Answers
Answer:
Option a.
Step-by-step explanation:
By looking at the options, we can assume that the function y(x) is something like:
[tex]y = \sqrt{4 + a*x^2}[/tex]
[tex]y' = (1/2)*\frac{1}{\sqrt{4 + a*x^2} }*(2*a*x) = \frac{a*x}{\sqrt{4 + a*x^2} }[/tex]
such that, y(0) = √4 = 2, as expected.
Now, we want to have:
[tex]y' = \frac{x*y}{2 + x^2}[/tex]
replacing y' and y we get:
[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]
Now we can try to solve this for "a".
[tex]\frac{a*x}{\sqrt{4 + a*x^2} } = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}[/tex]
If we multiply both sides by y(x), we get:
[tex]\frac{a*x}{\sqrt{4 + a*x^2} }*\sqrt{4 + a*x^2} = \frac{x*\sqrt{4 + a*x^2} }{2 + x^2}*\sqrt{4 + a*x^2}[/tex]
[tex]a*x = \frac{x*(4 + a*x^2)}{2 + x^2}[/tex]
We can remove the x factor in both numerators if we divide both sides by x, so we get:
[tex]a = \frac{4 + a*x^2}{2 + x^2}[/tex]
Now we just need to isolate "a"
[tex]a*(2 + x^2) = 4 + a*x^2[/tex]
[tex]2*a + a*x^2 = 4 + a*x^2[/tex]
Now we can subtract a*x^2 in both sides to get:
[tex]2*a = 4\\a = 4/2 = 2[/tex]
Then the solution is:
[tex]y = \sqrt{4 + 2*x^2}[/tex]
The correct option is option a.
Related Questions
what's the answer for this question
Answers
Answer:
B(3/4*1/2)
Step-by-step explanation:
So lets see, we have:
3/4 divded by 2
Any whole number, such as 2, will have a denominator like this:
2/1
So we can rewrite this as:
3/4 divided by 2/1
Now, we can actually rewrite this division as multipication. To do this, you must flip the dividing fraction, which was 2/1.
So now it is 1.2:
3/4*1/2
Looking at the anwers, this should be the seocnd one down.
Hope this helps!
f(x)=x^2-5 and g(x)=3x+1 then f(g(2))
Answers
Answer:
f(g(2)) = 44
Step-by-step explanation:
g(2) = 3(2) + 1 = 7
Plug 7 into f(x) since g(2) = 7
f(7) = 7² - 5 = 44
f(g(2)) = 44
(Please answer) Octavia is going to buy milkshakes for her friends. Small milkshakes cost $2.50 and large milkshakes cost $6.00. She needs to buy at least 20 milkshakes and she can spend no more than $90. How many small milkshakes Octavia should buy to serve her friends but stay on budget?
Octavia should buy less than 8 milkshakes.
Octavia should buy at least 8 small milkshakes.
Octavia should buy less than 12 milkshakes.
Octavia should buy at least 12 small milkshakes.
Answers
Answer:
Step-by-step explanation:
In this scenario, Octavia should buy at least 12 small milkshakes. At $2.50 each small milkshake, buying 12 would be a total of $30. Since she needs to buy atleast 20 total milkshakes, she would need to buy 8 large milkshakes which at $6 each would cost her a total of $48. Together this would sum up to be $78 for the 20 milkshakes which would mean that Octavia is still under her budget.
In a survey conducted at a pet store, 150 customers were asked if they owned
birds or fish. The survey data are shown in the relative frequency table.
What percentage of the people surveyed own fish?
A. 10%
B. 6%
C. 4%
D. 0.1%
Answers
Answer: the answer should be 10%
Step-by-step explanation:
Answer:
10% is correct!
Put 2 (n^2 + 8n + 16) in standard form
Answers
Answer: 2n^2 + 16n + 32
Step-by-step explanation:
Distribute 2 to all the terms inside parentheses.
2 (n^2 + 8n + 16)
2n^2 + 16n + 32
Hope this helped!
Find f(3) please. I need help. Thank you
Answers
Answer:
f(3) = -4
Step-by-step explanation:
3 is between 2 and 5 so we use the second piece of the function
f(3) = -4
Answer: f = 0
Step-by-step explanation:
f(3) = 0
f•(3) = 0
3f = 0
f = 0
Please someone help me with my math work?
Answers
Answer:
20 plus 20 is equla to 5000
PLEASE HELP
Find the measure of angle.
Answers
Answer:
39
Step-by-step explanation:
180-73-68
Use the line of best fit to predict the total amount of money earned in tips after working 12 hours. (8,80)(2,20)
Answers
Answer:
The line of best fit will look like this (see attatchement):
The total amount of money earned in tips after working 12 hours is $120.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given coordinate points are (8, 80) and (2, 20).
Here, slope (m) = (20-80)/(2-8)
= 10
Substitute m=10 and (x, y)=(8, 80) in y=mx+c, we get
80=10×8+c
c=0
So, the equation of a line is y=10x
Here, x=12
Then, y=120
Therefore, the total amount of money earned in tips after working 12 hours is $120.
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I’m kinda stuck on this question, can y’all please help me?
Answers
Points J, K and M form a triangle.
In this triangle you are given the angles for JKM (50) and KJM (60)
The 3 inside angles of a triangle need to equal 180.
The third angle JMK would be 180 minus the two given angles:
JMK = 180 - 50 - 60 = 70
JMK = 70 degrees
I need help asap. Evaluate Expressions
Answers
Answer:
1:
p-r/6=-6-(-6)/6=-6+1=-5
2:
p-(m-n)= -1-(-4-4)=-1-(-8)=-1+8=7
3:
(z+y)/2)3=(-5-4)/3=-9/3=-3
4:
m/6-n=6/6-6=1-6=-5
5:
k³-h=3³-(-2)=27+2=29
6:
p-(p-(m-3))=5-(5-(4-3))=5-(5-1)=5-4=1
7:
(k)(k-j)+3=(5)(5-5)+3=5*0+3=3
8.
p²/6-q=6²/6-4=6-4=2
9;
zx+3³=6*4+3³=24+27=51.
10:
y+z-(y-x)=5+4-(5-2)=9-3=6
Some basic rules:
+. +. +=+
+. * +=+
+. ÷ +=+
+. - +=+
and
+. +. -=add and put sigh of greater one.
-. * +=-sigh
-÷-=+sigh
- - -=add and put - sigh
pls help ASAP!! person who gives correct answer will be marked brainliest
Answers
Answer:
w+76=180(being supplementary angle)
w=180-76
w=104
Graph y = -2 – 6.
could someone graph this on a khan academy number line?
Answers
Answer:
plot ur x,y coordinates as (0,-8) (1,-8)
A man bought a house for 3600 Naira he repairs the house with 150 Naira if he sold the house for 4950 Naira . Find his percentage profit
Answers
Step-by-step explanation:
profit%=
[tex] \frac{selling \: price - cost \: price}{cost \: price} \times 100\%[/tex]
[tex] \frac{4950 \: naira - 3600 \: naira + 150 \: naira}{3750 \: naira} \times 100\%[/tex]
[tex] \frac{4950 - 3750}{3750} \times 100\%[/tex]
[tex] \frac{1200}{3750} \times 100\%[/tex]
=36%
Plz help me well mark brainliest if correct
Answers
all of the above which is e
If Susie is late for school one particular day of the week, the probability she arrives on time the next day is 0.8. If she arrives on time one day, the probability she arrives late the following day is 0.3. Susie was on time on Monday. What is the probability she was late on Thursday
Answers
Answer:
0.273 = 27.3% probability that she was late on Thursday.
Step-by-step explanation:
On time on Monday, late on Thursday:
Possible outcomes (tuesday-wednesday-thursday).
on time(0.7 probability) - on time(0.7 probability) - late(0.3 probability)
on time(0.7 probability) - late(0.3 probability) - late(0.2 probability)
late(0.3 probability) - on time(0.8 probability) - late(0.3 probability)
late(0.3 probability) - late(0.2 probability) - late(0.2 probability).
What is the probability she was late on Thursday?
Sum of these four outcomes. So
[tex]p = 0.7*0.7*0.3 + 0.7*0.3*0.2 + 0.3*0.8*0.3+0.3*0.2*0.2 = 0.273[/tex]
0.273 = 27.3% probability that she was late on Thursday.
WILL GIVE U BRAINLIEST
What is the value of X by CPCTC?
A. 11
B. 8
C. 3
D. 7
E. Not enough info
Answers
The value of x by CPCTC is 3.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
We need to find the value of x.
CPCT theorem states that if two or more triangles which are congruent to each other are taken then the corresponding angles and the sides of the triangles are also congruent to each other.
The side x is congruent to the quadrilateral having length 3.
the value of x is 3
Hence, the value of x by CPCTC is 3.
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WILL GIVE U BRAINLIEST!!!
What is an alternate exterior angle to angle 2?
A. 7
B. 6
C. 5
D. 4
Answers
Answer:
A. 7
Step-by-step explanation:
Alternate exterior angles are formed when we have two parallel lines that are intercepted by a transversal line in such a way that the exterior angles formed is outside the two parallel lines and they alternate each other along the transversal line.
Thus,
Angle 2 is an exterior angle along the transversal line and alternates angle 7, which is another exterior angle.
Therefore, an alternate exterior angle to angle 2 is angle 7.
please help me i’m like so over this.
Answers
Find the integration of (1-cos2x)/(1+cos2x)
Answers
Given:
The expression is:
[tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex]
To find:
The integration of the given expression.
Solution:
We need to find the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex].
Let us consider,
[tex]I=\int \dfrac{1-\cos 2x}{1+\cos 2x}dx[/tex]
[tex]I=\int \dfrac{2\sin^2x}{2\cos^2x}dx[/tex] [tex][\because 1+\cos 2x=2\cos^2x,1-\cos 2x=2\sin^2x][/tex]
[tex]I=\int \dfrac{\sin^2x}{\cos^2x}dx[/tex]
[tex]I=\int \tan^2xdx[/tex] [tex]\left[\because \tan \theta =\dfrac{\sin \theta}{\cos \theta}\right][/tex]
It can be written as:
[tex]I=\int (\sec^2x-1)dx[/tex] [tex][\because 1+\tan^2 \theta =\sec^2 \theta][/tex]
[tex]I=\int \sec^2xdx-\int 1dx[/tex]
[tex]I=\tan x-x+C[/tex]
Therefore, the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex] is [tex]I=\tan x-x+C[/tex].
HELP ME FAST PLESSE!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Read below
Step-by-step explanation:
They want green
out of all spinner results 3 of them were green
it was spun 40 times total
3/40=0,075 to the nearest hundred is 0,08
3/41=0,0731 to the nearest hundred is 0,07
I'm not sure but it is probably one of these answers
Which point is the image of point R(4, -7) first reflected across the x-axis and then across the y-axis?
Answers
Answer:
(-4, 7)
Step-by-step explanation:
It would be the exact opposite of point R because it was rotated about 180 degrees from it's original location
Please help me I am super confused I would really appreciate it ♥️♥️
Answers
QUICKK!! GIVING BRAINLIEST TO CORRECT ANSWER
Answers
Step-by-step explanation:
Insufficient information!
however, volume will remain same in both of these figures!
a bookstore sells 9 books for $90. Which table represents the relationship between number of books and the total price?
Answers
Answer:
Step-by-step explanation:
Answer:
Table B
first find cost of 1 book
cost of 1 book=$90/9
=$10
now cost cost of 10 books
cost of 11 books=$10*10
=$100
cost of 11 book =$10*11
=$110
Step-by-step explanation:
since the cost of 10 and 11 books match in table B ,it is the correct answer
what are adjacent angles
Answers
Answer:
Two angles having the same vertex and having a common side between them.
Which matrix equation can be used to solve the system?
(2x+ 5y = 15
X + 3y = 18
Answers
THE CORRECT OPTION IS A where the input data is correct
Answer:
option 3
Step-by-step explanation:
[tex]AX = B\\X = A^{-1}B\\\\A = \left[\begin{array}{CC}\\2&5\\1&3\end{array}\right]\\\\\\B =\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\X =\left[\begin{array}{C}\\x&y\end{array}\right][/tex]
[tex]det A = 1\\\\adj A = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right][/tex]
[tex]A^{-1} = \frac{1}{det A} \times Adj A[/tex]
[tex]= 1 \times \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\\\\\\= \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right][/tex]
Therefore,
[tex]X = A^{-1}B\\\\\\\left[\begin{array}{C}\\x&y\end{array}\right] = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\[/tex]
No links!!! A student population in a school was 972. Next year they are projected to have a 25% increase in student population. How many students will they have next year?
Answers
Answer:
1215
Step-by-step explanation:
If you have a 25% or 1/4 increase, this would mean that you divided the total number of students and add the quotient to the main thing.
So: 972 divided by 1/4 = 972/4 = 243.
972 + 243 = 1215.
Answer:
1215 Students
Step-by-step explanation:
25% is equal to 1/4 correct? (It is :D) So divide 972/4 to know what 25% of the school's population is. 972/4 = 243. So then 243 is 25% of the students. To get the 25% increase add 972 (for the students that will be back next year) and 243 (for the new students). I may have explained this in a really detailed way but it isn't that hard when you think about it!
1. 972/4 (to find 25%)
2. 25% = 243
3. 974 + 243 (old + new)
4. 1215 Students
What is the next term in the geometric sequence below?
3, -6, 12, -24, _, ...
A. 48
B. -48
C. -36
D. 36
Answers
Answer:
a. 48
Step-by-step explanation:
first of all find the num that can divide through equally
for ex. 3 x -2 = -6
-6×-2=12
12×-2=-24
-24×-2=48
therefore the num divisible is -2
Find the value of x. 12x - 14 = 34 *
Answers
Answer:
x = 4
Step-by-step explanation:
12x - 14 = 34
Add 14 to both sides
12x = 48
Divide both sides by 12
x = 4
12x = 48
X= 4