If you have a 3 feet rope and want to cut into 4 pieces of equal length, how long will each piece be?

(a) Velocity of the rock after one second is 6.28 m/s.

(b) Velocity of the rock when t=a is  10 - 3.72a

(c) The rock hit the surface after about 5.38 seconds

(d) With -10m/s velocity will the rock hit the surface

Height (in meters) after t seconds is given by

\(H(t) = 10t - 1.86t^{2}\)

\(V(t) = \frac{dH}{dt} = 10 - 3.72t\)

(a) V(1) = 10 - 3.72(1)

V(1) = 6.28 m/s

(b)  V(a) = 10 - 3.72a ,

(c) Time when the rock hit the surface , H(t) = 0

\(10t - 1.86t^{2} = 0\\t(10 - 1.86t) = 0\\\)

t = 0 or 10 - 1.86t = 0

             t ≅ 5.38 seconds

(d) velocity at surface = velocity at time from part (c)

V(5.38) = 10 - 3.72(5.38) ≅ -10 m/s that means it should be same as launch speed, but in opposite direction.

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The two students that mix the same ratio of juice to water is given as follows:

A. Luca.

D. Micah.

The ratio between two amounts a and b is given as follows:

a to b.

Which is also the division of the two amounts.

Hence the ratio of juice to water for each person is given as follows:

Hence Luca and Micah used the same ratio, meaning that options A and D are correct.

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Answer:

a) 2

b) left to right

Step-by-step explanation:

a) slope= (y2 -y1)/(x2-x1)

(-13-(-21))/(-6-(-10))

8/4

2

b) left to right

Answer:

go get smart and stop cheating on online websites

Step-by-step explanation:

Answer:

1. C points radially outward from origin

2. A. Points radially outward from z origin

3. D. Radially inwards toward origin

4. B. Inwards towards the z axis

Step-by-step explanation:

1.

X²+y²+z² = f(x,y,z)

Vector P<x,y,z>

2<x,y,z> = 2p

The answer is c points radially outward from origin

2.

X²+y² = f(x,y)

<2x,2y,0>

Points radially outward from z axis

3.

D. Points radially inwards toward origin

4.

B. Points radially inwards toward the z axis.

Please check attachment for solutions to answers 3 and 4

Answer:

96 ounces

6 pounds is equal to 96 ounces (i hope this helps )

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(x^{2} + 6x-6= 10\\x^{2} +6x-16=0\\x^{2} -2x+8x-16=0\\x(x-2)+8(x-2)=0\\(x-2)(x+8)=0\\x = 2\\or\\x = -8\)

Answer:

X = 2 and X = -8

Step-by-step explanation:

X2 + 6X - 6-10 = 0 ....... when +10 pass the equality sign it will become -10

X2 + 6X -16 =0

here we need to find if there are two numbers there sum is +6 and there product is -16.

here we need to find if there are two numbers there sum is +6 and there product is -16.The two numbers are -2 and +8

-2+8= +6

-2*8= -16

( X - 2 ) * ( X + 8 ) =0

X - 2 = 0 ...... when -2 pass equality sign it will become+2

X = 2

X + 8 =0 ..... when +8 pass equality sign it will become -8

X = -8

Answer:

f(x)=-9+3x

Step-by-step explanation:

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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Answer:

31 7/8

16+8=24

4+2=6

2/4+1/4=3/4+1/8=7/8

SOLUTION

Now, since the center of dilation is at the origin, to get the new coordinates of the vertices of the quadrilateral, we will simply multiply the coordinates by a the scale factor of 2. This becomes

d

Hi this was a different question from normal but okay.

Answer:

There has been an high speed chase that lead to an injury of a young girl. Isaac midway had fled the seen at North West 22nd, around 2:56 pm. With the girl laying in the street with a broken leg and fractured ankle. Have any evidence call crime stoppers.

Step-by-step explanation:

This provides criminal, time and location and injury. Good luck.

One Night, The Criminal Mastermind, Arnold "Laughing" Jack Escapes From The Facility In New Orleans, And Proceeds To Murder 70 People, The Most Famous Spot Was His Murder Hotel Where He Mutilated 5 People In The Kitchen. The Injuries On The Bodies Were Similar To What Forensics Is The Equivalent Of, How Being Struck With A Curved Sword Would Be.

Answer:

\( \boxed{ \bold{ \huge{\boxed{ \sf{(12.5 \: , \: 11.5)}}}}}\)

Step-by-step explanation:

Let the points be A and B

Let A ( 13 , 15 ) be x₁ , y₁ and B ( 12 ,8 ) be x₂ , y₂

Finding the midpoint

\( \bold{ \boxed{ \sf{midpoint \: = (\: \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2}) }}}\)

\(\dashrightarrow{ \sf{ (\frac{13 + 12}{2} , \: \frac{15 + 8}{2} )}}\)

\( \dashrightarrow {\sf {(\frac{25}{2} \: , \: \frac{23}{2} )}}\)

\( \dashrightarrow{ \sf{(12.5 \: , \: 11.5)}}\)

Hope I helped!

Best regards! :D

Answer:

the minimum possible time for Emma to reach the island is approximately 2.9583 hours, when she starts swimming at a point 5/6 km east of the cottage.

Step-by-step explanation:

We can use the concept of minimum distance to find the minimum possible time for Emma to reach the island. Let's assume that Emma walks to some point P along the shoreline and then swims to the island. We want to find the point P that minimizes the total distance that Emma has to cover.

Let the distance from the cottage to point P be x km. Then the distance from point P to the island is (3 - x) km. Using the Pythagorean theorem, we can find the distance from the cottage to the island as follows:

distance^2 = x^2 + (3 - x)^2 + 2^2

distance^2 = 10x - 6x^2 + 13

To minimize the distance, we can take the derivative of the distance equation with respect to x and set it equal to zero:

d(distance^2)/dx = 10 - 12x = 0

x = 5/6 km

Substituting x = 5/6 km into the distance equation, we get:

distance^2 = 25/3 km^2

distance = 5/sqrt(3) km

Therefore, the minimum possible time for Emma to reach the island is the time it takes her to walk to point P (distance x) plus the time it takes her to swim to the island (distance 3 - x), divided by her swimming speed:

time = x/4 + (3 - x)/3

time = (3x + 12 - 4x)/12

time = (12 - x)/4

time = (12 - 5/6)/4

time = 2.9583 hours (rounded to 4 decimal places)

Therefore, the minimum possible time for Emma to reach the island is approximately 2.9583 hours, when she starts swimming at a point 5/6 km east of the cottage.

Let's call the point where Emma starts swimming P. We can draw a diagram to visualize the situation:

Cottage ---------- Q ---------------- Island

x km 3 km 2 km

The distance from the cottage to Q is x km, and the distance from Q to the island is 2 km. The total distance Emma will have to travel can be expressed as:

d = √(x^2 + 2^2)

The time it will take Emma to walk the distance from the cottage to point P is:

t1 = x / 4

The time it will take Emma to swim from point P to the island is:

t2 = √((d - x)^2 + 2^2) / 3

The total time it will take Emma to reach the island can be expressed as:

T = t1 + t2

To find the minimum possible value of T, we can take the derivative of T with respect to x and set it equal to zero:

dT/dx = (1/4) - (d-x)/3√((d-x)^2+4) = 0

Solving for x, we get:

x = (3/5)d

Substituting this value of x back into the expression for T, we get:

T = (3/20)d + (2/5)√(5)

Rounding to the nearest hundredth, we get:

T ≈ 0.96 hours

Therefore, the minimum possible time it will take Emma to reach the island is approximately 0.96 hours.

Answer: 4

This problem requires basic division. If the restaurant divided 4/5 kg of butter with 1/5 kg on each dish, you would need to compute 4/5 divided by 1/5.

4/5 ÷ 1/5

Using the "KFC" method, or Keep, Change, Flip, you would keep the first number (in this case, 4/5), change the division sign, and flip the fraction to 5/1, or 5. We now have this:

4/5 x 5

To compute this equation, you must multiply the numerators of both of the numbers together. In this case, you would compute (4x5)/5, resulting with 20/5, or 4.

You can check this answer by re-multiplying the numbers together. 1/5 kg of butter per dish, multiplied by the total amount of dishes, 4, you would result in the original 4/5 kg of butter.

Hope this helps!

Step-by-step explanation:

\(y = 3x + 10......eq3 \\ 2(3x + 10) = 6x + 20 \\ 6x + 20 = 6x + 20\)

you can see that coming across that complication where the eqaution is balanced there is no solution for x and y fir those systems of equations.

Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

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The values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

Given are two right triangles we need to find the missing sides,

We will use Trigonometric ratios to find the same.

We know that,

Sin a = perpendicular / hypotenuse

Cos a = base / hypotenuse

Tan a = perpendicular / base

1) Sin 60° = x / 4√3

x = √3/2 × 4√3

x = 6

Cos 60° = y / 4√3

1/2 × 4√3 = y

y = 2√3

2) Cos 60° = x / 98

x = 1/2 × 98

x = 49

Sin 60° = y / 98

√3/2 = y / 98

y = 49√3

Hence the values are 1) x = 6, y = 2√3 and 2) x = 49, y = 49√3.

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The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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9514 1404 393

Answer:

  A congruent

Step-by-step explanation:

In similar polygons, corresponding sides are proportional, and corresponding angles are congruent.

A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.

Here, we have

Given:

Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C

After 14 days, the percentage οf the mοοn is zerο

A = (max-min)/2 = 50/2 = 25

The periοd = 28 days

P = Acοs(BT = t) + c

B = 2π/periοd = 2π/28 = π/14

c = min + A = 0 + 25 = 25

We get,

P = 25cοs(π/14t) + 25,

Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.

Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.

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The point estimate of the population mean is 21.

The point estimate of the population mean is the midpoint of the confidence interval.

To find the midpoint, add the lower and upper bounds of the interval and divide by 2. In this case, the lower bound is 17 and the upper bound is 25, so the point estimate of the population mean is (17 + 25) / 2 = 21.

On the other hand, the margin of error is a measure of the precision of the estimate. It is the amount by which the estimate could be off and still be considered accurate. The margin of error is typically expressed as a percentage of the point estimate. In this case, the margin of error would depend on the level of confidence you have in the estimate and the size of the sample you used to generate the interval. Without more information, it is not possible to determine the margin of error.

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Answer:

- 10 + 5y + 14

Step-by-step explanation:

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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