Find the equation of the tangent plane to (a) z = 4x 2 − y 2 + 2y at (−1, 2, 4)

Answers

Answer 1

cuase it would be eaiser

Related Questions

"suppose we are comparing the implementations of algorithm a and algorithm b on the same machine. for inputs of size n, algorithm a runs in 2n steps, and algorithm b runs in 5√n steps. for which values of n does algorithm a beat algorithm b?"

Answers

The solution is : n = 9

What is multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Explanation:

To find the answer we need to check at what point the running time of algorithm A is equal the running time of B:

1000*n*n = n*n*n*n*n

1000 = n*n*n = n^3

n = ∛(1000) = 10 (when n equals ten A equal B)

For any integer greater than ten B > A and for any integer smaller than ten B < A.

The greatest integer for which B < A is nine, therefore nine is our answer.

A B

1000n^2 n^5

n = 8 64000 < 32768

n = 9 81000 < 59049

n = 10 100000 = 100000

n = 11 121000 > 161051

n = 12 144000 > 248832

therefore nine is our answer.

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For [tex]$ n = 0, 1, 2, 3, 4, 5, 6 $[/tex], Algorithm A (which runs in [tex]$ 2n $[/tex] steps) beats Algorithm B (which runs in [tex]$ 5\sqrt{n} $[/tex] steps).

To determine for which values of [tex]$ n $[/tex] Algorithm A beats Algorithm B in terms of running time, we compare their complexities:

Algorithm A runs in [tex]$ 2n $[/tex] steps.

Algorithm B runs in [tex]$ 5\sqrt{n} $[/tex] steps.

Algorithm A beats Algorithm B if [tex]$ 2n < 5\sqrt{n} $[/tex].

Let's solve this inequality step by step:

1. Square both sides to eliminate the square root (valid since [tex]$ n \geq 0 $[/tex]):

[tex]\[ (2n)^2 < (5\sqrt{n})^2 \][/tex]

[tex]\[ 4n^2 < 25n \][/tex]

2. Bring all terms to one side to form a quadratic inequality:

[tex]\[ 4n^2 - 25n < 0 \][/tex]

3. Factorize the quadratic inequality if possible:

[tex]\[ n(4n - 25) < 0 \][/tex]

4. Find the values of [tex]$ n $[/tex] that satisfy the inequality:

[tex]$ n(4n - 25) < 0 $[/tex] holds when one factor is negative, and the other is positive:

[tex]$ n < 0 $[/tex] and [tex]$ 4n - 25 > 0 $[/tex]: No valid solutions since [tex]$ n \geq 0 $[/tex].

[tex]$ n > 0 $[/tex] and [tex]$ 4n - 25 < 0 $[/tex]:

[tex]\[ 4n < 25 \Rightarrow n < \frac{25}{4} = 6.25 \][/tex]

[tex]$ n < 0 $ and $ 4n - 25 < 0 $[/tex]: All [tex]$ n \geq 0 $[/tex] satisfy this condition.

5. Determine the integer values of [tex]$ n $[/tex]:

Since [tex]$ n $[/tex] must be non-negative, the integer values of [tex]$ n $[/tex] that satisfy [tex]$ 4n^2 - 25n < 0 $[/tex] are [tex]$ n = 0, 1, 2, 3, 4, 5, 6 $[/tex].

The local home improvement store wants to increase their inventory. Last year 40 lawn mowers cost them $4,776.
At the same cost, how much would 120 lawn mowers cost them this year?

Answers

To solve this, set up a proportion where X is the amount that 120 lawn mowers would cost. It would look like [tex] \frac{40}{4776}=\frac{120}{x} [/tex].

Then cross-multiply to get 40x = 120(4776) or 40x = 573120. Now divide each side by 40 to isolate the variable.

X = 14328.

120 lawn mowers would cost $14,328.

Answer:14,328

Step-by-step explanation:

Write 7.085 × 10-14 as an ordinary number

Answers

Final answer:

To convert [tex]7.085 * 10^-{14}[/tex] to an ordinary number, move the decimal point 14 places to the left, resulting in 0.00000000000007085.

Explanation:

To write [tex]7.085 * 10^-{14}[/tex] as an ordinary number, you need to move the decimal point 14 places to the left because the exponent is negative. This means the number is very small. The process is similar to changing other numbers from scientific to standard notation, for example, changing [tex]7.5 x 10^{-3}[/tex] to 0.0075 by moving the decimal point three places to the left.

For [tex]7.085 * 10^-{14}[/tex], you will end up with 0.00000000000007085. The number has thirteen zeros after the decimal point and before the 7085 because we move the decimal 14 places.

Use this equation to find dy/dx. 9y cos(x) = x2 + y2

Answers

using product rule to differentiate LHS
9y×-sin(x) + cos(x) 9dy/dx
differentiate RHS
2x+2ydy/dx
equate LHS - RHS
-9ysin(x) +9cos(x)|dy/dx = 2x + 2y|dy/dx
9cos(x)dy/dx - 2ydy/dx = 2x + 9ysin(x)
(9cos(x) -2y) |dy/dx = 2x+9ysin(x)
dy/dx = (2x+9ysin(x) ) / (9cos(x) -2y)

Final answer:

The derivative dy/dx for the equation 9y cos(x) = x² + y² is found by applying implicit differentiation. Rearranging terms after differentiation, dy/dx is obtained as the fraction (9y sin(x) + 2x) / (9 cos(x) - 2y).

Explanation:

The question asks for the derivative of dy/dx using the equation 9y cos(x) = x2 + y2. To find dy/dx, we can apply implicit differentiation, which implies taking the derivative of both sides with respect to x while treating y as a function of x (y(x)).

Let's differentiate both sides:

The left side: d/dx [9y cos(x)] = d/dx [9y] cos(x) + 9y d/dx[cos(x)] = 9(dy/dx) cos(x) - 9y sin(x)

The right side: d/dx [x2 + y2] = 2x + 2y(dy/dx)

Equating both the derivatives, we have:

9(dy/dx) cos(x) - 9y sin(x) = 2x + 2y(dy/dx)

Now, solving for dy/dx gives us:

dy/dx = (9y sin(x) + 2x) / (9 cos(x) - 2y)

There are 25 students performing in their holiday concert. Of students 11 are boys. What decimal represents the fraction of the students that are boys

Answers

Hello!

The fraction would be: 11/25

11/25 as a decimal is: 0.44

So, 0.44 of the 25 students are boys.

I really hope this helped you out! :)

That would be 11/25 = 0.44.

Find the radius of convergence of the power series \sum_{n=1}^\infty \frac{x^n}{\root 9 \of n}

Answers

Assuming "root 9 of n" is supposed to mean "the ninth root of n", that is [tex]\sqrt[9]n[/tex] we can use the ratio test, which says the series converges whenever

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{\sqrt[9]{n+1}}}{\frac{x^n}{\sqrt[9]n}}\right|<1[/tex]

We have

[tex]\displaystyle|x|\lim_{n\to\infty}\frac{\sqrt[9]n}{\sqrt[9]{n+1}}=|x|\sqrt[9]{\lim_{n\to\infty}\frac n{n+1}}=|x|<1[/tex]

which means the radius of convergence for this power series is 1.

the letters that spell WAIKIKI are each written on separate tiles laying face down on a table. A tile is selected at random, the letter is recorded, and then the letter is placed face down on the table. Then the process repeats. What is the theoretical probability of choosing a tile with the letter A?
A. 1/7
B. 1/4
C. 2/7
D. 3/7

Answers

Answer:

the Answer is. A 1/7

Step-by-step explanation:

i did the test

Name the property of equality that justifies: If x = 3 and y = x + 5, then y = 8

Answers

Substitution. This is because we put in x as 3 in the equation.

Hope this helps!

Farmer Jack needs 1,800 square feet of garden space to have enough corn for a year. His garden space is currently 10 5⁄6 feet by 18 feet. How much more land does farmer Jack need to plant the rest of his corn?

Answers

5/6 can be simplified to 0.83. 10.83*18=194.94 square feet. 1,800 minus 194.94 is 1605.06 more square feet required

Final answer:

Farmer Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.

Explanation:

To find out how much more land Farmer Jack needs to plant the rest of his corn, we need to calculate the area of his current garden and subtract it from the required area of 1,800 square feet. Farmer Jack's garden is 10 5/6 feet by 18 feet, so we can multiply these two dimensions to get the area of his current garden. Then, we subtract this area from 1,800 to find out how much more land he needs:

Area of Farmer Jack's garden: 10 5/6 feet * 18 feet = 197 1/3 square feet

More land needed by Farmer Jack: 1,800 square feet - 197 1/3 square feet = 1,602 2/3 square feet

Farm Jack needs an additional 1,602 2/3 square feet of land to plant the rest of his corn.

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choose the equation below that represent the line that passes through the point (7,-2) and has a slope of -3

Answers

y+2= -3(x-7)

y+2=-3x+21

y= -3x+19

Find tanθ exactly if sinθ=-9/41, and θ is in the fourth quadrant

Answers

keep in mind that, in the IV quadrant, sine or the y-coordinate is negative, and the cosine or x-coordinate is positive, whilst the hypotenuse or radius, is just a distance unit and is never negative.

now, we know the angle is in the IV quadrant, therefore the opposite side or "y" is negative, thus

[tex]\bf sin(\theta )=-\cfrac{9}{41}\implies sin(\theta )=\cfrac{\stackrel{opposite}{-9}}{\stackrel{hypotenuse}{41}} \\\\\\ \textit{so, now let's find the \underline{adjacent side} then} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf \pm\sqrt{41^2-(-9)^2}=a\implies \pm\sqrt{1600}=a\implies \pm 40=a \\\\\\ \stackrel{\textit{in the IV quadrant}}{+40=a}\\\\ -------------------------------\\\\ tan(\theta)=\cfrac{opposite}{adjacent}\qquad tan(\theta)=\cfrac{-9}{40}[/tex]

the pitch, or frequency, of a vibrating string varies directly with the square root of the tension. if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds, find the frequency when the tension is 72 pounds.

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \begin{array}{llll} \stackrel{frequency}{f}\textit{ of a vibrating string varies directly}\\ \qquad \qquad \textit{with the square root of the tension }\stackrel{tension}{t} \end{array}[/tex]

[tex]\bf f=k\sqrt{t}\quad \textit{we also know that } \begin{cases} f=300\\ t=8 \end{cases}\implies 300=k\sqrt{8} \\\\\\ \cfrac{300}{\sqrt{8}}=k\implies \cfrac{300}{\sqrt{2^2\cdot 2}}=k\implies \cfrac{300}{2\sqrt{2}}=k\implies \cfrac{150}{\sqrt{2}}=k \\\\\\ \textit{and we can \underline{rationalize} it to }\cfrac{150\sqrt{2}}{2}\implies 75\sqrt{2}=k[/tex]

[tex]\bf thus\qquad f=\stackrel{k}{75\sqrt{2}}\sqrt{t}\implies \boxed{f=75\sqrt{2t}}\\\\ -------------------------------\\\\ \textit{now, when t = 72, what is \underline{f}?}\qquad f=75\sqrt{2(72)}[/tex]

Answer:

when the tension is 72 pounds , the frequency is 900 hertz

Step-by-step explanation:

Hello, I think I can help you with this.

you can easily solve this by using a rule of three.

According to the question data:

the pitch, or frequency, of a vibrating string varies directly with the square root of the tension.in mathematical terms it is:

f ∝ √T

where f is the pitch or frequency and T is the tension

Step 1

if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds

300 hertz ∝ √8 pounds

300⇔√8

what is the frequency when the tension is 72 pounds

x⇔√72

Step 2

Let

300⇔√8

x⇔√72

the relation is

[tex]\frac{300}{\sqrt{8} } =\frac{x}{\sqrt{72} }\\\\ Now, solve\ for\ x\\\\\\\frac{300*\sqrt{72} }{\sqrt{8} } =x\\x=\frac{300*\sqrt{72} }{\sqrt{8} } \\x=\frac{300*\sqrt{8*9}}{\sqrt{8}} \\x=\frac{300*\sqrt{8}*\sqrt{9}}{\sqrt{8}} \\x=300*\sqrt{9}\\x=300*3\\x=900[/tex]

when the tension is 72 pounds , the frequency is 900 hertz

have a good day.

The first truck in a convoy will carry 12 tons of dirt while each additional truck will carry 8 tons of dirt. Write a rule to model th situation. Then use the rule to find how many tons of dirt can be carried by 7 trucks. Let n represent the number of trucks and t represent the tons of dirt.

Answers

12 + 8n = t

68 tons of dirt will be hauled

Final answer:

To model the situation, use the rule t = 12 + 8(n - 1), where n is the number of trucks. Applying this rule, 7 trucks can carry a total of 60 tons of dirt.

Explanation:

The student should write a rule to model the situation where the first truck carries 12 tons of dirt and each subsequent truck carries 8 tons. The rule can be defined as t = 12 + 8(n - 1), where n represents the number of trucks and t represents the total tons of dirt carried. For 7 trucks, we can plug in the value of n into the equation:

t = 12 + 8(7 - 1)

t = 12 + 8(6)

t = 12 + 48

t = 60 tons

Therefore, 7 trucks can carry a total of 60 tons of dirt.

what is the interqueartile range for the data set 13,14,17,18,23,27,28,31,34

Answers

Fortunately, the data is already arranged in ascending order, which is a requirement when we're looking for quadrants and the IQR. There are 9 data points, where 9 is an odd number, so the middle data point, 23, is the median.

We must now find Q1 and Q3. To the left of 23 we have 13, 14, 17, 18. Take the median of these four points: It is the average of 14 and 17, or 15.5.
Similarly, find the mediation of 27, 28, 31, 34; it is the average of 28 and 31, or 29.5.

The IQR is the difference between Q3 and Q1; here, that difference is 29.5 - 15.5 = 14.

Mr. River's car averages 25 3/4 miles per gallon. Express the miles per gallon as a decimal

Answers

25.75 is 25 3/4 in decimal form

PLEASE ANSWER
Solve the Equation
-2=3x/5+1

Answers

-2 = 3x/5 + 1
-2 - 1 = 3x/5
-3 = 3x/5
-3 * 5 = 3x
-15 = 3x
x = -15/3
x = -5

how many tiles in figure 0? Where is the Y intercept?

Answers

ahemmm how many tiles or rectangles in the grid? well, notice, each quadrant is a 9x11 rectangles, so there are 9*11 rectangles in each quadrant, there are 4 quadrants, thus 4 * 9 * 11 rectangles in the grid.

where's the y-intercept? well, just look at the line, what are coordinates where the graph touches or intercepts the y-axis? well, is at (0,3).

Use the distributive property to write the products as sums:7(4n-5m-2)

Answers

Final answer:

The distributive property is used to multiply 7 by each term inside the parentheses (4n, -5m, -2) resulting in the expression 28n - 35m - 14.

Explanation:

To apply the distributive property to the expression 7(4n-5m-2), you multiply each term inside the parentheses by 7. The distributive property allows us to multiply a single term outside a parenthesis with each term inside the parenthesis, effectively distributing the multiplication.

First term: 7 × 4n = 28nSecond term: 7 × -5m = -35mThird term: 7 × -2 = -14

Therefore, the product written as a sum, using the distributive property, is 28n - 35m - 14.

10 POINTS!!! I WILL GIVE BRAINLIEST!
Bens barbeque charges a setup fee to $52 for catering a barbeque party plus an additional $6.25 per person. Robert is planning to hire Ben's barbeque to cater a picnic. Robert has no more than $175 to spend on the picnic. What is the greatest number of people who can attend the picnic? (*WRITE AND SOLVE AN INEQUALITY TO SOLVE THIS PROBLEM*)

Answers

The inequality would be 6.25x + 52 < or = 175. If you solved the inequality for x, the answer would be 19.68. This means that the answer would be, the greatest number of people who can attend the picnic is 19, because you can not have .68 of a person.

175-52=123
123/6.25=19.68
you can't have 19.68 people, so the max amount of people that could attend would be 18. Hope it helped:)

_____ require a date signature amount and pay to the order of. (1 point)

Credit Cards
Debit Cards
Checks
Loan Documents

Answers

well, for a Credit Card all you need is to swipe it, and enter your pin number, and the transaction is electronically done, from the buyer to the seller.

for a Debit Card, is the same as above, they're just a different type of arrangement as the Credit Card.

for Loan Documents, you're not being paid or are paying anything, you're loaning an amount, it requires signatures and some dates, amounts and loaner info...but is not a payment per se.

so, that leaves the obvious one. for Cheques you do need a signature, amount, date and person to whom it goes, and you have to write it in ink, or something non-erasable that easily.

The answer is; c.) checks!

Find a formula for the function whose graph is given below.

Answers

y=(x-2)^2+3
^^^^^^^^^^^^^^^^

The equation of parabola is y = ( x - 2 )² + 3

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k - p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

The vertex of the parabola is given as A ( 2 , 3 )

Now ,

The equation of parabola is given by

y = a ( x - h )² + k

where the vertex of the parabola is A ( h , k )

a = 1

So , substituting the values of vertex in the equation of parabola , we get

y = ( x - 2 )² + 3

Hence , the equation of parabola is y = ( x - 2 )² + 3

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Latrell bought 4 bags of powdered sugar. He got a total of 5 1/2 cups of sugar. How many cups of sugar were in each bag?

Answers

so all 4 bags of sugar yielded 5 and 1/2 cups..... well.. how many in each one? well, let's split the 5 and 1/2 evenly in 4 pieces.

[tex]\bf \stackrel{mixed}{5}\frac{1}{2}\implies \cfrac{5\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{11}{2}}\\\\ -------------------------------\\\\ \cfrac{\quad\frac{11}{2} \quad }{4}\implies \cfrac{\quad\frac{11}{2} \quad }{\frac{4}{1}}\implies \cfrac{11}{2}\cdot \cfrac{1}{4}\implies \cfrac{11}{8}\implies \stackrel{cups}{1\frac{3}{8} }[/tex]

Each bag contained 1.375 cups of sugar.

To find out how many cups of sugar were in each bag that Latrell bought, we need to divide the total amount of sugar by the number of bags. Latrell has a total of 5 1/2 cups of sugar, which is the same as 5.5 cups when converted to a decimal. He bought 4 bags of sugar. Therefore, the calculation we need to perform is:

5.5 cups / 4 bags = 1.375 cups per bag

So, each bag contained 1.375 cups of sugar.

The price of a technology stock has risen to $9.73 today. Yesterday's price was $9.60 . Find the percentage increase. Round your answer to the nearest tenth of a percent.

Answers

Hello! To find this answer, we have to do change/original. 9.73 - 9.60= 0.13. 0.13/9.60 = 0.01354 and other numbers behind it or 1.4% when rounded to the nearest tenth. You have to multiply the decimal by 100 in order to to get the percent form. It rounds up to 1.4 instead of back down to 1.3, because the 5 is in the hundredths place, and when anything 5 or more appears behind the digit you are rounding to, you go up. The percent increase is about 1.4%.

Explain why you think slope-intercept form makes sense as a name for y = mx +
b. explain why you think point-slope form make sense as a name for y - y1 = m(x - x1)

Answers

Final answer:

The slope-intercept form y = mx + b shows how the slope and y-intercept values are used in the equation, while the point-slope form y - y₁ = m(x - x₁) defines a line using a point and the slope.

Explanation:

The slope-intercept form, y = mx + b, makes sense as a name because it explicitly shows how the slope and y-intercept values are used in the equation.

The 'm' represents the slope, which describes the steepness of the line, and the 'b' represents the y-intercept, which indicates where the line intersects the y-axis.

For example, in the equation y = 2x + 3, the slope is 2 and the y-intercept is 3.

The point-slope form, y - y₁ = m(x - x₁), is called so because it defines a line using a single point (x₁, y₁) and the slope 'm'. This form makes it easier to determine the equation of a line when given a point and the slope.

For instance, in the equation y - 2 = -3(x - 4), the point (4, 2) and the slope -3 are used to specify the line equation.

Solve the quadratic equation of 2x^2-5x+1=0

Answers

there are two solutions:

[tex]x = (5 + \sqrt{17} ) \div 4[/tex]
OR
[tex]x = (5 - \sqrt{17} ) \div 4[/tex]

how do you solve 3 - 1 3/4

Answers

Hey there!

To make this "easier" for you to solve

You can solve the "mixed fraction" (1 3/4)

So, 1 3/4 = 7/4 (or you can say 3/4)

Our problem becomes: 3 - 3/4

Now, 3 - 3/4 = 9/4

Answer: 9/4

Good luck on your assignment and enjoy your day

~MeIsKaitlyn:)

If a drug has a concentration of 350 mg per 10 mL, how many milliliters are needed to deliver 2 grams of the drug? Express your answer rounded to the nearest milliliter.

Answers

Final answer:

To deliver 2 grams of a drug with a concentration of 350 mg per 10 mL, convert 2 grams to milligrams (2000 mg), and then divide this value by the concentration in mg/mL (350 mg/10 mL) to find the volume in milliliters. After calculation, this results in approximately 6 milliliters, when rounded to the nearest milliliter.

Explanation:

To calculate how many milliliters are needed to deliver 2 grams of the drug when the concentration is 350 mg per 10 mL, we start with the conversion of grams to milligrams since the concentration is provided in milligrams. Remember, 1 gram equals 1000 milligrams:

Convert 2 grams to milligrams: 2 grams × 1000 = 2000 mg.Determine how many milliliters provide 350 mg: 10 mL corresponds to 350 mg.Calculate the proportion: (2000 mg) / (350 mg/mL) = Number of milliliters needed.Perform the calculation: 2000 / 350 = 5.71428571 mL.Round to the nearest milliliter: Approximately 6 mL.

Therefore, approximately 6 milliliters of the drug are needed to deliver a dose of 2 grams.

10 mi.= _________ft.

Answers

there is 5280 feet in 1 mile

5280 x 10 = 52800

52800 ft is your answer

hope this helps

The Junior Soccer League takes 12-person vans to the tournament. The league has 146 players and 14 coaches. How many vans are needed and how many people are left over?

Answers

Final answer:

The Junior Soccer League will need a total of 14 vans to transport 160 people, with 4 people left over after filling the 13th van.

Explanation:

To calculate the number of 12-person vans needed for the Junior Soccer League event, we first need to determine the total number of people that require transportation. This includes both players and coaches.

We have 146 players and 14 coaches, giving us a total of 160 people. If each van holds 12 people, the next step is to divide the total number of people by the capacity of the van.

Divide the total number of people by the capacity of the van (12).Calculate the number of full vans required.Determine if there are any people left over.

160 ÷ 12 = 13 vans with 4 people left over because 12 vans can only carry 144 people (12 × 12), and 16 people are remaining, which requires another van to accommodate them.

So, the league will need a total of 14 vans for transportation, and there will be 4 people left over after filling the 13th van.

Let f(X)=1/x+1

Use the limit definition of the derivative to find:

i) f(-4)
ii) f(-3)
iii) f(1)
iv) f(3)

Answers

[tex]\bf f(x)=\cfrac{1}{x+1}\qquad \qquad \stackrel{d e f in i tion~of~a~derivative}{\lim\limits_{h\to 0}~\cfrac{f(t+h)-f(t)}{h}} \\\\\\ \lim\limits_{h\to 0}~\cfrac{\frac{1}{x+h+1}-\frac{1}{x+1}}{h}\implies \cfrac{\frac{(x+1)~-~(x+h+1)}{(x+h+1)(x+1)}}{h} \\\\\\ \cfrac{\frac{x+1-x-h-1}{(x+h+1)(x+1)}}{h}\implies \cfrac{\frac{\underline{x+1}\underline{-x}-h\underline{-1}}{(x+h+1)(x+1)}}{h}\implies \cfrac{\frac{-h}{(x+h+1)(x+1)}}{h} [/tex]

[tex]\bf \cfrac{\frac{-h}{x^2+xh+2x+h+1}}{h}\implies \cfrac{-h}{x^2+xh+2x+h+1}\cdot \cfrac{1}{h} \\\\\\ \lim\limits_{h\to 0}~\cfrac{-1}{x^2+xh+2x+h+1}\implies \cfrac{-1}{x^2+x(0)+2x+0+1} \\\\\\ \lim\limits_{h\to 0}~\cfrac{-1}{x^2+2x+1}[/tex]

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What are pigments?A.Small dots that appear to create new colorsB.Substances that absorb certain parts of the light spectrumC.Theories about the relationships between colorsD.Methods of creating optical effects Generally, courts have ruled that teachers may be fired for: Write an equation of four lines that intersect to form the sides of a parallelogram Self sacrificing behavior is a form of what type of behavior? awnsers.com What is conflagration Which celestial body would have the strongest gravitational pull on a satellite orbiting 100 km above its surface? Explain your answer Cereal costs $2.79 for 16.4 ounces. At this rate how much does 25 ounces of cereal cost? Purpose of the anaconda plan What is the solution of the system? Use the elimination method. 2x+y=206x5y=12 Enter your answer in the boxes. what is the common ration between successive term in the sequance? 2,-4,8,-16,32,-64 Kendrick adds 3/4cup of chicken stock to a pot. Then he takes 3/4 cup of stock out of the pot. What is the overall increase or decrease in the amount of chicken stock in the pot? Question 1Read the excerpt from State of the Union Address by John F. Kennedy January 30, 1961. Then answer the question that follows. Excerpt from State of the Union Address by John F. Kennedy January 30, 1961 The present state of our economy is disturbing. We take office in the wake of seven months of recession, three and one-half years of slack, seven years of diminished economic growth, and nine years of falling farm income. Business bankruptcies have reached their highest level since the Great Depression. Since 1951 farm income has been squeezed down by 25 percent. Save for a brief period in 1958, insured unemployment is at the highest peak in our history. Of some five and one-half million Americans who are without jobs, more than one million have been searching for work for more than four months. And during each month some 150,000 workers are exhausting their already meager jobless benefit rights. Nearly one-eighth of those who are without jobs live almost without hope in nearly one hundred especially depressed and troubled areas. The rest include new school graduates unable to use their talents, farmers forced to give up their part-time jobs which helped balance their family budgets, skilled and unskilled workers laid off in such important industries as metals, machinery, automobiles and apparel. Our recovery from the 1958 recession, moreover, was anemic and incomplete. Our Gross National Product never regained its full potential. Unemployment never returned to normal levels. Maximum use of our national industrial capacity was never restored. In short, the American economy is in trouble. The most resourceful industrialized country on earth ranks among the last in the rate of economic growth. Since last spring our economic growth rate has actually receded. Business investment is in a decline. Profits have fallen below predicted levels. Construction is off. A million unsold automobiles are in inventory. Fewer people are workingand the average work week has shrunk well below 40 hours. Yet prices have continued to riseso that now too many Americans have less to spend for items that cost more to buy. Economic prophecy is at best an uncertain artas demonstrated by the prediction one year ago from this same podium that 1960 would be, and I quote, "the most prosperous year in our history." Nevertheless, forecasts of continued slack and only slightly reduced unemployment through 1961 and 1962 have been made with alarming unanimityand this Administration does not intend to stand helplessly by. We cannot afford to waste idle hours and empty plants while awaiting the end of the recession. We must show the world what a free economy can doto reduce unemployment, to put unused capacity to work, to spur new productivity, and to foster higher economic growth within a range of sound fiscal policies and relative price stability. I will propose to the Congress within the next 14 days measures to improve unemployment compensation through temporary increases in duration on a self-supporting basisto provide more food for the families of the unemployed, and to aid their needy childrento redevelop our areas of chronic labor surplusto expand the services of the U.S. Employment Officesto stimulate housing and constructionto secure more purchasing power for our lowest paid workers by raising and expanding the minimum wageto offer tax incentives for sound plant investmentto increase the development of our natural resourcesto encourage price stabilityand to take other steps aimed at insuring a prompt recovery and paving the way for increased long-range growth. This is not a partisan program concentrating on our weaknessesit is, I hope, a national program to realize our national strength. Which statement best summarizes the central idea of President Kennedys speech? Question 1 options: A. Prices for consumer goods continued to increase. B. The American economy was stagnant and faltering. C. Many Americans were unemployed or underemployed. D. Bankruptcies had reached a very high level. Nerve fibers that are housed within the same nerve tract share all of the following things in common, EXCEPT: Which theory of motivation emphasizes genetically predisposed behaviors? hierarchy of needs theory drive-reduction theory instinct theory arousal theory? A pulmonary embolism can cause __________ oxygen in the blood, which can cause atp production in cells to __________. 56/x^2-2x-15 - 6/x+3 = 7/x-5 A body of mass 25kg, moving at 3 ms per second on a rough horizontal floor brought to rest after sliding through a distance of 2.5m on the floor. calculate the coefficient of sliding friction [g = 10.0 ms per second per second] WILL MARK AS BRAINLIESTName the following ionic compounds. What is the reciprocal of 6 4/5?A.) 5/34B.) 29/5C.) 34/5D.) 15/5 If I have 550 students in my grade and I rank as 40, is that good? As in class rank? Steam Workshop Downloader