find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.

The length of the suspension line from the harness to the edge of the open chute is approximately 10.97 ft.

To find the length of the suspension line, we can use the Pythagorean theorem. The distance from the parachute to the center of the diameter is the radius of the parachute, which is half the diameter. Therefore, the radius is 15 ft / 2 = 7.5 ft. The suspension line is the hypotenuse of a right triangle with one leg being the radius and the other leg being the distance from the parachute to the edge of the open chute. Using the Pythagorean theorem, we can calculate the length of the suspension line as follows:

https://brainly.com/question/30506629

#SPJ12

Answer:

domain:   (-∞, ∞) ; range: [-5, 0]

Step-by-step explanation:

Let's begin with the basics:

The domain of cos x is (-∞, ∞); the range is [-1, 1].

The domain of cos²x is still (-∞, ∞).

Likewise, the domain of -5 cos²x is(-∞, ∞).

The range of cos²x differs: it is [0, 1] because squaring a negative number results in a positive output.

Multiplying cos²x by 5 expands the range to [0, 5].

Finally, multiplying 5 cos²x by -1 changes the range to [-5, 0].

Answer:

C

Step-by-step explanation:

Cuz edge

Answer:

A

Step-by-step explanation:

The formula for the Perimeter of a rectangle is P = 2W + 2L.

Let's equate this to 60 units and substitute 11 for W and 24 units for L:

2(11 units) + 2(24 units) = 22 units + 48 units = 70 units.  NO (Answer A)

Answer:

[tex]7\frac{1}{2}\ plates[/tex]

Step-by-step explanation:

we know that

The recipe calls for 2/3 cups of cheese for each plate of nachos

so

using proportion

Find out how many plates can she make with five cups of cheese

let

x ----> the number of plates

[tex]\frac{1}{(2/3)}\frac{plate}{cups} =\frac{x}{5} \frac{plates}{cups}\\ \\x=5/(2/3)\\ \\x=7.5\ plates[/tex]

Convert to mixed number

[tex]7.5=\frac{14}{2}+\frac{1}{2}=7\frac{1}{2}\ plates[/tex]

She can make 7.5plates with 5 cups of cheese

According to the question, we are told that the recipe calls for 2/3 cups of cheese for each plate of nachos. This is expressed as:

2/3 cups of cheese = 1 plate of nachos

In order to calculate the number of plates she can make with  five cups of cheese

5 cups  = x

Cross multiply

2/3x = 5

2x = 15

x = 7.5 plates

Hence she can make 7.5plates with 5 cups of cheese

learn more on ratios and proportions here: https://brainly.com/question/2328454

If a random student has a 33% probability of belonging to a minority, then there is a 67% chance that they do not. In a sample of 10 students, the probability that exactly 4 do not belong to a minority is

[tex]\dbinom{10}40.67^4(1-0.67)^{10-4}\approx0.0547[/tex]

Answer:

Is it a decimal?

Step-by-step explanation:

Answer:

Final answer is [tex]\frac{21x-7}{3x^2-2}[/tex]

Step-by-step explanation:

We have been given two terms [tex]\frac{21x}{3x^2-2}[/tex]

and [tex]\frac{7}{3x^2-2}[/tex]

Now we need to find their difference. So let's subtract them

[tex]\frac{21x}{3x^2-2}-\frac{7}{3x^2-2}[/tex]

Denominators are equal so we can easily subtract numerators

[tex]=\frac{21x-7}{3x^2-2}[/tex]

We may factor the numerator but we won't get any factor in denominator that can be cancelled with numerator.

Hence final answer is [tex]\frac{21x-7}{3x^2-2}[/tex]

Answer:

72

Step-by-step explanation:

The two acute angles add up to 90 degrees. That's because the given triangle is a right triangle.

So x + 4x + 90 = 180           All triangles = 180°. Combine left side terms.

5x + 90 = 180                      Subtract 90°

5x + 90 - 90 = 180 - 90      Combine

5x = 90                                Divide by 5

5x/5 = 90/5                         Combine

x = 18

The larger angle is 4x so

The larger angle = 4*18 = 72

Answer:

Both

Step-by-step explanation:

The total number of options that will be are 6. The representation made by both Elroy and Rose is correct.

The total number of options available is the product of a total number of options available in different sectors.

Given that number of colors is 3 while the number of formats is two. Therefore, the total number of options that are available will be 6 which is the product of the two.

As we can see that both have pointed out each of the six options, therefore, the representation made by both Elroy and Rose is correct.

Learn more about Number of options:

https://brainly.com/question/11185799

Answer:

Step-by-step explanation:

The angle you can get right away is z.

z + 93 = 180

z + 93 - 93 = 180 - 93

z = 87

===============

The next step is to solve for y. You need to draw a line from  y to the center and another one from z to the center.

The triangle containing part of y and part of z has a central angle of 106 degrees.

Part of y + partz + 106 = 180

part of y + partz = 74

part of y = partz = 37                The triangle is isosceles because 2 of the legs are radii.

Do the same thing from 93 to the center and the other part of y to the center.

The central angle is 58

The two other angles are equal

part of y + part of 93 + 58 = 180

partofy + partof93 = 180 - 58

partofy + partof93 = 122

partofy = part93 = 61

So

y = 61 + 37 = 98

========================

x + y = 180 (opposite angles in a quadrillateral that fits in a circle = 180)

x + 98 = 180

x = 82

====================

x = 82

y = 98

z = 87

Answer:

A

Step-by-step explanation:

There are calculators online that you can use to answer this, some even show you the work step by step

Answer:3/4

Step-by-step explanation: Since he read 1/4 on Monday and 2/4 on Tuesday that would add up to 3/4

I believe it’s B. hope it’s right!

Answer:

y = 1/2

Step-by-step explanation:

If two variables x and y vary inversely, then:

xy = k

where k is the constant variation.

In this case:

xy = 6

When x = 12:

12y = 6

y = 1/2

The value of y when x is 12 is 2 (option C)

Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases. Example is the price of a commodity and the quantity acquired, the higher the price, the lower of commodity bought and vice- versa.

here, we have,

Inverse relationship between two quantities x and y is expressed as:

x= ky

where k is the constant

k = 6

when x = 12

12 = 6y

divide both sides by 6

y = 12/6

y = 2

therefore the value of y when x is 12 is 2

learn more about inverse variation from

brainly.com/question/13998680

#SPJ3

Answer:

[tex]y=-2x-1[/tex]

Step-by-step explanation:

Let the first coordinate point be (x_1,y_1) and the second coordinate point be (x_2,y_2)

So

x_1 = -2

y_1 = 3

x_2 = -4

y_2 = 7

Now we can use the formula for equation of line to figure it our.

Equation of line formula is  [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Plugging in the known values and arranging in slope-intercept form, we have:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-3=\frac{7-3}{-4-(-2)}(x-(-2))\\y-3=\frac{4}{-2}(x+2)\\y-3=-2(x+2)\\y-3=-2x-4\\y=-2x-4+3\\y=-2x-1[/tex]

This is the equation of the line passing through the points ( -2, 3) and ( -4, 7)

Final answer:

To find the equation of the line, the slope is calculated as -2, using the point-slope form with one of the points yields y - 3 = -2(x + 2). Simplifying this, the equation of the line is y = -2x - 1.

Explanation:

To find the equation of a line passing through two points, first, determine the slope (m) of the line. The slope is calculated as the change in y (vertical) divided by the change in x (horizontal). For the points (-2, 3) and (-4, 7), the slope is:

m = (y2 - y1) / (x2 - x1) = (7 - 3) / (-4 + 2) = 4 / (-2) = -2.

Next, use the point-slope form:

y - y1 = m(x - x1),

where (x1, y1) is a point the line passes through. Using point (-2, 3) and the slope -2:

y - 3 = -2(x + 2).

Rewrite this equation in slope-intercept form (y = mx + b) by simplifying and solving for y:

y = -2x - 4 + 3,

y = -2x - 1.

Therefore, the equation of the line passing through the points ( -2, 3) and ( -4, 7) is y = -2x - 1.

Answer:

B

Step-by-step explanation:

First

Get totals for food items:

Pizza $14.95 ×2=$29.90

Salad=$4.35

Drinks $2.49 ×4=$9.76

Total Bill

$29.90

$ 4.35

+$ 9.76

$44.21 Food Bill

Second Step

Find Tip Amount Before Tax

Total Bill $44.21 × .15=$6.63 Tip

Third Step

Find Tax on Total Food Bill

$44.21 × .07675=$3.39

Fourth Step

Find amount left from paying bill with tax.

Total Bill including tax:

$44.21 (bill) +$3.39 tax=$47.60

Cash $ 50.00

Total Bill - $47.60

$ 2.40 Change left over

Fifth Step

Find amount needed to give $6.63 tip from above.

We have $2.40 we need $6.63

Subtract $6.33 -$2.40=$4.23 more money needed for tip

The correct option is B. $ 4.23. Mr. Wright needs an additional $4.23 to leave a 15% tip.

First, we need to calculate the total cost of the meal before tax and tip. The Wright family ordered two pizzas at $14.95 each, a salad at $4.35, and four drinks at $2.49 each. So, the cost of the pizzas is [tex]2 \times $14.95[/tex], the salad is $4.35, and the drinks are 4 \times $2.49.

Cost of pizzas: [tex]2 \times $14.95 = $29.90[/tex]

Cost of salad: $4.35

Cost of drinks: [tex]4 \times $2.49 = $9.96[/tex]

Total cost before tax: [tex]\$29.90 +\$\4.35 + \$\9.96 = \$\44.[/tex]21

Next, we calculate the sales tax, which is 7.675% of the total cost before tax.

Sales tax: [tex]\$\44.21 \times 7.675% = \$\44.21 \times 0.07675 = \$\3.39[/tex]

Now, we add the sales tax to the total cost before tax to get the total cost including tax.

Total cost with tax: [tex]\$\44.21 + \$\3.39 = \$\47.60[/tex]

Mr. Wright wants to leave a 15% tip on the total bill before tax. So, we calculate 15% of the total cost before tax.

Tip: [tex]\$\44.21 \times 15% = \$\44.21 \times \$\0.15 \times \$\ 6.63[/tex]

Mr. Wright paid with a $50 bill, so we subtract the total cost with tax from $50 to find out how much change he should receive.

Change from [tex]\$50: $50 - $47.60 = $2.40\[/tex]

To find out how much more money Mr. Wright needs to leave a 15% tip, we subtract the change he receives from the tip amount.

Additional money needed: [tex]\$6.63 - $2.40 = $4.23\[/tex]

Therefore, Mr. Wright needs an additional $4.23 to leave a 15% tip.

Answer:

Option B.

Step-by-step explanation:

If a quadratic equation is defined as

[tex]ax^2+bx+c=0[/tex]         .... (1)

then the quadratic formula is

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

The given equation is

[tex]10x^2=6+9x[/tex]

It can rewritten as

[tex]10x^2-9x-6=0[/tex]            .... (2)

On comparing (1) and (2) we get

[tex]a=10,b=-9,c=-6[/tex]

Using quadratic formula we get

[tex]x=\dfrac{-(-9)\pm \sqrt{(-9)^2-4(10)(-6)}}{2(10)}[/tex]

[tex]x=\dfrac{9\pm \sqrt{81+240}}{20}[/tex]

[tex]x=\dfrac{9\pm \sqrt{321}}{20}[/tex]

Therefore, the correct option is B.

Answer:

B

Step-by-step explanation:

I got it right

Answer:

49.999999999999974312306505198184 V

Step-by-step explanation:

Step 1: you see 45°, which gives you a easy conversion [tex]\frac \pi 4[/tex]).

Now, [tex]t = 392.7 \mu s = 392.7* 10^{-6} s[/tex], start replacing.

[tex]V= 50 cos ( 2* 10^3 * 392.7 *10^{-6} -\frac \pi 4) = 50 cos (0.7854 - \frac \pi 4) =\\ 49.999999999999974312306505198184 V[/tex]

BC also has length 12 because arcs DC and CE add up to 117 degrees in measure, so that arc DE is congruent to arc BC, and the chords DE and BC that respectively intercept these arcs must also be congruent.

Answer:

Length = 13

x = 80

Step-by-step explanation:

Question One

Let the width = x

Let the length = x + 5

Area = 104

Equation

Area = L * W

Area = (x+5)*x

Solution

x ( x + 5) = 104                  Remove the brackets

x^2 + 5x = 104                  Subtract 104 from both sides.

x^2 + 5x - 104 = 104 - 104

x^2 + 5x - 104 =  0            Factor the equation    

(x + 13)(x - 8) = 0

Only x - 8 = 0 works

x = 8

The width = 8

The Length = 8 + 5 = 13

Question Two

Draw AP

<BAP = 20o                     The triangle (APB) is isosceles: 2 sides are radii

<BPA = 180 - 20 - 20      The three angles of a triangle = 180

<BPA = 140                      Combine

Similarly <CAP = 140       Go through exactly the same steps.

<BPA + <CAP + X = 360  The total of the 3 angles in the center = 360

140 + 140 + X = 360         Combine

280 + X = 360                 Subtract 280 from both sides.

x = 80

The answer in the first quadrant is

(2,3)

Answer:

The median price of a new home

Step-by-step explanation:

Answer:

T= 2.35 seconds

Step-by-step explanation:

⇒The question is on the time of flight.

⇒Time of flight is the time taken for a projected object to reach the ground.It depends on the projectile angle and the initial velocity of the projectile

Given;

Initial velocity of ball= 110ft./sec.

The projectile angle= 20°

Acceleration due to gravity, g=32 ft./s²

⇒Formulae for time of fright T= (2×u×sin Ф)/g

Where T=time of fright, u=initial velocity of projectile, Ф=projectile angle and g=acceleration due o gravity.

Substituting values

T= (2×u×sin Ф)/g

T=( 2×110×sin 20°) / 32

T= 2.35 seconds

Answer:

Option B - Time taken for the ball to hit the ground is 2.47 seconds.

Step-by-step explanation:

Given :  A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees above the ground from a height of 4.5 ft.

To find : How long does it take for the ball to hit the ground?

Solution :

According to question,

The equation that models the height of the ball in feet as a function of time is

[tex]h(t) = h_0 + v_0t -16t^2[/tex]

Where, [tex]h_0[/tex] is the initial height,

[tex]v_0[/tex] is the initial velocity and

t is the time in seconds.

We have given,

Initial height, [tex]h_0=4.5 ft.[/tex]

A ball is thrown with a slingshot at a velocity of 110 ft./sec. at an angle 20 degrees.

The initial speed, [tex]v_0=110\times \sin(206\circ)[/tex]

[tex]v_0=37.62ft/s[/tex]

We have to find the time for the ball to hit the ground i.e. h(t)=0

Substitute all the values in the formula,

[tex]0 =4.5+ 37.62t -16t^2[/tex]

Applying quadratic formula to solve the equation,

The solution of quadratic general equation [tex]ax^2+bc+c=0[/tex] is

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Where, a=-16 , b=37.62 , c=4.5

Substituting in the formula,

[tex]t=\frac{-37.62\±\sqrt{(37.62)^2 -4(-16)(4.5)}}{2(-16)}[/tex]

[tex]t=\frac{-37.62\±\sqrt{1703.2644}}{-32}[/tex]

[tex]t=\frac{-37.62\±41.270}{-32}[/tex]

[tex]t=\frac{-37.62+41.270}{-32},\frac{-37.62-41.270}{-32}[/tex]

[tex]t=-0.114,2.47[/tex]

neglecting the negative value

t=2.47 seconds

Therefore,Option B is correct.

Time taken for the ball to hit the ground is 2.47 seconds.

Answer:

D) π/2 and 3π/2

Step-by-step explanation:

The equation can be factored:

(1 -sin(x))(1 +sin(x)) = 0

The factors will be zero when ...

sin(x) = 1 ⇒ x = π/2

sin(x) = -1 ⇒ x = 3π/2

Answer:

Step-by-step explanation:

Notice that the greatest number of dots is over the '70,' indicating that 70% of the students in the town enjoy playing video games.

This problem has to do as much with your ability to interpret graphs as to apply statistics concepts correctly.

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~AB}{\cfrac{4}{3}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{3}{4}}\qquad \stackrel{negative~reciprocal}{-\cfrac{3}{4}}}\impliedby \textit{slope of QA} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf A(\stackrel{x_1}{6}~,~\stackrel{y_1}{-5})\qquad Q(\stackrel{x_2}{2}~,~\stackrel{y_2}{y}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-(-5)}{2-6}=\stackrel{\textit{QA's slope}}{-\cfrac{3}{4}}\implies \cfrac{y+5}{-4}=\cfrac{-3}{4} \\\\\\ 4y+20=12\implies 4y=-8\implies y=\cfrac{-8}{4}\implies \boxed{y=-2}[/tex]

Add 8 to both sides of the equation.

You need to get x by itself. The only way to do that here is to do the opposite of subtracting 8, which is adding 8.

Also, when you do something to one side of the equation, you have to also do it to the other side to keep the equation equal.

Answer: Add 8 to both sides of the equation

Step-by-step explanation:

d - 8 = 9

in this equation you need to solve for d. To do that you have to get d by itself.

By adding 8 to both sides of the equation you cancel out the -8 and add 8 to 9 which solves for d.

Answer:

[tex]\$14.18[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$10\\ r=0.035\\n=12[/tex]  

substitute in the formula above  

[tex]A=P(1+\frac{0.035}{12})^{12*10}=\$14.18[/tex]  

Answer:

The measure of angle theta is [tex]\theta=2.25\ radians[/tex]

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=20\ ft[/tex]

substitute

[tex]C=2\pi (20)[/tex]

[tex]C=40\pi\ ft[/tex]

step 2

Find the measure of angle theta

we know that

The circumference of a circle subtends a central angle of [tex]2\pi\ radians[/tex]

so

using proportion

Find out the measure of the central angle by a length of arc equal to 45 ft

[tex]\frac{40\pi}{2\pi}=\frac{45}{\theta}\\ \\\theta=2*45/40\\ \\ \theta=2.25\ radians[/tex]

Answer: 2.25 radians

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The line passes through the points (-3,-7) and (9,1).

The slope of the line can be calculted using formula

[tex]\dfrac{y_2-y_1}{x_2-x_1}.[/tex]

Thus, the slope of the given line is

[tex]\dfrac{1-(-7)}{9-(-3)}=\dfrac{8}{12}=\dfrac{2}{3}.[/tex]

Answer:

A

Step-by-step explanation:

slope is given by the formula:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We need 2 points to find a line's slope.

Plugging these into the slope formula, we will get the slope:

[tex]\frac{1--7}{9--3}\\=\frac{1+7}{9+3}\\=\frac{8}{12}\\=\frac{2}{3}[/tex]

correct answer is A