use the level curves to predict the location of the critical points of f and determine whether f has a saddle point, local maximum, or local minimum at each point. then use the second derivatives test to confirm your predictions. (if an answer does not exist, enter dne.)
(0,0) is a saddle point and (1,1) is a local minimum.
The point as in domain of something like the functions with the lowest value is known as the local minimum. You can calculate the local minimum by determining the function's derivative.A saddle point of minimax point is a location on the graph's surface where the slopes of all orthogonal derivatives are zero (a crucial point), but which isn't the function's local extremum.From the contour map, the level curves intersect at (0,0) . Hence (0,0) is a saddle point.
and the center of level curve 3.2 (1,1) is a local minimum.
Hence (0,0) is a saddle point and (1,1) is a local minimum.
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Zachary purchased a computer for $1.900 on a payment plan. Three months after he purchased the computer, his balance was $1.525. Eight months after he purchased the computer, his balance was
$900. What is an equation that models the balance y after x months?
The equation models the balance y after x months.
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer)
The equation that models the balance of the payment plan loan, y, after x months is y = -125x + 1900.
What is an equation?An equation is a mathematical statement claiming that two mathematical expressions are equal or equivalent.
Equations are depicted using the equation sign (=) to show the equality of values.
Slope-Intercept Formula:y = mx+b
y = y-coordinate
m = slope
x = x coordinate
b = y-intercept
Purchase PlanPayment Period Balance
12 months $1,900
9 months (3 months after) $1,525
4 months (8 months after) $900
Let 12m = 1900 ... Equation 1
9m = 1525 ... Equation 2
4m = 900 ... Equation 3
Subtract Equation 3 from Equation 1:
12m = 1900
- 4m = 900
= 8m = 1000
m = 125 (1000/8)
Equation modeling the balance y after x months:
y = -125x + 1900
Thus, a model equation for the balance of the payment plan loan after x months is y = -125x + 1900.
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Which function is an extended function for f(x) = StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction that is continuous for all values of x?
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row negative 2, x = negative 1, 1.
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row negative 2, x = 1.
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row 4, x = negative 1, 1.
g (x) = StartLayout Enlarged left-brace First row StartFraction x cubed + 3 x squared minus x minus 3 Over x squared minus 1 EndFraction, x not-equals negative 1, 1 Second row 4, x = 1.
The function is f(x)=(x³+3x²-x-3)/(x²-1). The continuous function option A is correct.
Given that,
The function is f(x)=(x³+3x²-x-3)/(x²-1)
We have find the continuous function.
If the function's curve DOES NOT break at the point x = a, it is said to be a continuous function at that point in calculus. The mathematical definition of a function's continuity is given below. If x = a, then f(x) is continuous at that moment.
f(a) exists;
limₓ → ₐ f(x) exists;
limₓ → ₐ₋ f(x) = limₓ → ₐ₊ f(x) and
Both of the above values are equal.
Now, limₓ → ₐ f(x) = f(a).
The function g(x)=[tex]\left \{ {{\frac{x^{3}+3x^{2}-x-3 }{x^{2} -1} }, x\neq -1,1 \atop {-2, x=-1,1}} \right.[/tex]
Therefore, the continuous function option A is correct.
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Random sampling complicates the analysis of cross-sectional data.
a. True
b. False
Random sampling do not complicates the analysis of cross-sectional data
Sampling is just an action of taking samples or subsets of a given data set for analysis. This means that when sampling is done, the next stage for the samples, are for them to be analyzed.
There different methods of sampling including random sampling. In this type, each member of the samples have equally probability of being chosen.
A cross-sectional data analysis is the analysis of samples or subsets at a fixed point in time. A systematic random sampling method is used in the analysis of cross-sectional data. And when this used, then each combinations of individuals samples in a data set has an equal chance of being selected.
Hence, the statements that says random sampling complicates the analysis of cross-sectional data is False.
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If $a$ is 4 percent of $b$ and $b$ is 25 percent of $c$, what percent of $a$ is $c$?
c is 10,000 percent of a.
Here we are given that a is 4 percent of b and b is 25 percent of c.
Let us assume the value of c to be x
Then the value of b will be-
25 percent of x
= (25/100)x
= (1/4)x
= x/4
Now, the value of a will be-
4 percent of b
= 4 percent of x/4
= ( 4/100 )( x/4 )
= x/100
Thus, we have a = x/100 and c = x
Hence, the value of c as a percent of a can be calculated as follows-
x/( x/100 )*100
= ( 100x/x )*100
= 100*100
= 10,000
Thus, c is 10,000 percent of a.
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what is 42,400 at 13% for 2 years
The amount 42,400 at 13% for 2 years will be 53,424 in total with the interest 11,024.
we calculate the simple interest by multiplying the principal amount by the number of periods and the interest rate. Simple interest does not compound, and you don’t have to pay interest on interest. In simple interest, the payment applies to the month’s interest, and the remainder of the payment will reduce the principal amount.
The simple interest calculated by the following mathematical formula:
A = P (1+rt)
P = Principal Amount
R = Rate of interest
t = Number of years
A = Total accrued amount (Both principal and the interest)
Interest = A – P.
A= 42,400(1+0.13×2)
A= 53,424
Interest = A-P
53,424- 42,400 = 11,024.
Thus the amount will be 53,424 and Interest will be 11,024.
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The amount ₹ 42400 at 13% for 2 years will be ₹ 53424 with ₹ 11024 interest.
What is Simple Interest ?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
How Simple Interest is calculated ?Simple Interest is calculated using the following formula: SI = P × R × T/100, where P = Principal, R = Rate of Interest, and T = Time period. Here, the rate is given in percentage (r%) is written as r/100. And the principal is the sum of money that remains constant for every year in the case of simple interest.
What is Amount ?Amount is the total money paid back at the end of the time period for which it was borrowed.
How Amount is calculated ?The total amount formula in case of simple interest can also be written as: A = P + SI, where P = Principal and SI = Simple Interest.
In this question,
P = ₹ 42400
R = 13%
T = 2 years
SI = P x R x T / 100
= 42400 x 13 x 2 / 100
= 424 x 13 x 2
SI = ₹ 11024
Amount = P + SI
= ₹(42400 + 11024)
= ₹ 53424
The amount ₹ 42400 at 13% for 2 years will be ₹ 53424 with ₹ 11024 interest.
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HELPPPPPPPPPPPPPPP
Determine if the table shows a proportional relationship.
Time (hours) 0 7 14 21 28
Pay (dollars) 0 91 182 273 364
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 12 dollars per hour.
Yes, it is proportional because the ratios for dollars per hour are all equivalent to 13 dollars per hour.
No, it is not proportional because 91 over 7 does not equal 273 over 21.
No, it is not proportional because 273 over 21 does not equal 364 over 28.
Answer: Yes, it is proportional because the ratios for dollars per hour are all equivalent to 13 dollars per hour.
Step-by-step explanation:
By multiplying all of the hours by 13 they equal the pay in dollars therefore we can conclude that the ratio is proportional because all of the ratios are equal and the dollars per hour are equivalent to 13 dollars per hour.
To solve this system by substitution, which variable in which equation should be isolated?
{(4x+5y=4),(2x+y=7):}
x in the first equation
y in the first equation
x in the second equation
y in the second equation
Answer:
I would go for y in the first equation
Step-by-step explanation:
Eliminating x and isolating y is easierYou get y from the first equation I guess. The question is a bit confusing though.
Simon's bank account has a balance of -$28.16. He goes to the bank and deposits $40.25. How much money is in his account after the deposit?
What operation is needed to solve this problem? Explain how you know and then solve.
The money in his bank account after the deposit is $12.09.
The balance amount in Simon's bank account is -$28.16.We can clearly see that the balance amount is a negative number.Simon goes to the bank and deposits $40.25.He deposits the money in the bank. It means we need to add the amount deposited by him to the existing balance amount in his bank account.We need to perform an addition operation to solve the problem.Let the amount of money in his account after the deposit be "x".x is equal to the sum of the amount before the deposit and the money deposited.x = -$28.16 + $40.25x = $12.09To learn more about addition, visit :
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HELPPPPP
the question is attached
The value of the equation illustrated by E = 50q + 80000 is 5248000.
What is an equation?Simply put, an equation shows the relationship that exist between the variables that are given.
The equation given is illustrated as:
E = 50q + 80000
where q = (80p + 100000)
Substitute q into the equation
E = 50q + 80000
E = 50(80q + 100000) + 80000
E = 4000p + 5000000 + 8000
E = 4000p + 5080000
Substitute 42 for p
E = 4000(42) + 5080000
E = 168000 + 5080000
E = 5248000
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Can you solve for X inside the correct code for question four?
Answer
CIAD
Step-by-step explanation
The Pythagorean theorem states:
[tex]c^2=a^2+b^2[/tex]where a and b are the legs and c is the hypotenuse of a right triangle.
Applying this theorem to triangle 1:
[tex]\begin{gathered} x^2=77^2+36^2 \\ x^2=5929+1296 \\ x^2=7225 \\ x=\sqrt{7225} \\ x=85 \end{gathered}[/tex]Then, the first letter is C.
Applying the theorem to triangle 2:
[tex]\begin{gathered} x^2=39^2+80^2 \\ x^2=1521+6400 \\ x^2=7921 \\ x=\sqrt{7921} \\ x=89 \end{gathered}[/tex]Then, the second letter is I.
Applying the theorem to triangle 3:
[tex]\begin{gathered} x^2=25^2+100^2 \\ x^2=625+10000 \\ x^2=10625 \\ x=\sqrt{10625} \\ x=103.08 \end{gathered}[/tex]Then, the third letter is A.
Applying the theorem to triangle 4:
[tex]\begin{gathered} x^2=17^2+52^2 \\ x^2=289+2704 \\ x^2=2993 \\ x=\sqrt{2993} \\ x=54.71 \end{gathered}[/tex]Then, the fourth letter is D.
Simplify
Rewrite the expression in the form 5".
510
512
Answer:
510 by 2 is 255
255 by 2 is 127.5
127.5=63.75.63.75 by 2=31.875
31.875. by 2=15.9375
15.9375 by 2=7.96875
512 by 2=256
256 by 2=128
128 by 2=64
64 by 2=32
32 by 2=16
Multiple Choice
1. How many tenths are in two fifths?
A.
B. 1
C. 4
D. 100
ASAP please Hurry
For the equation y = 2x + 1
Shawn bought a 10-pound turkey to serve for Thanksgiving. He plans to serve eachadult 2/5 of a pound.Write an equation to represent the number of adult servings, x, Shawn canget from the 10-pound turkey. Use your equation to determine the number of adultservings.
Since each serving contains 2/5 of a pound, then, the total weight of x servings would be:
[tex]\frac{2}{5}x[/tex]If the total weight of x servings should be equal to the weight of the turkey, then:
[tex]\frac{2}{5}x=10[/tex]Multiply both sides of the equation by 5/2:
[tex]\frac{5}{2}\cdot\frac{2}{5}x=\frac{5}{2}\cdot10[/tex]Simplify the expressions on both sides of the equation:
[tex]x=25[/tex]Therefore, the number of adult servings from a 10 pound turkey, will be 25.
At its highest point, the elevation of a county is 5,776 feet above sea level. At its lowest point, the elevation of the county is 8 feet below sea level. Answer parts a through c. (Don’t simply
The difference or distance between the two points is 5768ft
The Difference in ElevationTo solve this problem, we have to find the difference between the highest point and lowest point of the county.
highest point = 5776ftlowest point = 8ftWhen the height of a point is its vertical distance above or below the surface of a reference plane* you have selected, it is called the elevation* of that point.
When the height of a point is its vertical distance above or below mean sea level (as the reference plane), it is called the altitude* of the point.
The difference between the points of elevation in this question is
[tex]5776 - 8 = 5768ft[/tex]
The difference in elevation is given as 5768ft
The complete question is-
At the highest point, the elevation of a county is 5,667 feet above sea level. At its lowest the elevation of the county is 7 feet below sea level. Answer parts a through c. Write an expression using integers to represent the difference between the elevations.
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Given ABC with coordinates A(1,3). B(4,5), and C(5,2). what are the coordinates of A'BC after the glide reflection described by T(-1,1)Ry-axis?A =B =C=
Let's begin by listing out the information given to us:
[tex]A\mleft(1,3\mright);B\mleft(4,5\mright);C\mleft(5,2\mright)[/tex]When this is glided by T(-1, 1); ry−axis(x, y) → (−x, y)
[tex]\begin{gathered} A\mleft(1,3\mright)\rightarrow A^{\prime}(^{}-1,3) \\ B(4,5)\rightarrow B^{\prime}(-4,5) \\ C(5,2)\rightarrow C^{\prime}(-5,2) \end{gathered}[/tex]Enter the polnomial function f(x) in standard form given that f has leading coefficient 3 and roots 4, sqrt(2), and -sqrt(2)
Here is a picture of what I mean
Using the Factor Theorem, the polynomial function that has leading coefficient of 3 and the given roots is given as follows:
f(x) = 3x³ - 12x² - 6x + 24.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule presented as follows.
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
a is the leading coefficient of the function f(x), determining if it is positive(a positive) or negative(a negative).
In the context of this problem, the leading coefficient and the roots are given as follows:
f(x) = 3(x - 4)(x - sqrt(2))(x + sqrt(2))
Applying the subtraction of perfect squares, the square root is simplified as follows:
(x - sqrt(2))(x + sqrt(2)) = x² - 2.
Hence the function is defined as follows:
f(x) = 3(x - 4)(x² - 2)
f(x) = 3(x³ - 4x² - 2x + 8)
f(x) = 3x³ - 12x² - 6x + 24.
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When solving an equation, the goal is to ____________________ the variable.
The answer for the missing piece is to 'find' the variable.
Suppose sin(A) = 1/4. Use the trig identity sin^2(A) + cos^2(A) = 1 to find cos(A) in quadrant 2. Round to ten-thousandth.
Using the given trigonometric identity, the cosine of the angle in the second quadrant is given by:
cos(A) = 0.9682.
What is the cosine of angle A?The cosine and the sine of the angle are related according to the following relation:
sin²(A) + cos²(A) = 1.
Hence, knowing the sine of the angle, as we do in this problem, we can find the cosine of the same angle solving the above equality.
The value of the sine of angle A is given by:
sin(A) = 1/4.
Hence the equation can be solved for the cosine as follows:
cos²(A) = 1 - sin²(A)
cos²(A) = 1 - (1/4)²
cos²(A) = 1 - (1/16)
cos²(A) = (16/16) - (1/16)
cos²(A) = 15/16
The inverse of the square is the square root, hence:
cos(A) = ± sqrt(15/16)
In the second quadrant, the cosine is negative, hence:
cos(A) = -sqrt(15/16)
cos(A) = -0.9682.
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what is the probability of rolling a 5 on a six sided number cube
please help asap thank u so much!!
Answer:
Step-by-step explanation:
I think the answer is 1/6.
There are six sides and only one side has a 5 on it.
So, one side with a five/six sides in total
help if your smartest person in the world
Answer:
First one, the answer could be 1, 2, or 3, because the fraction you made is less than one. Second one, the answer could be any number above 4 (5, 6, 7, and so forth), because the fraction you made is greater than one.
Which expression is equivalent to 4sin²(x) - 8sin²(x/2)
4(cos(x) - cos²(x))
4(-cos(x) - cos²(x))
4(2-cos(x) - cos²(x))
4(2 + cos(x) - cos²(x))
After solving 4sin²(x) - 8sin²(x/2), we get 4(cos(x) - cos²(x)) as an answer i.e, option (A) is the answer.
Trigonometry expression : 4sin²(x) - 8sin²(x/2)
What is Trigonometry expression?
The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosec , cosine , cotangent , secant , sine , and tan.
Given expression, 4sin²(x) - 8sin²(x/2)
=> 4(sin²(x) - 2sin²(x/2))
=> 4(sin²x - 2(√(1 - cos x) / 2)²)
=> 4(sin²x - 2(1 - cos x) / 2)
=> 4(1 - cos²x - 1 + cos x)
=> 4(cos(x) - cos²(x))
Therefore, the answer is option(a) i.e,4(cos(x) - cos²(x)).
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The sum of the three angles of
any triangle is [ ? ]0.
1 pointIf A=(-1-7,0) and B(-8,8-10), find ||AB||. Round to 3 decimal places.Type your answer.
Basically we need to find the distance between A and B, so:
[tex]\begin{gathered} \mleft\Vert AB\mright||=d=\sqrt[]{(x2-x1)^2+(y2-y1)^2+(z2-z1)^2} \\ where \\ A=(x1,y1,z1)=(-1,-7,0) \\ B=(x2,y2,z2)=(-8,8,-10) \\ \Vert AB||=\sqrt[]{(-8-(-1))^2+(8-(-7))^2+(-10-0)^2} \\ \Vert AB||=\sqrt[]{49+225+100} \\ \Vert AB||=\sqrt[]{374} \\ \Vert AB||\approx19.339 \end{gathered}[/tex]elba constructs a cube made of glass panels. Each panel has a side length of 3··4foot. What is the total surface area, in square feet, of the cube? Show your work.
The surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions.
Surface area=6(3.4)^2=69.36 square feet
What is surface area?
A solid object's surface area is a measurement of the overall space that the object's surface takes up.
The quantity of space enclosing a three-dimensional shape's exterior is its surface area.
A 3D object's surface area is the entire area that all of its faces cover. For instance, if we need to calculate how much paint is required to paint a cube, we can use the cube's surface area. determine how much paint is needed to paint it. It is consistently expressed in square units.
As a refresher, the surface area of an object is the sum of the areas of all of its faces, or the exterior surfaces of its three dimensions.
Surface area=6(3.4)^2=69.36 square feet
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given the cost function C(x)=85,000+125x where x represents the area of a house, what is the cost of building a house with 5,425 square feet?
The cost of building a house with the area 5,425 square feet is $763,125.
The given function is C(x)=85,000+125x.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here, x represents the area of a house is 5,425 square feet.
Put x=5425 in the given function, that is
The total cost = C(5425)=85,000+125 × 5425
= $763,125
Therefore, the cost of building a house with the area 5,425 square feet is $763,125.
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Which equation represents a line which is parallel to the line 8x – 7y = 35?A) y=8/7x+8B) y= -8/7x-6C) y= -7/8x+5D) y= 7/8x+2
The easiest way to solve this is to write the line in slope-intercept form.
The slope intercept is of the form:
[tex]y=ax+b[/tex]Where a is the slope of the line, any lines that ahve the same slope are parallel.
Then, we solve for y the equation of the line given:
[tex]\begin{gathered} 8x-7y=35 \\ 7y=8x-35 \\ y=\frac{8}{7}x-5 \end{gathered}[/tex]The slope of the line in the problem is 8/7. Then if we look at the options, the only one that has a slope of 8/7 is option B, which is the correct answer.
-30 = 3 (w + 6) + 5w solve for w and simplify your answer as much as possible
Answer: w = -6
Step-by-step explanation:
-30 = 3(w + 6) + 5w
-30 = 3w + 18 + 5w
-30 = 8w + 18
-48 = 8w
w = -6
Hope this helps
Hector got 42 out of 50 questions
correct on a math test. What percent of
the questions did Hector get correct?
Answer:
84%
Step-by-step explanation:
To solve this, the equation to find percent is AMOUNT divided by the TOTAL * 100. So 42 questions were right, divided by the total, 50. Therefore it would be 0.84 * 100, 84%
