16+8+4+2+1+1/2+1/4+1/8+....
Find the sum of the infinite geometric series.

Answer:

a. 22.3°

b. 2940.16 ft/s

Step-by-step explanation:

Here is the complete question

A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point (x, y) at the relationship cot theta = 2x/2y + gt^2 where theta is the angle of elevation of the launcher and g is the acceleration due to gravity (32.2 feet/second^2). An artillery man is firing at an enemy barker located 2275 feet up the side of a hill that is 6325 feet away. He fires a round, and exactly 2.84 seconds later he scores a direct hit.

a. What angle of elevation did he use? theta = degree (Do not round until the final answer. Then round to one decimal place as needed.)

b. f the angle of elevation is also given by sec theta = v_0 t/x, where v_0 is the velocity of the weapon, find the muzzle velocity of the artillery piece he used. v_0 = feet/second (Round to two decimal places as needed.)

Solution

(a) What angle of elevation did he use?

Given that cosθ = 2x/(2y + gt²) where x = horizontal distance of projectile = 6175 feet away,y = vertical distance of projectile = 2450 feet up, g = acceleration due to gravity = 32 ft/s² and t = time of hit = 2.27 s

So, cosθ = 2x/(2y + gt²)

cotθ = 2 × 6175 ft/(2 × 2450 ft + 32 ft/s² × (2.27 s)²)

cotθ = 12350 ft/(4900 ft + 32 ft/s² × 5.1529 s²)

cotθ = 12350 ft/(4900 ft + 164.8928 ft)

cotθ = 12350 ft/(5064.8928 ft)

1/tanθ = 2.4384

tanθ = 1/2.4384

tanθ = 0.4101

θ = tan⁻¹(0.4101)

θ = 22.3°

(b) If the angle of elevation is also given by sec θ = υ0t/x. where υ0 is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.

Making u0 subject of the formula, we have

u0 = xsecθ/t

u0 = x/tcosθ

since x = 6175ft, t = 2.27 s and θ = 22.3°, then

u0 = x/tcosθ

u0 = 6175 ft/(2.27 s × cos22.3°)

u0 = 6175 ft/(2.27 s × 0.9252)

u0 = 6175 ft/(2.1 s)

u0 = 2940.16 ft/s

Answer:

The correct solution is "x=3 or x=9".

Step-by-step explanation:

The given equation is:

⇒  [tex]x^2 - 12x + 49 = 22[/tex]

On subtracting "22" from both sides, we get

⇒  [tex]x^2-12x+49-22=22-22[/tex]

⇒          [tex]x^2-12x+27=0[/tex]

On factorizing the above equation, we get

⇒  [tex]x^2-9x-3x-27=0[/tex]

By taking common, we get

⇒  [tex]x(x-9)-3(x-9)=0[/tex]

⇒          [tex](x-3)(x-9)=0[/tex]

⇒                        [tex]x-3=0[/tex]

                                 [tex]x=3[/tex]

Or,

⇒                        [tex]x-9=0[/tex]

                                [tex]x=9[/tex]

Answer:

0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

What is the probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials?

2.45 standard deviations above the mean is Z = 2.45, so this probability is the p-value of Z = 2.45.

Looking at the z-table, Z = 2.45 has a p-value of 0.9929.

0.9929 = 99.29% probability that the carbon fiber composite material can withstand pressure less than 2.45 standard deviations above the mean when compared to the individual materials

Answer:

I think the answer it b and a

Answer:

j < 20

19

Step-by-step explanation:

60 > 3j

Divide both sides by 3

20 > j

Flip

j < 20

greatest whole-dollar amount Joyce could have earned?

19

Answer:

D. Both of the dot A and B have the same mean

Answer:

15m^2

Step-by-step explanation:

2m*3m = 6m^2

3m*3m = 9m^2

Answer: 6m^2 + 9m^2 = 15m^2

Feel free to mark as brainliest :D

Answer:

the mean of those numbers is 17.1

Answer:

The M.A.D (mean absolute deviation) is 2.3

Bonus (Just in case you need it): The Mean is 17.1

Have a good day!

Answer:

h^9

Step-by-step explanation:

When divided you subtract exponents 14-5=9

The expression using a single exponent is (d) h^9

From the question, we have the following parameters that can be used in our computation:

h^14 over h^5

This means that

h^14/h^5

Apply the law of indices

So, we have

h^14/h^5 = h^(14 - 5)

This gives

h^14/h^5 = h^9

Hence, the solution is (d) h^9

Read more about expressions at

https://brainly.com/question/30492964

#SPJ6

Answer:

2/3 km per minute

Step-by-step explanation:

kilometers

1 1/3 - 2/3 = 2/3km

Minutes

2 - 1 = 1 minute

----------------------------

Spped

(2/3 km) / (1 minute)

2/3 km per minute

Answer:

the diameter is 7

Answer:

[tex](6 \times 5) + (2 \times 3) \\ 30 + 6 \\ = 36cm^{2} [/tex]

Answer:

The first one

Step-by-step explanation:

I did this and got it right and I solved it

8×3 equal 24/1 so make it to a whole number 24

Answer:

D (1, 2), (2, 4), (4,8)

Step-by-step explanation:

Points lying on the same line:

If three points lie on the same line, the change in y has to be always the same when x changes by 1.

А. (0, 1), (-1, 3), (1, 3)

(-1,3) to (0,1): x changes by 1, y by -2

(0,1) to (1,3): x changes by 1, y by 2

So these points are not on the same line.

B. (4, 2), (2, 1), (4, -2)

Two values for y when x = 4, so not on the same straight line.

C (0, 0), (8, 0), (0, 8)

Two values for y when x = 0, so not on the same straight line.

D (1, 2), (2, 4), (4,8)

Here, when x changed by 1(from 1 to 2), y changed by 2.

When x changed by 2(from 2 to 4), y changed by 2*2 = 4.

So these points are on a straight line, and D is the correct answer.

Answer:

The answer is "[tex]28^{\circ}[/tex]"

Step-by-step explanation:

Please find the complete question in the file.  

The angle F measure is identical to the angle C measure.

The adjacent BC and the hypotenuse AC have been developed. That would be used cosine.

[tex]\cos C = \frac{15}{17}\\\\C =\ cos^{-1}\frac{15}{17} = 28.07\approx 28^{\circ}[/tex]

Answer:

90

Step-by-step explanation:

72 is the least and 90 is the greatest

87 is the second most greatest and 83 is the third most.

Therefore the answer is 90

Answer:

d. 128

Step-by-step explanation:

a. 0

b. 4

c. 64

d. 128

Answer:

656×756÷765+656+65=

Step-by-step explanation:

it was soo easy now i get what it is talking about no

Answer:

The Rule of 72 is a simplified formula that calculates how long it'll take for an investment to double in value, based on its rate of return. The Rule of 72 applies to compounded interest rates and is reasonably accurate for interest rates that fall in the range of 6% and 10%.

Answer:

100

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

trust me bro

Answer:

If in the ones place of a number contains digits like 0,2,4,6 or 8 then we can say that the number is divisible by 2.

Answer:

[tex] \frac{20}{29} [/tex]

Step-by-step explanation:

Let x replace theta.

Apply pythagorean trig identity

[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]

[tex] (\frac{21}{29} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]

[tex] \frac{441}{841} + \cos {}^{2} (x) = 1[/tex]

[tex] \cos {}^{2} (x) = 1 - \frac{441}{841} [/tex]

[tex] \cos {}^{2} (x) = \frac{400}{841} [/tex]

[tex] \cos(x) = \frac{20}{29} [/tex]

Cosine is positve in 1st quadrant so the answer is

[tex] \frac{20}{29} [/tex]

at lunch four friends drink 8 pints of milk. how many fluid ounces is this equal to?

128 FL

Answer:

The answer is choice #1 or 128 Fluid ounces

Step-by-step explanation:

8 pints = 128 oz

Answer:

No, a 25-year-old job applicant cannot be two standard deviations below the mean

Step-by-step explanation:

There are two frequencies 25 and 65

Mean of the two frequencies = 25+65/2 = 45

Standard deviation =

[tex]\frac{65-25}{\sqrt{12} } \\= 11.55[/tex]

Mean - 2 x standard deviation [tex]= 45 - 2 * 11.55 = 21.9[/tex]

[tex]21.9 < 25[/tex]

Thus, a 25-year-old job applicant cannot be two standard deviations below the mean

Answer:

22 in. or B

Step-by-step explanation:

add all the sides

Answer:

The Answer would be B)22 in.

Step-by-step explanation:

if you add the sides together then multiply by 2 you will get 22 in. I hope this helpped!

Answer: THE ONE ABOVE IS WRONG

A= 3V/h

​

Step-by-step explanation:

Formulas may contain multiple variables, along with known numbers and letters that stand for known constants like \piπpi.

We can highlight a certain variable in the formula by treating the formula as an equation where we want to solve for that variable.

In this case, we need to solve the equation V =\dfrac{1}{3}AhV=

3

1

​

AhV, equals, start fraction, 1, divided by, 3, end fraction, A, h for AAA.

Hint #22 / 3

\begin{aligned} V&=\dfrac{1}{3}Ah \\\\ \dfrac{3V}{h}&=A \end{aligned}

V

h

3V

​

​

=

3

1

​

Ah

=A

​

Hint #33 / 3

This is the result of rearranging the formula to highlight the base area:

A=\dfrac{3V}{h}A=

h

3V

​ It works I did it in Khan

Answer:

Sample means and the grand mean

Step-by-step explanation:

The total sum of squares present in the sample can be partitioned into two parts.

1) Within sum of squares ( also called error sum of squares)

2) Between sum of squares

The first part is the sum of squares of deviations of the observations from the sample mean and is called the within sum of squares ( also called error sum of squares).

The second part is the weighted sum of the square of deviations of the sample means from the grand mean and is called between sum of squares.

Thus symbolically

Totastal SS = Within SS + Between SS

Answer:

2.8 liters

Step-by-step explanation:

6 - 3.20 = 2.8

Answer:

2 4/5

Step-by-step explanation:

6-3 1/5 = 2 4/5