Answer:
Step-by-step explanation:
Since r=2 and |r|>1 the sum does not converge to any value. The sum does not exist for this infinite geometric series.
The sum to infinity of the sequence is -18
Sum to infinity of a geometric sequenceThe formula for calculating the sum to infinity of a geometric sequence is expressed as:
Sinfty = a/1-r
where
a is the first term
r is the common ratio
From the nth term
a = 18
r = 2
Substitute
Sinfty = 18/1-2
Sinfty = -18
Hence the sum to infinity of the sequence is -18
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Compute the discriminant D(x,y)D(x,y) of the function. f(x,y)=x3+y4−6x−2y2+3 f(x,y)=x3+y4−6x−2y2+3 (Express numbers in exact form. Use symbolic notation and fractions where needed.) D(x,y)=D(x,y)= Which of these points are saddle points? (2⎯⎯√,0)(2,0) (2⎯⎯√,1)(2,1) (−2⎯⎯√,1)(−2,1) (2⎯⎯√,−1)(2,−1) (−2⎯⎯√,−1)(−2,−1) (−2⎯⎯√,0)(−2,0) Which of these points are local minima?
The discriminant of function [tex]f(x,y)=x^3 + y^4 - 6x-2y^2+3[/tex] is 72xy³ – 24x and points (√2,0), (-√2, 1) and (-√2, -1) are saddle point, and points (√2, 1) and (√2, -1) are local minima.
A function is an expression in terms of one or more variable.
If f(x, y) is a two-dimensional function that has a local extremum at a point ([tex]x_o, y_o[/tex]) and has continuous partial derivatives at this point, then [tex]f_x (x_o, y_o)=0[/tex] and [tex]f_y (x_o, y_o)=0[/tex]. The second partial derivatives test classifies the point as a local maximum or local minimum.
Then
1. If D > 0 and [tex]f_{xx}(x_o, y_o) > 0[/tex] , the point is a local minimum.
2. If D > 0 and [tex]f_x_x (x_o, y_o) < 0[/tex], the point is a local maximum.
3. If D < 0, the point is a saddle point.
4. If D = 0, higher order tests must be used.
Given that
[tex]f(x,y)=x^3 + y^4 - 6x-2y^2+3[/tex]
[tex]f_x = 3x^2-6[/tex]
[tex]f_x = 0[/tex] implies that [tex]x = \pm\sqrt2[/tex]
[tex]f_y= 4y^3-4y[/tex]
[tex]f_y= 0[/tex] implies that y = 0; y = [tex]\pm[/tex]1.
Thus, the critical points are (√2,0), (√2,1), (√2, -1);(-√2,0), (-√2,1); (√2, -1).
[tex]f_{xx} = 6x[/tex]; [tex]f_y_y = 12y^3 - 4[/tex], [tex]f_{xy}= 0[/tex]
D(x, y) = [tex]f_{xx}f_{yy} - f_{xy}^2[/tex]
= 6x × (12y³ – 4)
D(√2, 0) = -24√2 < 0 implies (√2,0) is a saddle point.
D(√2, 1) = 48√2 > 0 ; [tex]f_{xx}(2, 1) = 6\sqrt2 > 0[/tex] implies (√2, 1) is local minimum.
D(√2, -1) = 48√2 > 0; [tex]f_{xx}(2, -1) = 6\sqrt2 > 0[/tex] implies (√2, -1) is local minimum.
D(-√2, 0) = 24√2 > 0; [tex]f_{xx}(-2,0) = -6\sqrt2 < 0[/tex] implies (-√2, 0) is local maximum.
D(-√2, 1) = -48√2 < 0 implies (-√2, 1) is a saddle point.
D(-√2, -1) = -48√2 < 0 implies (-√2, -1) is a saddle point.
Thus, (√2,0), (-√2, 1) and (-√2, -1) are saddle point, and (√2, 1) and (√2, -1) are local minima.
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Twelve friends met for for dinner. They learned that three-twelfths of them
were born in Texas, two-twelfths in New York and the rest in Idaho.
How many friends were born in Idaho?
the answer is seven twelfth
PRETTY MUCH A FREE BRAINLIEST IF UR RIGHT, GOOD LUCK :D. Value of x is greater than or equal to 14
Options:
x>14
x<14
x≥14
x≤14
Answer:
3rd choice down. . . . . . .
x≥14 plz give me brainlyest
1/8+ c = 4/5
27/20 = c
Answer: the answer will be for c is 27 over 40
Step-by-step explanation:
The net of a rectangular prism is shown below. What is the total surface area of the prism in square centimeters?
A. 208 cm2
B. 96 cm2
C. 160 cm2
D. 144 cm2
Answer:
B.96
Step-by-step explanation:
Looking for help with some geometry questions today!
Please only answer if you know the answer and can support it by showing you work. If you have a comment or do not know the answer, tell me that in the comment section, do not answer the question. Don't take my points and I want take yours!
Anyways, please show all of you work and explain your thinking! Answer all 5 parts of this question! Good luck!
Answer:
A) Central angle has same value as intercepted arc
GD is the diameter ⇒ mGFED = 180°mDE + mGF = 180° - 90°mDE = 90° - mGF = 90° - 46° = 44°B) Inscribed angle is half of the intercepted arc:
∠WTV = 1/2(90°) = 45°C) Sum of angles of triangle is 180° and inscribed angle is half of the intercepted arc:
m∠RST = (180° - 67° - 102°/2) = 62°D) Inscribed angle is half of the intercepted arc:
m∠HJK = 1/2(80° + 84°) = 62°mHJ = 2*81° - 84° = 98°E) Tangent chord angle is half of the intercepted arc:
m∠XYZ = 1/2(188°) = 94°If you are given the diameter, how can you calculate the radius
Answer:
divide the diameter by 2
please help me asap
Answer:
add the two bases together: 19.5 + 14.5 = 34 x 8 (height) = 272 divided by 2 (times half) = 136cm is your answer.
Formula of a trapezoid:
Base 1 + Base 2 times height times height (basically dividing by 2)
AY
1500-
1400
1300
Optional: How much compound
interest is earned at 35 years?
(looks to be in the middle)
compound interest
Total amount (dollars)
1200
1100
1000
900
800
700
600
500
400
300
200
100
Optional: How much simple
interest is earned at 35 years?
(looks close to the whole number)
simple interest
(a) How much more compound
interest than simple interest is
earned after 35 years?
0
5 10 15 20 25 30 35 40 45 50
Number of years
Answer:
How much compound interest is earned at 35 years? 850
How much simple interest is earned at 35 years? 600
How much more compound interest than simple interest is earned after 35 years? 250
Step-by-step explanation:
-3/4 ( 8y - 12 ) + 1/5 ( 15y - 30 )
The owner of a restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a drink from the beverage fountain instead of filling the cup with water. The owner randomly selected 90 people who order a water cup and found that 21 of those customers filled the cup with a soft drink.a. Construct and interpret a 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain. b. The owner estimates that each customer who asks for a water cup but fills it with a soft drink costs the restaurant $0.35. Suppose that in the month of June 2,500 customers ask for a water cup when placing an order. Use the confidence interval constructed in part (a) to give an interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soft drink.
Answer:
This is very confusing.
Can you try and make this a shorter question for me to answer?
Step-by-step explanation:
Solve For X
(This is arcs and i could use some help)
Answer:
x = - 4
Step-by-step explanation:
Since we are looking at a circle, we know that the sum of all arc angles should add up to 360°. This means that the following...
- 32x - 3 = 360 - 85 - 35 - 115
- 32x - 3 = 125
- 32x = 125 + 3
- 32x = 128
x = 128 / (-32)
x = - 4
Terry’s garden is in the shape of a quarter-circle with radius 24 meters. What is the area of her garden?
Answer: 1809.56 let me know if it is right?
Step-by-step explanation:
Find the measure of the arc.
D
А
146°E
B
mĒDF = [?]°
Enter
Answer: 214
hope this helped.
The measure of the arc is 214 degrees
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The measure of the arc FE is 146 degrees.
Measure ED is 90 degrees.
To find the measure of the arc EDF we have to find the measure of DF.
146+90+x=360
236+x=360
Subtract 236 from both sides
x=360-236
x=124
Now let us find the arc measure EDF =Measure of ED + Measure of DF
=90+124
=214 degrees
Hence, the measure of the arc is 214 degrees
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Somebody HURRY I NEED HELP
Answer:
1/5^3
Step-by-step explanation:
5 ^ -3 = 1 / 5^3 = 1 / 125
Hi i need help. I will give brainliest
I need help with #18
Answer:
1. a
2.60
3.g
Step-by-step explanation:
Parallelogram WXYZ.
WX = 13x + 15
YZ = 19x - 9
Find the values of x and y.
Answer:
Step-by-step
sum of the adjacent angles of parallelogram is supplementary.
Therefore,
Q + R = 180°
4y+7 + 10y-37 = 180°
14y - 30° = 180°
14y = 210°
y = 210°/14
y = 15°
Could not found X in the question.
Answer: 3.27
Step-by-step explanation:
Help for brainiest
please explain how you got it :D it would help so I can understand how to do the rest
Answer:
Option D
Step-by-step explanation:
Formula to use: V=[tex]\frac{1}{2}(b*a)*h\\[/tex]
b=base of triangle a=altitude of triangle h=height of prism
Doing [tex]\frac{1}{2}(b*a)[/tex] is essentially finding the area of the triangle and after multiplying by h will give you the volume of the triangular prism.
Solve: V = [tex]\frac{1}{2}(3*3)*7[/tex] or option D
Ps. Altitude is perpendicular or 90 degrees to the side I used for the base, so it wouldn't be option C.
Which of the following points are part of the solution set to the inequality
y ≤ −1\3 x +7
A.
(-9, 1)
B.
(3, 13)
C.
(12, -4)
D.
(3, 7)
Answer:
45
St45-by-step explanation:
ramu and ravi borrowed rs 8000
Answer: Rs. 11,520
Step-by-step explanation:
As the method of compounding is not stated, the default of simple interest will be used.
Simple interest is a fixed amount that is paid over the course of the loan and is based on the original amount borrowed.
Formula is:
Amount owed = Amount borrowed * ( 1 + rate * time)
= 8,000 * ( 1 + 8% * 5.5 years)
= 8,000 * 1.44
= rs 11,520
please help me, I’m very confused
Please answer this for me
Answer:
6+p=120
Step-by-step explanation:
p=14 and thats because there are 6 p and 6+14 is 20 right, and 20x6 is 120 :D hope you understood me
2. Which of the following statements shows the distributive property?
5 + (4 – 2) = 20 – 10
5(4 – 2) = 20 – 10
5 + (4 – 2) = 9 + 3
5(4 – 2) = 9 – 7
PLEASE HELP ME!!! ITS A MONTH PAST DEW! I NEED HELP ASAP!
Determine the perimeter of a rectangle that is 10 inches long and 9 inches wide.
inches
Answer:
38
Step-by-step explanation:
2(l + b)
2(10 + 9)
2(19)
2*19
38
the point (2, -3 ) is reflected in the line x = 0 find the image
Answer:
The image of [tex]P(x,y) = (2,-3)[/tex] is [tex]P'(x,y) = (-2, -3)[/tex].
Step-by-step explanation:
According to this statement, we need to find the image of a given point by reflection with respect to the y-axis. The reflection can be done by following operation:
[tex]P(x,y) = (x, y) \to P'(x,y) = (-x, y)[/tex] (1)
Where:
[tex]P(x,y)[/tex] - Original point.
[tex]P'(x,y)[/tex] - Reflected point.
If we know that [tex]x = 2[/tex] and [tex]y = -3[/tex], then the reflecting point is:
[tex]P'(x,y) = (-2, -3)[/tex]
The image of [tex]P(x,y) = (2,-3)[/tex] is [tex]P'(x,y) = (-2, -3)[/tex].
Which is the approximate solution to the system y= 0.5x + 3.5 and y= -2/3x + 1/3 shown on the graph?
Answer: 1. 4, 2. 1x.
Step-by-step explanation:
The width of the rectangle below is 9 cm, and its length is 17
cm. What is its area?
Its area is _ cm?
Answer:
Area=153 cm²
Step-by-step explanation:
Length × Width= Area
17×9=153
Answer:
153
Step-by-step explanation:
Area= length x width
area= 17 x 9
I need help please anyone help me???????
A lottery game requires that 3 different numbers are picked from 1 to 9 if someone picks all 3 winning numbers the person wins 9 million complete parts a and b
What is the sum?
х 3
+
X+3 X+ 3
+
X+ 3
اله اثر)
X+5
X + 3
X+5
3x+27
6x
X+3
Answer:
there is no question like that
Step-by-step explanation:
are you fooling AROUND