if i = 10 sin α, what is i at α = 30°

Answer:

20

Step-by-step explanation: you have to find the amount of change then determine the percent of increase and round it to the nearest percent

       32 -56=24     then round to the nearest number you get 20

Answer:

please mark brainiest thank you

1, 5^5!9

2. 20.

3. 6.

4. 16r/25

Answer:

$10

Step-by-step explanation:

The hardcover books are $12 each which would be $60 out of the $100. There are four more paperbacks meaning they would be $10 each and cost $40 total.

I hope this helped!!! :)

The price of hardcover book is $12.Identity equations and conditional equations are the two types of equations. All possible values of the variables result in an identity.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. An equation is created by joining two expressions with the equals sign ("=").

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this article, let's learn more about math equations.

Given ,

We suggest a set of equations for this situation:

Let a be the variable for the price of hardback books.

B: Make the variable for the price of paperback books.

The statement information we have indicates:

\(5a+4b=100\)

\(b=a-b\)

Adding the second equation to the first one results in:

\(5a+4(a-2)= 100\\5a+4 a- 8= 100\\9a =100+8\\9 a=108\\a=108/9\\a=12\)

Consequently, hardcover books are $12.

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The integrate is W = 12 ∫[0 to 1] (1 + 3t)^(3/2) dt + 27 ∫[0 to 1] (1 + 2t) √(1 + 3t) dt.

To find the work done by the force field F in moving an object from point A to point B, we can use the line integral of the force field along the path connecting A and B. The line integral is given by the formula:

W = ∫[C] F · dr

where C represents the curve connecting points A and B, F is the force field, dr is the differential displacement vector along the curve, and · denotes the dot product.

First, let's calculate the differential displacement vector dr. Since we are moving from point A(1, 1) to point B(3, 4), the differential displacement vector dr can be expressed as:

dr = dx i + dy j

Now, let's determine the curve C connecting A and B. The curve can be parametrized as follows:

x(t) = 1 + 2t

y(t) = 1 + 3t

where t varies from 0 to 1.

Differentiating these parametric equations, we obtain:

dx = 2 dt

dy = 3 dt

Substituting these values into the differential displacement vector dr, we have:

dr = 2 dt i + 3 dt j

Next, let's calculate the force field F at each point along the curve C. Given that F(x, y) = 6y^(3/2) i + 9x √y j, we can substitute the parametric equations for x and y into F:

F = 6(1 + 3t)^(3/2) i + 9(1 + 2t) √(1 + 3t) j

Now, let's evaluate the line integral by substituting the values of F and dr into the integral expression:

W = ∫[0 to 1] (6(1 + 3t)^(3/2) i + 9(1 + 2t) √(1 + 3t) j) · (2 dt i + 3 dt j)

Expanding the dot product, we have:

W = ∫[0 to 1] (12(1 + 3t)^(3/2) dt + 27(1 + 2t) √(1 + 3t) dt)

Now, we can simplify and integrate each term separately:

W = 12 ∫[0 to 1] (1 + 3t)^(3/2) dt + 27 ∫[0 to 1] (1 + 2t) √(1 + 3t) dt

To evaluate these integrals, we can use appropriate substitution or integration techniques. After integrating both terms, we will have the value of the work done by the force field F in moving the object from A to B along the curve C.

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a) The future value of the ordinary annuity is $19,144.99.

b) The future value of the ordinary annuity is $48,956.03.

c) The present value of the ordinary annuity is $13,384.15.

d) Robin will have $488,215.78 in the account after 30 years.

a) To find the future value of the ordinary annuity for the first scenario, we use the formula:

FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)

Where:

FV = Future Value

P = Payment per period

r = Annual interest rate

n = Number of compounding periods per year

t = Number of years

Plugging in the given values: P = $1100, r = 0.08 (8%/year), n = 2 (semiannual compounding), t = 9 years, we calculate FV = $19,144.99.

b) For the second scenario, we use the same formula:

FV = P * [(1 + r/n)^(n*t) - 1] / (r/n)

Plugging in the given values: P = $110, r = 0.13 (13%/year), n = 12 (monthly compounding), t = 17 years, we calculate FV = $48,956.03.

c) To find the present value of the ordinary annuity, we use the formula:

PV = P * [1 - (1 + r/n)^(-n*t)] / (r/n)

Plugging in the given values: P = $3400, r = 0.12 (12%/year), n = 2 (semiannual compounding), t = 7 years, we calculate PV = $13,384.15.

d) For the final scenario, to find the future value of Robin's Keogh account, we can use the compound interest formula:

FV = P * (1 + r)^t

Plugging in the given values: P = $4500, r = 0.085 (8.5%/year), t = 30 years, we calculate FV = $488,215.78.

Therefore, after 30 years, Robin will have approximately $488,215.78 in his Keogh account.

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The cost of the shirt, in dollars, after the 30% discount is $17.50.

What is discount?

A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. Discounts can be offered for a variety of reasons, such as to attract customers, increase sales, or clear out inventory. Discounts can be expressed as a percentage or a fixed amount, and they can be applied at the time of purchase or deducted from an invoice or bill. Discounts are often used in sales promotions, marketing campaigns, and loyalty programs to incentivize customers to buy or use a product or service.

If a store is offering a 30% discount on shirts that cost $25 originally, then the discount amount is:

30% of $25 = 0.30 x $25 = $7.50

The discount amount is $7.50, so the new price of the shirt after the discount is:

$25 - $7.50 = $17.50

Therefore, the cost of the shirt, in dollars, after the 30% discount is $17.50.

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If the decision variables for a problem have to be integers, rounding the linear programming optimal solution for that problem will always result in a feasible solution.

However, this solution may not always be optimal. It may result in either a feasible or infeasible solution depending on the problem constraints.

Rounding may also result in an optimal solution if the optimal solution happens to already have integer values for the decision variables. Therefore, rounding may result in a feasible and optimal solution or just a feasible solution but not necessarily always optimal.

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This can be calculated by dividing the initial reserves of 300 million tonsThe year when the cumulative extraction reaches or exceeds 300 million tons will be the time when the mineral reserves are exhausted.

a) If the extraction of minerals is kept constant at 50 million tons per year, the reserves will be exhausted in 6 years. This can be calculated by dividing the initial reserves of 300 million tons by the annual extraction rate of 50 million tons.

b) If the extraction of minerals declines by 15 percent each year due to increasing extraction costs, we need to determine how long the mineral reserves will last.

To do this, we can calculate the cumulative extraction each year until it reaches or exceeds the initial reserves of 300 million tons. Assuming the extraction declines by 15 percent each year, we can calculate the extraction in each subsequent year and add it to the cumulative extraction from previous years. The year when the cumulative extraction reaches or exceeds 300 million tons will be the time when the mineral reserves are exhausted.

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Answer:

D is the correct answer.

ZY + YX = ZX

Answer:

66, 114, 114

Step-by-step explanation:

angle 3=angle 1=66

angle 2=angle 4=180- angle 3=114

Answer:

the answer is 12

Step-by-step explanation:

The n 1/2 of the se 1/4 of the sw 1/4 and the ne 1/4 of the sw 1/4 of Section 19 contains 40 acres.

The method used for land surveying is called the government rectangular survey system.

This system is commonly known as the Public Land Survey System (PLSS) of the United States. It is based on a grid network. The grid is formed with meridians and baselines.

The meridians are the imaginary lines running north to south, and the baselines are the imaginary lines running east to west. The meridians and baselines are named as ranges and townships, respectively.

Each range is 6 miles wide and numbered consecutively, beginning with the one on the far west side of the state. The townships are numbered from 1 to 36, in sequence, beginning at the southeast corner of the state. The government rectangular survey system divides the land into smaller units as follows:

Each township is further divided into 36 sections, each section is one square mile, or 640 acres.

Each section is further divided into halves, or 320 acres, and each half is divided into quarters, or 160 acres, and each quarter is divided into quarters again, or 40 acres.

Finally, each 40-acre parcel is divided into quarters, or 10 acres.

Therefore, the n 1/2 of the se 1/4 of the sw 1/4 and the ne 1/4 of the sw 1/4 of section 19 contains 40 acres.

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Answer:

30.

Step-by-step explanation:

first term = a

3r term = ar^2

So here ar^2/ a  = r^2

r^2 = 5/180 = 1/36

r = 1/6

So missing term = 180 * 1/6 = 30.

Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

The equations of the tangents are:y = -3/2 + sqrt(37)/2(x - 10) (smaller slope)y = -3/2 - sqrt(37)/2(x - 10) (larger slope):y=-\frac{3}{2}+\frac{\sqrt{37}}{2}(x-10) (smaller slope)y=-\frac{3}{2}-\frac{\sqrt{37}}{2}(x-10) (larger slope).

Curve isx = 6t^2 + 4, y = 4t^3 + 4the slope of tangent of this curve dy/dx is dy/dx=12t/(3t^2+2)Then, equation of tangent with slope m and passing through (x1, y1) is given by(y - y1) = m(x - x1) ............(1)Here, point is (10,8)Therefore, equation of tangent passing through (10, 8) will be of the form(y - 8) = m(x - 10)Let this tangent intersect the curve at point P. Then, the coordinates of point P are given byx = 6t^2 + 4y = 4t^3 + 4.

Equating this with equation (1), we get:4t^3 + 4 - 8 = m(6t^2 - 6)4t^3 = 6m(t^2 - 1)2t^3 = 3m(t^2 - 1)2t^3 + 3mt - 3m = 0t = -m/2 ± sqrt(m^2/4 + 3m)Therefore, the two tangents are given by:y - 8 = m1(x - 10), where m1 = -3/2 + sqrt(37)/2y - 8 = m2(x - 10), where m2 = -3/2 - sqrt(37)/2Hence, the equations of the tangents are:y = -3/2 + sqrt(37)/2(x - 10) (smaller slope)y = -3/2 - sqrt(37)/2(x - 10) (larger slope):y=-\frac{3}{2}+\frac{\sqrt{37}}{2}(x-10) (smaller slope)y=-\frac{3}{2}-\frac{\sqrt{37}}{2}(x-10) (larger slope).

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Answer:5.0

Step-by-step explanation:

The radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

To find the radius of the silo, we need to determine the radius of the cylindrical section.

The volume of the cylindrical section can be calculated using the formula:

\(V_{cylinder} = \pi * r^2 * h\)

where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.

Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:

\(V_{cylinder} = \pi * r^2 * 30\)

To find the radius, we can rearrange the formula:

\(r^2 = V_{cylinder} / (\pi * 30)\)

Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:

\(r^2 = 10,000 / (\pi * 30)\)

Simplifying further:

\(r^2 = 106.103\)

Taking the square root of both sides, we find:

\(r = \sqrt{106.103} = 10.3\)

Therefore, the radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

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Answer:

1/3

Step-by-step explanation:

1/2 * 2/3 = 2/6 = 1/3

Answer:

no

Step-by-step explanation:

Answer:

3 times greater

Step-by-step explanation:

To find out how many times greater the population of Chicago is than Austin, we can divide the population of Chicago by the population of Austin:

Population of Chicago / Population of Austin = 2,720,546 / 900,000

Simplifying the expression by dividing both the numerator and denominator by 100,000, we get:

Population of Chicago / Population of Austin = 27.20546 / 9

Dividing these numbers, we get:

Population of Chicago / Population of Austin = 3.022838

Therefore, the population of Chicago is about 3 times greater than the population of Austin.

The measure of the side 'x' is 16.31 m. The correct option is C.

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is a fundamental part of geometry that has many practical applications in fields such as physics, engineering, navigation, and surveying.

Given that in a right-angled triangle, the value of side RS is x, angle R is 25° and the side RT is 18 m.

The value of x will be calculated as,

sin65° = x / 18

x = 18 x sin65°

x = 16.31 m

Hence, the correct option is C.

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The original fraction is -5. Note that this is a negative fraction, which may not be meaningful in certain contexts.

Let's call the original fraction "x".

From the first condition, we have:

x + 4 / x's denominator = 3/4

From the second condition, we have:

x / (x's denominator + 2) = 1/2

We can substitute x's denominator in the first equation with (x's denominator + 2) from the second equation:

x + 4 / (x's denominator + 2) = 3/4

Next, we can cross-multiply and solve for x:

4x + 16 = 3x's denominator + 6

x's denominator = 4x + 10

Substituting back into the second equation:

x / (4x + 10) = 1/2

Multiplying both sides by (4x + 10) to isolate x:

2x = 4x + 10

Solving for x:

-2x = 10

x = -5

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The height of the cylindrical water tank should be approximately 8.04 meters to hold 2000L of water with a radius of 500 cm.

The formula to calculate the volume of a cylinder is:

V = π\(r^2h\)

where V is the volume, r is the radius, and h is the height.

We know that the manufacturer plans to make a cylindrical water tank that can hold 2000L of water. We also know that the radius of the tank is 500 cm.

First, we need to convert the volume from liters to cubic centimeters (\(cm^3\)) because the units of radius and height are in centimeters:

2000L = 2,000,000\(cm^3\)

Substituting these values into the formula, we get:

2,000,000 = π\((500)^2\)h

Solving for h, we get:

h = 2,000,000 / (π\((500)^2\))

h ≈ 8.04 cm

Therefore, the height of the cylindrical water tank should be approximately 8.04 meters to hold 2000L of water with a radius of 500 cm.

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y = -3

to get to 20 characters

let me tell you the complicated progress

y = -3 as you can see

(or)

y = ax + b

-3 = -2a + b

-3 = 3a + b

a = 0

b = -3

So y = 0x - 3

y = -3

Answer: 3

Step-by-step explanation: 12/1 × 1/4

Answer:

15u + 141 = 420

Step-by-step explanation:

So basically we are modelling how much the coach is spending. Each player is given a uniform and a basketball

We can use 'u' as the cost of a single uniform

We can use 'b' as the cost of a single basketball

Since there is 15 players we must give a ball and uniform to each so

15u + 15b = 420

The problem gives us the cost of each basketball: 9.40

so now 15u + 15(9.4) = 420

15u + 141 = 420

Answer:

20 hours

Step-by-step explanation:

Mathematically we know that;

time = distance/ speed

distance = 239,000 miles

Time = 200 miles per minute

time = 239,000/200 = 1195 minutes

Let us convert this to hours by dividing by 60 (since 60 minutes equal an hour

So we have 1195/60 = 19.91

This is approximately 20 hours

Answer:

D

Step-by-step explanation:

20 hours

Statement 1:  2AB = AC

Reason 1: Given

--------------------------------------------

Statement 2:  AC = AB+BC

Reason 2: Segment addition postulate (which your teacher abbreviated to "Seg + Post")

--------------------------------------------

Statement 3: 2AB = AB+BC

Reason 3: Substitution

--------------------------------------------

Statement 4:  2AB-AB = AB+BC-AB

Reason 4: Subtraction Property of Equality

---------------------------------------------

Statement 5: AB = BC

Reason 5: Combine like terms

----------------------------------------------

Notes:

The two adjacent angle according to the given question are angle 1 (60 degree)  and angle 5 ( 30 degree)

what is adjacent angle?

In geometry, an adjacent angle refers to an angle that shares a common vertex and a common side with another angle. The word "adjacent" means "next to" or "near to." Therefore, two angles are adjacent if they are next to each other and share a side. When two adjacent angles are added together, they form a larger angle known as a linear pair. Adjacent angles are important in many areas of geometry, including trigonometry, where they are used to calculate the values of trigonometric functions such as sine, cosine, and tangent. In real-life applications, adjacent angles can be found in various geometric shapes, such as triangles, rectangles, and polygons, and are used to determine the measurements and properties of these shapes.

Adjacent angles are important in geometry and are used to calculate the values of trigonometric functions such as sine, cosine, and tangent.

Therefore, The two adjacent angle according to the given question are angle 1 (60 degree)  and angle 5 ( 30 degree)

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Answer:

the first choice

Step-by-step explanation:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.

then it means if the events are independent then the probability is multiplying the probability of each event.

The two plants would have the same height in 7 weeks and the height would be 31 inches.

The form of the expression that represents the length of the plant on the window sill is:

initial length + (length of growth per week x number of weeks)

3 + (4 x w)

3 + 4w

The form of the expression that represents the length of the plant on the coffee table is:

initial length + (length of growth per week x number of weeks)

17 + (2 x w)

17 + 2w

When the two plants have the same height, the two expressions would be equal:

17 + 2w = 3 + 4w

17 - 3 = 4w - 2w

14 = 2w

w = 14/2

w = 7 weeks

Height of the plant = 3 + 4(7)

3 + 28 = 31 inches

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