Answer:
(g ⚬ f)(x)
Step-by-step explanation:
(g ⚬ f)(x)
Find the slope of the line tangent to the graph of (x^2)-((xy)^(1/2))=(2y^2)+3x at the point (4,1).
Compute [tex]\frac{\mathrm dy}{\mathrm dx}[/tex] using implicit differentiation:
[tex]x^2-(xy)^{1/2}=2y^2+3x[/tex]
[tex]\dfrac{\mathrm d(x^2)}{\mathrm dx}-\dfrac{\mathrm d(xy)^{1/2}}{\mathrm dx}=\dfrac{\mathrm d(2y^2)}{\mathrm dx}+\dfrac{\mathrm d(3x)}{\mathrm dx}[/tex]
[tex]2x-\dfrac1{2(xy)^{1/2}}\left(\dfrac{\mathrm dx}{\mathrm dx}y+x\dfrac{\mathrm dy}{\mathrm dx}\right)=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-\dfrac1{2(xy)^{1/2}}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-\dfrac12\left(\dfrac yx\right)^{1/2}-\dfrac12\left(\dfrac xy\right)^{1/2}\dfrac{\mathrm dy}{\mathrm dx}=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-3-\dfrac12\left(\dfrac yx\right)^{1/2}=\left(4y+\dfrac12\left(\dfrac xy\right)^{1/2}\right)\right)\dfrac{\mathrm dy}{\mathrm dx}[/tex]
[tex]4x-6-\left(\dfrac yx\right)^{1/2}=\left(8y+\left(\dfrac xy\right)^{1/2}\right)\right)\dfrac{\mathrm dy}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x-6-\left(\frac yx\right)^{1/2}}{8y+\left(\frac xy\right)^{1/2}}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x(xy)^{1/2}-6(xy)^{1/2}-y}{8y(xy)^{1/2}+x}[/tex]
Plug in x = 4 and y = 1 to find that the tangent line's slope is 19/20.
What is 1/8 of 72 bottles of water
Bella lost 10 points 7 times playing a video game she then lost an additional a hundred points for going over the time limit what was the total change in her score
ga fa gza ca Morgan aca she moaned so hard
How are the entries of the matrix named by position?
Answer:
6=a23
8=a35
2=a32
Step-by-step explanation:
HELP PLEASE
I need help ASAP
Answer:
1032
Step-by-step explanation:
can someone help me
Answer:
a. fig. 2 has 8 tiles, 3 has 11 and 4 gas 14
b. It changed when they added sides, 2 to the up and down left part and 1 on the right left part
Jordan’s credit card has an APR of 10.59%, compounded monthly. He is required to make a minimum payment of 3.96% of his current balance every month. At the beginning of March, Jordan had a balance of $628.16 on his credit card. The following table shows his credit card purchases over the next few months. Month Cost ($) March 50.81 March 48.04 April 77.36 April 32.40 April 49.20 May 25.79 May 79.39 May 79.08 If Jordan makes only the minimum monthly payments in March, April, and May, what will his balance be after he makes the minimum payment for May? (Assume that interest is compounded before the monthly payment is made, and that the monthly payment is applied at the end of the month. Round all dollar values to the nearest cent.) a. $1,094.10 b. $988.97 c. $967.60 d. $1,070.23
Answer:
b. 988.97
Step-by-step explanation:
got a 100 on the test
The balance at the end of May after the minimum payment is made is
$571.64.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $628.16
r = 10.59%
n = 12
t = 1/12
The amount after March.
A = 628.16 [tex](1 + 0.1059)^{12\times0.08[/tex]
A = $633.48
Monthly payment.
= 3.96/100 x 633.48
= $25.09
Remaining amount.
= 633.48 - 25.09
= $609.39
The amount after April.
A = 609.39 [tex](1 + 0.1059)^{12\times0.08[/tex]
A = $614.55
Monthly payment.
= 3.96/100 x 614.55
= $24.34
Remaining amount.
= 614.55 - 24.34
= $590.21
The amount after May.
A = 590.21 [tex](1 + 0.1059)^{12\times0.08[/tex]
A = $595.21
Monthly payment.
= 3.96/100 x 595.21
= $23.57
Remaining amount.
= 595.21 - 23.57
= $571.64
Thus,
The balance at the end of May is $571.64.
Learn more about compound interest here:
https://brainly.com/question/13155407
#SPJ3
Which numbers is a factor of 100? 8 12 15 20
Answer:
20
Step-by-step explanation:
[tex]100 = 20 \times 5[/tex]
what number is greater than -4 but less then -2
Answer:
-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
-3 is greater than -4 on the number line but less than -2 on the number line. Therefore, the number is -3
hope I helped.
Susan is buying three different colors of tiles for her kitchen floor. She is buying 107 red tiles, and three times as many navy blue tiles as beige tiles. If susan buys 435 tilea all together, how many tiles of each color does susan buy?
2x-2 ???????????????????????????????????????????????????
Joey Page earns $5.75 per hour at his part-time job. Last week he worked 25 hours. What was his gross
pay for the week
Answer:
143.75
Step-by-step explanation:
idk man use google or something
Would 2-3 have the same answer as 3-2? Why or why not?
Answer:
No
Step-by-step explanation:
2-3= -1
3-2 = 1
( 5 - 2i)2 Write answer in standard form a +bi. Remember you can not have i2 in your answer it is a number.
Answer:
Step-by-step explanation:
(5 - 2i)^2
25 - 10i - 10i + 4I^2
25 -20i - 4
21 - 20i
what is the slope of the line ?
from the product of 30 and 70 take the sum of the two numbers
Huh? Is yo question finished
There are ten pieces of pizza. Anthony ate 4 9 of the pizza for dinner. He ate 1 6 of the pizza for a bedtime snack. How much of the pizza has he eaten in all? Give your answer as a fraction, reduced to lowest terms.
Answer:
7/18
Step-by-step explanation:
Convert the 10, 9, and 6 to a common denominator which would be 90. So you would have 90/90, 40/90, and 15/90. Then you would add the 15/90 and 40/90 together getting 55/90. Then you subtract 90/90 by 40/90. You would then get 35/90 and then simplify to 7/18.
Anthony had eaten an (11/18) fraction of pizza in all.
What are fractions?A fraction is a portion of a whole or, more broadly, any number of equal pieces.
It is written in the form p/q, read as "p by q", where p is called the numerator and q is called the denominator, and the fraction p/q represents p number of equal parts from q number of equal parts.
How to solve the given question?In the question, we are informed that there There are ten pieces of pizza. Anthony ate a 4/9th fraction of the pizza for dinner. He ate a 1/6th fraction of the pizza for a bedtime snack.
We are asked to find how much of the pizza has he eaten in all.
Total pizza Anthony had = Pizza he had for dinner + Pizza he ate as a bedtime snack.
or, Total pizza Anthony had = {(4/9) + (1/6)} fraction of pizza,
or, Total pizza Anthony had = {(8/18) + (3/18)} fraction of pizza,
or, Total pizza Anthony had = {11/18}th fraction of pizza.
Therefore, Anthony had eaten an (11/18) fraction of pizza in all.
Learn more about fractions at
brainly.com/question/11562149
#SPJ2
Fraction Operation pls help
A right triangle has one angle that measures 5°. What is the measure of the other acute angle?
Answer:
85
Step-by-step explanation:
There are three angles in a triangle
Since it is a right triangle one angle is 90 degrees
We are given one angle is 5 degrees
Let the third angle be x
The sum of the angles of a triangle is 180
x+5+90 =180
Combine like terms
x+95 = 180
Subtract 95 from each side
X+95-95 = 180-95
x = 85
round 355,668 to the nearest hundred thousands
Answer:
400,000
Step-by-step explanation:
Let's find
1/2+3/7
First write the addition with a common denominator.
Then add.
1/2+3/7=
Answer:
7/14+6/14=13/14
Step-by-step explanation:
find the common denominator(14)
change both fractions
1/2*7/7(2*7=14)=7/14
3/7*2/2(7*2=14)6/14
then add.
Lucas ran 9 miles in 3/4 of an hour. He took a break then returns by traveling that same 9 miles in 2/3 of an hour. How many more miles can lucas run per hour with his new rate
Answer:
He can run more 4.5 miles [total 13.5 miles in one hour]
Step-by-step explanation:
check the attachment for explanation
The monthly rents (in dollars) paid by 8 people are given below. (Note that these are already ordered from least to greatest.) 545, 945, 970, 995, 1015, 1030, 1040, 1124 Suppose that one of the people moves. His rent changes from $545 to $905.
Answer the following. (a) What happens to the median? It decreases by s[ It increases by se It stays the same. It decreases bys] (b) What happens to the mean? It increases by It stays the same.
Answer:
Step-by-step explanation:
Before: 545, 945, 970, 995 , 1015, 1030 , 1040 , 1124
Now: 905, 945, 970, 995 , 1015, 1030 , 1040 , 1124
a) Median stays same.
As number of data's is 8, median is the average of 4th and 5th term
Median = (995 + 1015)/2 = 2010/2 =
Median = 1005
When rent changes from $545 to $ 905, the 4th and 5th term remains same.
So, median stays same
b) Mean increases 45
Before: 545, 945, 970, 995 , 1015, 1030 , 1040 , 1124
Mean = Sum of rents ÷ 8
= (545 + 945+ 970+ 995 + 1015 +1030 + 1040 + 1124)/8
=7664/8
= 958
Now : 905, 945, 970, 995 , 1015, 1030 , 1040 , 1124
Mean = (905 + 945+ 970+ 995 + 1015 +1030 + 1040 + 1124)/8
= 8024/8
= 1003
Mean increases by 1003 - 958 = 45
please help!!! urgent
Answer:
E
Step-by-step explanation:
is the answer
suppose four more people voted and they all voted for Jocelyn.what fraction of the vote would be for Jocelyn?
Answer:
The Answer is 113/348
Step-by-step explanation:
The graph of f(x)=2^x is shown in black (k). Match each transformation of this function with a graph below.
Answer:
Step-by-step explanation:
From the graph attached,
Black curve represents a function f(x) = 2ˣ
When this curve is reflected over the x-axis image of the function will be,
g(x) = -[tex]2^{x}[/tex] [Red curve]
Similarly, curve represented by h(x) = [tex]2^{-x}[/tex] is the blue curve [image of f(x) reflected over y-axis]
When this curve is reflected over the x-axis, image of the function will be,
h'(x) = [tex]-2^{-x}[/tex] [green curve]
[tex]-2^{x}[/tex] → Red
[tex]-2^{-x}[/tex] → Green
[tex]2^{-x}[/tex] → Blue
Courtney and Malik are buying a rug to fit in a
50-square-foot space, which rug should they
purchase? Explain.
$99 Rug Sa
4 1/2 x 2 3/5 what is the answer simplified into fraction
Answer:I tnink its 21 sorry if wrong
Step-by-step explanation:
You are given the list of numbers, -9, 8, 3.0,
2
5'
2.42, 1. Which numbers are rational? Irrational?
x=4-k over 6, what is k
Answer:
k = -6x+4Step-by-step explanation:
[tex]x =\frac{4-k}{6}[/tex]
Cross Multiply
[tex]x \times 6 = (4-k)\times 1\\\\6x = 4-k[/tex]
Isolate k
[tex]6x -4 =-k[/tex]
Divide through by -1
[tex]\frac{6x}{-1} -\frac{-4}{-1} = \frac{-k}{-1}\\ \\-6x+4 =k\\\\k =-6x+4[/tex]