2 + h^2
Let's expand this to c^2 -2cx + x^2 = a^2 + h^2
Isolate a^2 and we now have a^2 = c^2 -2cx + x^2 + h^2
pls vote me brainliest if i was able to help you!! <3
give the distance between two points with the given coordinates.
-10.3 and -12.1
Solve for w.
|5w + 7) = |5w + 8)
please help :)
Answer:
w=3/2
Step-by-step explanation:
[tex]|5w+7|=|5w+8|\\5w + 7 =\pm (5w+8)\\5w + 7 = 5w + 8 \text{ or } 5w + 7 = -5w-8\\7 = 8 (\text{abusrd}) \text{ or } 10 w =15\\w= 15/10 = 3/2.[/tex]
cho hàm số y= x^{3} +3x^{2} -1 .viết phương trình tiếp tuyến tại điểm có hoành độ bằng -1
hope you do not mind expressing this on in English ♂️
8= 8 + 4x +5x
can anyone help me with this
Answer:
0= x
Step-by-step explanation:
8= 8 + 4x +5x
Combine like terms
8 = 8+9x
Subtract 8 from each side
8-8 =8+9x-8
0 = 9x
Divide by 9
0/9 = 9x/9
0= x
Tính đạo hàm cấp n của hàm số f(x) = 3x − 1
4x + 3
Answer:
so fx 3x-1 '4x+3
Step-by-step explanation:
please mark me brainliest answer
how do you simplify this question x^3z^7/x^5z
Answer:
go to symbolab and it will simplify for you, brainly is useless with these kinds of questions. Symbolab.com very easy to use and gives you answer right away instead of have to wait for some oaf like me to solve your problems.
Step-by-step explanation:
One airline carried 3,720 people on 31 flights between Portland and Los Angeles. If there were the same number on each flight, how many people were on each flight?
Please help ASAP!
Divide total people by total flights:
3720/31 = 120
There was 120 people on each flight
