An object is launched vertically in the air at 41.65 meters per second from a 7-meter-tall platform. using the projectile motion model h(t)=-4.9t^2+v0t+h0, where h(t) is the height of the projectile t seconds after it’s departure, v0 is the initial velocity in meters per second, and h0 is the initial height in meters, determine how long it will take for the object to reach its maximum height. what is the maximum height?

The requried dimension of the original rectangle is given as length = 25 cm, width = 10 cm.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

Let the length and width of the original rectangle be x and y,
According to the quesiton,

The perimeter of a rectangle is 70 cm.
2 [x + y] = 70
x  + y = 35 - - - -(1)

Now,
its length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 cm².
Area of the new rectangle = area of the original rectangle + 50
(x  - 5)(y + 5) = xy + 50

from equation 1,

(x - 5)(35 - x + 5) = x(35 - x) + 50
-x² - 200 + 40x + 5x = 35x - x² + 50
45x - 35x = 50 + 200
10x = 250
x = 25

Now,
y = 35 - 25
y = 10

Thus, the requried dimension of the original rectangle is given as length = 25 cm, width = 10 cm.

Learn more about rectangles here:

brainly.com/question/15019502

#SPJ1

The equation for the least-squares regression line for the given data and the average chance of admission for a student who scores a 305 on the GRE are options b) 51% (or 0.51).

To find the equation for the least-squares regression line, we need to first calculate the slope and y-intercept. Let x be the predictor variable (GRE score) and y be the response variable (admission chance). Then, we have:

n = 10 (number of data points)

Σx = 3100

Σy = 52.1

Σxy = 161750

Σx^2 = 96100

Σy^2 = 24.71

The slope, b, can be calculated as:

b = (nΣxy - ΣxΣy) / (nΣx^2 - Σx^2)

= (10(161750) - (3100)(52.1)) / (10(96100) - 3100^2)

= 0.0644

The y-intercept, a, can be calculated as:

a = (Σy - bΣx) / n

= (52.1 - (0.0644)(3100)) / 10

= 0.336

Therefore, the equation for the least-squares regression line is:

y = 0.0644x + 0.336

To find the average chance of admission for a student who scores a 305 on the GRE, we simply substitute x = 305 into the equation and solve for y:

y = 0.0644(305) + 0.336

= 0.5136

So the average chance of admission for a student who scores a 305 on the GRE is b) 51% (or 0.51).

For more questions like Regression click the link below:

https://brainly.com/question/28178214

#SPJ11

The price elasticity of demand measured using midpoint method, for a price change between $10 and $2 can be determined as follows:Price elasticity of demand (mid-point method) = [ΔQ / {(Q1 + Q2)/2}] ÷ [ΔP / {(P1 + P2)/2}]Given that P1 = $10, P2 = $2, Q1 = Q2, and the price has decreased from $10 to $2.

Therefore, the midpoint price (P) = (P1 + P2) / 2 = ($10 + $2) / 2 = $6The midpoint quantity (Q) = (Q1 + Q2) / 2 = Q1 / 2 + Q2 / 2 = Q / 2 + Q / 2 = Q.ΔP = $2 − $10 = −$8ΔQ = Q − Q = 0Hence, the absolute value of the price elasticity of demand using the midpoint method for a change in price from $10 to $2 is :Price elasticity of demand (mid-point method) = [ΔQ / {(Q1 + Q2)/2}] ÷ [ΔP / {(P1 + P2)/2}]E = [0 / {Q / 2}] ÷ [−8 / $6]E = 0 ÷ −1.3333E = 0

So, the correct answer is option B: 1.

To know more about elasticity visit:

https://brainly.com/question/30999432

#SPJ11

Answer:  37

Step-by-step explanation: i did it i think ¯\(°_o)/¯

In Korea, tofu is typically offered during breakfast.

Describe breakfast.

The first meal of the day, known as breakfast, is often had in the morning. After an overnight fast, it is a crucial meal that gives the body and brain fuel. Protein and carbs are generally found in breakfast foods such eggs, bacon, oatmeal, toast, pancakes, yoghurt, cereal, and fruits. A nutritious breakfast may boost energy levels, jump-start the metabolism, and enhance focus and memory. A nutritious breakfast can also aid in lowering mid-day snacking and preventing overeating in the evening. Make sure to incorporate breakfast in your daily schedule since eating breakfast is crucial to living a healthy lifestyle.

For such more question on tofu.

https://brainly.com/question/12099097

#SPJ4

Answer:

Step-by-step explanation:

√40 = √4*√10

        = 2√10 is one equivalent expression

Answer:

90

Step-by-step explanation:

multiply 30 by 3

Answer:

Hi,

I hope you are searching for this answer.

The lcm of an expression is calculated by taking the common factor and multiply the common factor with the remaining one, alright.

or, simply the lcm of an expression is calculated by the product of common factors and the factors which are not common.

Hope it helps...

The reservoir level h needed to maintain a flow of 10 L/s through the given commercial steel annulus is 0.226 m.

To estimate the reservoir level h needed to maintain a flow of 10 lit/sec, we can use the Darcy-Weisbach equation:

ΔP = f (L/D) (ρV²/2)

where: ΔP = pressure drop (Pa), f = friction factor, L = length of pipe (m), D = diameter of pipe (m), ρ = density of water (kg/m³), V = velocity of water (m/s)

To find the velocity of water, we can use the continuity equation:

A₁V₁ = A₂V₂

where: A₁ = cross-sectional area of the pipe at the inlet (m²), A₂ = cross-sectional area of the pipe at the outlet (m²)

Assuming the pipe is horizontal and the flow is steady, the continuity equation simplifies to:

V = Q / A

where:

Q = flow rate (m³/s)

We can convert the flow rate of 10 L/s to m³/s by dividing by 1000:

Q = 10 / 1000 = 0.01 m³/s

The cross-sectional area of the pipe at the inlet can be calculated as:

A₁ = π/4 (D₁)²

where: D₁ = inner diameter of the pipe

Substituting the given values, we get:

D₁ = 60 mm = 0.06 m

A₁ = π/4 (0.06)² = 0.002827 m²

The cross-sectional area of the pipe at the outlet is the same as the inlet, so A₂ = A₁.

Using the continuity equation, we can find the velocity of water:

V = Q / A₁ = 0.01 / 0.002827 = 3.541 m/s

Now, we can use the Darcy-Weisbach equation to find the pressure drop:

ΔP = f (L/D) (ρV²/2)

where: L = 50 m, D = 0.1 m (100 mm outside diameter - 60 mm inner diameter), ρ = 1000 kg/m³ (density of water)

Substituting the given values, we get:

ΔP = 0.0232 (50 / 0.1) (1000 × 3.541² / 2) = 2217.55 Pa

To maintain a flow of 10 L/s, this pressure drop must be balanced by the hydrostatic pressure due to the difference in height between the inlet and outlet of the pipe:

h = ΔP / (ρg)

here:

g = acceleration due to gravity = 9.81 m/s²

Substituting the given values, we get:

h = 2217.55 / (1000 × 9.81) = 0.226 m

Therefore, the reservoir level h  is 0.226 m.

To know more about Reservoir level:

https://brainly.com/question/30736964

#SPJ4

Answer: In mathematics, the additive inverse of a number is the number that, when added to the original number, results in zero.

Step-by-step explanation: The additive inverse of 21.9 can be found by simply negating the value, which means changing the sign from positive to negative, or vice versa. Therefore, the additive inverse of 21.9 is -21.9, because 21.9 + (-21.9) = 0.

Answer:

946 milliliter can

Step-by-step explanation:

She should consider how much is in it. Which one will last longer and is better. The bigger can has more in it so that one should be bought.

Hope this helps!

The steps for adding and subtracting fractions with whole numbers:

- Write the whole number in the form of a fraction.

- Convert the fractions to like fractions.

- Add/Subtract the numerators while the denominator remains the same.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part of fraction is denominator.

consider a fraction 1/8.

Here, numerator is 1, denominator is 8

When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8

In case of adding and subtracting fractions with whole numbers:

Let us assume that 'a' represents the whole number and \(\frac{x}{y}\) be fraction

First we write the whole number in the form of a fraction.

So, a = \(a = \frac{a}{1}\)

Now we find the LCM of the denominators of fractions \(\frac{a}{1} ,\frac{x}{y}\) and then convert the given fractions to like fractions.

Let m be the LCM of the denominators of fractions \(\frac{a}{1} ,\frac{x}{y}\)

So, the fractions becomes  \(\frac{a}{m} ,\frac{x}{m}\)

Last we Add/Subtract the numerators while the denominator remains the same.

i.e., \(\frac{a\pm x}{m}\)

Learn more about fraction here:

brainly.com/question/24638688

#SPJ4

The complete question is:

How to add /subtract fractions with whole numbers?

Answer: (-4,2) ,  (-2,1) , (1,4) , (4,4)

Step-by-step explanation: according to the table, we can identify that the domain of the relationship is:  (-4,2) ,  (-2,1) , (1,4) , (4,4)

The forecast value for time period 2 is 210, and the forecast error is -110 when the actual value is 100. Option B

To calculate the forecast value for time period 2, we substitute W = 2 into the regression equation:

y = 200 + W + 2W^2

= 200 + 2 + 2(2^2)

= 200 + 2 + 2(4)

= 200 + 2 + 8

= 210

Therefore, the forecast value for time period 2 is 210.

To calculate the forecast error, we compare the forecasted value with the actual value for time period 2. Given that the actual value is 100, the forecast error can be calculated as the difference between the actual value and the forecast value:

Forecast error = Actual value - Forecast value

= 100 - 210

= -110

Hence, the forecast error is -110.

Therefore, the correct answer is:

Forecast value = 210; forecast error is -110. So Option B is correct.

For more question on time visit:

https://brainly.com/question/53809

#SPJ8

To solve a proportion like x/a = b/c, you need to find the value of x that makes the two ratios equal. You can do this by cross-multiplying, which involves multiplying the numerator of one ratio by the denominator of the other ratio, and vice versa. We start by multiplying both sides by ac, giving us x = (ab)/c.

In summary, to solve a proportion of this form in just three steps, we multiply both sides by the product of the denominators, then simplify the resulting expression to get the value of x. To solve a proportion like x/a = b/c, you need to find the value of x that makes the two ratios equal. You can do this by cross-multiplying, which involves multiplying the numerator of one ratio by the denominator of the other ratio, and vice versa.

Following the cross-multiplying method, you multiply the two numbers that are diagonally opposite each other, then do the same for the remaining two numbers. In this case, multiply 'a' by 'c' and 'x' by 'b'. This results in the equation: x * b = a * c. To find the value of x, divide both sides of the equation by 'b'. This will give you the final equation: x = (a * c) / b. By plugging in the values for a, b, and c, you can easily solve for x and find the value that satisfies the proportion x/a = b/c.

To know more about ratios visit:-

https://brainly.com/question/28345307

#SPJ11

Answer:

3/10

Step-by-step explanation:

you do 3/5 times 1/2 which is 3/10

half of 3/5 is 3/10

hope this helps

correct me if this is wrong

Answer:  Top one is trapezoid, middle one is rectangle, bottom one is triangle

Step-by-step explanation:

I took the test and got them all right, so this one must also be right

The shape is formed by each cross-section shown is Top is a trapezoid, the middle is a rectangle, the bottom is a triangle.

A branch of mathematics that offers the dimension, houses, and relationships of points, traces, angles, surfaces, and solids broadly: the take a look at houses of given elements that continue to be invariant beneath detailed ameliorations.

The definition of geometry is a department of math that makes a specialty of the measurement and courting of lines, angles, surfaces, solids, and points. An instance of geometry is the calculation of a triangle's angles.

Learn more about geometry here:-https://brainly.com/question/24375372

#SPJ2

To find the value of c such that the limit of B(t) exists as t approaches 2, we need to ensure that the two pieces of the function B(t) agree at t = 2. By setting the expressions for B(t) equal to each other and solving for c, we can determine the value of c.

1. We set the expressions for B(t) equal to each other:

  4 - (1/2)t = √t + c

2. We simplify the equation:

  √t + c = 4 - (1/2)t

3. To remove the square root, we square both sides of the equation:

  (√t + \(c)^2 = (4 - (1/2)t)^2\)

4. Expanding both sides of the equation:

  t + 2c√t + \(c^2 = 16 - 4t + (1/4)t^2\)

5. Rearranging the terms:

  \((1/4)t^2 + (4 + 2c)t + (c^2\) - 16) + 2c√t = 0

6. To satisfy the condition for the limit, the quadratic equation must have only one solution when t = 2. This occurs when the discriminant is zero.

7. Setting the discriminant equal to zero:

  (4 + \(2c)^2 - 4(1/4)(c^2\)- 16) = 0

8. Simplifying the equation:

  16 + 16c + \(4c^2 - (c^2\) - 16) = 0

9. Combining like terms:

 \(3c^2\) + 16c = 0

10. Factoring out c:

   c(3c + 16) = 0

11. Solving for c:

   c = 0 or c = -16/3

Therefore, the two possible values for c are 0 and -16/3. Either of these values will ensure that the limit of B(t) exists as t approaches 2.

For more such questions on expressions, click on:

https://brainly.com/question/28036476

#SPJ8

Answer:

10

Step-by-step explanation:

a^2+b^2=c^2

9^2+3^2=c^2

81+9=c^2

100=c^2

c=10

Answer:

x-intercept = (-9,0)

y-intercept = (0,27)

Step-by-step explanation:

So first we will convert 9x - 3y = -81 into slope intercept form (y=mx+b).

Subtract 9x on both sides to get -3y = -9x -81. Next divide -3 on both sides to get y = 3x + 27.

Since b is the y-intercept, in y=mx+b and 27 is in the position of b, we can already tell that 27 is the y-intercept. So we will write it as (0,27) because coordinates are supposed to be written as (x,y).

Now in order to find the x-intercept, we will have to plug in 0 for y, in the original equation, so we can solve for x.

So we have: 9x -3(0) = -81

Since 3 × 0 = 0, we now have 9x - 0 = -81. So next we add 0 on both sides to get 9x = -81, and then we divide by 9 to get x = -9. So we will write this as (-9,0).

Hope this helps you :)

Answer:

64 dimes and 34 quarters.

Step-by-step explanation:

Let d represent the amount of dimes and q represent the amount of quarter Julie has.

She has in total 98 coins. Therefore:

\(d+q=98\)

Each dime is worth 0.10 and each quarter is worth 0.25. Together, they are worth in total $14.90. Therefore:

\(0.1d+0.25q=14.90\)

We have a system of equations. We can solve this using substitution.

First, we can multiply the second equation by 100 to simplify. So:

\(10d+25q=1490\)

From the first equation, we can subtract q from both sides:

\(d=98-q\)

Substitute this into the second equation:

\(10(98-q)+25q=1490\)

Distribute:

\(980-10q+25q=1490\)

Combine like term:

\(15q+980=1490\)

Subtract:

\(15q=510\)

Therefore:

\(q=34\)

So, Julie has 34 quarters.

Returning to our first equation:

\(d+q=98\)

Substitute:

\(d+34=98\)

Therefore:

\(d=64\)

Thus, Julie has 64 dimes and 34 quarters.

No, the equation solved is not correct.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given that, an equation, -6 +2x = -10

The solution of step 2 is not correct because, 2 should be divided by every term in the equation, in the step 2, 2 is not divided by -6, the first term which is making the equation in correct,

The correct solution is as follows,

-6 +2x = -10

2x = -10+6

2x = -4

x = -2

Hence, the equation solved is not correct.

Learn more about equations, click;

https://brainly.com/question/29657988

#SPJ1

Answer:

407.4

Step-by-step explanation:

Answer:

Partial product 1: 194

Partial product 2: 388

Answer: 407.4

The height of the cliff is approximately 269 feet.

We will be using the tangent function to find the height of the cliff.
Draw a right triangle with the rowboat at one corner, the cliff's base as the adjacent side, and the cliff's height as the opposite side.

The angle of elevation (73.8 degrees) is between the rowboat and the cliff's base.
We are given the adjacent side (75 feet) and we need to find the opposite side (height of the cliff).

To do this, we will use the tangent function:
tan(angle) = opposite side / adjacent side
Plug in the given values:
tan(73.8) = height / 75
Solve for the height:
height = tan(73.8) * 75
Calculate the value:
height ≈ 269.4 feet
Round the height to the nearest foot:
height ≈ 269 feet.

For similar question on function.

https://brainly.com/question/24748644

#SPJ11

Answer: y=-3x-5

Step-by-step explanation:

(0,-5)   (-1,-2)

\(\displaystyle\\\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}\)

x₁=0     x₂=-1     y₁=-5    y₂=-2

\(\displaystyle\\\frac{x-0}{-1-0}=\frac{y-(-5)}{-2-(-5)} \\\\\frac{x}{-1} =\frac{y+5}{-2+5} \\\\-x=\frac{y+5}{3}\)

Multiply both parts of the equation by 3:

\(-3x=y+5\\\\-3x-5=y+5-5\\\\-3x-5=y\)

\(Thus,\ y=-3x-5\)

Answer:

0

Step-by-step explanation

Because sin 0 = cos 0 when 0 = 0 degrees because it wouldn't change it would stay the same so it's just 0 cause it's to the 0 power.

Answer:

2, 1

Step-by-step explanation:

half of 64 is 32

half of 32 is 16

half of 16 is 8

half of 8 is 4

half of 4 is 2

half of 2 is 1

Answer:

2, 1

Step-by-step explanation:

you are dividing it in half or by two