The diameter of a tree was 23 inches. During the following year, the circumference increased 2.8 inches. Use differentials to approximate the following: About how much did the tree's diameter increase? About how much did the tree's cross-sectional area increase?

9514 1404 393

Answer:

  340 ft^2

Step-by-step explanation:

The length of one side is 1/4 of the perimeter, so is 10 ft.

The area of the base is the square of the length of the side:

  base area = (10 ft)^2 = 100 ft^2

__

The lateral area is the area of four triangles, each with a base of 10 ft and a height of 12 ft.

  lateral area = 4(1/2)(10 ft)(12 ft) = 240 ft^2

__

The total surface area is the sum of the base area and the lateral area:

  surface area = base area + lateral area

  surface area = (100 ft^2) +(240 ft^2) = 340 ft^2

Answer:

x = 1

Step-by-step explanation:

a^2 + b^2 = c^2

The hypotenuse (c) and a side length is already given, so:

x^2 + 12 = 13

x^2 = 1

Square root of 1 = 1

So, x = 1

You can check it by 1+12=13

The general solution to the third differential equation is y(x) = u(x)y1(x), where y1(x) = e^(-x) and u(x) is an arbitrary function of x.

To solve the first differential equation using reduction of order, we assume the general solution to be of the form y(x) = u(x)y1(x), where y1(x) is the known solution (in this case, y1(x) = x^(-1)) and u(x) is a function to be determined.

We begin by computing the first and second derivatives of y1(x):

y1'(x) = -x^(-2)

y1''(x) = 2x^(-3)

Substituting these into the original differential equation, we have:

x(2x^(-3)) + (2 + 2x)(2x^(-3)) - 2(x^(-1)) = 0

Simplifying the equation:

2x^(-2) + 2(2x^(-2)) + 2x^(-2) = 0

6x^(-2) = 0

Since x^(-2) cannot be equal to zero for any value of x, we conclude that there is no nontrivial solution satisfying the differential equation with y1(x) = x^(-1).

Similarly, for the second differential equation, we assume the general solution to be of the form y(x) = u(x)y1(x), where y1(x) = x*sin(x) and u(x) is a function to be determined.

We get the first and second derivatives of y1(x):

y1'(x) = xcos(x) + sin(x)

y1''(x) = 2cos(x) - x*sin(x)

Substituting these into the original differential equation, we have:

x^2(2cos(x) - xsin(x)) - 2x(xcos(x) + sin(x)) + (x^2 + 2)(xsin(x)) = 0

Simplifying the equation:

2x^2cos(x) - x^3sin(x) - 2x^2cos(x) - 2xsin(x) + x^3sin(x) + 2xsin(x) = 0

0 = 0

Since the equation simplifies to 0 = 0, it means that any function y(x) of the form y(x) = u(x)y1(x) satisfies the differential equation, where y1(x) = x*sin(x) and u(x) is an arbitrary function.

For the third differential equation, we assume the general solution to be of the form y(x) = u(x)y1(x), where y1(x) = e^(-x) and u(x) is a function to be determined.

We get the first and second derivatives of y1(x):

y1'(x) = -e^(-x)

y1''(x) = e^(-x)

Substituting these into the original differential equation, we have:

(x+1)(e^(-x)) + x(-e^(-x)) - (e^(-x)) = (x+1)^2

Simplifying the equation:

xe^(-x) + e^(-x) - xe^(-x) - e^(-x) = (x+1)^2

0 = (x+1)^2

Expanding the equation, we get:

0 = x^2 + 2x + 1

This is a quadratic equation with the solution x = -1.

Therefore, the general solution to the third differential equation is y(x) = u(x)y1(x), where y1(x) = e^(-x) and u(x) is an arbitrary function of x.

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A "full table of 5" refers to a multiplication table that includes all of the products of the number 5 multiplied by the integers from 1 to some maximum value.

Here is an example of a full table of 5:

5 x 1 = 5

5 x 2 = 10

5 x 3 = 15

5 x 4 = 20

5 x 5 = 25

5 x 6 = 30

5 x 7 = 35

5 x 8 = 40

5 x 9 = 45

5 x 10 = 50

In this example, the maximum value for the multiplier is 10, but a full table of 5 can continue with any number of rows. This table is useful for memorizing the multiplication facts of 5, and also to see the pattern of the multiples of 5.

It's worth to mention that if you are looking for a way to calculate the products you could use a loop or a function that takes the maximum value of the multipliers as an input and prints the full table of 5.

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One tablespoon (tbsp) is equal to approximately 14.7867648 milliliters (ml).

To convert tablespoons to milliliters, you can use this conversion factor.For example, to convert 1 tablespoon to milliliters, you would multiply 1 by 14.7867648, which would give you 14.7867648 milliliters.It's important to note that tablespoon and milliliter are both units of measurement for volume.

tablespoon is used in cooking recipes in the United States, Canada and the United Kingdom. While the milliliter is used in the International System of Units (SI).

It's important to know the correct conversion factors to ensure accuracy when working with measurements in different units. These conversion factors can be memorized or looked up in a conversion table or calculator.It's also worth noting that for larger volume measurements, you can use the liter (L) instead of the milliliter, since 1 L = 1000ml, and 1 tablespoon = 14.7867648ml.

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Answer:

x-3=-x+3

2x=6

x=3 y=0

the solution is the intersection of those two lines!

cost = $187.60

20% down

4 months of $39.40

1.- Calculate the 20%

187,6 ------------------- 100

x -------------------- 20

x = (20 x 187.6) / 100

x = 3752/100

x = 37.52

2.- Calculate the final price

Price paid = 37.52 + 4(39.40)

Price paid = 37.52 + 157.6

= $195.12

2.- Finance charge

= 195.12 - 37.52

= $157.6

Answer:

Step-by-step explanation:

10 + 3k = 22

3k = 22 - 10

k = 12 / 3

k = 4

therefore, the answer is D. 4

Answer:

3

Step-by-step explanation:

(8y-3)+(-8y+6)=

8y + -8y = 0

-3 + 6 = 3

0 + 3 = 3

To answer this question, we need to have some basic knowledge about the lunar cycle. based on the assumption that the student saw a full moon on the 1st of the month, we can estimate that they would see the next third quarter moon about 22-23 days later, or around the 23rd of the month.

The lunar cycle is the period of time it takes for the moon to go through all its phases, which includes the new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, third quarter, and waning crescent. This cycle takes approximately 29.5 days to complete.
Now, let's look at the question again. The student saw a full moon one evening, which means they were observing the moon at the full moon phase. If we assume that the student saw the full moon on the 1st of the month, for example, we can estimate that the next third quarter moon would occur about 22-23 days later.
Why 22-23 days? Because the third quarter moon occurs approximately halfway through the lunar cycle, or 14-15 days after the full moon. So, if the full moon was observed on the 1st of the month, we would add 14-15 days to that date to get the approximate date of the third quarter moon. This would give us a date of around the 15th of the month. However, the lunar cycle is not exactly 29.5 days long, so we need to adjust our estimate slightly. On average, the lunar cycle is about 29.53 days long, so if we add 14-15 days to the 1st of the month, we get a date of around the 23rd of the month for the next third quarter moon.

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Answer:

2 y=471

Step-by-step explanation:

Answer:

Well I cant really graph it for you cause I don't know how to do that but the first one plot the point at 0,-1 and rise 3 and run 2

Step-by-step explanation: Just remember that

I really wish I could graph it for you but I don't know how to do that sorry

Answer:

470 is your awnser

Step-by-step explanation:

Answer:

50 + 30 * 14 = 470

Step-by-step explanation:

  50 + 30 * 14

= 50 + 420

= 470

Answer:

-1 1/2 if you need a mixed number then choose -1 1/2

Answer: There are many possible fractions, here is all of them.

-3/2 = -6/4 = -9/6 = -12/8

= -15/10 = -18/12 = -21/14 = -24/16

= -27/18 = -30/20 = -33/22 = -36/24

= -39/26 = -42/28 = -45/30 = -48/32

= -51/34 = -54/36 = -57/38 = -60/40

= -63/42 = -66/44 = -69/46 = -72/48

= -75/50 = -78/52 = -81/54 = -84/56

= -87/58 = -90/60 = -93/62 = -96/64

= -99/66 = -102/68 = -105/70 = -108/72

= -111/74 = -114/76 = -117/78 = -120/80

= -123/82 = -126/84 = -129/86 = -132/88

= -135/90 = -138/92 = -141/94 = -144/96

= -147/98 = -150/100 = -153/102 = -156/104

= -159/106 = -162/108 = -165/110 = -168/112

= -171/114 = -174/116 = -177/118 = -180/120

= -183/122 = -186/124 = -189/126 = -192/128

= -195/130 = -198/132 = -201/134 = -204/136

= -207/138 = -210/140 = -213/142 = -216/144

= -219/146 = -222/148 = -225/150 = -228/152

= -231/154 = -234/156 = -237/158 = -240/160

= -243/162 = -246/164 = -249/166 = -252/168

= -255/170 = -258/172 = -261/174 = -264/176

= -267/178 = -270/180 = -273/182 = -276/184

= -279/186 = -282/188 = -285/190 = -288/192

= -291/194 = -294/196 = -297/198 = -300/200

Step-by-step explanation:

If you have any questions feel free to ask

Answer:

15/9 :))

is your answerrr

Answer:

15/9

Step-by-step explanation:

For this all you have to do is add the numerators.

So 7 + 8 = 15

The number is 15/9

Hope this helps ya!!

Answer:

(3x + 11y)^2

Step-by-step explanation:

The polynomial is a perfect square trinomial, because:

1) √ [9x^2] = 3x

2) √121y^2] = 11y

3) 66xy = 2 *(3x)(11y)

Then it is factored as a square binomial, being the factored expression:

[ 3x + 11y]^2

Now you can verify working backwar, i.e expanding the parenthesis.

Remember that the expansion of a square binomial is:

- square of the first term => (3x)^2 = 9x^2

- double product of first term times second term =>2 (3x)(11y) = 66xy

- square of the second term => (11y)^2 = 121y^2

=> [3x + 11y]^2 = 9x^2 + 66xy + 121y^2, which is the original polynomial.

The factors of the equation are \(\rm (3x+11y)(3x+11y)\).

Given

Equation \(\rm 9x^2+66xy+121y^2\)

Factors of a number are numbers that divide evenly into another number.

Factorization writes a number as the product of smaller numbers.

The factors of the equation are given by using the following formula;

\(\rm (a+b)^2=a^2+b^2+2ab\)

Then,

The factor of the equation is

\(\rm 9x^2+66xy+121y^2\\\\(3x)^2+(11y)^2+2(3x)(11y)\\\\(3x+11y)^2\\\\(3x+11y)(3x+11y)\)

Hence, the factors of the equation are \(\rm (3x+11y)(3x+11y)\).

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Q1: The strength of the electric field at (x, y)=(2.0m,3.0m) is 1100 V/m.

Q2: The direction of the electric field at (x,y)=(2.0m,3.0m) is 319.4 degrees counter-clockwise from the positive x-axis.

The electric potential in a region of space is given by the equation V=(210 x^2− 120 y^2)V, where x and y are in meters. We are asked to find the strength and direction of the electric field at the point (x,y)=(2.0m,3.0m).

Q1: To find the strength of the electric field, we need to take the negative gradient of the electric potential. The gradient of a function is given by the partial derivatives with respect to x and y:

∇V= ( ∂V/∂x , ∂V/∂y )

∇V= ( 420x , -240y )

At the point (x,y)=(2.0m,3.0m), the gradient of the electric potential is:

∇V= ( 420(2.0) , -240(3.0) ) = ( 840 , -720 )

The strength of the electric field is the magnitude of the gradient:

|∇V|= √(840^2 + (-720)^2) = 1100 V/m

Q2: To find the direction of the electric field, we need to find the angle of the gradient vector counter clockwise from the positive x-axis. The angle θ is given by:

θ= tan^(-1)(∂V/∂y / ∂V/∂x)

θ= tan^(-1)(-720/840) = -40.6 degrees

Since we want the angle counter clockwise from the positive x-axis, we need to add 360 degrees:

θ= -40.6 + 360 = 319.4 degrees

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Therefore , We can perform operations on complex numbers by following below steps.

Complex numbers are those that are expressed as expression of a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).

Here,

Operations on Complex Numbers

Here, fundamental algebraic operations on complex numbers are covered.

z1 = a1 + ib1 and z2 = a2 + ib2

Addition of Two Complex Numbers

=> \(z1+z2 = ( a1+a2 )+ i( b1+b2 )\)

Subtraction(Difference) of Two Complex Numbers

=> \(z1-z2 = ( a1-a2 )-i( b1-b2 )\)

Multiplication of Two Complex Numbers

=>z1*z2 = (a1*a2) -(b1*b2)

Division of Two Complex Numbers.

=>z1/z2 = \(\frac{a1*a2 + b1*b2}{a^{2} _{2} + b^{2} _{2} }\) + \(i\frac{b1*a2 + a1*b2}{a^{2} _{2} + b^{2} _{2} }\)

Therefore , We can perform operations on complex numbers by following above steps.

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Answer:

81 + 144i

Step-by-step explanation:

Original equation

\((-3\sqrt{-81})(-5+\sqrt-9) + 9i\)

Rewrite the radicals

\((-3\sqrt{81} * \sqrt{-1})(-5+\sqrt{9} * \sqrt{-1}) + 9i\)

Simplify the radicals

\((-3 * 9i)(-5+3i) + 9i\)

Simplify further

\((-27i)(-5+3i) + 9i\)

Distribute the -27i

\(135i - 81i^2 + 9i\)

Add like terms

\(- 81i^2 + 144i\)

Square the i

\(- 81 * (-1) + 144i\)

Simplify

\(81 + 144i\)

Answer:

x=8

Step-by-step explanation:

x-3=5

+3=+3(cancel 3)

_____________

x=8

a. The sold 35 delta strangle would generally receive more premium compared to the sold 25 delta strangle.

b. A 25 delta risk reversal for USDCAD trading at no cost suggests that the market perceives an equal probability of future directional movement in either direction.

c. It is possible for the same underlying asset and maturity to have the 35 delta risk reversal trading at 1% and the 10 delta risk reversal at -2% based on market conditions and participants' expectations.

a. The delta of an option measures its sensitivity to changes in the underlying asset's price. A higher delta indicates a higher probability of the option being in-the-money. Therefore, the sold 35 delta strangle, which has a higher delta compared to the 25 delta strangle, would generally receive more premium as it carries a higher risk.

b. A 25 delta risk reversal trading at no cost suggests that the implied volatility for call options and put options with the same delta is equal. This implies that market participants perceive an equal probability of the underlying asset moving in either direction, as the cost of protection (via put options) and speculation (via call options) is balanced.

c. It is possible for the same underlying asset and maturity to have different delta risk reversal levels due to market conditions and participants' expectations. Market dynamics, such as supply and demand for options at different strike prices, can impact the pricing of different delta risk reversals. Factors such as market sentiment, volatility expectations, and positioning by market participants can influence the pricing of options at different deltas, leading to varying levels of risk reversal.

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Answer:

4212 square feet.

Step-by-step explanation:

If the blueprint's scale is 1 inch : 9 feet.

Square both sides

(1in)² = (9ft)²

1in² = 81ft²

Given the  gym's  area as 52 square inches, hence;

52in² = x

Divide both expressions

1/52 = 81/x

x = 52 * 81

x = 4212ft²

Hence the area of the actual gym  is 4212 square feet.

Answer:

((−3r^3)(s^5))2−r^6s^10

=9r^6s10+−r^6s^10

Combine Like Terms:

=9r^6s^10+−r^6s^10

=(9r6s10+−r6s10)

=8r6s10

Answer:

=8r^6s1^0

Step-by-step explanation:

Answer:

\(8 {r}^{6} {s}^{10} \)

Step-by-step explanation:

\(( - {3r}^{3} {s}^{5} {)}^{2} - {r}^{6} {s}^{10} \)

\(9 {r}^{6} {s}^{10} - {r}^{6} {s}^{10} \\ 8 {r}^{6} {s}^{10} \: (collect \: the \: like \: terms)\)

Answer:

Pretty sure it's SQ.

Step-by-step explanation:

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Answer:

hi

Step-by-step explanation:

bye

Answer:

b. 408

Step-by-step explanation:

did the work

give brainliest please

There are 15890700 different selections to win at lotto at a certain state.

To find the number of different selections that are possible, you can use the combination formula. The combination formula is:

C(n , r) = n! / (r! × (n - r)!)

where C(n , r) represents the number of combinations, n represents the total number of items, and r represents the number of items being chosen at a time.

In this case, n is 50 and r is 6, so the number of different selections is:

C(50 , 6) = 50! / (6! × (50 - 6)!) = 50!/6!44! = 15890700

Therefore, there are 15890700 different selections that are possible.

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Their present ages are given as follows:

The present ages are obtained solving a system of equations, for which the variables are given as follows:

Five years ago, the father's age was five times the son's age, hence:

x - 5 = 5(y - 5)

x = 5y - 20

In ten years' time, the father will be twice as old as his son, hence:

x + 10 = 2(y + 10)

x = 2y + 10.

Equaling both equations, the value of y is given as follows:

5y - 20 = 2y + 10

3y = 30

y = 10.

The value of x is given as follows:

x = 2(10) + 10 = 30.

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