A sequence of positive numbers is defined by
given that a1=2
find a2 and a3 leaving your answer in a surd form

If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

Given that,

The combined length and girth of a priority mail package cannot exceed 171 inches, according to postal standards.

We have to find calculate the size of the largest volume, cylindrical container that can be sent via priority mail.

We know that,

Let

Length= Breadth =x

Height=y

Volume can be written as

V=x²y

Now,

Combined length and girth is

7x+y=171

y=171-7x

V(x)=x²(171-7x)

V(x)=171x²-7x³

Differentiating with respect to x.

V'(x)=343x-21x²

The maximum value

V'(x)=0

343x-21x²=0

7x(49-3x)=0

x=0

and

49-3x=0

3x=49

x=49/3

Once again differentiating with respect to x.

V''(x)=343-42x

V''(x)=343-42(0)=343>0(min)

V''(x)=343-42(49/3)=-343<0(max)

The maximum volume is

Vmax=V(49/3)=(49/3)(171-7(49/3))

Vmax=925

Therefore, If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.

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Answer:

C

Step-by-step explanation:

Formula to get the area

A = r^2π

A = 16^2π

A= 804.24 cm^2

As per the given data, the approximate area of the shaded sector is 283 square cm, which is option D.

Area is a measure of the amount of space inside a two-dimensional shape or a flat surface. It is typically measured in square units, such as square meters or square feet.

To find the area of the shaded sector, we need to first find the area of the whole circle, and then multiply it by the fraction of the circle that is shaded.

The area of a circle is given by the formula:

A = \(\pi r^2\)

Where r is the radius of the circle. In this case, we are given that the radius of the circle is 18 cm, so we can substitute this value into the formula:

A = \(\pi 18^2\)

A = 324π

So, the area of the whole circle is 324π square cm.

The shaded sector has a central angle of 100 degrees, which is a fraction of the total central angle of 360 degrees. So, the fraction of the circle that is shaded is:

100° / 360° = 5/18

Therefore, the area of the shaded sector is:

A = (5/18) * 324π

A = 90π

Using 3.14 as an approximation for π, we get:

A ≈ 90 * 3.14

A ≈ 283

Thus, the approximate area of the shaded sector is 283 square cm, which is option D.

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Answer:

Step-by-step explanation:

S.I =720×6×5/100×365

=21600/36500

=0.59178

So balance will be 720+0.59178

=720.59178

Answer:

Hypotenuse is the longest side in a triangle.

a^2=b^2+c^2.

5^2=4^2+c^2.

c^2=25-16.

c^2=9.

c=√9.

c=3cm.

The point-slope form of the equations of the line are listed below:

Case 1: y - 4 = 2 · (x + 2)

Case 2: y - 1 = - 3 · (x - 2)

Case 3: y + 1 = - (x + 4)

Case 4: y + 2 = 5 · (x - 4)

In this problem we must derive the point-slope form of the equation of the line for each of four cases described in statement. This form is introduced below:

y - k = m · (x - h)

Where:

Now we proceed to determine the resulting expression for each case:

Case 1

y - 4 = 2 · (x + 2)

Case 2

y - 1 = - 3 · (x - 2)

Case 3

y + 1 = - (x + 4)

Case 4

y + 2 = 5 · (x - 4)

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Answer: Your answer is 23.5in²

Hope it helped :D

Good Luck!

Answer: The answer is 148 square feet.

Step-by-step explanation:

So if we are given the information to the area of the composite figure, we just first have to find the area of the smaller shapes and then add them all together to achieve the total.

1. The larger rectangle is a 10 by 14 rectangle.

2. The smaller rectangle is a 1 by 8 rectangle.

How did I get around to 8 feet?

Subtract 3 and 3 from 14, and you'll get 8 for the side.

Now just find the areas of each of the rectangles:

1. 10 times 14 = 140

2. 1 times 8 = 8

Now add them together:

140 + 8 = 148

The answer is 148 square feet.

Answer:

Step-by-step explanation:

Given

We can see from the equations that

So greater use of unit B brings greater profit. We don't want any unit is left over, so get this equation.

Is the equation set to indicate use of the units A and B

Solving we get

It this case all the units are used and profit is maximum

Answer:

Roots are basically the x-intercepts (of a parabola)

Step-by-step explanation:

When you are doing quadratic equations, whenever the line touches the x-intercept, it is called a root.

The absolute minimum of the function is f ( -10 ) = -1

Given data ,

Let the function be represented as f ( x )

Now , the function f ( x ) is plotted on the graph

where the minimum of a function is the smallest value that the function takes on over its entire domain.

It is the point on the graph of the function that is the lowest possible point

So , the function has the minimum value of - 1 at the point x = -10

Hence , the minimum of function is f ( -10 ) = -1

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Answer:

In this case, the Leading Coefficient is 9 and the Trailing Constant is 2. The factor (s) are: of the Leading Coefficient : 1,3 ,9 of the Trailing Constant

Step-by-step explanation:

m + 14 ) 2 + ( 3 m ) 2 = ( 5 m ) 2.

Answer:

Mark me as Brainliest

\(fx^{-1} (x)=x+3\)

Step-by-step explanation:

To find the inverse of a function, just “trade” x and y and solve for the “new” y. The graph of the inverse is the reflection of the original function over the line y=x.

Rewrite the function

\(f(x)=x+3\)

as the equation, y=x+3

Trade x and y.

X=y+3

The symbol for the inverse if \(fx^{-1} (x)\)

\(fx^{-1} (x)=x+3\)

Answer:

x-3

Step-by-step explanation:

hlo therre!!

f(x)=x+3

let f(x) be y;

y=x+3

now; interchanging the value of x and y;

i.e. x=y+3

y=x-3

f(x)^-1 = x - 3...

this is the required inverse function..

thank u!! hope it helps!

Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

Answer:

3053.63 inches cube

Step-by-step explanation:

V =4 3

------nr

3

4/3×22/7×9×9×9

=

3053.63

please mark as brainliest answer as it will also give you 3 pts

hii! i just wanted to say hope you're having a fantastic day and hope that things are going well (: stay strong and stay safe!

The triangle congruence criteria that can be used to prove that DEF and D'EF are congruent is the SAS rule.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The SAS rule states that "If two sides and the included angle of one triangle are equal to corresponding two sides and included angle of another triangle, then the triangles are congruent"

From ΔDEF and ΔD'EF

DE = D'E

m∠DEF = m∠D'EF

EF = EF

ΔDEF ≈ ΔD'EF

Thus,

The triangle congruence criteria that can be used is the SAS rule.

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Final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.

Let's break down the steps to determine the final speed:

Step 1: Convert the speed from miles per minute to miles per hour.

Since you're driving one and a half miles per minute, we need to convert it to miles per hour. There are 60 minutes in an hour, so we multiply 1.5 by 60 to get 90 miles per hour.

Step 2: Slow down by 15 miles per hour.

Subtract 15 from the initial speed of 90 miles per hour, resulting in 75 miles per hour.

Step 3: Reduce the speed by one third.

To find one third of 75 miles per hour, we divide it by 3, which gives us 25 miles per hour.

Therefore, the final speed after slowing down by 15 miles per hour and reducing the speed by one third is 25 miles per hour.

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The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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Answer:

volume of this sphere is 4.19 cm³

Explanation:

volume of sphere: \(\frac{4}{3}\)πr³

Here the radius of the sphere is 1 meter.

Using the formula:

\(\frac{4}{3}\) * 3.14 * 1³

4.19 cm³

Answer:

\({\purple{\boxed{4.19}}}\) cubic meters.

Step-by-step explanation:

DIAGRAM :

\(\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bf{1\ m}}\end{picture}\)

\(\begin{gathered}\end{gathered}\)

SOLUTION :

Here's the required formula to find the volume of sphere :

\(\longrightarrow{\pmb{\sf{V_{(Sphere)} = \dfrac{4}{3} \pi {r}^{3}}}}\)

Substituting all the given values in the formula to find the volume of sphere :

\(\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \pi {r}^{3}}}\)

\(\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times {(1)}^{3}}}\)

\({\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times {(1 \times 1 \times 1)}}}}\)

\({\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times {(1 \times 1)}}}}\)

\({\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times {(1)}}}}\)

\({\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 1}}}\)

\({\longrightarrow{\sf{V_{(Sphere)} = \dfrac{4}{3} \times 3.14}}}\)

\({\longrightarrow{\sf{V_{(Sphere)} = \dfrac{12.56}{3}}}}\)

\({\longrightarrow{\sf{V_{(Sphere)} \approx 4.19}}}\)

\(\star{\underline{\boxed{\sf{\red{V_{(Sphere)} \approx 4.19 \: {m}^{3}}}}}}\)

Hence, the volume of sphere is 4.19 m³.

\(\begin{gathered}\end{gathered}\)

LEARN MORE :

\(\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}\)

\(\rule{300}{2.5}\)

Answer:

B

y = -4x

Step-by-step explanation:

PLZ mark brainliest

The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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(a) The shape of the distribution of donations is rectangular.

(b) The proportion of donations are at least 75 cents id 0.24

(a)The density curve is rectangular in shape.

This indicates that donations are distributed uniformly.

(b) From the question, we have

The probability of donations at least 75 cents as follows:

\(P(X\geq 75) =\int\limits^a_b {\frac{1}{99-0} } \, dx \\\)

Substituting the limits,  we get

\(P(X\geq 75) =\frac{99-75}{99} \\=\frac{24}{99} \\=0.24\)

Probability:

Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

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Answer:

2·2·2·2 = 16

Step-by-step explanation:

everytime a number is raised by another, that means you are going to multiply the base number  times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:

2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:

2² = 2 · 2 = 4

2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:

2³ = 2 · 2 · 2 = 8

In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:

2^4 = 2·2·2·2 = 16

the same format will be used regardless of the base number and the exponent

i hope this helps! :)

Answer:

A

Step-by-step explanation:

\(\sqrt{x^3}\) = \(x\sqrt{x}\)

\(\sqrt{16x^3}\) = \(4x\sqrt{x}\)

\(x\sqrt{x}\) + \(4x\sqrt{x}\)  \(-3x\sqrt{x}\)

= \(5x\sqrt{x}\) \(-3x\sqrt{x}\)

= \(2x\sqrt{x}\)

The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

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Answer:

37.50 UNITS SQUARE.

Step-by-step explanation:

add 6 to 9 you get 15

multiply 15 by 5 you get 75

divide 75 by 2

37.5

I hope it helps bye