The value of fx(1, 0) equal to -(1/√(3)) and fy(1, 0) is equal to -20/√3.
To find fx(1, 0) and fy(1, 0), we need to take the partial derivative of the given equation with respect to x and y respectively, and then evaluate the derivatives at the point (1,0).
First, we have f(x, y) = √(4 - x² - 4y²)
To find fx(1, 0), we'll take the partial derivative of f(x, y) with respect to x:
fx(x, y) = ∂f/∂x = -(x/√(4 - x² - 4y²))
Therefore, fx(1, 0) = -(1/√(4 - 1² - 4×0²)) = -(1/√(3))
fx(1, 0) = -(1/√(3))
To find fy(1,0), we'll take the partial derivative of f(x, y) with respect to y:
fy(x, y) = ∂f/∂y
= -2y/√(4 - x² - 4y²)
Therefore, fy(1, 0) = -20/√(4 - 1² - 4×0²) = -20/ √3
These numbers, fx(1, 0) and fy(1, 0), can be interpreted as slopes of the equation. The slope in this case represents the rate of change of the function in the x and y directions. A negative value for fx(1,0) means that as x increases by a small amount, the function value decreases by a small amount, while a value of 0 for fy(1,0) means that as y increases by a small amount, the function value does not change.
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Find the value of 2π√l /g
when π=3⅐, l= 98 and g = 32
Answer:
Step-by-step explanation:
2π√l/g = (2*3.14*sqrt(98))/32 = 10.945
31. Grace solved the equation 2 1/2y = 5/8. Her steps for the solution are shown in the table but are all mixed up. Write her steps I. The correct order on the right side of the table
The correct steps in the solution of the fraction are;
Step 1 ; 2 1/2y = 5/8Step 2 ; 5/2 y = 5/8Step 3 ; y = 5/8 . 2/5Step 4 ; y = 10/40 or 1/4What are the steps in the solution?We know that when we talk about a fraction what we mean is just a part of a whole. There are some steps that we would need in the solution of the question and the steps have not been arranged in the proper order in the image that is attached here.
The task that we have then is to be able to arrange the steps that we need to take in the proper order and as such, we are going to have that;
Step 1 ; 2 1/2y = 5/8
Step 2 ; 5/2 y = 5/8
Step 3 ; y = 5/8 . 2/5
Step 4 ; y = 10/40 or 1/4
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ABCD is a regular tetrahedron. MandN are the mid points of the edges AB and CD. It the length of AB is a, then |MN|^2 = ...?
4/3 is the valve of |MN| ^2 of a given tetrahedron in which M AND N are the mid points of the edges AB and CD . is explained below:
on observing the diagram we can estimate that image of point D in the plane is given by ABC is [tex](2\sqrt{2} , 0 , -2 )[/tex] and volume of tetrahedron ACBM is 4/3
AB=BC=CD=AD =a
hence a =[tex]2\sqrt{2}[/tex] then MA =2 ; 2b^2 =4 ; therefore , b=[tex]\sqrt{2}[/tex]
then value of B ([tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex] then according to the theorem we get as
[tex]MA^{2} + MB^{2} = AB^{2}[/tex] we have condition by diagram as MA ⊥ MB similarly
MA ⊥ MC , MB ⊥ MC hence , MA.MC =-2z =0
hence MB.MC= [tex]\sqrt{2x} +\sqrt{2y} =0[/tex] therefore we get y=-x and z=0 hence the coordinates for C(x ,-x ,0)
and also MC^2 =2x^2=MA^2 =4 ; x=[tex]\sqrt{2}\\[/tex] (x>0)
hence C[tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex] hence
|MN|^2 = [tex]\frac{1}{6} |MA| . |MB| . |MC| = \frac{4}{3}[/tex]
hence the value of |MN|^2 = 4/3
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Please HELP me ASAP... Don't answer if you don't know all of the questions
In an AP, a1,a2,a3,.....an, where a1 represents first term and an represents nth term, what is the common difference d?
Answer:
a2 - a1
Step-by-step explanation:
Tn= a+(n-1)d
Tn = a1 (an -1) a2-a1
find the roots of the factored polynomial. (x 1)2(x 2) write your answer as a list of values separated by commas.
The (x-1)2(x+2) factored polynomial has roots of 5 and -2. In mathematics, a polynomial is a statement with variables.
what are polynomial ?A polynomial is a mathematical expression that solely uses additions, subtractions, multiplications, and powers of positive integer variables. It is composed of coefficients and uncertainty. A single indeterminate x polynomial is indicated by the expression x2 4x + 7. In mathematics, a polynomial is a mathematical equation made up of variables (sometimes called indeterminates) and coefficients that can be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is a statement in mathematics involving variables and coefficients. The only operations that can be included in an expression are addition, subtraction, multiplication, and non-negative integer exponents. These formulas are known as polynomials.
given
(x - 5)(x + 2) = 0
Using the 0 product property:
Case 1
x - 5 = 0
x = 5
Case 2
x + 2= 0
x = -2
The (x-1)2(x+2) factored polynomial has roots of 5 and -2. In mathematics, a polynomial is a statement with variables.
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In parallelogram PQRS, the measure of angle P is five times the measure of angle Q. What is the measure of angle R , in degrees?
The measure of angle R, in degrees, is 150°.
A parallelogram is a quadrilateral or four-sided shape, that has opposite sides that are parallel to each other. The opposite sides of a parallelogram are equal in length, and the opposite angles are also equal in measure.
In a parallelogram, opposite angles are equal, so if the measure of angle P is five times the measure of angle Q, then the measure of angle R must also be five times the measure of angle Q.
Let's call the measure of angle Q "x". Then the measure of angle P is 5x, and the measure of angle R is 5x.
Therefore, the measure of angle R in degrees is 5x degrees.
We know,
All of the angles added together = 360°
∠5Q +∠Q+∠5Q+∠Q = 360 Solve for Q
∠12Q = 360
⇒ ∠Q = 30°
then ∠P = ∠5Q = 5(30) = 150°
and,
∠P = ∠R
⇒ ∠R = 150°
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19. Two consecutive odd numbers are such that the difference of twice the larger number and twice the smaller number is 21. Find the product of the numbers.
There are no two consecutive odd numbers that satisfy the given condition.
What are the consecutive numbers?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
consecutive numbers are defined as numbers that follow each other in the natural sequence of numbers either from largest to smallest or from smallest to largest.
Let x be the smaller odd number and y be the larger odd number. Since y is larger than x, we know that y = x + 2.
The problem states that:
2y - 2x = 21
We can substitute in the value of y:
2(x + 2) - 2x = 21
Solving for x:
2x + 4 - 2x = 21
4 = 21
This is a contradiction, so there are no two consecutive odd numbers that satisfy the given condition.
Hence, there are no two consecutive odd numbers that satisfy the given condition.
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on a certain clock the minute hand is 8 in long and the hour hand is 6 in long. how fast is the distance between the tips of the hands when changing at 9 o'clock
The distance between the tips of the hands is changing at a rate of 55 inches per minute at 9 o'clock.
To find the distance between the tips of the hands, we can use the Pythagorean theorem:
distance = $\sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10$
As the clock moves, the minute hand will rotate 360 degrees in 60 minutes, or 6 degrees per minute, and the hour hand will rotate 360 degrees in 12 hours or 0.5 degrees per minute.
To find the rate at which the distance between the tips of the hands is changing, we need to find the rate at which the angle between the hands is changing.
We can use the fact that the angle between the hands is equal to the difference in the angular velocities of the hands.
Angular velocity of the minute hand = 6 degrees/minute
Angular velocity of the hour hand = 0.5 degrees/minute
Angular velocity of the distance between the tips of the hands = 6 - 0.5 = 5.5 degrees/minute
To convert this to distance per minute, we can use the fact that the distance between the tips of the hands is equal to the length of the hour and minute hand multiplied by the sine of the angle between them.
Distance per minute = 10 * 5.5 degrees/minute = 55 inches/minute
So, the distance between the tips of the hands is changing at a rate of 55 inches per minute at 9 o'clock.
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An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. talk and the initial velocity of the ball is 40 ft per sec. The height s of the hall in feet is given by the equation s=-2.7t^2 + 40t+6.5 , where the number of seconds after the ball was thrown. After how many seconds in the ball 22ft above the moons surface?
Answer:
Step-by-step explanation:
Using the given equation, we can solve for t when s is equal to 22.
22 = -2.7t^2 + 40t + 6.5
Subtracting 6.5 from both sides, we get:
15.5 = -2.7t^2 + 40t
Adding 2.7t^2 to both sides, we get:
18.2t^2 = 15.5 + 40t
Subtracting 40t from both sides, we get:
18.2t^2 - 40t = 15.5
Dividing both sides by 18.2, we get:
t^2 - 2.2t = 0.855
Factoring, we get:
(t - 1)(t - 0.855) = 0
Setting each factor equal to 0 and solving, we get:
t = 1 and t = 0.855
Therefore, the ball will reach a height of 22ft after 1 second and 0.855 seconds.
What is the y-intercept of the line shown? (4 points)
−1
0
0.5
1
Allie is creating an art project using pieces of paper that are each 8. 06 inches long. If she tapes 5. 4 pieces together end-to-end, what will the total length be?
According to the formula of area of rectangle, the length of each piece is 1.49 inches.
The formula to calculate the area of the rectangle is written as,
A = l x b
where l refers the length and b refers the breadth of the rectangle.
Here we have know that Allie is creating an art project using pieces of paper that are each 8. 06 inches long.
Here we also know that she tapes 5. 4 pieces together end-to-end.
Here the value 8.06 refers the total area of the paper and the value 5.4 refers the breadth of the paper.
Then according to the formula, the length is calculated as,
=> l = 8.06/5.4
=> 1.49
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Last month the average price of gas was $2.20 per gallon. This month, the average price has increased by 75%. What is the average price of gas per gallon this month?
The average price of gas per gallon this month is
(don't forget $)
The average price of gas per gallon this month: $3.85 per gallon.
Define the term percentage increase?The degree, intensity, extent, or value of a variable can change to a greater or lesser extent as measured by percent rise and percent decrease. By comparing the original (or before) as well as final (or after) amounts in accordance with a predetermined formula, the figures are derived.For the stated question-
Average price of gas last month = $2.20 per gallon.
Percentage increase = 75%.
75% of 2.20 = 75*2.20 / 100
= 1.65
Average price of gas this month = $2.20 + $1.65 per gallon
= $3.85 per gallon
Thus, the average price of gas per gallon this month: $3.85 per gallon.
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alex thinks $163$ degree angles are neat. what is the maximum number of interior angles of a convex polygon that can have measure $163$ degrees?
The maximum number of interior angles of a convex polygon would be 7.
Imagine operating a small vehicle on a track with a polygonal shape. Your compass is handy (directional, not one for drawing circles). The automobile concludes the lap in the same direction as it began. If there was a compass, it has completed one full rotation.
180 - 131 = 49°
360/49 = 7.346938775510204
So 7 interior angles max
A convex polygon's outside angles add up to 360 degrees.
131 degrees for the inside angles and 49 degrees for the outside angles. The vehicle is capable of seven rotations at 49 degrees and one turn at 17 degrees, for a total of 360 degrees in one lap.
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The question is wrong the correction:
Alex thinks 131 degrees are neat. What is the maximum number of interior angles of a convex n-gon that can measure 131 degrees?
what is 4 2/3 - 3 1/3
Answer:
1.33333333333
Step-by-step explanation:
1.33333333333
a company produces steel rods. the lengths of the steel rods are normally distributed with a mean of 97-cm and a standard deviation of 1-cm. for shipment, 15 steel rods are bundled together. find the probability that the average length of a randomly selected bundle of steel rods is less than 97.1-cm.
The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Steel rods are produced by a firm. The lengths of the steel rods have a mean of 97 cm and a standard deviation of 1 cm, and they are regularly distributed. 15 steel rods are packaged together for shipping. determine the likelihood that the average length of a bundle of steel rods chosen at random is less than 140.7 cm.
mean is N (M) (109,1.6)
Looking for P(M 108.7) to P(z ???) conversion utilizing N(0,1) z-statistic transformation
P(z [M - population mean]/[SD/square root(sample size)]) = P(z [108.7-109)/[1.6/sqrt(27)] = P(z -0.974] = 0.165.
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there are 260 plants in a garden. 2/20 are flowers. how many plants are not flowers?
Answer:
To find out how many plants are not flowers, we need to subtract the number of flowers from the total number of plants.
We know that 2/20 of the plants are flowers, and we can use this information to find out how many plants are flowers. To do this, we can multiply the total number of plants (260) by the fraction of plants that are flowers (2/20).
260 x (2/20) = 260 x 0.1 = 26
So there are 26 plants that are flowers.
To find the number of plants that are not flowers, we subtract the number of flower plants from the total number of plants:
260 - 26 = 234
So there are 234 plants that are not flowers.
ABCD i a trapezoid. = 1 cm and = 5 cm, and the area = 7. 5 cm2. What i the altitude of the trapezoid?
The required altitude of the trapezoid ABCD is 2.5 cm.
What is trapezoid?The Greek roots of the term trapezoid are trapeza, which means "table," and -oeides, which means "formed." A trapezoid is shaped like a table. It has two parallel sides, which are often referred to as the figure's bases. Take the average of the bases and multiply it by the height to determine the area of a trapezoid.
According to question:Here, we must utilise the area of a trapezoid formula, which is
where h is the height or altitude and b1 and b2 are the two bases.
[tex]Area =\frac{ (b_{1}+b_{2})h}{2}[/tex]
Given are the values of Area = 7.5, b1 = 1, b2 = 5, and h is unknown.
Then,
7.5 = (1+5)h/2
7.5 = 3h
h = 2.5cm
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write 6x^5/8 in radical form
the radial form is, 6 times the eight root of x to the fifth power.
What is radical form?Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.
here, given that,
6x^5/8
now,
the radial form is,
6 times the eight root of x to the fifth power.
Hence, the radical form is, 6 times the eight root of x to the fifth power.
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Determine the number of positive integers n that satisfy 1/2 < n/(n +1) < 99/101. Do any negative integers satisfy this inequality? Hint: Tackle 1/2 < n/(n + 1) and n/(n +1) < 99/101 separately.
Answer:
No
Step-by-step :
n/n + 1 > 1/2, (n + 1)/n < 2, (n+1)/n - 2 < 0, [(n + 1) - 2n]/n < 0, (1 - n)/n < 0, n > 0, 1 - n < 0, n > 1
n/n + 1 < 99/101, (n + 1)/n > 101/99, [99(n+1)]/n > 101, [(99n + 99)]/n > 101, [(99n + 99)]/n - 101 > 0, (99n + 99 - 101n)/n > 0
(99 - 2n)/n > 0, n > 0, 99 - 2n > 0, 2n < 99, n < 99/2
1 < n < 49.5
You pick a card at random. 2 3 4 5 What is P(3)?
If you picked a card at random, then the probability of picking a three is 1 / 4 or 25 %.
How to find the probability ?The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
The probability that an event will occur is determined by the probability formula. The ratio of positive outcomes to all possible outcomes is used as the formula to determine an event's probability.
The probability that you can pick a three out of the cards given is:
= Number of cards of 3 / Number of total cards
= 1 / 4
= 25 %
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the ratio of boys to girls in ms.cano's class is 7 to 21. there are 49 girls in the class. what is the total number of students in mr.cano's class?
The ratio of boys to girls in Ms. Cano's class is 7 to 21, there are 49 girls in the class. The total number of students in Mr. Cano's class is 196
Ratio:
In mathematics, ratios indicate the number of times one number contains another number. For example, if you have 8 oranges and 6 lemons in your fruit bowl, the ratio of oranges to lemons is 8 to 6 (that is, a ratio of 8:6, or 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to whole fruit is 8:14 (or 4:7). Ratios can be given by giving both constituent numbers written "a to b" or "a : b", or by giving only the value of their quotient a/b.
When comparing one data point (A) to another data point (B), the formula is A/B. That is, divide information A by information B. For example, if A is 5 and B is 10, the ratio is 5/10. Solve the equation. Divide data A by data B to get the ratio.
According to the Question:
Given:
The ratio of boys to girls is 7: 21,
and there are 49 boys,
Let number of boys be x and number of girls be y.
49/7 × 11 = 77 girls
Therefore,
Total number of boys and girls in the classroom is
77 + 49 = 126.
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Make y the subject of the formula.- A=r(y + 2 ) / 5
Answer:
y = 5A/r - 2
Step-by-step explanation:
It is a simple algebra. pkease see the above
Answer:
Step-by-step explanation:
(Graphing Linear Equations MC)
A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 54
5 48
7 44
10 38
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 49
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
The solution is Option C.
The equation of line is given by y = -2x + 58
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 2 , 54 )
Let the second point be Q ( 5 , 48 )
The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 54 - 48 ) / ( 2 - 5 )
On simplifying the equation , we get
Slope m = 6 / -3
Slope m = -2
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 54 = -2 ( x - 2 )
On simplifying the equation , we get
y - 54 = 2x + 4
Adding 54 on both sides of the equation , we get
y = -2x + 58
Therefore , the graph is plotted through the points ( 0 , 58 ) , ( 1 , 56 )
Hence , the equation of line is y = -2x + 58
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Alexandra is fishing from a small boat. A fish swimming at the same depth as the hook
at the end of her fishing line is 5 meters away from the hook. If Alexandra is 13 meters away
from the fish, how far below Alexandra is the hook?
Answer:
12 m
Step-by-step explanation:
Here's a picture to show the problem.
boat
--------------------------------------------
~~~~~~~~~~~\ /~~~~~~~~~~~~~~~~~~~~~~~~
\-----------Alexandra ---------/ surface of the water
|\
| \
| \
| \
d | \ 13 m
| \
| \
| \
| --- rt < \
hook -----|------------------------------ fish
5 m
There is a right angle at the hook. We have a right triangle with leg d, the distance we need to find, leg 5 m, and hypotenuse 13 m.
a² + b² = c²
5² + b² = 13²
25 + b² = 169
b² = 144
b = √144
b = 12
Answer: 12 m
Solve the word problem below using the steps given in the lesson above. Show your equation and each step you take to solve it. Neil and Tom love to collect baseball cards. Neil has 83 more baseball cards than Tom. Neil has 517 baseball cards. How many baseball cards does Tom have
In linear equation , the number of baseball cards Tom has is 434.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
We need to find the amount of cards Tom has.
The number of cards Tom has is 434.
Let the number of baseball cards Tom has be X .
Neil has 83 more baseball cards than Tom so
X + 83 is the number of baseball cards that Neil has.
The number of baseball cards Neil has is 517
So,
x + 83 = 517
x = 517 - 83
x = 434
Hence, the number of baseball cards Tom has is 434.
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Find the slope of the image below
Answer: First question for the slope that passes through (-7, -2) and (6,-2) is m = 0. For the line that passes through (5, 3) and 5, -7) is m = 1/0.
I hope this helps!
Step-by-step explanation:
(−7,−2) and (6,−2)
(x₁,y₁) = (−7,−2)
(x₂,y₂) = (6,−2)
y₂ − y₁ / x₂−x₁
= −2 − −2 / 6 − −7
= 0/13
m = 0
m = y₂ − y₁ / x₂ − x₁
= −7 − 3 / 5 - 5
= −100
m = 1/0
which angles must be less than 146 degrees? please list both angles and support your answer by stating the theorem that will support your conclusion.
Any two angles whose sum is 146 degrees must both be less than 146 degrees. This can be supported by the Triangle Sum Theorem, which states that the sum of the measure of the interior angles of a triangle is 180 degrees.
The Triangle Sum TheoremThe Triangle Sum Theorem states that the sum of the measure of the interior angles of a triangle is always 180 degrees. Therefore, if two angles add up to 146 degrees, then both of those angles must be less than 146 degrees. This is because the remaining angle must make up the difference to reach the total of 180 degrees.
For example, if two angles measure 80 degrees and 66 degrees, then the third angle must measure 34 degrees in order to sum up to 180 degrees.Therefore, any two angles whose sum is 146 degrees must both be less than 146 degrees.
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find the volume of the largest right circular cylinder (in units^3) that fits in a sphere of radius 4 units.
The volume of the largest right circular cylinder (in cubic units) that fits in a sphere of radius 4 units is 154.7 cubic units.
First, draw a diagram. The diagram shows the cylinder inscribed in the sphere. Given that in the diagram the height, h, we can find the radius of the cylinder in terms of r using the Pythagorean Theorem.
h represents half of the total height of the cylinder. choose h instead of h² to simplify things better.
To find the volume of the cylinder, we need to multiply the area of the top by the total height of the cylinder. In other words;
V = π(radius of cylinder)²(height of cylinder)
V = π(√r²−h²)²(2h)
V = 2πh(r²−h²)
V = 2π(r²h−h³)
d/dxV(h) = 2π(r²−3h²) = 0
The 2π divides out and we are left with;
r²−3h² = 0
After some rearranging;
h² = r²/3
Take the square root of both sides.
h = r/√3
To find the volume, we need to put this into the volume equation.
V = 2πh(r²−h²) = 2π(r/√3){r²−(r/√3)²}
V = (2πr/√3)(r²−r²/3)
V = (2πr/√3){(3r²−r²)/3}
V = (2πr/√3)(2r²/3)
V = 4πr³/3√3
V = 4√3πr³/9
Now, put the value of r in the above equation, and we get
V = 4√3π(4)³/9
V = 256√3π/9
V = 154.7 cubic units
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8 ÷ 28 *has to be in decimal form*
Answer: 0.28571428571
Step-by-step explanation: 8 dived by 28
