At what projection angle will the range of a projectile equal to 6 times its maximum height?

Answers

Answer 1

i not sure but it might be 60 kilogrames

Answer 2

The formula for maximum height is:

H = v²sin²θ/2g

The formula for range is:

R = v²sin(2θ)/g

The relationship between the two is written as:
R = 6H
v²sin(2θ)/g = 6(v²sin²θ/2g)
v²sin(2θ)/g = 3v²sin²θ/g)
Cancelling out like terms,
sin(2θ) = 3sin²θ
Solving for θ using a scientific calculator,
θ = 33.7°

Related Questions

Five sixths of Forty two

Answers

Hello,

Five sixths of forty two is = 35.

If bethany earned $51,740 last year, how much did she earn per week?

Answers

52.14 dollars per week.

What is the difference between the mean and the median of the data set? {22, 8, 10 ,18 ,12, 20} 0 2 4 6

Answers

Answer: The correct option is (A) 0.

Step-by-step explanation: We are given to find the difference between the mean and median of the following data set:

{22, 8, 10 ,18 ,12, 20}.

MEAN: It is the sum of all the values together divided by the number of values in the set.

So, the MEAN of the given data set is

[tex]m=\dfrac{22+8+10+18+12+20}{6}\\\\\\\Rightarrow m=\dfrac{90}{6}\\\\\Rightarrow m=15.[/tex]

MEDIAN: The median of a data set is given by the middle-most value in the data.

If there is an even number of items in the data set, then the median is found by taking the mean of the two middlemost numbers.

Arranging the given data in ascending order, we have

8, 10, 12, 18, 20, 22.

Since there are 6 values, that is even number of values. so the MEDIAN is given by

[tex]M=\dfrac{12+18}{2}\\\\\Rightarrow M=\dfrac{30}{2}\\\\\Rightarrow M=15.[/tex]

Therefore, m = M.

That is, mean and median of the given data are equal.

Hence, the difference is

m - M = 15 - 15 = 0.

Thus, option (A) is CORRECT.

Answer:

Option A - 0

Step-by-step explanation:

Given : Data set {22, 8, 10 ,18 ,12, 20}

To find : What is the difference between the mean and the median of the data set?

Solution :

Data set in increasing order {8, 10 ,12,18, 20,22}

Mean is defined as the division of sum of set values by total number of values.

[tex]M=\frac{\sum x}{n}[/tex]

Substitute the values we get,

[tex]M=\frac{8+10+12+18+20+22}{6}[/tex]

[tex]M=\frac{90}{6}[/tex]

[tex]M=15[/tex]

So, The mean of the set is 15.

Median of even numbers is the average of two middle terms.

[tex]m=\frac{3rd+4th}{2}[/tex]

[tex]m=\frac{12+18}{2}[/tex]

[tex]m=\frac{30}{2}[/tex]

[tex]m=15[/tex]

So, The median of the set is 15.

Now, The difference of the mean and the median of the set is

[tex]d=M-m[/tex]

[tex]d=15-15[/tex]

[tex]d=0[/tex]

Therefore,Option A is correct.

The difference of the mean and the median of the set is 0.

Sebastian made the following model to find the product of 17X24
Is his model correct? Expalin

Answers

Sebastian's model is not correct because 20x7 does not equal 14.
17x24= 408

®PLEASE MARK AS BRAINLIEST TO HELP ME LEVEL UP®

1.5x+0.5y=12
solve for y

Answers

Y=-3x+24

Hope this helps :)

The fracture toughness (in ) of a particular steel alloy is known to be normally distributed with a mean of 28.3 and a standard deviation of 0.77. We select one sample of this alloy at random and measure its fracture toughness. Given that the fracture toughness is at least 27, what is the probability that the fracture toughness will be between 29 and 40.3? is it just P(X <= 40.3) - P(X <= 29)? How do I use the 27?

Answers

This is a conditional probability question.

The conditional probability is given as follows: The probability of an event A given B is given by

[tex]P(A|B)= \frac{P(A\cap B)}{P(B)} [/tex]

Thus, given that the fracture toughness of a particular steel alloy is known to be normally distributed with a mean of 28.3 and a standard deviation of 0.77.

The probability that the fracture toughness will be between 29 and 40.3 given that the fracture toughness is at least 27 is given by

[tex]P(29 \leq X \leq 40.3 \, | \, X \geq 27)= \frac{P(29 \leq X \leq 40.3)\cap P(X \geq 27)}{P(X \geq 27)} \\ \\ =\frac{P(29 \leq X \leq 40.3)}{P(X \geq 27)}[/tex]

[tex]P(29 \leq X \leq 40.3)=P\left(z \ \textless \ \frac{40.3-28.3}{0.77}\right)- P\left(z \ \textless \ \frac{29-28.3}{0.77}\right) \\ \\ =P(z\ \textless \ 15.58)-P(z\ \textless \ 0.91)=1-0.81835=0.18165[/tex]

[tex]P(X \geq 27)=1-P(x\ \textless \ 27) \\ \\ =1-P\left(z\ \textless \ \frac{27-28.3}{0.77}\right)=1-P(z\ \textless \ -1.688) \\ \\ =1-0.04568=0.95432[/tex]

Thus, the probability that the fracture toughness will be between 29 and 40.3 given that the fracture toughness is at least 27 is given by

[tex]\frac{P(29 \leq X \leq 40.3)}{P(X \geq 27)}= \frac{0.18165}{0.95432} =\bold{0.1903}[/tex]

To determine a 72 percent level of confidence for a proportion, the value of z is approximately:

Answers

To solve this problem, we have to make use of the standard probability distribution tables for z test.

Since we are asked to find for the 72 percent level confidence, then this means we are to look for the value of z which gives (100-72)/2 = 14% on both sides of the tail.

So at 14% tail on one side, the z value is approximately:

1.08

Answer:

± 1.08

A round pizza, with a 12.0 in diameter, is cut into 8 pie shaped pieces. What is the area of each slice (sector) of pizza?

Answers

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\pi \theta r^2}{360}\quad \begin{cases} d=diameter\\ r=radius\\ \theta =angle~in\\ \qquad degrees\\ -------\\ r=\frac{d}{2}=6\\ \theta =\frac{360}{8}=45 \end{cases}\implies A=\cfrac{\pi \cdot 45\cdot 6^2}{360}[/tex]

Determine the unit rate. Use mental math when you can. 6 golf balls for $15. 2 dozen tennis balls for $36. 4lb meat for $18. 24 tickets for $480.

Answers

Final answer:

To determine the unit rate for each item, divide the total cost by the number of units. This gives us $2.50 per golf ball, $1.50 per tennis ball, $4.50 per pound of meat, and $20 per ticket.

Explanation:

The question involves determining the unit rate of different items. A unit rate is the cost per one unit of an item. To calculate each unit rate, we divide the total cost by the number of units.

For 6 golf balls for $15, the unit rate is $15 ÷ 6 = $2.50 per golf ball.For 2 dozen (24) tennis balls for $36, the unit rate is $36 ÷ 24 = $1.50 per tennis ball.For 4lb of meat for $18, the unit rate is $18 ÷ 4 = $4.50 per pound of meat.For 24 tickets for $480, the unit rate is $480 ÷ 24 = $20 per ticket.

These calculations can often be made using mental math, especially when dealing with simple numbers or common multiples.

5y-x=10 (solve for y).

Answers

To solve 5y - x = 10 for y, add x to both sides and then divide by 5, resulting in the solution y = (x + 10) / 5.

To solve the equation 5y - x = 10 for y, follow these steps:

Add x to both sides of the equation to isolate terms with y on one side: 5y = x + 10.

Now, divide both sides of the equation by 5 to solve for y:

y = (x + 10) / 5.

The solution for y when given an equation of the form 5y - x = 10 is y = (x + 10) / 5.

what is absolute value of these set of numbers?

Answers

= (6×-2) - (-3×-4)
= -12 - 12 = -24
that's the determinant tho, not absolute value

is 30 x 10 to the 4th power equal 3,000,000

Answers

It is not because 30×10^4 is 300,000.
The answer would then be...
30×10^5
Hope this helps!

Marcus works for 8 hours a day for 2 days at the bank and earned $165.12 how much did he earn per hour

Answers

$10.32 an hour.

165.12/16

16= hours worked

$165.12= pay for those 16 hours worked

Answer is $10.32 per hour

165.12/2= 82.56
82.56/8=10.32
I believe Marcus earns $10.32 Per hour

0.27 repeating in simplest form

Answers

.27 repeating is 3/11

The standard notation for a repeating decimal is to put a bar over the repeating digits, that is, 0.27272727...=0.27 repeating

0.27 (repeating) = 27/99 which reduces to 3/11 <==

** if u have 1 number repeating, like 0.222, then u put that 1 number over 9...2/9

if u have 2 numbers repeating, like 0.1414, then u put those 2 numbers over 99....14/99

if u have 3 numbers repeating, like 0.234234, then u put those 3 numbers over 999.....234/999

9x-5y=-32 in slope intercept form

Answers

The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x:

y = a + bxb is the slopea is a constant term. It is the y intercept, the place where the line crosses the y axis.

Example 1

y = -13 + 7x

This equation is in slope intercept form. The y intercept is (0,-13) and the slope is 7.

Example 2

4x + 3y = 12

Rewrite this equation in slope intercept form.

3y = 12 - 4x

The equation is now in slope intercept form. The y intercept is (0,4) and the slope is
-4/3.

Example 3

5x - 3y - 15 = 0

Rewrite this equation in slope intercept form.

3y = -15 + 5x

The equation is now in slope intercept form. The y intercept is (0,-5) and the slope is
5/3.

Example 4

The equation is now in slope intercept form. The y intercept is (0,-7.5) and the slope is
1.5.

Find the dimensions of the rectangle with area 120 square inches and smallest possible perimeter

Answers

Here, A = L*W and P=2L+2W. Maximize P. Subst. L = A/W for L in the 2nd equation:

P=2(A/W) + 2W. This is to be minimized.

dP/dW = 2[-A/(W^2)) + 2W. But A = 120 sq in:

dP/dW = 2[-120/(W^2)) + 2W set this equal to 0 and solve for W.
Once you have W, find L: L=120/W

Let 2[-120/(W^2)) + W] = 0. Then [-120/(W^2)) + W] = 0

Multiplying all terms by W^2 gives us -120 + W^3 = 0.

w^3 = 120 cubic inches. Find the cube root to find W.

W = cube root of 120 = 4.93 inches. L = 120/W, or L = 120/4.93 inches

Summary: W = 4.93 inches and L = 24.33 inches (answer)

Six sandwiches are being divided evenly among 4 friends.

How many sandwiches will each friend receive?

A. 2

B. 3/2

C. 2/3

D. 3/4

Answers

Hello! Six sandwiches are being split between 4 friends. To find out how much each friend gets, all we have to do is divide the number of sandwiches by friends. 6/4 is 1.5 or 3/2 in improper fraction form. Each friend will get 3/2 of a sandwich. The answer is B: 3/2.

it should be 1 and a half each

What is the slope of y=1/5x - 4?

Answers

1/5 because y=mx+b where m=the slope so in y=1/5x+-b, 1/5 is the slope.

Given that the equation is [tex]y= \frac{1}{5}x-4 [/tex]
the slope is [tex] \frac{1}{5}[/tex] and the -4 is the intercept or where the line crosses the y- axis

Find 1206 ×5 using expanded form. --------×5=

Answers

1000+200+00+6=1206 is how it looks in expanded form.

To calculate 1206 × 5 using expanded form, break 1206 into its place values, multiply each by 5, and then add the results. This gives 6030.

Finding 1206 × 5 Using Expanded Form

To find the product of 1206 and 5 using expanded form, we break down 1206 into its place values:

100020006

Now, we multiply each component by 5:

1000 × 5 = 5000200 × 5 = 10000 × 5 = 06 × 5 = 30

Finally, we add all these products together:

5000 + 1000 + 0 + 30 = 6030

Therefore, 1206 × 5 equals 6030.

by which conversion factor can 800 meters be multiplied to change in to miles?

Answers

there are 1000 meters in 1 kilometer.

and there are 1.609 kilometers in 1 mile.

if there are 1.609 kilometers in 1 mile, then there are 1.609 * 1000 meters in 1 mile, or 1609 meters

[tex]\bf \cfrac{800~\underline{m}}{1}\cdot \cfrac{mile}{1609~\underline{m}}\implies \cfrac{800}{1609}~mile\implies 800\cdot \cfrac{1}{1609}~mile[/tex]

Find the solution set of 3x +2y = 12 if each variable represents a positive integer.

Answers

3x+2y=12
(3/2)x-6=y

All real numbers

3×2 = 6
2×3 = 6
6+6 = 12
X = 2
Y = 3

The time required to cook a pizza at a neighborhood pizza joint is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes. find the time for each event. (round your answers to 2 decimal places.)
a. highest 5 percent min.
b. lowest 50 percent min.
c. middle 95 percent min. to min.
d. lowest 80 percent min.

Answers

Final answer:

a. The highest 5 percent time is approximately 15.29 minutes. b. The lowest 50 percent time is 12 minutes. c. The middle 95 percent interval is approximately 8.08 minutes to 15.92 minutes. d. The lowest 80 percent time is approximately 10.32 minutes.

Explanation:

a. To find the highest 5 percent, we need to find the value that separates the highest 5 percent from the rest. This value is called the upper 5th percentile. Using the z-score formula, z = (x - mean) / standard deviation, we can find the z-score associated with the upper 5th percentile. By looking up this z-score in the z-table, we can find the corresponding value. In this case, the z-score is approximately 1.645. Using the formula, x = z * standard deviation + mean, we can calculate the time needed for the highest 5 percent: x = 1.645 * 2 + 12 = 15.29 minutes.

b. To find the lowest 50 percent, we need to find the value that separates the lowest 50 percent from the rest. This value is called the median. The median of a normally distributed data set is equal to the mean. Hence, the lowest 50 percent time is the mean of 12 minutes.

c. To find the time for the middle 95 percent interval, we need to find the values that separate the middle 95 percent from the rest. These values are called the lower 2.5th percentile and the upper 2.5th percentile. Using the z-score formula, we can find the z-scores associated with the lower and upper 2.5th percentiles. By looking up these z-scores in the z-table, we can find the corresponding values. In this case, the z-scores are approximately -1.960 and 1.960. Using the formula, x = z * standard deviation + mean, we can calculate the times: lower 2.5th percentile = -1.960 * 2 + 12 = 8.08 minutes, and upper 2.5th percentile = 1.960 * 2 + 12 = 15.92 minutes.

d. To find the lowest 80 percent, we need to find the value that separates the lowest 80 percent from the rest. This value is called the lower 20th percentile. Using the z-score formula, we can find the z-score associated with the lower 20th percentile. By looking up this z-score in the z-table, we can find the corresponding value. In this case, the z-score is approximately -0.841. Using the formula, x = z * standard deviation + mean, we can calculate the time needed for the lowest 80 percent: x = -0.841 * 2 + 12 = 10.32 minutes.

use the multiplication table. describe a pattern you see, 5, 10, 15

Answers

Final answer:

The sequence 5, 10, 15 represents multiples of 5, where each number is 5 units apart from the last.

This pattern can also be observed in a multiplication table in the row or column of the number 5.

Explanation:

The question asks us to describe a pattern in the sequence 5, 10, 15.

This sequence represents the multiples of 5. A clear pattern that can be observed is that each number increases by 5 to get to the next multiple.

For instance, starting with 5, adding 5 gives us 10, and adding another 5 to 10 gives us 15.

This pattern continues indefinitely with the series 20, 25, 30, and so on.

The expression 1/3b−1/3 factored is

Answers

(1/3)(b-1) is the simplest set of factors.

Answer:

[tex]\frac{1}{3}[b-1][/tex]

Step-by-step explanation:

we have

[tex]\frac{1}{3}b-\frac{1}{3}[/tex]

Factor the coefficient [tex]\frac{1}{3}[/tex] of both terms

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

What is the value of x in diagram

Answers

Answer is below........

What is the largest flag jake can draw

Answers

Final answer:

In the painting 'Three Flags' by Jasper Johns, the size of the largest flag would depend on the canvas or surface used.

Explanation:

In the painting Three Flags by Jasper Johns, he used his encaustic process to create the artwork. Each flag reduced about twenty-five percent in scale as he stacked canvas flags, with the largest one receding into the background. The congealed wax drippings gave the painting a dimensional sculptural appearance.

The stripes and stars on the flags also grow smaller, adding to the illusion of three separate elements. Therefore, in terms of the largest flag Jake can draw, it would depend on the size of the canvas or surface that he is working with.

How do you write .625 as a fraction

Answers

Since there are 3 digits in this problem it means that the number for the denominator will be 1000. the answer to this is 625/1000

To turn a decimal into a fraction, first notice that the number to the right of the decimal point is 625. The 6 represents the tens, the 2 represents the hundreds, and the 5 represents the thousands. So, we can put 625 over 1000 or 625/1000.

Notice that the fraction [tex]\frac{625}{1000}[/tex] is not in lowest terms. To turn the fraction into lowest terms, we can divide both the numerator and the denominator by 125.

[tex]\frac{625}{1000}[/tex] ÷ [tex]\frac{125}{125}[/tex] = [tex]\frac{5}{8}[/tex]

Therefore, .625 can be written as the fraction 5/8, which is in lowest terms.

ANYONE????
Use infinite geometric summation to write 0.18 as a fraction whose numerator and denominator have no common factors. Recall that 0.18 means 0.18181818 . . . .

Answers

Your denominator is going to be 4 digits. "18,18,18,18".

The Waverly bush company issued 4,000 shares of common stock worth $2000,000.00 total. What is the par value of each share

Answers

I'm pretty sure it's $500 bc 2,000,000.00 divided by 4,000 is 500.

A bird leaves its nest and travels 12 miles per hour downwind for x hours. On the return trip, the bird travels 2 miles per hour slower and has 3 miles left after x hours. What is the distance of the entire trip? How long does the entire trip take?

Answers

3 hours

On the way there, 1.5x12 = 18
On the way back, 1.5x10 = 15

12x = 10x + 3

Subtract 10x from both sides

2x = 3

Divide by two on each side

x = 3/2 or 1 1/2 hours

Distance of the trip:

12 * 2 * 3/2 = 36 miles

How long does the trip take:

3/2 + 3/2 + 3/10 = 3 3/10 hours

3 hours

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