4(cos⁶A-sin6A) = cos³2A+3cos2A​

Answer:

vertex = (- 2, - 4 )

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

y = (x + 2)² - 4 ← is in vertex form

with (h, k ) = (- 2, - 4 ) ← vertex

Answer:

Each person gets 1 pie

Step-by-step explanation:

Becasue if there are 4 pies and 4 people than since the amount of pies and people are equal it cancels out, meaning there are no pies left to be eaten and no people left that dont  have a pie to eat    

Option B. $9,255.75, Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of

To find the present value of an infinite stream of cash flows, we can use the formula:

PV = CF / r

where PV is the present value, CF is the cash flow per period, and r is the interest rate per period.

In this case, CF = $100 (received at the end of each year forever) and r = 10%.

Plugging in the numbers, we get:

PV = $100 / 0.10 = $1,000

So the present value of the infinite stream of cash flows is $1,000.

However, we need to adjust for the fact that the cash flows are received at the end of each year, not at the beginning. To do this, we can use the formula:

PV = CF / (r - g)

where g is the growth rate of the cash flows, which in this case is 0 (since the cash flows are constant).

Plugging in the numbers, we get:

PV = $100 / (0.10 - 0) = $1,000

So the present value of the infinite stream of cash flows received at the end of each year is also $1,000.

Therefore, the answer must include the present value of an infinite stream of cash flows. Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of cash flows.

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Answer:

Step-by-step explanation:

\(a = b \times h \\ \\ a = 9 \: \: {yd}^{2} \\ b = 6 \: \: yd \\ \\ 9 = 6 \times h \\ h = \frac{9}{6} \\ h = 1.5 \: \: yd\)

I hope that is useful for you :)

Answer:

  90 inches

Step-by-step explanation:

The perimeter of the inscribed triangle is 1/2 that of the enclosing triangle. So, the total of perimeters is ...

  (3·16 in)(1 +1/2 +1/4 +1/8) = (48 in)(15/8) = 90 inches

Answer:

See below.

Step-by-step explanation:

They invested in a ratio of Julie:Kristen of 5:12.

5 + 12 = 17

Julie invested 5/17 of the amount, and Kristen invested 12/17 of the mount.

a.

Julie: 5/17 * $51,000 = $15,000

Kristen: 12/17 * $51,000 = $36,000

b.

Kristen owns 12/17 of the business.

As a percent, 12/17 = 12/17 * 100% = 70.6%

c.

The percent of the business each owns does not change with the amount the company is worth.

Kristen owns 70.6%, so Julie owns 100% - 70.6% = 29.4%

per fluid ounce  is 20 cents

the series is convergent or divergent. [infinity] k = 1 k2 k2 − 2k 9 convergent divergent if it is convergent, find its sum. (if the quantity diverges, enter diverges.) is convergent.

To determine whether the series is convergent or divergent, we can use the limit comparison test. We can compare the given series with the p-series 1/k^2, which is a known convergent series.

Using the limit comparison test, we have:

lim (k→∞) (k^2/(k^2-2k+9))/(1/k^2) = lim (k→∞) k^4/(k^2-2k+9)

Using L'Hopital's rule, we can evaluate the limit as:

lim (k→∞) 4k^3/(2k-2) = ∞

Since the limit is greater than zero, we can conclude that the given series converges if and only if the p-series 1/k^2 converges. Since the p-series converges, the given series also converges.

The series is convergent. However, we are not asked to find the sum of the series in this question.

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Answer:

1) \(4\frac{1}{2}\)

2)\(5\frac{3}{35}\)

Step-by-step explanation:

The rate of change of the demand is -16.538 per month.

Given that:

A price p (in dollars) and demand x for a product are related by:

2x² + 3xp + 50p² = 28000

Substitute p = 20.

2x² + 60x + 50(20²) = 28000

2x² + 60x - 8000 = 0

2(x² + 30x - 4000) = 0

x² + 30x - 4000 = 0

This can be factorized as:

(x + 80)(x - 50) = 0

So, x = -80 or x = 50

Negative demand is not possible.

So, x = 50.

Consider :

2x² + 3xp + 50p² = 28000

Differentiate this with respect to time.

4x (dx/dt) + 3x(dp/dt) + 3p(dx/dt) + 100p(dp/dt) = 0

(dp/dt)(3x + 100p) + (dx/dt)(4x + 3p) = 0

Substitute p = 20, x = 50, and dp/dt = 2.

2(150 + 2000) + (dx/dt)(200 + 60) = 0

260 (dx/dt) = -4300

dx/dt = -16.538

Hence the demand is decreasing at a rate of -16.538 per month.

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Answer:

E) 150°

Step-by-step explanation:

angle adjacent to 70° angle is 110°

the angle supplemental to 'x' must be 180-(40+110) or 30°

this means 'x' must be 150°

Answer:

7/15

Step-by-step explanation:

First, we have to make the bottom part the same:

2/3 - 1/5 = 10/15 - 3/15

10 - 3 = 7 = 7/15

Answer:

y = x - 1 (third answer choice)

Step-by-step explanation:

From the given we see immediately that the slope of this line is -1.  The slope of a line perpendicular to this one is +1, which is the negative reciprocal of -1.  The slope-intercept form is y = mx + b.  To find b, the y-intercept, we make the following substitutions:  m = -1, y = -2, x = -2:

-2 = +1(-2) + b, or +1 = 2 + b, or b = -1

and so the desired equation is y = x - 1 (third answer choice)

Answer:

We can simplify the expression as follows:

- First, we can simplify inside the parenthesis: 12 - 3 + 6x = 9 + 6x.

- Next, we can substitute this simplified expression back into the original expression:

-1/3(9 + 6x) = -3 - 2x, distributing the -1/3 through.

Therefore, -1/3(12-3+6x) is equivalent to -3-2x.

The plan that is most useful for demonstrating a new technology or service or to reach a market that is widely spread out is a proof-of-concept website

The statement about the market section of the classic business plan that is not true is that some people prefer to relocate the competition and competitive advantage section from the market section to the industry section.

A critical risk to the success of your business plan is Overlooked competition.

The pitch deck categories that is sometimes given in the form of a user's experience is Problem slide.

There are two goals you can seek in the "ask" of your elevator pitch. One is to build your network and the other is to get the listener to Make a micro-commitment

A good marketing strategy is most likely to focus on the longer-term competitive plan.

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To find the volume of a solid obtained by rotating a region bounded by curves around an axis, we can use the disk or washer method.

Suppose we want to find the volume of a solid obtained by rotating the region bounded by the curves y = f(x), y = g(x), and the lines x = a and x = b around the x-axis.

We can divide the region into vertical slices of width Δx, and rotate each slice around the x-axis to obtain a disk or washer. The volume of each disk or washer can be approximated as the area of the base times the thickness, or π(R² - r²) Δx, where R and r are the outer and inner radii of the disk or washer, respectively.

To find the exact volume, we take the limit as Δx approaches zero and sum up the volumes of all the disks or washers using integration:

V = ∫[a, b] π(R² - r²) dx

where R = f(x) and r = g(x).

Alternatively, if we want to rotate the region around the y-axis, we can divide the region into horizontal slices of width Δy, and rotate each slice around the y-axis to obtain a disk or washer. The volume of each disk or washer can be approximated as π(R² - r²)Δy, where R and r are the outer and inner radii of the disk or washer, respectively.

The exact volume can be found using integration as:

V = ∫[c ,d] π(R² - r²) dy

where R = f(y) and r = g(y), and c and d are the y-coordinates of the endpoints of the region.

In either case, it is important to sketch the region and identify the appropriate radii before setting up the integral.

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Answer:

there is no graphs to go of sorry

Step-by-step explanation:

For the given coordinates the area of the triangle will be 248.5 square units.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,triangle TABLE has vertices M(-7,-1) A(5,6) L(2,-3)

x₁,y₁=(-7,-1)

x₂,y₂=(5,6)

x₃,y₃=(2,-3)

We must utilize the triangle's vertices to calculate the area of the triangle in order to obtain the equation,

S=1/2[-7(6-(-3)+5(-3-(-1)+2(-1-(6)]

S=248.5

Thus, for the given coordinates the area of the triangle will be 248.5 square units.

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Based on the given table, the profit-maximizing level of output for company Econislife is 4 units. At this quantity, the company's profit is $40.

To determine the profit-maximizing level of output, we need to analyze the relationship between total revenue (TR) and total costs (TC) for different quantities of output. The profit can be calculated as the difference between total revenue and total costs.

Looking at the table, we can see that as the quantity increases from 1 to 5, both total revenue and total costs increase. However, at a certain point, the increase in total costs outpaces the increase in total revenue, leading to a decrease in profit.

To find the profit-maximizing level of output, we compare the profits at different quantities.

Quantity 1: TR = $28, TC = $40, Profit = TR - TC = $28 - $40 = -$12

Quantity 2: TR = $56, TC = $45, Profit = TR - TC = $56 - $45 = $11

Quantity 3: TR = $84, TC = $55, Profit = TR - TC = $84 - $55 = $29

Quantity 4: TR = $112, TC = $72, Profit = TR - TC = $112 - $72 = $40

Quantity 5: TR = $140, TC = $120, Profit = TR - TC = $140 - $120 = $20

From the above calculations, it is evident that the profit is highest at Quantity 4. Therefore, the profit-maximizing level of output for company Econislife is 4 units. At this quantity, the company's profit is $40.

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1) Considering this data set, we need to rewrite them orderly:

4,7,8,10, 11, 14, 16, 19

2) Note that there are 8 data points. So the Median can be found this way:

Therefore, the measures of VP, VQ, and VR are: 5 units, 7 units and 12 units.

A triangle is a two-dimensional geometric shape that is formed by connecting three non-collinear points with straight line segments. The points are called the vertices of the triangle, and the line segments that connect them are called the sides of the triangle. Triangles are one of the most basic shapes in geometry, and they have many interesting properties and applications in mathematics, science, and engineering. Some common types of triangles include equilateral triangles (where all three sides have the same length), isosceles triangles (where two sides have the same length), and scalene triangles (where no two sides have the same length).

Here,

To solve this problem, we can use the following properties of the centroid of a triangle:

The centroid of a triangle divides each median into two segments, one that is twice as long as the other.

The centroid is located two-thirds of the way from each vertex to the midpoint of the opposite side.

Let's label some additional points on the figure:

Let M be the midpoint of SR.

Let N be the midpoint of PQ.

Let W be the intersection of PT and SR.

Using property 1 above, we know that VW is twice as long as VU. Therefore, VW = 2 * VU = 16.

Using property 2 above, we know that VN = 2 * VQ and VM = 2 * VP. Since N is the midpoint of PQ, we have PQ = 2 * PN = 2 * VN / 3. Similarly, SR = 2 * SM = 2 * VM / 3.

Therefore:

PQ = 2 * VN / 3 = 2 * 3 * VP / 2 = 3 * VP

SR = 2 * VM / 3 = 2 * 3 * VQ / 2 = 3 * VQ

Now we can set up a system of equations to solve for VP, VQ, and VR:

VP + VQ + VR = V

PQ = 3 * VP

SR = 3 * VQ

VW = 16

PW + WQ = 15

We can substitute the second and third equations into the first equation to get:

4 * VP + 4 * VQ + VR = V

Using the fact that VW = 16, we can write:

PW = PT - TW = PT - VW/2 = 15 - 8 = 7

WQ = SR - SW = SR - VW/2 = 21 - 8 = 13

Substituting these values into the last equation, we get:

3 * VP + 3 * VQ = 8 + 2 * PW + 2 * WQ = 8 + 2 * 7 + 2 * 13 = 48

Now we can substitute this equation into the equation we derived earlier and solve for VR:

4 * VP + 4 * VQ + VR = V

4 * VP + 4 * VQ + (V - VP - VQ) = V

3 * VP + 3 * VQ = V

VR = V - 3 * VP - 3 * VQ

VR = V - 3/4 * (3 * VP + 3 * VQ)

VR = V - 9/4 * VP - 9/4 * VQ

VR = V - 9/4 * (8 * VP + 8 * VQ) / 4

VR = V - 18

Finally, we can substitute VP = PQ / 3 and VQ = SR / 3 into the equation above to get:

VR = V - 18

VR = VP + VQ

VR = PQ/3 + SR/3

VR = 15/3 + 21/3

VR = 12

Therefore, the measures of VP, VQ, and VR are:

VP = PQ / 3 = 15 / 3 = 5

VQ = SR / 3 = 21 / 3 = 7

VR = 12

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1) To factor a polynomial by grouping, let's take 2 examples and do it step by step

2) Consider this quadratic equation, let's factor x² + 7x +12 by grouping

x² +7x +12 =0 Which two numbers whose sum is 7 and whose product is 12

S =___ + ___ = 7 4 + 3

P = ___x ___ = 12 4x 3

Then we can rewrite 7x as 4x +3x

x² +4x +3x +12 = 0 Let's group these terms into two parentheses:

(x² +4x) +(3x +12)

Now let's write them as factors, the GCD outside the parentheses x, 4x and 3, 12

x(x +4) +3(x +4)

Since we have a repetition of the factor (x +4) we can write it as a product

(x+4) (x+3) = x² +7x +12

Another example:

x³ -2x² +5x -10 Group them into two parentheses

(x³-2x²) +(5x -10) Factor out the GCD x³, 2x² =x² and 5, 10 =5

x²(x-2) +5(x-2) Now let's write them as a factor, (x -2x) is common to both

(x²+5) (x -2)

(x²+5) (x -2) = x³ -2x² +5x -10

3) So, in words.

1. Rewrite the polynomial into two parentheses grouping the terms

2. Factor out the GCD of the terms, leaving it outside the parentheses

3. Rewrite it as a product writing the outside factors into parentheses and the common term.

1. cos(y) = (3/4) / sin(x) = (3/4) / √(2/3) = √(3)/2

2.  the solution is:x = arccos(√(1/3)), y = arcsin(√(3)/12).

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

To solve this system of trigonometric equations, we can use a technique called "substitution." First, we isolate one of the variables in terms of the other in one of the equations, and then substitute it into the other equation. Here's how:

1. Solving for y in terms of x:

Let's start with the first equation: sin(x)*cos(y) = 3/4. Dividing both sides by cos(y), we get:

sin(x) = (3/4) / cos

Using the trigonometric identity sin²(x) + cos²(x) = 1, we can rewrite this as:

cos²(y) * sin²(x) + cos²(y) * cos²(x) = cos²

Dividing by cos²(y), we get:

sin²(x) + cos²(x) = 4/3

Using the trigonometric identity sin²(x) + cos²(x) = 1 again, we can rewrite this as:

1 - cos²(x) + cos²(x) = 4/3

Solving for cos(x), we get:

cos(x) = ±√(1/3)

Since 0 ≤ x,y ≤ π/2, we know that cos(x) and cos(y) are both positive. So, we take the positive solution for cos(x):

cos(x) = √(1/3)

Using the trigonometric identity sin²(x) + cos²(x) = 1, we can find sin(x):

sin(x) = ±√(2/3)

Since 0 ≤ x,y ≤ π/2, we know that sin(x) and sin(y) are both positive. So, we take the positive solution for sin(x):

sin(x) = √(2/3)

Using the first equation, we can find cos(y):

cos(y) = (3/4) / sin(x) = (3/4) / √(2/3) = √(3)/2

2. Substituting into the second equation:

Now we can substitute the values of cos(y) and sin(x) into the second equation:

sin(y) * cos(x) = 1/4

sin(y) * √(1/3) = 1/4

sin(y) = (1/4) / √(1/3) = √(3)/12

So, the solution is:

x = arccos(√(1/3)), y = arcsin(√(3)/12)

Note: There are two possible solutions for each angle, since the sine and cosine functions are periodic. In this case, we take the positive solutions for both trigonometric functions, since we know that x and y are in the first quadrant (0 ≤ x,y ≤ π/2).

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Answer:

85

Percentage Calculator: 357 is what percent of 420? = 85.

Answer:

85%

Step-by-step explanation:

357/420 reduces to 17/20 if you divide the numerator and denominator by 21 which is equivalent to .85

Answer:

Out of the 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 total students, 4 + 3 = 7 are freshmen so the answer is 7 / 30 * 100 = 23%.

Step-by-step explanation:

Assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

The current in the secondary coil is dependent on the voltage ratio of the primary and secondary coils. If the voltage ratio of the coils is the same as the turns ratio, then the current in the secondary coil will be identical to that in the primary coil. Therefore, assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

The current in the secondary coil is determined by the voltage ratio of the primary and secondary coils. The voltage ratio is equal to the turns ratio, which is the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. In an ideal transformer with 100% efficiency, the power output in the secondary coil will be equal to the power input in the primary coil. Since power is equal to voltage multiplied by current, and the voltage ratio is equal to the turns ratio, the current in the secondary coil will be the same as the current in the primary coil.

Therefore, assuming 100% efficiency, the current in the secondary coil will be the same as the current in the primary coil.

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