use your above answers to find an equation for the line through the point =(−2,3) perpendicular to the vector −3⃗ 6⃗ .

Answer: I III and IV

Step-by-step explanation:

The line intersects the x axis at (2,0) and the y axis at (0,-4) so the line goes through quadrants 1 3 and 4 so the answer is the middle or the 3rd from top

the speed of the boat is 5.418 km/h and the speed of the stream is 2.167 km/h

Let's define the variables:

B = speed of the boat in still water.

S = speed of the stream.

When the boat travels downstream, the total speed of the boat will be equal to the sum of the speed of the stream and the speed of the boat in still water:

speed = B + S

When the boat goes downstream, the speed will be:

speed = B - S

Now, also remember the relation:

speed*time = distance.

The given information is:

In 8 hours the boat can:

go 12 km upstream and 40km downstream.

We now need to define another variable, T, as the time that the boat travels upstream.

Then we can write this as:

12km = (B - S)*T

If the boat travels T hours upstream, and travels for a total of 8 hours, then the amount of time that travels downstream is 8h - T, then we can write:

40km = (S + B)*(8h - T)

Similarly, when we have:

"it can go 16 km upstream and 32 km downstream in the same time."

we can define a new variable T', and write:

16km = (B - S)*T'

32km = (S + B)*(8h - T')

Then we have a system of 4 equations:

16km = (B - S)*T'

32km = (S + B)*(8h - T')

40km = (S + B)*(8h - T)

12km = (B - S)*T

And we need to solve this for S and B.

To do it, we need to isolate one of the variables in one of the equations.

Let's isolate T in the last equation:

T = 12km/(B - S)

now we can replace that in the third equation to get:

40km = (S + B)*(8h - 12km/(B - S))

So now we have 3 equations:

16km = (B - S)*T'

32km = (S + B)*(8h - T')

40km = (S + B)*(8h - 12km/(S - B))

Now we need to do the same thing, this time let's isolate T' in the first equation and replace it in the second one:

T' = 16km/(B - S)

Replacing it in the second equation we get:

32km = (S + B)*(8h - T')

32km = (S + B)*(8h - 16km/(B - S))

So now we have two equations:

40km = (S + B)*(8h - 12km/(B - S))

32km = (S + B)*(8h - 16km/(B - S))

Let's simplify these:

40km = 8h*(S + B) - 12km*(S + B)/(B - S)

32km = 8h*(S + B) - 16km*(S+ B)/(B - S)

Now we can multiply both equations by (B - S) to get:

40km*(S - B) = 8h*(S + B)*(B - S) - 12km*(S + B)

32km*(S - B) = 8h*(S + B)*(B - S) - 16km*(S+ B)

Let's keep simplifying this:

40km*(B - S) + 12km*(S + B) =  8h*(S + B)*(B - S)

32km*(B - S)  + 16km*(S+ B) = 8h*(S + B)*(B - S)

Now we get:

52km*B - 28km*S = 8h*(S^2 + B^2)

48km*B - 16km*S = 8h*(S^2 + B^2)

Notice that the right side of these equations is the same thing, then we can write:

52km*B - 28km*S = 48km*B - 16km*S

(52km - 48km)*B = (28km - 18km)*S

4km*B  =  10km*S

B = (10/4)*S

B = (5/2)*S

Now we can replace this in one of our two equations, let's use the first one:

48km*B - 16km*S = 8h*(S^2 + B^2)

48km*(5/2)*S - 16km*S = 8h*( S^2 + ( (5/2)*S)^2)

Now we can solve this for S

104km*S = 8h*( S^2 + 25/4*S^2)

104km*S = 8h*(29/4*S^2) = 48h*S^2

104km*S = 48h*S^2

dividing at both sides by S we get:

104km = 48h*S

104km/48h = S = 2.167 km/h

And using B = (5/2)*S

We can find the speed of the boat:

B = (5/2)*2.167 km/h = 5.418 km/h

Then:

the speed of the boat is 5.418 km/h and the speed of the stream is 2.167 km/h

If you want to learn more about this topic, you can read:

https://brainly.com/question/17300107

Answer:

answer is D im pretty sure

Step-by-step explanation:

In the spherical coordinates, the triple integral of f(rho,θ,ϕ)=cosϕ, over the region 0≤θ≤2π, 0≤ϕ≤π/4, 3≤rho≤4 is  \(79\pi /3\).

Spherical coordinates of the gadget denoted as (r, θ, Φ) is the coordinate machine specifically used in three-dimensional systems. In 3 dimensional area, the round coordinate gadget is used for finding the surface region. those coordinates specify 3 numbers: radial distance, polar angles, and azimuthal perspective.

To convert a factor from spherical coordinates to Cartesian coordinates, use equations x=ρsinφcosθ,y=ρsinφsinθ, and z=ρcosφ. To transform a factor from Cartesian coordinates to spherical coordinates, use equations ρ2=x2+y2+z2,tanθ=yx, and φ=arccos(z√x2+y2+z2).

Consider the function:

f(0,0,0)=cos

35057

Spherical Coordinates:

x=psin cos

y=psin sine

z = p cos

DV = p² sin dpdøde

1=[[[psin p cos dpdøde

003

= "deƒân (20)deſp°dp

-(2x) (1-1) (343-27)

12

pm (316

34

3

79/3

Learn  more about spherical coordinates here https://brainly.com/question/4465072

#SPJ4

The calculated surface area of the figure is 3100.8 square feet

from the question, we have the following parameters that can be used in our computation:

SA = hp + 2B

From the figure, we have

B = 1/2 * (10 + 34) * 24.7 = 543.4

p = 2 * (34 + 19) = 106

h = 19

So, we have

SA = 19 * 106 + 2 *  543.4

Evaluate

SA = 3100.8

Hence, the surface area is 3100.8 square feet

Read more about surface area a

https://brainly.com/question/26403859

#SPJ1

-1, it's fairly clear just from the table...

Answer:

-1

Step-by-step explanation:

The slope of any line parallel to this line would be c) 3/7.

Parallel lines are those lines that are equal distances apart and often of the same length. So, for the given slope where we have parallel lines, we can expect to have lines of the same slope. Thus we can arrive at 3/7.  

Note that parallel lines have the same slope. So, since the first slope is 3/7, we can expect the second to be the same thing.

Learn more about parallel lines here:

https://brainly.com/question/24607467

#SPJ2

Answer:

im gonna say 24

Step-by-step explanation:

Answer:

Answer:

The answer is 3.98942, rounded its 3.99.

Step-by-step explanation:

Answer:

3.99 ft

Step-by-step explanation:

Volume of a cylinder = πr²h

π = 3.14

volume = 500 ft³

height = 10 ft

πr²h = 500

3.14×r²×10 = 500

r² = 500/3.14×10

= 15.92..

= √15.92

r = 3.9899.. ≈ 3.99 ft

Answer:

-(5x+8)(x - 3)

Step-by-step explanation:

add and subtract second term to expression and factor using grouping

Answer:

Translation

Step-by-step explanation:

Remember Translation as a 'Slide'

Answer:

translation

Step-by-step explanation:

hopes this help

Answer:

(2,-16) (4,-32) (8,-64)

Step-by-step explanation:

The distance between point F and point G is 2√5, while the volume of the traffic cone is 628.32 in³. Lastly the scientific notation form of 34.6 x 10⁵ is 3.46 x 10⁶

Distance Formula

The distance formula is derived from the Pythagorean theorem and is given by:

d = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

Given the coordinates of point F as (-1, 6) and point G as (3, 4), we can substitute these values into the distance formula:

d = \(\sqrt{(3 - (-1))^2 + (4 - 6)^2}\)

 = \(\sqrt{(3 + 1)^2 + (-2)^2}\)

 = √(16 + 4)

 = √20

 = 2√5

Therefore, the distance between point F and point G is 2√5 (approximately 4.47 units).

Volume

Use the formula for the volume of a cone, which is given by:

V = (1/3) * π * r² * h

Where:

V is the volume,

π is the constant approximately equal to 3.14,

r is the radius of the cone (half of the diameter), and

h is the height of the cone.

Given:

height = 2 feet (24 inches)

diameter = 10 inches

r = 10 inches / 2 = 5 inches

Now we can substitute the values into the volume formula:

V = (1/3) * 3.14 * (5 inches)² * 24 inches

 = (1/3) * 3.14 * 25 square inches * 24 inches

 = (1/3) * 3.14 * 600 cubic inches

 ≈ 628.32 cubic inches

Therefore, the approximate volume of the traffic cone is 628.32 cubic inches.

Scientific Notation

The number 34.6 × 10^5 can indeed be expressed in scientific notation. Scientific notation represents a number as a product of a decimal number between 1 and 10 (known as the coefficient) and a power of 10 (known as the exponent).

To express 34.6 × 10^5 in scientific notation, we can rewrite it as:

3.46 × 10^6

In this form, the coefficient is 3.46, and the exponent is 6.

Learn more about distance here:

https://brainly.com/question/28551043

#SPJ1

The expected number of people between 165 and 175 is 41.

The expected number of people taller than 168 is 39.

Given that the mean and standard deviation of people's heights (measured in centimeters) are 170 and 5 respectively. The heights of 60 people are revealed.

μ = 170

σ = 5

n = 60

(a) The probability would you expect to be between 165 and 175 cm tall;

P( 165 < x < 175 ) = P( (165 - 170)/5 < z < (175 - 170)/5 )

                            = P( -1 < z < 1 )

                            = P( z < 1) - P( z < -1 )

                            = 0.8413 - 0.1587

                            = 0.6826

Expected number of people between 165 and 175 = n * p

                                                                                    = 60 * 0.6826

                                                                                    = 40.956

                                                                                    ≅ 41

(b) The probability would you expect to be taller than 167 cm;

P( x >  167 ) = P( z > (167 - 170)/5 )

                   = P( z > -0.6 )

                   = 0.7257

Expected number of people taller than 168 = n * p

                                                                        = 60 * 0.7257

                                                                        = 43.542

                                                                        ≅ 39

Hence,

The expected number of people between 165 and 175 is 41.

The expected number of people taller than 168 is 39.

To learn more about probability click here:

brainly.com/question/11234923

#SPJ4

The questions are illustrations of inequalities

The inequality is given as:

x² - 18x < -77

Add 77 to both sides

x² - 18x + 77 < 0

Expand the inequality

x² - 7x - 11x + 77 < 0

Factorize the inequality

x(x - 7) - 11(x - 7) < 0

Factor out x - 7

(x- 7)(x - 11) < 0

Solve for x

x < 7 or x < 11

This means that the solution to the inequality is 7 < x < 11

The inequality expression is given as:

y ≤ x² + 2

See attachment for the graph of the inequality

The function is given as:

f(x) = |x| + 5

The smallest value of |x| is 0.

So, we have:

f(x) > 0 + 5

Evaluate

f(x) > 5

Hence, the range of the function is (c) R: {f(x) ∈ ℝ | f(x) > 5}

The inequality expression is given as:

|2x + 3| < 7

Remove the absolute expression

2x + 3 < 7 or 2x + 3 < -7

Subtract 3 from both sides

2x < 4 or 2x < -10

Divide both sides by 2

x < 2 or x < -5

Hence, the solution to the inequality is x < –5 or x > 2

Read more about inequality at:

https://brainly.com/question/11234618

#SPJ1

For this case we have the following variables:

x: represents time, in seconds at the start of the test.

y: represents the speed, in miles per hour.

We have then that:

x = 0 ---> y = 0

x = 12 ---> y = 0

Answer:

the electric car is not moving at 0 seconds and 12 seconds

I hope this helps!

the electric car is not moving at 0 seconds and 12 seconds

I hope this helps!

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

To learn more about parabola click :

https://brainly.com/question/24042022

#SPJ1

Answer:

everything except -1 will be the answer

Step-by-step explanation:

4n + 13 < 9

n < -1

if n is -1, the answer would be 9(INCORRECT)

if n is -2, the answer would be 5(CORRECT)

if n is -3, the answer would be 1(CORRECT)

if n is -4, the answer would be -3(CORRECT)

Answer:

D

Step-by-step explanation:

The circle has center (-3, 2) and radius 5. The line is a vertical line passing through the point (-8, 0).

We can see from the graph that the line does not intersect the circle at any point. Therefore, the correct answer is:

D. The line does not pass through the circle.

Answer:

x=5

Step-by-step explanation:

     May I have brainiest I'm trying to level up!

                 </3 PureBeauty

Answer:

x=5

Step-by-step explanation:

6x-3 = 3x +12

+3            +3

6x = 3x +15

-3x   -3x

3x = 15

divided both sides by 3 to get your answer

Step-by-step explanation:

-9x+15=3(2-x)

6-6x

2. collect like terms

-9x+15= 6-6x

15-6 = 6x+9x

11= 15x

3. divide both sides by the coefficient of X which is 15

x= 11/15

The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

We have,

Two functions:

f(x) = b^x

g(x) = log_b(x)

Now,

From the table,

f(0.699) = b^0.699 = 5

Taking the logarithm of both sides with base b.

log_b(5) = 0.699

b = 5^(1/0.699)

b = 8.343

Now, we can find the value of f(1.477).

f(1.477) = b^1.477 = 8.343^1.477 = 32.857

Similarly, we can find the value of g(20).

g(20) = log_b(20) = log_8.343(20) = 1.729

Thus,

The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

Answer:

b = -18

Step-by-step explanation:

to find be you need to isolate the variable. First, you have to multiply both sides by 13 to cancel the denominator. Then, add 8 to both sides to cancel the negative 8 on the left. You should be left with what x equals.

-8+b/13(13) = -2(13)

-8+b = -26

+8       +8

b = -18

Answer:

b = -18

Step-by-step explanation:

First multiply 13 on both sides which will give you

-8 + b = -26

Then add 8 to both sides and will give the answer

b = -18

The equation representing the given transformations is y = 3sin(x - 10°) + 3.

To create an equation in the form y = asin(x - d) + c given the transformations, we can start with the standard sine function and apply the given transformations step by step:

Vertical translation 1 unit up:

The standard sine function has a maximum value of 1 and a minimum value of -1.

To vertically translate it 1 unit up, we add 1 to the function.

This gives us a maximum value of 1 + 1 = 2 and a minimum value of -1 + 1 = 0.

Horizontal translation 10 degrees to the right:

The standard sine function completes one full period (i.e., goes from 0 to 2π) in 360 degrees.

To shift it 10 degrees to the right, we subtract 10 degrees from the angle inside the sine function.

This accounts for the horizontal translation.

Adjusting the amplitude:

To achieve a maximum value of 8, we need to adjust the amplitude of the function.

The amplitude represents the vertical stretch or compression of the graph.

In this case, the amplitude needs to be 8/2 = 4 since the original sine function has an amplitude of 1.

Putting it all together, the equation for the given transformations is:

y = 4sin(x - 10°) + 2

This equation represents a sine function that has been vertically translated 1 unit up, horizontally translated 10 degrees to the right, and has a maximum value of 8 and a minimum value of 2.

For similar question on standard sine function.

https://brainly.com/question/16300816  

#SPJ8

The hands of a 12-hour clock will coincide 22 times from 9 am today until 9 am tomorrow.

In a 12-hour clock, the hands coincide when the minute hand and the hour hand are on the same hour marks. For example, when the minute hand and hour hand coincide at 12 o'clock, the next time they will coincide is at 1 o'clock.

The minute hand moves 12 times faster than the hour hand, so for every hour that passes, the minute hand travels 12 hour marks. In a 12-hour clock, the minute hand will travel 360 degrees and the hour hand will travel 30 degrees in one hour. The minute hand travels 12 times faster than the hour hand. We can calculate the number of coincidences between the minute hand and hour hand over 24 hours as follows:

For each hour, the hour hand moves 30 degrees and the minute hand moves 360 degrees.

Therefore, the difference in degrees between the minute hand and hour hand is 330 degrees.Therefore, the hands of a 12-hour clock will coincide 22 times from 9 am today until 9 am tomorrow.

Know more about Clock here:

https://brainly.com/question/12528769

#SPJ11

Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

Given,

In the question:

A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.

To find the how many possible 3-course meals are there?

Now, According to the question:

Let's know:

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with  ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N=n_1\) × \(n_2\) × \(n_3\)... ×\(n_n\)

In this problem, considering the number of salads, main courses and desserts, we have that:

\(n_1=4 , n_2=5,n_3=3\)

The total number of options is given by:

N = 4 × 5 × 3

N = 60

Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.

Learn more about Fundamental Counting Theorem at:

https://brainly.com/question/28384306

#SPJ4

Therefore, the only claim that the interval would tend to refute is option E: The population mean is less than 125.

Based on the 90% confidence interval of 135 to 160, we can conclude that the population mean is likely to be within this interval with a 90% degree of confidence.

A. The claim that the population mean is more than 110 is not refuted by the confidence interval since the lower limit of the interval is above 110.

B. The claim that the population mean is less than 150 is not refuted by the confidence interval since the upper limit of the interval is above 150.

C. The claim that the population mean is between 140 and 150 is not refuted by the confidence interval since both values are within the interval.

D. The claim that the population mean is more than 140 is not refuted by the confidence interval since the lower limit of the interval is above 140.

E. The claim that the population mean is less than 125 is refuted by the confidence interval since the lower limit of the interval is above 125.

To know more about confidence interval,

https://brainly.com/question/27375978

#SPJ11

Answer:

4a=76°

2a=38°

X=104°

Step-by-step explanation:

the sum of angles triangle are 180°

so,

66°+4a+2a= 180°

or, 66°+6a=180°

or,6a= 180°-66°

or, a= 114°÷6

or, a= 19°

then, angle B = 4a= 4xa= 4x19°= 76°

angle C = 2x19°= 38°

lastly,

4a+x=180°[being straight angle]

76°+x=180°

x= 180°-76°

x= 104°.