Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.
In the given question, we have to verify the linear approximation at (0, 0).
f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y
Let f(x, y) = √(y+cos^{2}x)
f(x, y) ≈ f(a, b)+fx(a, b)(x-a)+fy(y-b)
f(x) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex]
f(y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]
f(x, y) ≈ 1+0(x-0)(1/2)(y-0)
f(x, y) ≈ 1+1/2y
Hence, left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.
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The complete question is:
Verify the linear approximation at (0, 0). f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y
Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) =.............. and fy(x, y) = ............. Both fx and fy are continuous functions for y >............ , so f is Differentiable at (0, 0) by this theorem. We have fx(0, 0) =........... and fy(0, 0) =............. , so the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)=........
Practice Triangle Ratios (Sides) Find the value of c. Round to the nearest tenth!
Answer:
30.6688
Step-by-step explanation:
We usually use the formula SOHCAHTOA meaning Sine = opposite side/hypotenuse Cosine = opposite side /hypotenuse then Tangent = Opposite side/Adjacent side. We then say Tan61°= x/17 to get the height as 30.6688 PS/ Hypotenuse is the slanting side of the triangle
PLEASE HELP WILL GIVE BRAINLIEST!
A dart board contains 20 equal sized sectors numbered 1 to 20. A dart is randomly tossed at the board 10 times. what is the probability that the dart lands in sector 20 exactly 5 times?
Answer:
1/2
Step-by-step explanation:
There are a total of 20 sections on the board. And a dart hit that the section labeled 20 a total of 5 times, throwing a total of 10 darts. So, if you take these two numbers and and put them into the fraction: 5/10 and then simplify it you will get 1/2. Hope this helps.
Answer:
It's 6.09 x 10^-5.
Step-by-step explanation:
These other answers did not pay attention in school.
He base rate for a state's workers compensation insurance for a service station attendant is $5.12 per $100.00 paid in wages the payroll for scott park service station for march is 5,784.00. What is the monthly premium for workers compensation insurance?
Answer:
$2961.41
Step-by-step explanation:
Base rate for a state workers compensation insurance = $5,12 per $100 paid in wages
Scott park payroll for march = $5784 ( inclusive of insurance payment )
Determine the monthly premium for insurance
$5.12 = $100
First; calculate how many $100 are in $5784
= 5784 / 100 = 578.4
Hence the monthly premium for workers compensation insurance
= $5.12 * 578.4
= $2961.41
the heights of the peach trees in an orchard are normally distributed with a mean of 12.5 feet and a standard deviation of 1.8 feet.
what is the height of a peach tree with a z-score of -0.5?
Enter your answer rounded to the nearest tenth, in the box.
Answer:
i think 1.8 not sure tho
Answer:
Z-score Formula: z = (x - μ)/σ
Plug in: -0.5 = (x - 12.5)/1.8
Solve: -0.5 * 1.8 = x - 12.5
-0.9 = x - 12.5
-0.9 + 12.5
x = 11.6
Therefore, the height of a peach tree with a z-score of -0.5 is 11.6 feet.
Ana participated in a charity walk. She
raised $0.25 for each 1/2
mile that she
walked. The first day, Ana walked 11 miles.
The second day, she walked 14 miles.
How much money did Ana raise?
Answer:
if $0.25 for each mile, then $1.00 =1 mile.
so the first day would be = $1=1mile
$n=11 miles
= 1n= 11×1=$ 11
Step-by-step explanation:
and the 2nd day is = 14×1= $14.
So the answer is 14+11=$25.00
...............................
In numerology, the letter Y can be a vowel or a consonant
Simplify the following expression: (2x2+3x−4)−(4x2−7x+1)
A
−2x2+10x−5
B
2x2−4x−3
C
−8x2+21x+4
D
−2x−4x−5
Urgent please help..
Answer: I’m pretty sure it’s 15 cm
Step-by-step explanation:
9.8 ft
4f
12 ft
Find the Area of this figure
3.71 × 1,000 pls need answer
Answer: 3,710
Step-by-step explanation:
What value of x makes x - 10 = -5 true?
-5
15
5
-15
Answer:
5
Step-by-step explanation:
x - 10 = -5
+ 10. +10
x = 5
hope this helps
Classify the triangle based on its sides
If you are helped with my answer pls tag me brianliest
I really want it
THANK YOU........
3. Find the balance of a savings account at the end of 15 years if the interest
earned each year is 6.3%. The principal is $700.
Answer:
The balance of the savings account in 15 years will be $1,750.24.
Help 15 points!!
A central angle of a circle of diameter 6 cm measures 86°. What is the length of the intercepted arc?
A)
2.8 cm
B)
4.5 cm
C)
5.1 cm
D)
9 cm
Answer:
B)
4.5 cm
Step-by-step explanation:
The formula for arc length when our central angle is in degrees =
2πr(θ/360)
θ = 86°
Diameter = 6cm Radius = Diameter /2
Radius = 6cm/2 = 3cm
Hence,
Intercepted arc length = 2 × π × 3 (86/360)
= 2 × π × 3 × 0.2388888889
= 4.5029494701 cm
Approximately = 4.5 cm
Option B is the correct answer
An urn contains 8 green and 9 white balls. Six balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 6 balls drawn from the urn are white? Round your answer to three decimal places.
Answer:
The probability is 0.022
Step-by-step explanation:
Firstly, we need to get the total number of balls in the urn
mathematically, we have this as ;
8 + 9 = 17
now, the probability of selecting a white ball will be the number of white balls divided by the total number of balls
Mathematically, we have this as 9/17
Now, since the event is carried out with replacement, the probability for the six times is the same
So, we have the probability as;
(9/17)^6 = 0.022
HELP ASAP!! Which of the following will result in an irrational number? Select all that apply.
A. -√3 +2
B. √2*√3
C. √27*√ 3
D. 3√7 + 2√7-5√7
Answer:
A and B.
Step-by-step explanation:
The irrational number are -√3 +2 and √2 x √3.
What is Irrational Number?Any number that cannot be stated as a fraction for any integers is considered to be irrational. The decimal expansions of irrational numbers are neither periodic nor do they come to an end. Every number that is transcendental is illogical.
Given:
A) -√3 +2 is an irrational number.
B) √2 x √3 = √6, which is an irrational number.
C) √27 x √ 3
= 3√3 x √3
= 3 x 3
= 9, which is a rational number.
D) 3√7 + 2√7-5√7
= 5√7- 5√7
= 0, which is a rational number.
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When 'x' is multiplied by a number inside the parentheses, it causes what type of
transformation:
The proportional relationship between the distance driven and the amount of time driving is shown in the
following graph.
Which statements about the graph are true ?
A. The y- coordinate of point A represents the distance driven in 4 hours.
B. The distance driven in 1 hour is 80 km
C. None of the above
The distance driven in 1 hour is 80 km. Therefore, option B is the correct answer.
The given time graph shows the proportional relationship between the distance driven and the amount of time driving.
What is a distance-time graph?If an object moves along a straight line, the distance travelled can be represented by a distance-time graph. In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.
From the graph, we can see that object A moved 400 km in 5 hours time.
So, in 1 hour the distance travelled by object =400/5=80 km
Therefore, option B is the correct answer.
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A girl successfully made 12 free throws yesterday today she made 150% as a nanny how many successful Fritos did she make today
Answer:
18 throws
Step-by-step explanation:
Given data
Number of throws= 12
Let us 150% if 12
=150/100*12
=1.5*12
=18 throws
Hence she made 18 throws today
Suppose y varies directly with x, and y = 14 when x = 2. What direct variation equation relates x and y? What is the value of y when x = 6? Explain. Show your work
A. The equation y = 2x relates x and y. When x = 6, y =2(6) or 12.
B. The equation y = 14x relates x and y. When x = 6, y =14(6) or 84.
C. The equation y = 7x relates x and y. When x = 6, y =7(6) or 42.
Answer: C. The equation y = 7x relates x and y. When x = 6, y =7(6) or 42.
Step-by-step explanation:
Using direct variation with the formula:
y = kx
Since y =14, when x = 2.
y = kx
14 = 2k
k = 14/2
k = 7
Therefore, y = 7x
The value of y when x = 6 will be:
y = kx
y = 6k
Recall that k = 7
y = 6 × 7
y = 42
Therefore, the equation y = 7x relates x and y. When x = 6, y =7(6) or 42.
what is the rate of change of y=0.5•x-2
Answer:
0.5
Step-by-step explanation:
rate of change is just a synonym for slope and the equation for slope is y=mx +b where m is the slope so 0.5=m and if m= slope then 0.5=slope=rate of change :)
ABCD is a trapizoid of bases [AB] and [DC], M and N are the midpoint of [AD] and [BC] if DC=11cm and MN=9cm then AB=
Answer:
[tex]AB = 7[/tex]
Step-by-step explanation:
Given
[tex]DC = 11[/tex]
[tex]MN = 9[/tex]
Required
Find AB
Since MN is the midpoint, then:
[tex]MN = \frac{1}{2}(AB + DC)[/tex]
[tex]9 = \frac{1}{2}(AB + 11)[/tex]
Multiply by 2
[tex]2 * 9 = \frac{1}{2}(AB + 11)*2[/tex]
[tex]18 = AB + 11[/tex]
[tex]AB = 18 - 11[/tex]
[tex]AB = 7[/tex]
help a girl out please
Answer:4
Step-by-step explanation:ts is = ed
A ball is dropped from a height of 180 meters. The height of the ball can be represented by
-5t2 + 180, in meters, when t represents the time in seconds since the ball was dropped.
Which expression represents the height of the ball In factored form?
A) -5(t+6)^2
B) -5(t-6)^2
C) -5(t+6)(t-6)
D) (5t-3)(80t+3)
Mark correct answer for wrong ones.
Except one needs to answers I haven't gotten to yet. Correct answer gets brainliest!
Answer: Can I see a better pic?
Step-by-step explanation:
Answer: D and C
Step-by-step explanation:
PPPPPPPPPPPPPPPPPLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLZZZZZZZZZZZZZZZZZZZZZ Help its due by end of day i relay need a good grade
Answer:
first question
AB=CD=15cm
BD=AC=8cm
Help please and Thanks :))
Please help me with this
2)
Okay so because the right side is two times the length and width of the left side, we need to divide 20 and 14 by 2 which gives us 10 and 7. That means x+2 = 10 so we need to subtract 2 from each side which gives you 8. Therefore, x = 8.
20/2 = 10
10 - 2 = 8
x = 8
find c
A. square root of 7 and 2
B. 14
C. 7
D. square root of 7 and 3
can you please help.
Answer:
3.74-a
7
2.64
4.58
Step-by-step explanation:
hope it helps please mark me as brainlist
Mario walked 250 ft south then 430 ft west. How far is he from the starting point? Round off answers to the nearest hundredths place.
Answer:
497.39 FEET
Step-by-step explanation:
Please check the attached image for a diagram of the bearings
This question can be solved using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
we want to determine the value of c
250² + 430² = 247400
c = √247400 = 497.39 feet