what is the smallest number of integer kilogram weights needed to weigh every whole kilogram between 1kg and 40kg?​

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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The equation in spherical coordinates will be a constant, as we are describing a spherical shell.

r(φ, θ) = 8 units.

The equation:

x^2 + y^2 + z^2 = R^2

Defines a sphere of radius R.

Then the equation:

x^2 + y^2 + z^2 = 64

Defines a sphere of radius √64 = 8.

Then we will have that the radius is a constant for any given angle, then we can write r, the radius, as a constant function of θ and φ, the equation will be:

r(φ, θ) = 8 units.

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The equation in spherical coordinates is r(φ, θ) = 8 units.

Spherical coordinates of the system denoted as (r, θ, Φ) is the coordinate system mainly used in three-dimensional systems.

The equation of the spherical coordinates is written as;

\(\rm x^2 + y^2 + z^2 = R^2\)

Where R is the sphere of radius.

The given equation of the spherical coordinates is;

\(\rm x^2 + y^2 + z^2 = 64^2\)

Here 8 is the sphere of radius.

Hence, the equation in spherical coordinates is r(φ, θ) = 8 units.

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Step-by-step explanation:

FYT and UYF are supplementary angles (together they cover all angles around Y on one side of the line TU, and that's is in total 180°).

so,

FYT = 180 - 42 1/8 = 137 7/8°

as 180 - 42 = 138, and then we subtract another 1/8. that gives 137 7/8.

Answer:

<X = 36

<Y = 72

<W = 108

<Z = 144

Step-by-step explanation:

Since this shape is a quadrilateral, all angles add up to 360

x + 3x + 4x + 2x = 360

10x = 360

x = 36

<X: x

36

<W: 3x

3(36) = 108

<Y: 2x

2(36) = 72

<Z: 4x

4(36) = 144

The quadratic equation of the graph is y = - 16 · x² + 12 · x + 1. (Correct choice: C)

In this question we know the graph of a quadratic equation, whose expression is described below:

y = a · x² + b · x + c, where a, b, c are real coefficients.

According to algebra, we can find the values of the real coefficients by knowing three distinct points of the graph. If we know that (x₁, y₁) = (0, 1), (x₂, y₂) = (0.4, 3.25) and (x₃, y₃) = (0.826, 0), then the coefficients of the quadratic equations are, respectively:

1 = c

3.25 = 0.16 · a  + 0.4 · b + c

0 = 0.683 · a + 0.826 · b + c

(a, b, c) = (- 16, 12, 1)

The quadratic equation is y = - 16 · x² + 12 · x + 1

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The correct deductions for Larren Buffett's paycheck are as follows: Social Security taxes: $317.68, Medicare taxes: $59.45, and Federal Income Tax withholding: $475.90.

Larren Buffett, who is paid a weekly salary of $4,100, is concerned about the accuracy of her deductions for Social Security, Medicare, and Federal Income Tax withholding (FIT). To determine the correct deductions, we need to consider her marital status, number of claimed deductions, and prior earnings. According to the information provided, Larren claims 3 deductions and has total earnings of $128,245. For Social Security, the rate of 6.2% applies to a maximum of $128,400, resulting in a deduction of $317.68. Medicare tax, calculated at 1.45%, amounts to $59.45. As for FIT, further details are not provided, so we cannot determine the exact amount without additional information.

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From the given figure the angle x° is quals to 38°.

Given triangle is a right-angled triangle,

In the right-angled triangle the opposite side of the triangle = 6.1

The hypotenuse of the triangle = 9.9

In a right-angled triangle, by using little big trigonometry we know that,

sin theta = opposite side of the triangle/hypotenuse side of the triangle

From the given figure sin x° = opposite side of x / hypotenuse side

sin x° = 6.1/9.9

x° = \(sin^{-1}\)  (6.1/9.9)

x° = 38.03°

From the above analysis, we can conclude that the angle of x° is equal to 38.03° ≅ 38°.

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the value of ∠LJM will be 25 degrees.

A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.

Given KLMJ is a parallelogram such as

∠LMR = 72°, ∠RMJ = 27°

Since,

∠LMR + ∠RMJ = ∠LMJ

∠LMJ = 72 + 27

∠LMJ = 99°

Since KLMJ is a parallelogram adjacent angles of it will be supplementary angles.

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 110° and angle 70° are supplementary angles because the sum of 110° and 70° is equal to 180°.

Thus,

∠kJM + ∠LMJ = 180

∠kJM + 99 = 180

∠kJM = 81°

As we can observe in the figure,

∠kJM = ∠KJL + ∠LJM

81 = 56 + ∠LJM

∠LJM = 81 -56

∠LJM = 25°

therefore, the value of ∠LJM will be 25 degrees.

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Answer:

The square of -3 is 9

Step-by-step explanation:

(-3)^2=9

Answer:

189.27in^2

Step-by-step explanation:

Area of the rectangle is l*w

15*10= 150

Area of the circle is π r^2

We don't have radius but we have diameter so 10/2 =5

so A= π 5^2

78.53982, but we need half that since its only half a circle.

78.53982/2 = 39.26991

39.26991 + 150 = 189.26991

The law of cosines serves as a generalization of the Pythagorean formula, which is applicable to all triangles.

Compare the total of the squares on the two smaller sides to the square on the largest side to determine if the triangle is acute, right, or obtuse. Because of the larger sum, the triangle is sharp.

The Pythagorean formula applies to all triangles and is generalised by the law of cosines. The square of one side of the triangle, c², is said to be equal to a² + b², the sum of the squares of the other two sides, minus 2ab cos C, which is the product of the two squares times the cosine of the opposite angle.

Three closed sides make up a triangle. The Pythagoras theorem and the Heron's formula are two significant formulas that pertain to triangles.

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Answer:

B. 0 ≤ y ≤ 5

Step-by-step explanation:

Range is the set of y-values outputted by function f(x).

We see that our y-values span from 0 to 5. Since both are closed dot, both are included in the range:

[0, 5] or 0 ≤ y ≤ 5

Answer:

135*

Step-by-step explanation:

trust me

Answer:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

Step-by-step explanation:

Swap f(x) and x position of the function, thus:

\(\displaystyle{x=7f(x)+3}\)

Then solve for f(x), subtract 3 both sides and then divide both by 7:

\(\displaystyle{x-3=7f(x)}\\\\\displaystyle{\dfrac{x}{7}-\dfrac{3}{7}=f(x)}\)

Since the function has been inverted, therefore:

\(\displaystyle{f^{-1}(x)=\dfrac{x}{7}-\dfrac{3}{7}}\)

And we can prove the answer by substituting x = 1 in f(x) which results in:

\(\displaystyle{f(1)=7(1)+3 = 10}\)

The output is 10, now invert the process by substituting x = 10 in \(f^{-1}(x)\):

\(\displaystyle{f^{-1}(10)=\dfrac{10}{7}-\dfrac{3}{7}}\\\\\displaystyle{f^{-1}(10)=\dfrac{7}{7}=1}\)

The input is 1. Hence, the solution is true.

Answer:

where is the graph

Step-by-step explanation:

Answer:

hyuh

Step-by-step explanation:

Answer:

C is the answers for the question

Step-by-step explanation:

please mark me as brainlest

the exact location of the object at time 2 is given by 2/3 + C, where C is the constant of integration that depends on the initial position of the object.

To determine the exact location of the object at time 2, we need to find the object's position function and evaluate it at t = 2.

The velocity function is given as (-5t) + 4t^2. To find the position function, we integrate the velocity function with respect to time:

∫((-5t) + 4t^2) dt

Integrating term by term, we get:

-∫(5t) dt + ∫(4t^2) dt

Simplifying and integrating, we have:

-5∫t dt + 4∫(t^2) dt

= -(5/2)t^2 + (4/3)t^3 + C

where C is the constant of integration.

Now, to find the exact location at time 2, we substitute t = 2 into the position function:

-(5/2)(2)^2 + (4/3)(2)^3 + C

= -(5/2)(4) + (4/3)(8) + C

= -10 + (32/3) + C

= (32/3) - (30/3) + C

= 2/3 + C

Therefore, the exact location of the object at time 2 is given by 2/3 + C, where C is the constant of integration that depends on the initial position of the object.

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Frank cannot recover the reward because he was unaware of the reward being offered by Emma.

In order to claim the reward, one typically needs to have knowledge of the reward prior to finding and returning the lost item or fulfilling the specified condition. Since Frank was unaware of the reward, he would not have had the opportunity to intentionally seek the dog with the expectation of receiving the reward. As a result, Emma is not obligated to provide the reward to Frank in this situation.

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Answer:

the new area is 1% smaller.

Step-by-step explanation:

the area of a rectangle is length times breadth.

let's call them a and b

Area = a × b

now, a is increased by 10%. that means it is multiplied by 11/10.

because 100% means the whole thing, 1% means a 1/100th part of the whole. and 10% then means 10 times the 1/100th part of 10 × 1/100 = 10/100 = 1/10

if then simmering increases by 10% it means that it is the original 100% plus 10%.

so, it is 100/100 + 10/100 = 10/10 + 1/10 = 11/10

therefore the new length is

a(new) = a(old)×11/10

in exactly the same way, when the breadth is reduced by 10% we get then

breadth(new) = breadth(old)×9/10

so, Area(new) = a(new)×b(new) = a(old)×11/10 × b(old)×9/10

remember, Area(old) = a(old)×b(old)

so, Area(new) = a(old)×b(old) × 11/10 × 9/10 =

= Area(old) × 11/10 × 9/10 =

= Area(old) × 99/100

that means the new area has lost compared to the old area 1/100th of its size. 1/100th = 1%

The least amount of money he could pay for the conditions that he will for the given information is = £ 3053.4

What about least amount?

In mathematics, the term "least amount" is not commonly used. However, a similar term that is often used is "minimum".

The minimum value of a set of numbers or a function is the smallest value within that set or function. For example, if we have the set of numbers {2, 5, 7, 8, 10}, the minimum value is 2.

Similarly, in the context of optimization problems, we often seek to find the minimum value of a function to achieve the best possible outcome. This can involve finding the minimum value of a cost function in order to minimize the cost of a process, or finding the minimum value of a profit function to maximize the profit of a business.

According to the given information:

Set the number of party bags pack as x , toy pack as y

Since, 105 party bags in a pack , £1.32

84 toys in a pack £4.15.

Hence, 105x = 84y , cost = 105x × 1.32x + 84y × 4.15 = 763.35x

Find the least common multiple

Hence, 84 × 5 = 420 , 105 × 4 = 420

x  =4

y =5

least cost = 105 × 1.32 × 4 + 84×4.15 ×5

= £3053.4

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Answer:

121/100

1.21

Step-by-step explanation:

Answer:

Decimal is 1.21

Fraction is 121/100

The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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