Knowing that sin 30° = 1/2, what is a?
30⁰
A. 8.66
OB. 2.5
C. 5
D. 10
5
60°

To write the equation in proper form, we can divide the entire equation by \(t^9\):

\[y^{(5)} - \frac{t^{-6}}{t^{-12}}y'' + 6t^{-9}y = 0\]

Simplifying further, we can multiply the equation by \(t^{12}\):

\[t^{12}y^{(5)} - t^3y'' + 6y = 0\]

Therefore, the given differential equation is:

\[t^{12}y^{(5)} - t^3y'' + 6y = 0\]

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If donna didn't stop, her average speed for the final 30 miles to 2 dp is; 57.39 mph

We are given;

Distance travelled by Donna = 70 miles

Average Speed of Donna = 40 mph

Additional Distance travelled = 30 miles

Average speed for entire journey = 44 mph

We know that;

time = distance/speed

Thus

Total time = (70 + 30)/44

Total time = 100/44 h

Time 1 = 70/40 = 7/4 hr

Time 2 = 30/v

Thus;

30/v + 7/4 = 100/44

Multiply through by 44 to get;

1320/v = 100 - 77

v = 1320/23

v = 57.39 mph

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The equation that best represents the depth of the pond each week is,

\(y=10(1.03)^{x}\)

A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation.

Given:

The given equation is,

\(y=P(1+r)^{x} \;\;\;\;\;-------equation(1)\)

Depth of the pond, P = 10 feet deep

Rate of pond increase, r = 3% = 0.03

Substitute the value of P and r in the equation (1),

\(y=10(1+0.03)^{x}\)

Therefore, The equation that best represents the depth of the pond each week is,

\(y=10(1.03)^{x}\)

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Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

Answer

x = 28

y = 32

Step-by-step explanation:

Non-vertical angles (top and bottom) are congruent

Thus

5x - 15 = 4x + 13

x = 28

and so each non-vertical is

5(28) -15 = 125

4(28) + 13 = 125

Diagonals bisect vertex angles (left and right) Thus we have one vertical angle as (y + y) = 2y

and another vertical angle as (y -9) + (y - 9) = 2y - 18

All the angles in a kite adds up to 360

So

125 + 125 + 2y + (2y - 18) = 360

250 + 4y - 18 = 360

4y = 128

y = 32

Answer:

draw it again

Step-by-step explanation:

draw it as it is you can use a mirror to look through while you are drawing good luck

Step-by-step explanation:

If

n

is a positive integer that is greater than

x

and

a

is a real number or a factor, then

a

x

n

=

n

√

a

x

.

a

x

n

=

n

√

a

x

Use the rule to convert

y

3

5

to a radical, where

a

=

,

x

=

, and

n

=

.

5

√

y

3

The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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Answer:

Please give me Brainliest :)

I think the answer is A.

Step-by-step explanation:

The smallest answer choices here are 1 and 2. One is decimal and the other is a fraction. To make our lives easier, let's turn both into decimals:

1. -4.5

2. 1/4 = 0.25

-4.25

This means that 1 is the smallest because, in negative numbers, the largest number is the least.

Answer:

D. 19.5 Ft.

Step-by-step explanation:

Formula: B · H = A

Substitution: 3.25 · 2 = 6.5

6.5 · 3 ( 3 Windows ) = 19.5 Ft.

No le quites puntos gratis a las personas que necesitan ayuda, gracias, Me hiciste eso a mi y a algunas atras personas y no es muy amable...

Bill before tax = $32

Tax = 10/100×32

= $3.2

Tip = 15/100×32

= $4.8

Total cost = 32 + 3.2 + 4.8

= $40

Answered by Gauthmath must click thanks and mark brainliest

Answer:

0.238

Step-by-step explanation:

1. On December 31, 2012, the consolidation worksheet journal entries for Matthews Co. are as follows

:Investment in Jackson account is debited for $55,000Patent account is credited for $18,000Common stock account is credited for $20,000Additional paid-in capital account is credited for $13,000The amount that is shown as the credit for the common stock account is $20,000, which is the result of multiplying the number of shares that Jackson has by the par value of the shares. Matthews Company records the difference between the purchase price and the book value as goodwill. The patent account is credited for $18,000, which is the result of multiplying the $60,000 book value of the patent by 30%.

2. On December 31, 2013, the consolidation worksheet journal entries for Matthews Co. are as follows

:Investment in Jackson account is debited for $48,000Goodwill account is credited for $10,000Retained earnings account is credited for $38,000Matthews Company records the difference between the purchase price and the book value as goodwill. Retained earnings are credited for the amount of Jackson Company's net income for the year.

3. The consolidation worksheet for December 31, 2013, is as follows

: ASSETSCash $45,000Accounts Receivable 60,000Inventory 110,000Equipment 240,000Investment in Jackson 672,000Total Assets $1,127,000LIABILITIESAccounts Payable $85,000Long-term debt 240,000Total Liabilities $325,000OWNERS' EQUITYMatthews Co. Common Stock $400,000Matthews Co. Additional Paid-In Capital 60,000Matthews Co. Retained Earnings 267,000Jackson Co. Common Stock 100,000Jackson Co. Additional Paid-In Capital 300,000Jackson Co. Retained Earnings 75,000Total Owners' Equity $1,202,000Total Liabilities and Owners' Equity $1,527,000

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Answer:

The answer is 20.

Step-by-step explanation:

4(d) - c

4(7) - c

28 - c

28 - 8

20 is the answer.

I hope this helps, have a nice day.

Answer:

Exact Form:

7 /4

Decimal Form:

1.75

Mixed Number Form:

1  3 /4

Step-by-step explanation:

:)

The radius of the circle tangent to sides AC and BC and to the circumcircle of triangle ABC.

r= 24.

Generally, the equation for side lengths AB is  mathematically given as

Triangle ABC has side lengths

Where

Hence

r √ 2 · (89 √ 2/2 − r √ 2) = r(89 − 2r),

r = 89 − 65

r= 24.

In conclusion, The radius of the circle tangent to sides AC and BC and to the circumcircle of triangle ABC.

r= 24.

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The value of x is 11.

It states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points.

From given figure,  \(A=3x+9,B=8x-4\)

                \(\angle B=2\angle A\\\\8x-4=2(3x+9)\\\\8x-4=6x+18\\\\8x-6x=18+4\\\\2x=22\\\\x=22/2=11\)

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A certain plane is described by 2x+3y+4z=16. Find the unit vector normal to the surface in the direction away from the origin.Firstly, we will obtain the coefficients of the x, y and z variables from the equation of the plane:2x + 3y + 4z = 16The coefficients are 2, 3, and 4 respectively.

Now, we will calculate the magnitude of the normal vector, ||N||, using the formula:||N|| = √(a² + b² + c²)where a, b, and c are the coefficients of the x, y, and z variables respectively.||N|| = √(2² + 3² + 4²)= √(4 + 9 + 16)= √29Therefore, the unit normal vector in the direction away from the origin is given by:N = (2/√29) i + (3/√29) j + (4/√29) k. Given the equation of a plane as 2x + 3y + 4z = 16, we have to find the unit vector normal to the surface in the direction away from the origin. Here's how we can do it:To find the unit vector normal to the surface, we first need to find the coefficients of the x, y, and z variables from the equation of the plane. In this case, the coefficients are 2, 3, and 4 respectively.Next, we can use the formula ||N|| = √(a² + b² + c²) to calculate the magnitude of the normal vector, where a, b, and c are the coefficients of the x, y, and z variables respectively. In this case, ||N|| = √(2² + 3² + 4²) = √29.Finally, we can find the unit normal vector in the direction away from the origin by dividing each coefficient by the magnitude of the normal vector, ||N||. Thus, the unit normal vector is:N = (2/√29) i + (3/√29) j + (4/√29) k

Therefore, the unit vector normal to the surface in the direction away from the origin is (2/√29) i + (3/√29) j + (4/√29) k.

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Answer:all real numbers

Step-by-step explanation:

To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350

Solving for W, we get:

W = 350 - 2L

Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:

L = x + y + z

Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:

Area = Length x Width

Therefore, the total area of the fenced-in region is:

Area = (xW) + (yW) + (zW)

Substituting W = 350 - 2L and L = x + y + z, we get:

Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))

Simplifying this equation, we get:

Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)

To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.

After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:

W = 350 - 2L

L = x + y + z

With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.

In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.

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Answer:

49

Step-by-step explanation:

A= a^2 = 7^2 =49

9514 1404 393

Answer:

  A.  {1, 7, 11}

Step-by-step explanation:

The constant in the equation is 1, so that is the value when x=0. No answer choice can be correct unless it includes the value 1. The only viable choice is A.

_____

If you want to go to the trouble to evaluate the expression for the different values of x, you can. It often works well to rewrite the expression to "Horner form":

  (2x -1)x +1

For x = -2, this is (2(-2) -1)(-2) +1 = (-5)(-2) +1 = 11

For x = 0, this is 1

For x = 2, this is (2(2) -1)(2) +1 = (3)(2) +1 = 7

So, the range for the given domain is {1, 7, 11} . . . . . matches choice A

Colligative properties depends on Properties that depend only on the concentration of the solute.

Colligative Characteristics Colligative qualities of solutions are characteristics that depend on the quantity of molecules or ions in the solute, but not on the kind of solute. Osmotic pressure, boiling point elevation, freezing point depression, and vapour pressure reduction are examples of ligand-like properties.

Given:

As, Colligative qualities of solutions are characteristics that depend on the quantity of molecules or ions in the solute, but not on the kind of solute.

Osmotic pressure, boiling point elevation, freezing point depression, and vapour pressure reduction are examples of ligand-like properties.

So, Colligative properties are dependent only on the number of non-volatile solute molecules or the concentration. They are independent of any other factor.

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Answer:

25

Step-by-step explanation:

The ounces will be the division of the numbers. This will be:

= $2.50 / $0.10

= 25

Answer:

42.39 yd²

Step-by-step explanation:

the sector area = (3π/4)/2π × 3.14 × 6²

= 3/8 × 3.14 ×36 = 42.39 yd²

Both statements are false. Consumer surplus decreases when the price is increased above the equilibrium, and producer surplus decreases when the price is decreased below the equilibrium.

(a) False.

The statement is not necessarily true. Consumer surplus is the difference between what consumers are willing to pay for a good or service and what they actually pay. At the equilibrium price, consumer surplus is maximized. However, if the price is increased above the equilibrium price, consumer surplus will generally decrease.

This is because as the price increases, fewer consumers are willing to purchase the good or service, resulting in a decrease in consumer surplus. T

herefore, at any price higher than the equilibrium price, the consumer surplus will generally be less than the consumer surplus at the equilibrium price.

(b) False.

Similar to the previous statement, the statement is not necessarily true. Producer surplus is the difference between the price producers receive for a good or service and the minimum price they are willing to accept. At the equilibrium price, producer surplus is maximized.

However, if the price is decreased below the equilibrium price, producer surplus will generally decrease. This is because as the price decreases, fewer producers are willing to supply the good or service, resulting in a decrease in producer surplus.

Therefore, at any price lower than the equilibrium price, the producer surplus will generally be less than the producer surplus at the equilibrium price.

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The volume of the three-dimensional figure formed if the  two-dimensional figure is rotated 360 degrees is 37.70 in³

Volume is the amount of space occupied by a three dimensional shape or object.

The volume of the three dimensional shape is:

Volume = volume of cylinder + volume of cone =  (π(2²) * 2) + [(1/3) * π * (2²) * 3] = 37.70 in³

The volume of the three-dimensional figure formed if the  two-dimensional figure is rotated 360 degrees is 37.70 in³

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The radius of the cone is 3 units

Here, given the volume of a right circular cone and the height of the cone, we want to get the radius of the cone

Mathematically, we need the formula for the volume of a right circular cone

We have this formula as;

We substitute the value of the volume and the height as follows;

Step-by-step explanation:

l^2=15^2+6^2

l^2=225+36

l^2=261

l=√261

The simple interest on 17,000 loan for 10 years will be 11,900

Solution:

As we know,  simple interest is the interest amount for a particular principal amount of money at some rate of interest.

Here given ,

Principle (P) = 17,000

Rate of interest (R) = 7%

Time (T)= 10 years

Simple Interest = (RxRxT)/100

Therefore,

S.I. = ( 17,000 x 7 x 10 ) / 100

     = 11,900

Hence,

The simple interest at the end of 10 years will be 11,900

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