Question 1 Post Math

Step-by-step explanation:

x = a cos t, y = b sin t

cos t = x / a, sin t = y / b

cos² t + sin² t = 1

(x / a)² + (y / b)² = 1

If a = b, the conic section is a circle.

If a and b are different, the conic section is an ellipse.

D.All interior angles are 90 degrees

Let's analyze each choice to determine which one is the exception, that is, a property that is not shared between a square and a rhombus:
A. Opposite pairs of sides are parallel:
This is true for both a square and a rhombus. By definition, both a square and a rhombus have opposite sides that are parallel.
B. Opposite pairs of sides are congruent:
This property also holds true for both squares and rhombi. In a square, all four sides are equal in length. In a rhombus, opposite sides are equal in length.
C. Pairs of interior and exterior angles are supplementary:
Again, this is a common feature of both squares and rhombuses. In any parallelogram (which includes both squares and rhombuses), each pair of interior and exterior angles on the same side are supplementary, totaling 180 degrees.
D. All interior angles are 90 degrees:
This is where we can find the exception. In a square, all four interior angles are indeed 90 degrees. However, this is not the case for a rhombus. A rhombus does not necessarily have right angles; its angles can be of any measure as long as opposite angles are equal and the sum of the angles is 360 degrees, which is true for any quadrilateral.
Therefore, the correct answer to the question is:
D. All interior angles are 90 degrees
This is the property that is not common between a square and a rhombus, making it the exception.

For this problem, you need to know how to use sin, cos, and tan or 'SOH-CAH-TOA' sin- opposite/hypotenuse cos-adjacent/hypotenuse toa- opposite/adjacent

in this case, you can use tan or toa

the equation should be set up like this:

4/x=1/0.848

solve, and you will get 3.39...

(you need to use the sin,cos,tan degree chart to find 0.848)

Answer:

The sum of the first 499 terms is 249001

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

 between each two consecutive terms n is the position of the

 number

- The sum of first n terms of an Arithmetic sequence is calculate from

 Sn = n/2[a + l], where a is the first term and l is the last term

* Now lets solve the problem

∵ The terms of the sequence are 1 , 3 , 5 , 7 , ......... , 997

∵ The first term is 1 and the second term is 3

∴ The common difference d = 3 - 1 = 2

∵ The first term is 1

∵ The last term is 997

∵ The common difference is 2

- Lets find how many terms in the sequence

∵ an = a + (n - 1) d

∴ 997 = 1 + (n - 1) 2 ⇒ subtract 1 from both sides

∴ 996 = (n - 1) 2 ⇒ divide both sides by 2

∴ 498 = n - 1 ⇒ add 1 for both sides

∴ n = 499

∴ The sequence has 499 terms

- Lets find the sum of the first 499 terms  

∵ Sn = n/2[a + l]

∵ n = 499 , a = 1 , l = 997

∴ S499 = 499/2[1 + 997] = 499/2 × 998 = 249001

* The sum of the first 499 terms is 249001

Final answer:

The sum of the series 1+3+5+7+...+997 is calculated using Gauss's approach for arithmetic series, resulting in a sum of 249500.

Explanation:

To find the sum of the series 1+3+5+7+...+997 using Gauss's approach, we first recognize that this is an arithmetic series where each term increases by a constant difference, in this case, 2. The first term, a, is 1 and the last term, l, is 997. We can find the number of terms, n, in the series using the formula: n = (l - a) / common difference + 1, which in this case is (997 - 1) / 2 + 1 = 499. Then, the sum of an arithmetic series can be found using the formula: Sum = n/2 * (a + l), so the sum of this series is 499/2 * (1 + 997) = 249500.

Answer:

The appropriate compound inequality is then 14 ft ≤ W ≤ 16 ft

Step-by-step explanation:

30 ft perimeter:  P = 30 ft = 2L + 2W = 2(8 ft) + 2W

Solving for W, we get:  30 ft - 16 ft = 14 ft.  The minimum width, W, is 14 ft.

32 ft perimeter:  

P = 32 ft = 2L + 2W = 2(8 ft) + 2W

Solving for W, we get:  32 ft - 16 ft = 16 ft.  The minimum width, W, is 16 ft.

The appropriate compound inequality is then 14 ft ≤ W ≤ 16 ft

Answer:

Range of width = [7,8]

Step-by-step explanation:

Let w be the width of garden,

The length of garden, l = 8 feet

We have perimeter = 2 x ( length + width)

Perimeter = 2 x ( 8 + w)

The perimeter of the garden must be at least 30 feet and no more than 32 feet.

That is

             30 ≤ 2 x ( 8 + w) ≤ 32

             15 ≤ 8 + w ≤ 16

              7 ≤ w ≤ 8

So range of width = [7,8]

Answer:

  8

Step-by-step explanation:

The minus sign outside parentheses changes the sign of what's inside parentheses when parentheses are eliminated:

  7 -(-1) = 7 +1 = 8

_____

Alternate way to think about it

Subtraction is the same as addition of the opposite. The opposite of -1 is +1, so subtracting -1 is the same as adding +1.

Answer:

    0.3643

Step-by-step explanation:

3.643×10^-1 = 3.643×(1/10) = 3.643×0.1 = 0.3643

Answer:

Step-by-step explanation:

This is a third degree polynomial because we are given three roots to multiply together to get it.  Even though we only see "2 + i" the conjugate rule tells us that 2 - i MUST also be a root.  Thus, the 3 roots are x = -4, x = 2 + i, x = 2 - i.

Setting those up as factors looks like this (keep in mind that the standard form for the imaginary unit in factor form is ALWAYS "x -"):

If x = -4, then the factor is (x + 4)

If x = 2 + i, then the factor is (x - (2 + i)) which simplifies to (x - 2 - i)

If x = 2 - i, then the factor is (x - (2 - i)) which simplifies to (x - 2 + i)

Now we can FOIL all three of those together, starting with the 2 imaginary factors first (it's just easier that way!):

(x - 2 - i)(x - 2 + i) = [tex]x^2-2x+ix-2x+4-2i-ix+2i-i^2[/tex]

Combining like terms and canceling out the things that cancel out leaves us with:

[tex]x^2-4x+4-i^2[/tex]

Remembr that [tex]i^2=-1[/tex], so we can rewrite that as

[tex]x^2-4x+4-(-1)[/tex] and

[tex]x^2-4x+4+1=x^2-4x+5[/tex]

That's the product of the 2 imaginary factors.  Now we need to FOIL in the real factor:

[tex](x+4)(x^2-4x+5)[/tex]

That product is

[tex]x^3-4x^2+5x+4x^2-16x+20[/tex]

which simplifies down to

[tex]x^3-11x+20[/tex]

And there you go!

Answer:

True

Step-by-step explanation:

The circumcenter is the center of the circumscribing circle, the circle that intersects each of the vertices. Since the points on a circle are equidistant from its center, the vertices of a triangle are equidistant from the circumcenter.

Final answer:

The circumcenter of a triangle is the point that is equidistant from the vertices of the triangle.

Explanation:

True

The circumcenter of a triangle is the point that is equidistant from the vertices of the triangle. This means that the distance from the circumcenter to each vertex of the triangle is the same.

For example, in an equilateral triangle, the circumcenter is the point where all the perpendicular bisectors of the sides intersect.

Check the picture below.

[tex]\bf (\stackrel{x}{1},\stackrel{y}{8})\qquad y=2x^3\implies 8=2(1)^3\implies 8\ne 2~~\bigotimes \\\\\\ (\stackrel{x}{-1},\stackrel{y}{-2})\qquad y=2x^3\implies -2=2(-1)^3\implies -2=-2~~\checkmark \\\\\\ (\stackrel{x}{0},\stackrel{y}{0})\qquad y=2x^3\implies 0=2(0)^3\implies 0=0~~\checkmark \\\\\\ (\stackrel{x}{2},\stackrel{y}{16})\qquad y=2x^3\implies 16=2(2)^3\implies 16=16~~\checkmark[/tex]

Answer:

  800,000,000

Step-by-step explanation:

Subtract the known numbers from the sum to find the missing number:

  800,903,402 - 900,000 -2 -3,000 -400 = 800,000,000

In the equation F=kx, F is the force, k is the spring constant, and x is the displacement.  Plug in and solve:

F=0.3(1.5)

F=0.45N

Hope this helps!!

Answer:

the answer is the 3 one I'm 90% sure

The volume and the surface area of the hemisphere in terms of π are 3888π in³ and 972π in² respectively.

The volume of a hemisphere can be found using the formula given below:

Volume = (2/3)πr^3

The surface area of a hemisphere can be found using the formula given below:

Surface Area = 3πr^2

The figure is provided. From the figure, we can see that the radius of the hemisphere is 18 inches.

The volume of the hemisphere can be found as shown below:

Volume = (2/3)π*18*18*18 in³

= 3888π in³

The surface area of a hemisphere can be found as shown below:

Surface Area = 3π*18*18 in²

= 972π in²

We have found the volume and the surface area of the hemisphere. The volume and the surface area of the hemisphere are 3888π in³ and 972π in² respectively.

Therefore, we have found that the volume and the surface area of the hemisphere in terms of π are 3888π in³ and 972π in² respectively. The correct answer is option B.

Learn more about hemispheres here: https://brainly.com/question/333717

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$50 per day x 6 days = 300

20% = 0.2, times t = 0.2t

The equation would be: f(t) = 300 + 0.2t

Answer:

Option D:[tex]f(t)=300+0.2 t[/tex]

Step-by-step explanation:

We are given that Mikayla is a waitress

She makes a guaranteed per day =$50

Her tips per day =20 % of weekly tips t

We have to find a function that represents the amount of money makes by Mikayla in one week

[tex]20% of t=\frac{20}{100}t=0.2t[/tex]

She works per week=6 days

She earns in 6 days=[tex]50\times 6[/tex]=$300

Total earning of Mikayla in one week =[tex]300+0.2t[/tex]

[tex]f(t)=300+0.2 t[/tex]

Hence, option D is true.

Answer:

none of the above

Step-by-step explanation:

All of the answer choices agree that the magnitude of the components is 150/√2 ≈ 106.1. The units of these components should be "mph", the same as the units of the magnitude of the given vector.

We only know the angle with respect to horizontal. We don't know whether that angle is measured with respect to the positive x-axis or the negative x-axis. Both of those are horizontal, and there is nothing in the problem statement that restricts the airplane to be traveling in one direction or the other.

Possible answers are ...

<106.1 mph, -106.1 mph> . . . . . . "horizontal" is +x direction

<-106.1 mph, -106.1 mph> . . . . . "horizontal" is -x direction

(The units are not degrees (°).)

since the diameter of the circle is 10, then its radius must be half that or 5.

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\pi \theta r}{180}~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=&5\\ \theta=&180 \end{cases}\implies s=\cfrac{\pi (180)(5)}{180}\implies s=5\pi \implies s\approx 15.71[/tex]

Answer:

The correct answer is 15.7 inches

Step-by-step explanation:

Points to remember

Circumference of a circle = 2πr

Where r is the radius of circle

To find the value of arc length

It is given that, diameter = 10 inches

Radius = diameter/2 = 10/2 = 5 inches

Circumference =  2πr

 = 2 * 3.14 * 5

 = 31.4

central angle of arc =180

Arc length = (180/360) * circumference

 = (1/2) * 31.4

 = 15.7 inches

Therefore the correct answer is 15.7 inches

x + y = 16

x = y^2 x 4

i hope this helps :)

good luck

Answer:

1

Step-by-step explanation:

-2(1) = -2

then -2 - 4 = -6

-6 = -6

Answer:

1

Step-by-step explanation:

Move all terms that don't contain x to the right side & solve.

I don’t know what answer Is I wish I could help

[tex]\bf (\stackrel{a}{2}~,~\stackrel{b}{-1})\qquad \begin{cases} r=\sqrt{a^2+b^2}\\\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ r=\sqrt{2^2+(-1)^2}\implies r=\sqrt{5} \\\\\\ \theta =tan^{-1}\left( \cfrac{-1}{2} \right)\implies \theta \approx -26.57^o\implies \theta \approx 333.43^o \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\sqrt{5}~~,~~333.43^o)~\hfill[/tex]

Answer:

[tex](r,\theta); (\sqrt{5} , tan^{-1}(\frac{x}{y}))\\(r,\theta); (-\sqrt{5} , -tan^{-1}(\frac{x}{y}))[/tex]

Step-by-step explanation:

Here we are given our rectangular coordinates as (2,-1) . We have to convert this into polar coordinates. The formula for conversion into polar form is

[tex]r=\sqrt{x^2+y^2}[/tex]

[tex]\theta=tan^{-1}(\frac{x}{y})[/tex]

Substituting the values of x and y in the above formulas we get

[tex]r=\sqrt{2^2+(-1)^2}\\r=\sqrt{4+1}\\r=\sqrt{5}\\r=-\sqrt{5}\\[/tex]

[tex]\theta=tan^{-1}(\frac{-1}{2})[/tex]

Hence our polar coordinates are

[tex]r=(\sqrt{5},tan^{-1}(\frac{-1}{2}) )\\r=(-\sqrt{5},tan^{-1}(\frac{-1}{2}) )\\[/tex]

D. Normal distributions are symmetric, so the mean is the same as the median.

Answer:

18

Step-by-step explanation:

Answer:

h=20

Step-by-step explanation:

h=3 (V/lw)

h= 3 (960/12*12)

Answer:

4.22 meters per second.

Step-by-step explanation:

First multiply the revs per second by pi:

= 11pi = 34.558.

Now multiply this by the diameter which is 2*6.1 = 12.2 cm = 0.122 m.

Linear velocity =  0.122 * 34.558

= 4.22 m/s.

Linear velocity of the gear in meters per second is  4.22 m/s.

Linear velocity is the measure of “the rate of change of displacement with respect to time when the object moves along a straight path.” It is a vector quantity.

Given

Gear of radius = 6.1 cm

Gear of diameter = [tex]2 \times 6.1 = 12.2 cm[/tex] = 0.122 m

Revolutions per second = [tex]11\pi[/tex] = 34.558

Linear velocity of the gear  =  diameter × Revolutions per second

Linear velocity = 0.122 × 34.558

= 4.22 m/s

Linear velocity of the gear in meters per second is  4.22 m/s.

Find out more information about linear velocity here

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Answer:

There are 288 cups left

Step-by-step explanation:

Take the amount that were there (395) and subtract the amount that were sold (177).  that is the amount that are left

395-177 = 218

There are 288 cups left

after selling 177 cups, there are 218 lemon ice cups still at the snack shop.

To calculate how many lemon ice cups are still at the snack shop after some were sold, we need to perform a simple subtraction operation. The initial quantity of lemon ice cups was 395. After selling 177 cups, we subtract 177 from 395 to find out how many are left.

Here's the calculation:

So, after selling 177 cups, there are 218 lemon ice cups still at the snack shop.

The answer should be 3840

Answer:

  (b)  3x -5

Step-by-step explanation:

You can slog through the entire long division process, or you can realize that the product of the quotient constant and the divisor constant must match the dividend constant. If we let q represent the quotient constant, you must have ...

  4q = -20

  q = -20/4 = -5

The only answer choice with a constant of -5 is choice B, 3x -5.

ANSWER

[tex]S_{26}=1300[/tex]

EXPLANATION

The sum of an arithmetic sequence whose first term and last terms are known is calculated using

[tex]S_{n}= \frac{n}{2} (a + l)[/tex]

From the given information, the first term of the series is

[tex]a = 7[/tex]

and the last term of the series is

[tex]l = 93[/tex]

The sum of the first 26 terms is

[tex]S_{26}= \frac{26}{2} (7 + 93)[/tex]

[tex]S_{26}= 13 (100)[/tex]

[tex]S_{26}=1300[/tex]

The sum of the first 26 terms of the given arithmetic series is 1300, obtained using the sum formula S = n/2 * (a1 + an) for arithmetic series.

To find the sum of the first 26 terms of an arithmetic series whose first term (a1) is 7 and the 26th term (a26) is 93, you can use the formula for the sum of an arithmetic series: S = n/2*(a1 + an). Here, n is the number of terms, a1 is the first term, and an is the nth term. In this case, we have n = 26, a1 = 7, and a26 = 93.

The sum, S, of the series is calculated as follows:
S = 26/2 * (7 + 93) = 13 * (100) = 1300.

Therefore, the sum of the first 26 terms of the arithmetic series is 1300.

Answer:

The inverse of f(x) is  [tex]f ^ {- 1}(x) = x + 2[/tex]

Step-by-step explanation:

To find the inverse of the function [tex]f (x) = x-2[/tex], perform the following steps:

1) do [tex]y = f (x)[/tex]

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

2) Solve the equation for the variable x.

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

[tex]y + 2 = x[/tex]

3) exchange the variable x with the variable y

[tex]y + 2 = x[/tex] ----> [tex]x + 2 = y[/tex]

4) Change the variable y by [tex]f ^{- 1}(x)[/tex]

Finally the inverse function is:

 [tex]f ^ {- 1} (x) = x + 2[/tex]

Answer:

f-1(x)=x+2

Step-by-step explanation:

Answer:

B. 25

Step-by-step explanation:

In order to find out the value of x + 2, you need to know what x is.  Let's solve for it then sub it back in to evaluate the expression.

3(x+2)=5(x-8) distributes out to give you

3x + 6 = 5x - 40.  Get like terms together on opposite sides of the equals sign:

46 = 2x and divide to get x = 23.  Now that we know that x = 23, that means that x + 2 is the same as 23 + 2 which is 25.