what is the difference between dot product and cross product?

Answer:

5% annual population growth rate

Step-by-step explanation:

Let the percent the population grows by be [tex]X\%[/tex]. The total population, [tex]f(x)[/tex], after [tex]t[/tex] years can be modeled by the function:

[tex]f(x)=40,000\cdot (\frac{X}{100}+1)^t[/tex]

Why?

Let's take a look at a simple example. If we said a number [tex]n[/tex] grew by 10%, we could represent the number after it grew by multiplying [tex]n[/tex] by [tex]1.10[/tex]. This is because growing by 10% is equivalent to taking [tex]100\%+10\%=110\%[/tex] of that number and we convert a percentage to a decimal by dividing by 100.

Therefore, if the population grew [tex]X\%[/tex], we would divide it by 100 to convert it to a decimal, then add 1 (100%) and raise to the power of [tex]t[/tex] (number of years) to multiply by the initial population of 40,000 to get the total population after [tex]t[/tex] years.

Since the population of the town after two years is 44,100, substitute [tex]f(x)=44,100[/tex] and [tex]t=2[/tex] into [tex]f(x)=40,000\cdot (\frac{X}{100}+1)^t[/tex]:

[tex]44,100=40,000\cdot (\frac{X}{100}+1)^2,\\\\(\frac{X}{100}+1)^2=\frac{44,100}{40,000},\\\\(\frac{X}{100}+1)^2=1.1025,\\\\(\frac{X}{100}+1)^2=\pm \sqrt{1.1025},\\\\\begin{cases}\frac{X}{100}+1=1.05,\frac{X}{100}=0.05, X=\boxed{5\%},\\*\text{negative case is extraneous since X must be positive}\end{cases}[/tex]

Therefore, the city has an annual population growth rate of 5%.

Answer:

C

Step-by-step explanation:

sin(theta)=7/8, theta=arcsin(7/8)=61

Answer:

Below!

Step-by-step explanation:

Please provide the two points (A & B) so I can help you out with the question or...

use the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where the first point = [tex](x_1,y_1)[/tex] & the second point: [tex](x_2,y_2)[/tex]

Answer:

x = 35

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

x^2 + 12^2 = (x+2)^2

FOIL

x^2+144=x^2+4x+4

Subtract x^2 from each side

144= 4x+4

Subtract 4 from each side

140 = 4x

Divide by 4

35 =x

Answer:

y=(3/7)*x+52/7

Step-by-step explanation:

The slope of the line will be (3/7). The equation of line will be y=(3/7)*x+52/7

Answer:

1/19

Step-by-step explanation:

There are a total of 36+2 = 38 spaces

2 are green

P(green) = green / total

             = 2/38

            =1/19

            .052631579

Answer:

[tex]thank \: you[/tex]

Answer:

Step-by-step explanation:

3-(2x-5)=-4(x+2)

We simplify the equation to the form, which is simple to understand

3-(2x-5)=-4(x+2)

Remove unnecessary parentheses

3-2x+5=-4*(x+2)

Reorder the terms in parentheses

3-2x+5=+(-4x-8)

Remove unnecessary parentheses

+3-2x+5=-4x-8

We move all terms containing x to the left and all other terms to the right.

-2x+4x=-8-3-5

We simplify left and right side of the equation.

+2x=-16

We divide both sides of the equation by 2 to get x.

x=-8

Answer:

x < - 8

Step-by-step explanation:

Given

3 - (2x - 5) < - 4(x + 2) ← distribute parenthesis on both sides

3 - 2x + 5 < - 4x - 8

- 2x + 8 < - 4x - 8 ( add 4x to both sides )

2x + 8 < - 8 ( subtract 8 from both sides )

2x < - 16 ( divide both sides by 2 )

x < - 8

I think the given integral reads

[tex]\displaystyle \int_{-3}^3 \int_0^{9-x^2} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

In cylindrical coordinates, we take

x ² + y ² = r ²

x = r cos(θ)

y = r sin(θ)

and leave z alone. The volume element becomes

dV = dx dy dz = r dr dθ dz

Then the integral in cylindrical coordinates is

[tex]\displaystyle \boxed{\int_0^\pi \int_0^{(\sqrt{35\cos^2(\theta)+1}-\sin(\theta))/(2\cos^2(\theta))} \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta}[/tex]

To arrive at this integral, first look at the "shadow" of the integration region in the x-y plane. It's the set

{(x, y) : -3 ≤ x ≤ 3 and 0 ≤ y ≤ 9 - x ²}

which is the area between a paraboloid and the x-axis in the upper half of the plane. So right away, you know θ will fall in the first two quadrants, so that 0 ≤ θ ≤ π.

Next, r describes the distance from the origin to the parabola y = 9 - x ². In cylindrical coordinates, this equation changes to

r sin(θ) = 9 - (r cos(θ))²

You can solve this explicitly for r as a function of θ :

r sin(θ) = 9 - r ² cos²(θ)

r ² cos²(θ) + r sin(θ) = 9

r ² + r sin(θ)/cos²(θ) = 9/cos²(θ)

(r + sin(θ)/(2 cos²(θ)))² = 9/cos²(θ) + sin²(θ)/(4 cos⁴(θ))

(r + sin(θ)/(2 cos²(θ)))² = (36 cos²(θ) + sin²(θ))/(4 cos⁴(θ))

(r + sin(θ)/(2 cos²(θ)))² = (35 cos²(θ) + 1)/(4 cos⁴(θ))

r + sin(θ)/(2 cos²(θ)) = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))]

r  = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))] - sin(θ)/(2 cos²(θ))

Then r ranges from 0 to this upper limit.

Lastly, the limits for z can be converted immediately since there's no underlying dependence on r or θ.

The expression above is a bit complicated, so I wonder if you are missing some square roots in the given integral... Perhaps you meant

[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

or

[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{\sqrt{9-x^2-y^2}} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

For either of these, the "shadow" in the x-y plane is a semicircle of radius 3, so the only difference is that the upper limit on r in either integral would be r = 3. The limits for z would essentially stay the same. So you'd have either

[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

or

[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{\sqrt{9-r^2}} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

Answer:

Step-by-step explanation:

(-4 - 5i)⋅(1 - i) = (-4)(1) + (-4)(-i) + (-5i)(1) + (-5i)(-i)

= -4 + 4i - 5i + 5i²

= -4 - i -5

= -9 - i

Answer:

please tell me the complete question

Answer: hello your question is poorly written attached below is the complete question

answer:

1 ) =  I (

2) = F

3) = Z

4) = D

Step-by-step explanation:

attached below is the required solution.

1 ) =  I ( The sequence diverges to infinity )

2) = F ( The sequence has a finite non-zero limit )

3) = Z ( The sequence converges to zero )

4) = D ( The sequence diverges )

Answer:

3

Step-by-step explanation:

Please Mark me brainliest

Answer:

aren't one of the numbers in the equations supposed to be negative?

Answer:

1

Step-by-step explanation:

Since the y value is the same, we only need to find the distance between the x points

1-0 = 1

The distance between the point is 1

Answer : 1 unit.

Explanation: Since ( 0,0 ) is at 0 on the x axis, ( 1,0 ) is one unit to the right of 0, 1.

Answer:

30

Step-by-step explanation:

To compare the numbers, divide the first number by the second number.

(7.4 x 10^8)/(2.5 x 10^7) = (74 x 10^7)/(2.5 x 10^7) = 74/2.5 = 29.6

Answer: 30

$121 and $12 ok isn't available in your ma er bishal bishal bishal

Answer:

A. A critical value is how far away our sample statistic can be from the true population parameter with a certain level of confidence.

Step-by-step explanation:

Test of a hypothesis:

When we are testing a hypothesis, we have a null hypothesis and an alternative hypothesis, and the conclusion depends on the test statistic, given by:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

The test statistic measures the number of standard errors that we have to move away from the sample mean, and the critical value is how much we can be far from the population parameter with a certain level of confidence, that is, before a certain value we do not reject the null hypothesis, after the value we reject, and this value is the critical value, and thus the correct answer is given by option a.

Hi! I'm happy to help!

To solve this problem, we need to divide the recipe amount in 1/6 amounts. So, we will do a fraction division problem like this:

15[tex]\frac{1}{6}[/tex]÷[tex]\frac{1}{6}[/tex]

This problem is hard to do with mixed numbers, so we need to turn 15[tex]\frac{1}{6}[/tex] into an improper fraction. To do that we need to multiply 15 by 6, because that is our denominator, then add the extra [tex]\frac{1}{6}[/tex].

(15×6)+1

90+1

91

So, our improper fraction would be[tex]\frac{91}{6}[/tex], now, let's solve.

[tex]\frac{91}{6}[/tex]÷[tex]\frac{1}{6}[/tex]

It is difficult to do division problems on their own, so we can change this into an easier problem. We can do the inverse operation and turn this into multiplication. We do this by changing it to multiplication (obviously), then flip the second fraction.

[tex]\frac{91}{6}[/tex]×[tex]\frac{6}{1}[/tex]

Now, we just multiply the top by the top, and bottom by the bottom.

[tex]\frac{546}{6}[/tex]

We could end it here, but we want a whole number, so, we simplify the number by dividing both the top and bottom by 6.

[tex]\frac{91}{1}[/tex]

Anything over 1, is just a whole number

91.

Therefore, the recipe should require 91 uses of the 1/6 cup.

I hope this was helpful, keep learning! :D

Answer:

the lower limit is 35% women believed and 65% of men believed in serial discrimination

Answer:

-12

Step-by-step explanation:

that is b

Answer:

Step-by-step explanation:multiple 5 times 108 and that gives you your answer..

The maximum length of the seesaw is option c  4.00 meters.

A right-angled triangle is one in which one of the angles is equal to 90 degrees. A 90 degree angle is called a right angle, which is why a triangle made up of right angle is termed a right angled triangle.

A right-angled triangle has three sides- hypotenuse, base and height. Hypotenuse is the longest and also the opposite side of the right angle of the triangle, base and height of a right triangle are always the sides adjacent to the right angle.

The formula for measuring the hypotenuse is,

Height / Hypotenuse = Sinθ , where θ is the angle opposite to the height of the triangle.

In the given question, the seesaw should make an angle of 30° with the ground and the maximum height it should rise is 2 meters so the height here is 2 meters. So the seesaw will make a right angled triangle.

Height = 2 meters, θ = 30°,

Now using the formula,

2 / Hypotenuse = Sin30°

Rearranging we get,

Hypotenuse = 2 / Sin30°

The value of Sin30° is 1/2 and putting the value we get,

Hypotenuse = 2 / (1/2)

                     = 2 × 2

                     = 4 meters.

Therefore, the maximum length of the seesaw (that is the hypotenuse ) is 4 meters.

To learn more about right-angled triangles and finding sides of it click here-brainly.com/question/10331046

#SPJ2

Answer:

there are infinite solutions

Step-by-step explanation:

if you add y-3 to both sides of the first equation, you will see that it is equal to the second equation, so they are the same line. Therefore, there are infinite solutions to this system

[tex]\\ \sf\longmapsto \dfrac{2}{3}x=10[/tex]

[tex]\\ \sf\longmapsto \dfrac{2x}{3}=10[/tex]

[tex]\\ \sf\longmapsto 2x=3(10)[/tex]

[tex]\\ \sf\longmapsto 2x=30[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{30}{2}[/tex]

[tex]\\ \sf\longmapsto x=15[/tex]

[tex] \begin{cases}\large\bf{\red{ \implies}} \tt \frac{2}{3} x \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt \frac{2x}{3} \: = \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 3 \: \times \: 10 \\ \\ \large\bf{\red{ \implies}} \tt 2x \: = \: 30 \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \:\frac{ \cancel{30} \: \: ^{15} }{ \cancel{2}} \\ \\ \large\bf{\red{ \implies}} \tt \: x \: = \: 15 \end{cases}[/tex]

Answer: k = 2/-3

Step-by-step explanation: Option (B)

Taking the test as we speak

ans: 257,256.59

if it was sold for $3.99

it would have been 86,047 × $3.99 = 343,303.59 and it was sold for $1 instead so automatically it's $86,047

therefore

343, 303.59

-86, 047 which is equal to a loss of $257, 256.59

Let missing side be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{6}{4}=\dfrac{x}{20-x}[/tex]

[tex]\\ \sf\longmapsto 6(20-x)=4x[/tex]

[tex]\\ \sf\longmapsto 120-6x=4x[/tex]

[tex]\\ \sf\longmapsto 120=6x+4x[/tex]

[tex]\\ \sf\longmapsto 120=10x[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{120}{10}[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]