What is the answer with the remainder

Answer:

The initial height from which the ball was dropped = 7.90 meters

Step-by-step explanation:

The correct question is:

In the video, I drop a ball off a three-story balcony. We know that objects in free fall follow the equation for height h, in meters, [tex]h = -4.9t^2 + c[/tex], where [tex]t[/tex] is time in seconds, and [tex]c[/tex] is the initial height. A student timed the drop at 1.27 seconds.

Use this to determine the height from which the ball was dropped, to at least 2 decimal places.

Solution:

The height [tex]h[/tex] of the free falling ball is represented by the equation as:

[tex]h=-4.9t^2+c[/tex] where [tex]t[/tex] is time in seconds, and c is the initial height.

To determine the initial height from which the ball was dropped.

The drop was timed at 1.27 seconds, we will plugin [tex]t=1.27[/tex] in the given height function to find [tex]h(1.27)[/tex]

[tex]h(1.27)=-4.9(1.27)^2+c[/tex]

[tex]h(1.27)=-7.90+c[/tex]

Since, the drop is timed at 1.27 seconds, so in the given time the ball will reach the ground, making [tex]h(1.27)=0[/tex]

So, we have.

[tex]0=-7.90+c[/tex]

Adding both sides by 7.90 to solve for [tex]c[/tex].

[tex]0+7.90=-7.90+7.90+c[/tex]

[tex]7.90=c[/tex]

∴ [tex]c=7.90\ m[/tex]

Thus, the initial height from which the ball was dropped = 7.90 meters

The first five terms of sequence is 4.5, -27, 162, -972, 5832

Solution:

Given that we have to find first five terms of recursive sequence

Given sequence is:

[tex]a_n = -6a_{n - 1}[/tex]

To find first five terms, substitute n = 2, 3, 4, 5

First term is given = [tex]a_1[/tex] = 4.5

Find second term:

Substitute n = 2 in given sequence

[tex]a_2 = -6a_{2 - 1}\\\\a_2 = -6a_1\\\\a_2 = -6(4.5) = -27[/tex]

Thus second term of given sequence is -27

Find third term:

Substitute n = 3 in given sequence

[tex]a_3 = -6a_{3-1}\\\\a_3 = -6a_2\\\\a_3 = -6(-27) = 162[/tex]

Thus third term of given sequence is 162

Find fourth term:

Substitute n = 4 in given sequence

[tex]a_4 = -6a_{4-1}\\\\a_4 = -6a_3\\\\a_4 = -6(162) = -972[/tex]

Thus fourth term of given sequence is -972

Find fifth term:

Substitute n = 5 in given sequence

[tex]a_5 = -6a_{5-1}\\\\a_5 = -6a_4\\\\a_5 = -6(-972) = 5832[/tex]

Thus the first five terms of sequence is 4.5, -27, 162, -972, 5832

Answer:

See below table

Step-by-step explanation:

[tex]\begin{array}{cccccccc}p&q&r&\sim q&\sim q\rightarrow p&r\vee(\sim q\rightarrow p)&\sim p&[r\vee (\sim q\rightarrow p)]\rightarrow \sim p\\ \\ \\ \\T&T&T&F&T&T&F&F\\ \\T$&T&F&F&T&T&F&F\\ \\T&F&T&T&T&T&F&F\\ \\T&F&F&T&T&T&F&F\\ \\ \\ \\F&T&T&F&T&T&T&T\\ \\F&T&F&F&T&T&T&T\\ \\F&F&T&T&F&T&T&T\\ \\F&F&F&T&F&F&T&T\end{array}[/tex]

Answer:

?

Step-by-step explanation:

Answer:

π(6²)

Step-by-step explanation:

The base of the cone is a circle with area (A) calculated as

A = πr² ← r is the radius

Here diameter = 12 , hence r = 12 ÷ 2 = 6, thus

A = π(6²)

Commission earned by William is $ 45.84

Given that,

William makes a commission of 6% percent on everything he sells

He sells a computer for $764.00

To find: Commission amount of William

Given that he makes a commission of 6 % on everything he sells. So he has received a commission of 6 % of $ 764.00

Commission amount of William = 6 % of $ 764.00

a % of b can be written in fraction as [tex]\frac{a}{100} \times b[/tex]

[tex]6 \% \text { of } 764=\frac{6}{100} \times 764=0.06 \times 764=45.84[/tex]

Thus commission earned by William is $ 45.84

Answer:

7.6875

Step-by-step explanation:

Answer:number 3

Step-by-step explanation:

Answer:

6.09864679092 minutes

Step-by-step explanation:

Mach 27= 33076.19km/h

3,362, at 33076.19km/h

3,362/33076.19

0.101644113182 hours

6.09864679092 minutes

Answer:

Around 6 minutes

Or in other words, fast

Answer:

π

Step-by-step explanation:

Y= 2 sin(2X)

Analytically,

The Amplitude is 2, while the Period is 2π/2, same as π

Answer:

The length of the ladder is 9.2m

Step-by-step explanation:

We need to find the false statement.

The first one is true (m<RPS=m<WPR because RU⊥SW).

The second statement is true because the two angles make a linear pair and are supplementary.

The third one is false because we only know that the angle pair is complimentary. Their measures are not equal.

answer: m∠SPT=m∠UPT

Answer:

−6y+13

Step-by-step explanation:

jsjsdjidedhue

Answer:

The speed of the boat in still water is 30 mph, and the speed of the current is 6 mph.

Step-by-step explanation:

Let's say b is the speed of the boat in still water, and c is the speed of the current.

Distance = rate × time

Going downstream:

504 = (b + c) × 14

36 = b + c

Going upstream:

504 = (b − c) × 21

24 = b − c

Two equations, two variables.  Solve with substitution or elimination.  To use elimination, add the equations together.

60 = 2b

b = 30

Plug into any equation to find c.

36 = b + c

36 = 30 + c

c = 6

The speed of the boat in still water is 30 mph, and the speed of the current is 6 mph.

The speed of the boat in still water will be 30 miles per hour and the speed of the current will be 6 miles per hour.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Let the speed of the boat in still water be x and the speed of water be y.

A boat traveled 504 miles downstream and back. The trip downstream took 14 hours. Then the equation will be

x + y = 504 / 14

x + y = 36      ...1

The trip back took 21 hours. Then the equation will be

x - y = 504 / 21

x - y = 24       ...2

Add equations 1 and 2, then the value of x will be

2x = 36 + 24

2x = 60

x = 30 miles per hour

Then the value of y will be

30 - y = 24

y = 6 miles per hour

The speed of the boat in still water will be 30 miles per hour and the speed of the current will be 6 miles per hour.

More about the solution of the equation link is given below.

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Answer:

120.35

Step-by-step explanation:

De tanque lleno de agua,se utilizan las dos quintas partes y luego los tres cuartos del resto. Si aún quedan 240 litros ¿cuántos litros tiene?

2/5- 3/4=-0.35

tienes 120 galones más el 0.35

120+0.35=120.35

que tengas un buen día!!!!!!!!!!!!!

The initial amount of water in the tank was 1600 liters.

Let's denote the initial amount of water in the tank as W.

First, two-fifths of the water are used, leaving [tex]\(\frac{3}{5}\)[/tex] of the water remaining.

[tex]\[\text{Remaining amount} = \frac{3}{5} \times W\][/tex]

Then, three-quarters of the remaining water are used, leaving \(\frac{1}{4}\) of the remaining water.

[tex]\[\text{Final amount} = \frac{1}{4} \times \left(\frac{3}{5} \times W\right)\][/tex]

According to the problem, the final amount is 240 liters:

[tex]\[\frac{1}{4} \times \left(\frac{3}{5} \times W\right) = 240\][/tex]

Now, solve for W:

[tex]\[\frac{3}{5} \times W = 240 \times 4\][/tex]

[tex]\[\frac{3}{5} \times W = 960\][/tex]

[tex]\[W = \frac{960 \times 5}{3}\][/tex]

[tex]\[W = 1600\][/tex]

So, the initial amount of water in the tank was 1600 liters.

The right answer is Option B: 5(x+3)=12

Step-by-step explanation:

“The product of five and the sum of a number x and three is twelve”

First;

The sum of a number x and 3 = x+3

Product means multiplication,

Therefore,

Product of five and sum of a number x and three = 5(x+3)

is twelve means that the answer will be 12

5(x+3)=12

The right answer is Option B: 5(x+3)=12

Keywords: linear equation, addition

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Answer:

The right answer is Option B: 5(x+3)=12

Step-by-step explanation:

“The product of five and the sum of a number x and three is twelve”

First;

The sum of a number x and 3 = x+3

Product means multiplication,

Therefore,

Product of five and sum of a number x and three = 5(x+3)

is twelve means that the answer will be 12

5(x+3)=12

The right answer is Option B: 5(x+3)=12

Keywords: linear equation, addition

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Step-by-step explanation:

Answer:

18.18%

Step-by-step explanation:

Cross-multiply

11 years ------------ 100% of life

2 years ------------- x% of life

11/2 = 100/x ===> 11x = 2*100 ===> 11x = 200 ===> x = 200/11 ===> x = 18.18%

Answer:

50 possible codes.

Step-by-step explanation:

The first digit must be 1, 3, 5, 7 or 9. -  5 possibilities.

The second digit is one of the numbers from 0 to 9, -  10 possibilities.

So the number of possible codes = 5 * 10 = 50.

Final answer:

To solve both 3/8 x 4 and 3/6 x 4, we multiply the numerator by 4 and simplify the resulting fraction if necessary, resulting in 1.5 for the first expression and 2 for the second.

Explanation:

To solve the problem 3/8 x 4 and 3/6 x 4, we need to perform multiplication of a fraction by a whole number. For the first part, we multiply the numerator (3) by the whole number (4) and keep the denominator (8) to get 12/8, which simplifies to 1 1/2 or 1.5. For the second part, we simplify the fraction 3/6 to 1/2 since both the numerator and denominator can be divided by 3. Then, again, we multiply the numerator (1) by the whole number (4) and keep the denominator (2), resulting in 4/2, which simplifies to 2.

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slope = difference in y/difference in x

Substitute values in:

slope = (1 - 9)/(-2- (-9)

slope = -7/7

slope = -1

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Answer: -6.5x+4.4

Step-by-step explanation:

Answer:230

Step-by-step explanation:

To get to 100% you need to do 20% 5 times so if 46 people is 20% 46x5 will give you 100% of people surveyed

For this case we have to by definition, if two lines are perpendicular then the product of its slopes is -1, that is:

[tex]m_ {1} * m_ {2} = - 1[/tex]

So, if we have the slope [tex]m_ {1} = - \frac {1} {3}[/tex]

A perpendicular line will have a slope m_ {2}:

[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {- \frac {1} {3}}\\m_ {2} = 3[/tex]

Thus, the perpendicular line will have slope [tex]m_ {2} = 3[/tex]

Answer:

The perpendicular line will have slope [tex]m_ {2} = 3[/tex]

Answer: C. Line EF.

Step-by-step explanation: Correct on edge.

Answer:

Part 1) [tex]f(g(x))=3(x^2)+2[/tex]

Part 2) [tex]g(f(5))=289[/tex]

Step-by-step explanation:

we know that

A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function

we have

[tex]f(x)=3x+2[/tex]

[tex]g(x)=x^{2}[/tex]

Part 1) Determine f(g(x))

To find f(g(x)) substitute the function g(x) as the variable in function f(x)

so

[tex]f(g(x))=3(x^2)+2[/tex]

Part 2) Determine g(f(x))

To find g(f(x)) substitute the function f(x) as the variable in function g(x)

so

[tex]g(f(x))=(3x+2)^2[/tex]

For x=5

[tex]g(f(5))=(3(5)+2)^2[/tex]

[tex]g(f(5))=289[/tex]

Answer:

its definitely A, because it is some number to the power of 4

Step-by-step explanation:

Answer:

θ= 30° or θ= 60°

Step-by-step explanation:

Please see attached picture for full solution.

Since √ 3/2 is positive, look at first 2 quadrant. (CAST diagram)

Answer:

No! {-2, 1} is not a solution set to the given equation.

Step-by-step explanation:

The statement  X squared take away 2X Takeaway three equals X take away one can be written in mathematical terms as follows:

X² - 2X - 3 = X - 1

⇒ X² - 2X - 3 - X + 1 =0

⇒ X² - 3X - 2 = 0

Now, substitute x= -2 and see if the equation is satisfied.

⇒ (-2)² -3(-2) - 2 = 4 + 6 - 2

= 8 ≠ 0

So, -2 is not a solution to the equation.

Now, check for x = 1.

⇒ (1)² - 3(1) - 2 = 1 - 3 - 2

= -4 ≠ 0

⇒ x = 1 is not a solution as well.

Answer:

gradient = 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

Rearrange 2y - 6x = - 8 into this form

Add 6x to both sides

2y = 6x - 8 ( divide all terms by 2 )

y = 3x - 4 ← in slope- intercept form

with gradient m = 3

Answer:

x=-7

Step-by-step explanation:

The value of x if,  Lines 1 and 2 are parallel, LINE 1: (-2,5) and (0,0) LINE 2: (x,12) and (-3,2) is -7.

An object having an endless length and no width, depth, or curvature is called a line. Since lines can exist in two, three, or higher-dimensional environments, they are one-dimensional things.

Given:

Line 1 and line 2 are parallel,

The coordinates of lines are given as,

LINE 1: (-2, 5) and (0, 0) LINE 2: (x, 12) and (-3, 2)

As we know that the slope of the parallel lines is equal,

Calculate the slope of Line 1 as shown below,

Slope = 0 - 5 / 0 - (-2)

Slope = -5 / 2

Thus, for the second line,

The slope of Line 2 = (2 - 12) / (-3 - x)

-5 / 2 = -10 / -3 - x

-5(-3 - x) = -20

15 + 5x = -20

5x = -20 - 15

x = -35 / 5

x = -7

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Answer:

Infinitely many

Step-by-step explanation: