The general term Tn of a sequence is
4+n
2n
Find the 4th term and the 6th term in the sequence.

Given:

\(x^{\frac{5}{4}}=100\)

\(x=\sqrt[a]{100}^b\)

To find:

The values of a and b.

Solution:

We have,

\(x^{\frac{5}{4}}=100\)

It can be written as

\(x^{\frac{5}{4}\times \frac{4}{5}}=100^{\frac{4}{5}}\)

\(x^{1}=\left[100^{\frac{1}{5}}\right]^4\)       \([\because a^{mn}=(a^m)^n]\)

\(x=\left[\sqrt[5]{100}\right]^4\)       \([\because a^{\frac{1}{n}}=\sqrt[n]{a}]\)

\(x=\sqrt[5]{100}^4\)

On comparing this with \(x=\sqrt[a]{100}^b\), we get

\(a=5\)

\(b=4\)

Therefore, the value of a is 5 and value of b is 4.

Answer: i don't really know how you want me to solve it

Use the formula x =−b/2a (b over 2a)

(1 second

to find the maximum and minimum.

6t^(2 )+ 12t + 30

which should give you this answer

6(t2+2t+5)

what i did was factor 6 out of 6t^(2 )+ 12t + 30

Answer: 1 second

Step-by-step explanation:

There are two ways to solve this:

1. Graph it. You will see an inverted parabola with time (in seconds) on the x axis and height (in feet) on the y axis. The top of the parabola is point (1, 36) which means at 1 second the ball will be at 36 feet. Since the balcony is at 30 feet, the ball only goes up 6 feet before it changes direction toward the ground.

2. Take the first derivative and set it equal to zero. The first derivative will give us the slope, or rate of change, of the parabola for any point t (on the x-axis). The rate of change when the ball reaches its maximum height will be zero, when it goes from a positive value (going up) to a negative value (going down).

-6t^2 + 12t + 30

First derivative = h'(t) = -12t + 12

Set h'(t) to zero: 0 = -12t + 12

t = 1 second

Either way works. Put 1 second into the original equation and it will return 36 feet. That's 36 feet aboove ground. 6 feet above the balcony from which it is thrown. You can throw better then that, I assume.

Answer:

x=1

Step-by-step explanation:

According to the given statement the absolute value of just about any complex number Ia + biI seems to be the distance between (a, b) and (0, 0) in the complex plane is √(a² + b²).

After dividing one number by another, the modulo operation yields the remainder or signed remainder of the division. A modulo n seems to be the remainder of something like the Euclidean division on a by n, where an is the dividend and n is the divisor, given two positive numbers a and n.

The modulus operator can be used in a variety of situations. It is frequently used to decrease a randomly generated number to a randomly generated number in a smaller range, and it may also rapidly tell you if one integer is a factor of another.

The modulus of any complex number is its absolute value, regarding which there is a modulus formula. √(a² + b²).

where a and b are integers

Please see the attached file for the complex plane of the provided points (a,b) (0,0).

The separation of two points (x1 ,y1) and (x2 ,y2) will be:

√((x1 - y1)² + (x2 - y2)²)

We need to calculate the distance between (a,b) because (0,0)

We will obtain by replacing the numbers in the distance formula.

√((0 - a)² + (0 - b)²).

The given statement the absolute value of just about any complex number a + bi seems to be the distance between (a, b) and (0, 0) in the complex plane is √(a² + b²).

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I understand that the question you are looking for is:

now examine |a + bi| and complete the definition below. the absolute value of any complex number a + bi is the from (a, b) to (0, 0) in the complex plane.

Answer: distance , positive real on edge

Step-by-step explanation:

if cos(x) + sin(y) = 5 then, \(y'' = (-cos(x)cos^3(y) - sin(y)sin^2(x)) / cos^4(y)\)

To find y'', we need to differentiate the given equation twice with respect to x.

First, we take the first derivative of both sides:

-sin(x) + cos(y) * y' = 0

Then, we take the second derivative:

\(-cos(x) - sin(y) * (y')^2 + cos(y) * y'' = 0\)

We want to solve for y'', so we can rearrange the equation:

\(y'' = (cos(x) + sin(y) * (y')^2) / cos(y)\)

Now we just need to substitute the values we have and simplify:

cos(x) + sin(y) = 5

\((y')^2 = sin^2(x) / cos^2(y)\)

\(y' = sin(x) / cos(y) or y' = -sin(x) / cos(y)\)

(Note that there are two possible values for y', depending on whether we use the positive or negative square root. We'll need to plug in both values to get both possible solutions for y''.)

Substituting y' into our equation for y'':

\(y'' = (cos(x) + sin(y) * sin^2(x) / cos^3(y)) / cos(y)\)

\(y'' = (cos(x)cos^3(y) + sin(y)sin^2(x)) / cos^4(y) or\)

\(y'' = (-cos(x)cos^3(y) - sin(y)sin^2(x)) / cos^4(y)\)

Therefore, there are two possible solutions for y'':

\(y'' = (cos(x)cos^3(y) + sin(y)sin^2(x)) / cos^4(y)\)

or

\(y'' = (-cos(x)cos^3(y) - sin(y)sin^2(x)) / cos^4(y)\)

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The water level is rising at a rate of 1/3 ft/min.

The trough has the shape of isosceles triangles at its ends.

Height of the trough = 12 ft

Base of the isosceles triangle, b =  5 x h' = 5h' [since the width across the top of the trough is 5 ft]

Let h be the height of the isosceles triangle which is the depth of the water.

Base area of the trough = Area of the triangle

                                        = 1/2 x 5h x h

                                        = 5/2 h²sq. ft.

Volume of the trough, V = Base area x height of the trough

                                         = 5/2 h² x 12

                                         = 30h² cubic ft

Differentiating V with respect to t,

dV/dt = 30 x 2h x dh/dt = 60h dh/dt,

where dh/dt is the rate of change in the water level.

The rate of water being filled in the trough, dV/dt = 15 ft³/min.

Substituting dV/dt and when h = 9 inches = 3/4 ft,

⇒ 15 = 60 x 3/4 x dh/dt

⇒ dh/dt = 15 /(45)

⇒ dh/dt = 1/3 ft/min

So the water level is rising at a rate of 1/3  ft/min.

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Answer: Yeah and ?

Step-by-step explanation:

Answer:

(15,-5)

Step-by-step explanation:

The value of x from the given expression is -10

Given the following expression

AC = x + 24,

AB = 2x + 28,

and BC = 6.

Using the addition property, we will have:

AC = AB + BC

Substitute the expression to have:

x+24 = 2x + 28 + 6

x-2x = 34 - 24

-x = 10

x = -10

Hence the value of x from the given expression is -10

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Answer:

X=-10

Step-by-step explanation:

In this case, "X+24" is the sum of "2x+28" and "6"

The correct equation would be:

2x+34=x+24

Now, subtract X from both sides and add 34 to both sides

Now:

x=-10

Hence, -10 is the answer

Answer:

i believe 13

your welcome

Answer:

2

Step-by-step explanation:

6 sides by 6 adding 4x4=12

Answer: 263.088

Step-by-step explanation:

Multiply the equation

¨What does Multiply mean?¨

To compute a product; to perform a multiplication.

(8.1) x (8.12) x 4

Answer    c

Step-by-step explanation: I did the test i hope this help unlike that girl who just wrote random numbers anyways have a good day

Answer:c

Step-by-step explanation:

Answer:

Rs 1425

Step-by-step explanation:

=(30×40) + (15×15)

=1425

Answer:

the first person, y=4-3x

the second person, y=2+3x

The way that X and Y vary can be used to determine if a table is linear. A table is linear if, when X rises by 1, Y increases at a steady pace. By locating the initial difference, you may get the constant rate.

X  Y

1  2

2  4

3  6

4  8

It's linear in this table. There is a difference of two between Y1 and Y2, Y2 and Y3, and Y3 and Y4. As a result, Y's constant rate is 2.

X  Y

1  6

2  9

3  1

4  40

NOT a linear table, this one. Y does not rise at a consistent pace when X increases by 1, as evidenced by the differences of 3, 8, and 39 between Y1 and Y2, Y2 and Y3, and Y3 and Y4. This shows that there is no linear link between the two.

What is table of linear function ?

Well, a linear function is proportional, a straight line (on a graph). And the numbers must not have the same answer. For instance, if the X input is 5, and the Y output is 7. And then another X input is 5, and the Y output is 8, that's non-linear.

So, the Answer would be the third graph. This is because the X values are steadily increasing, and so are the Y values.

For the X and Y values, for each time X increases by 1, Y increases by -8. This is, linear because both sides are constantly and evenly increasing.

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Probability that the first ball drawn is a red ball if the second ball drawn is yellow = 7/12

Number of yellow balls, N(Y) = 5

Number of red balls, N(R) = 7

Total number of balls, N(Total) = 7+5

N(Total) = 12

Probability of picking a yellow a ball

Pr(Y) = N(Y) / N(Total)

Pr(Y) = 5/12

Probability of picking a red ball

Pr(R) = N(R) / N(Total)

Pr(R) = 7/12

Probability of the two balls are red and yellow

Pr(RnY) = 5/12 x 7/12

Pr(RnY) = 35/144

Probability that the first ball drawn is a red ball if the second ball drawn is yellow

Pr(R|Y) = Pr(RnY)/P(Y)

Pr(R|Y) = 35/144 ÷ 5/12

Pr(R|Y) = 35/144 x 12/5

Pr(R|Y) = 7/12

Probability that the first ball drawn is a red ball if the second ball drawn is yellow = 7/12

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A two-step experiment consists of tossing a six-sided die and flipping a coin. The sample space for this experiment consists of all possible outcomes that could result from both steps. To find the number of elements in the sample space, we need to multiply the number of possible outcomes for each step.

The first step involves rolling a six-sided die, which has six possible outcomes. The second step involves flipping a coin, which has two possible outcomes. To find the total number of elements in the sample space, we need to multiply these two numbers together:

6 x 2 = 12

Therefore, the sample space for this two-step experiment consists of 12 elements, each representing a unique outcome that could result from rolling the die and flipping the coin. This could be represented in a tree diagram, where each branch represents a possible outcome at each step, and the endpoints of the branches represent the final outcomes in the sample space.

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Answer:

d = 3

Step-by-step explanation:

2d + 1 = 7

7 -1

2d = 6

2 divided by 2(cancels out), 6 divided by 2 is 3.

d = 3

Answer:

76

Step-by-step explanation:

The formula for the area of the Trapezoid is:

\(A=\frac{a+b}{2}h=\frac{7+7}{2}2=14\)

The formula for the area of the rectangle is:

\(A=wl=6*15=90\)

Now you rest 90 - 14 and it gives you 76.

The particular solution is:

y = -1 - e^(3x)

We have the differential equation:

y' - 3y = 3

To find the integrating factor, we multiply both sides by e^(-3x):

e^(-3x)y' - 3e^(-3x)y = 3e^(-3x)

Notice that the left-hand side is the product rule of (e^(-3x)y), so we can write:

d/dx (e^(-3x)y) = 3e^(-3x)

Integrating both sides with respect to x, we get:

e^(-3x)y = ∫ 3e^(-3x) dx + C

e^(-3x)y = -e^(-3x) + C

y = -1 + Ce^(3x)

Using the initial condition y(0) = -1, we can find the value of C:

-1 = -1 + Ce^(3*0)

C = -1

So the particular solution is:

y = -1 - e^(3x)

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Explanation:

1 hat = 45 dollars

6 hats = 6*45 = 270 dollars

1 phone = 40 dollars

4 phones = 4*40 = 160 dollars

total = $270 + $160 = $430

Felicia spent a total of $430. Since this amount of money leaves her account, this means we write a negative sign out front to end up with the final answer of -430

In other words, her account balance went down by $430 which is why we use a negative. If someone gave her $430, then the answer would be positive.

slope intercept form = y=mx+b

m= slope

b= y-intercept

the slope is rise over run, so if the points are (1, -6) and (5, -6), the slope is 0

the y intercept is -6

y = 0x-6

or

y = -6

Answer:

Step-by-step explanation:

Hello : let  A(3,-8)    B(-1,-2)

the slope is :   (YB - YA)/(XB -XA)

(-2+8)/(-1-3)  = 6/-4 =-3/2

Answer:

y = 1/2x + 2

Step-by-step explanation:

The y-intercept is 2 because it passes through the y axis at (0,2) and the slope if 1/2

Hope that helps and have a great day!

Answer:

\(y=\frac{1}{2}x+2\)

Step-by-step explanation:

To find the equation for the line, lets try to find the slope and y-intercept of the line.

From looking at the graph, we can see that the line intersects the y-axis at y = 2. So the y-intercept would be 2.

The slope of the line would be the rise divided by the run. Looking at the graph, we can see that for every 2 the line moves in the x-direction, it moves 1 in the y-direction. This means that the rise is 1 and the run is 2. So the slope would be 1/2.

So we now know that the slope is 1/2 and the y-intercept is 2, we can now plug the information into the slope-intercept form.

Slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

Plugging in we get

\(y=\frac{1}{2}x+2\)

And now we have the equation of the line.

I hope you find my answer and explanation to be helpful. Happy studying.

The area of a shape is the amount of space it occupies

The area of the rhombus is 24.7 square inches

Start by calculating the length BO using the following Pythagoras theorem

\(BC^2 = AO^2 + BO^2\)

So, we have:

\(5^2 = 3.8^2 + BO^2\)

Evaluate the exponents

\(25 = 14.44 + BO^2\)

Collect like terms

\(BO^2 = 25 - 14.44\)

\(BO^2 = 10.56\)

Take the square roots

\(BO = 3.25\)

The area of the rhombus is then calculated as:

\(Area = \frac{2BO * 2AO}{2}\)

This gives

\(Area = \frac{2 * 3.25 * 2 * 3.8}{2}\)

\(Area = 24.7\)

Hence, the area of the rhombus is 24.7 square inches

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Answer:

300000 km per second

18000000 km per minute

126000000 km in 7 minutes

Step-by-step explanation:

In 10 minutes there are (10*60) seconds, which is 600 seconds.

180000000/600 = 300000

To find km per minute,

180000000/10 = 18000000

To find km in 7 minutes,

18000000*7=126000000

Light travels 18000000 kilometers per minute and 300000 kilometers per second.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, light travels about 180000000 kilometers in 10 minutes.

A) We know that, 1 minute =60 seconds

10 minutes =600 seconds

Now, number of kilometers per second

= 180000000/600

= 300000 kilometers/second

B) Number of kilometers per minute

= 180000000/10

= 18000000 kilometers per minute

C) Number of kilometer light travel in 7 minutes

= 18000000×7

= 126000000

Therefore, light travels 18000000 kilometers per minute and 300000 kilometers per second.

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A continuous function is a function where small changes in the input result in small changes in the output, with no abrupt jumps or breaks in the function's graph.

Since f(x,y) is independent of x, we can write it as f(x,y) = g(y). We are given that the integral of g(x) from 0.3 to 10 is 1, so we can write:

∫0.3^10 g(x) dx = 1

Using this information, we can find g(y) by integrating g(x) with respect to x:

g(y) = ∫0.3^10 g(x) dx / ∫0^10 dx
g(y) = 1 / 9.7

Now, we can find f(x,y) by substituting g(y) into f(x,y) = g(y):

f(x,y) = g(y) = 1 / 9.7

We need to find the integral of f(x,y) over the rectangle R, which is:

∫0^3 ∫0^10 f(x,y) dy dx
∫0^3 ∫0^10 1 / 9.7 dy dx
(1 / 9.7) ∫0^3 ∫0^10 dy dx
(1 / 9.7) * 3 * 10
= 3.0928

Therefore, the value of the integral of f(x,y) over the rectangle R is 3.0928.

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