can someone help me with part b of question please.

Answer:

hypotenuse

Step-by-step explanation:

The side opposite the right angle has a special name - hypotenuse

The other two sides of the right triangle are called legs

Answer:

Therefore, the maximum height reached by the rocket is approximately 2080 feet.

Step-by-step explanation:

The given equation is y = -16x² + 400x + 80.

This is a quadratic function with a negative coefficient of x², which means that it is a downward facing parabola. The maximum point of this parabola represents the highest point reached by the rocket.

The x-coordinate of the vertex of the parabola can be found using the formula x = -b/2a, where a = -16 and b = 400.

x = -400/(2*(-16)) = 12.5

So the maximum height is reached 12.5 seconds after launch.

To find the corresponding y-coordinate, we substitute x = 12.5 into the equation:

y = -16(12.5)² + 400(12.5) + 80 = 2080

Answer:  550 ft

Step-by-step explanation:

the equation they gave is a quadratic/parabola.  To find the max you  will need to find the vertex because the max/min of a parabola is the vertex

y is your height

x is your time in sec

y = -16x² + 160x +150

To find vertex use \(x = -\frac{b}{2a}\)

a = -16

b = 160

c = 150

\(x = -\frac{160}{2(-16)}\)

x = 5      This is the time that it happens 5 sec

Plug back in to find max/vertex height

y = -16x² + 160x +150

y = -16(5)² + 160(5) +150

y=550

Max height is at 550 ft

Answer:

3.14

Step-by-step explanation:

area=pi times the square of radius

1^2 = 1 x 3.14=3.14

Answer:

A. (0,4)

Step-by-step explanation:

You can calculate the y intercept when x = 0.

Substitute 0 for x:

y = (-4/3)(0) + 4

= 0 + 4

= 4

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Answer:

$60

Step-by-step explanation:

Let's say we need t $2 bills and v $5 bills.

We need 9 more $2 bills than $5 bills, so:

t = 9 + v

We also know that the amount of money in t $2 bills is 2 * t = 2t. The amount of money in v + 9 $5 bills is 5 * (v + 9) = 5v + 45. These amounts are equal:

5v + 45 = 2t

Plug v + 9 in for t in 5v = 2t + 18:

5v = 2t + 18

5v = 2 * (9 + v) + 18

5v = 18 + 2v + 18

3v = 36

v = 12

We have 12 $5 bills, so that total cost is 12 * 5 = $60.

~ an aesthetics lover

One of the primary factors determining your card's A.P.R. is your credit score is "True". The correct answer is B.

Credit card issuers evaluate applicants' creditworthiness based on their credit scores, among other factors, and use this information to determine the interest rate they will be charged. Higher credit scores generally result in lower A.P.R.s, reflecting a lower risk profile.

However, it is important to note that the specific A.P.R. offered to an individual may also depend on other factors, such as the card's terms and conditions, the applicant's income, and the card issuer's policies. It is incorrect to assume that most cardholders pay the lowest rate listed when given a range of A.P.R.s, as individual circumstances and creditworthiness vary.

Additionally, higher A.P.R.s do not benefit cardholders, as they result in increased interest charges. The notion that A.P.R.s on credit cards are usually fixed and not adjusted is also incorrect, as A.P.R.s can be variable and subject to change based on various factors.

Therefore, the correct answer is B) One of the primary factors determining your card's A.P.R. is your credit score.

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Note: The question would be as

Reading through a credit card disclosure (aka the Schumer Box), you see the A.P.R. for a specific card is set at 9.99% -23.99%. Which of the following statements is probably TRUE?

a. When given a range of A.PR.s like this, you can assume most cardholders pay the lowest rate listed

b. One of the primary factors determining your card's A.P.R. is your credit score

c. With credit card A.PR.s, cardholders like higher A.P.R.s because they earn more

d. The A.PR. on credit cards is usually fixed so they won't be adjusted as long as you are a cardholder

Answer:

:)

Step-by-step explanation:

The average rate of change between the PVC (x=0) and point 1000 is 0.03.

What is average?

The average of a function is defined as the sum of all the terms that are present in the function divided by the total number of terms in the function.

Here the function is \(f(x)=-0.00002x^{2} +0.05x+1600\)

To find the rate of the function differentiate it with respect to x

\(f('x)=-0.00004x+0.05\)

Now put the value x = 0

\(f('0)=0.05 (i\)

Now, put x = 1000

\(f('1000)=-0.04+0.05=0.01 (ii\)

Now, the average of the PVC at x= 0 and the x=1000

Average is \(\frac{0.05+0.01}{2}\\ \frac{0.06}{2}=0.03\)

Hence, the average rate change is 0.03.

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The probability of Z being greater than 4 is nearly 0 (option D). Therefore, the answer is D.

Let's assume that the weight of a grapefruit follows a normal distribution with mean 0.9 pounds and standard deviation 0.1 pounds. Then, the weight of three grapefruits will follow a normal distribution with mean 2.7 pounds (3 x 0.9) and standard deviation 0.1732 pounds (sqrt(3) x 0.1).

Now, we need to find the probability that the total weight of three grapefruits is more than 3.4 pounds. We can standardize the distribution by subtracting the mean from 3.4 and dividing by the standard deviation:

Z = (3.4 - 2.7) / 0.1732 = 4

Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than 4 is nearly 0 (option D). Therefore, the answer is D.

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Answer:

A) One hundred random students

Step-by-step explanation:

Answer: A)  -4.6

b) 4.6 spaces left from the original spot

c) the totaal distance travled was 18.2 cm

Step-by-step explanation:

for a you add the amounts together, if you go left that's negative so you use subtraction

for b you count the amount you have from zero

for c you add all the numbers together and forget the signs

The recursive rule for the number of acres at the beginning of the nth day in a forest fire that grows by 20% each day and is battled by firefighters who can put out 15 acres per day is given by: A(n) = 1.2 * A(n-1) - 15, where A(n) represents the number of acres at the beginning of the nth day. Using this rule, we can calculate that there are 89.6 acres burning at the beginning of the 8th day.

Explanation: To determine the recursive rule for the number of acres at the beginning of the nth day, we need to consider the given information. The forest fire initially covers 60 acres and grows by 20% each day. This means that the number of acres at the beginning of the next day (n+1) is 1.2 times the number of acres at the beginning of the current day (n). However, the firefighters are able to put out 15 acres of fire per day.

Therefore, to calculate A(n), we start with the initial number of acres, which is 60, and apply the recursive rule. A(n) = 1.2 * A(n-1) - 15. This formula takes into account the growth of the fire by 20% and the reduction of 15 acres due to the firefighters' efforts. By substituting the values, we can calculate the number of acres at the beginning of each day.

To find the number of acres burning at the 8th day, we substitute n = 8 into the recursive rule. A(8) = 1.2 * A(7) - 15. We need to determine A(7) first by substituting n = 7, and so on, until we reach the initial value A(1) = 60. Once we have calculated A(8), we can determine that there are 89.6 acres burning at the beginning of the 8th day

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Yes, infrared spectroscopy would indeed be helpful in determining,

if the dehydration reaction of cyclohexanol to form cyclohexene was successful in an organic chemistry lab.

Infrared spectroscopy (IR spectroscopy) is a widely used analytical technique in organic chemistry,

That provides information about the functional groups present in a compound.

It measures the absorption of infrared radiation by the sample,

Which corresponds to the vibrations of different chemical bonds in the molecule.

In the case of cyclohexanol and cyclohexene, there is a significant difference in their functional groups.

Cyclohexanol contains an -OH group alcohol, whereas cyclohexene contains a carbon-carbon double bond alkene.

These functional groups have characteristic absorption bands in the IR spectrum.

By comparing the IR spectra of the starting material cyclohexanol and the desired product cyclohexene.

One can determine if the dehydration reaction was successful.

The presence or absence of characteristic absorption bands for the alcohol (-OH) and the alkene (C=C).

In the product spectrum can provide evidence of the reaction's success.

If the desired cyclohexene is formed, the absorption band corresponding to the -OH group should disappear,

Indicating the removal of the alcohol functionality.

Additionally, a new absorption band corresponding to the C=C bond should appear in the product spectrum.

Therefore, IR spectroscopy can be a valuable tool in confirming the success of the dehydration reaction and characterizing the functional groups present in the resulting product.

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Answer:

___________________________________________________________

By finding the product of a point's x coordinate times the next point's y coordinate, then subtracting the y coordinate of the first point times the x coordinate of the second coordinate and dividing by two, you will find the area of the polygon.

___________________________________________________________

Answer:

20 pts

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

20,000 divided by 20 is 1,000!

Answer:

2/9 and 3/12

Step-by-step explanation:

2/9 = 8/36

3/12 = 9/36

Answer:

3.7

Step-by-step explanation:

The lenght of an arc with a radius of 3m and substended angle of 70 degrees is 3.7meters

The length of an arc is expressed as:

L = r theta

Given the following parameters

r = 3m

theta = 70 degrees = 70π/180

L = 3(70π/180)

L = 3.7 metres

Hence the lenght of an arc is 3.7meters

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The order of every element in (Z18, +) is as follows:

Order 1: 0

Order 3: 6, 12

Order 6: 3, 9, 15

Order 9: 2, 4, 8, 10, 14, 16

Order 18: 1, 5, 7, 11, 13, 17

The set (Z18, +) represents the additive group of integers modulo 18. In this group, the order of an element refers to the smallest positive integer n such that n times the element yields the identity element (0). Let's find the order of every element in (Z18, +):

Element 0: The identity element in any group has an order of 1 since multiplying it by any integer will result in the identity itself. Thus, the order of 0 is 1.

Elements 1, 5, 7, 11, 13, 17: These elements have an order of 18 since multiplying them by any integer from 1 to 18 will eventually yield 0. For example, 1 * 18 ≡ 0 (mod 18).

Elements 2, 4, 8, 10, 14, 16: These elements have an order of 9. We can see that multiplying them by 9 will yield 0. For example, 2 * 9 ≡ 0 (mod 18).

Elements 3, 9, 15: These elements have an order of 6. Multiplying them by 6 will yield 0. For example, 3 * 6 ≡ 0 (mod 18).

Elements 6, 12: These elements have an order of 3. Multiplying them by 3 will yield 0. For example, 6 * 3 ≡ 0 (mod 18).

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All correct proportions include the following:

A. \(\frac{AC}{CE} =\frac{BD}{DF}\)

D. \(\frac{CE}{DF} =\frac{AE}{BF}\)

In Mathematics and Geometry, two geometric figures are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Hence, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar.

Since line segment AB is parallel to line segment CD and parallel to line segment EF, we can logically deduce that they are congruent because they can undergo rigid motions. Therefore, we have the following proportional side lengths;

\(\frac{AC}{CE} =\frac{BD}{DF}\)

\(\frac{CE}{DF} =\frac{AE}{BF}\)

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The planet that has the larger mass is the planet B and the measurements in standard forms are

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

Planet A = 5*10^26 kilograms

Planet B = 2*10^28 kilograms

Rewrite the masses properly

So, we have

Planet A = 5*10²⁶ kilograms

Planet B = 2*10²⁸ kilograms

The exponent 28 is greater than the exponent 26

This means that

2*10²⁸ is greater than 5*10²⁶

So, we have

Planet B has the larger mass

When the measurements are expressed in standard forms, we have

Planet A = 500000000000000000000000000 kilograms

Planet B = 20000000000000000000000000000 kilograms

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Let's determine the height of the building using ratios and proportions.

Where,

h = height of the building

We get,

Therefore, the height of the building is approximately 105 m.

Answer:

2/5*180=72

360/72=5

as simple as that you just need to read on polygons

Step-by-step explanation:

pls give me brainlyist

First, let's define variables:

A = adults

C = children

Okay, now that's done, time to set up the two equations required to solve:

10a + 7c = 6549

a + c = 783

One way you can solve this is to set up the second equation to isolate a variable. For example,

a = -c + 783

Using this, we can plug it into the first equation and solve for c.

10(-c+783) + 7c = 6549

-3c = -1281

c = 427

Now, use the value of 427and plug it in either equation to solve for a.

a + 427 = 783

a = 356

356 adult tickets were sold, and 427 children tickets were sold.

The value for a = -2 and b = 0, the absolute minimum of f(x, y) is 0, and the absolute maximum is 2.

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To find the critical points of the function f(x, y) = √(2² - x² - y²) restricted to the boundary of D, we need to consider the condition x² + y² = 2².

Let's solve for x² + y² = 2² and substitute it into the function f(x, y):

x² + y² = 2²

Simplifying, we have:

x² + y² = 4

Substituting this into f(x, y), we get:

f(x, y) = √(2² - x² - y²) = √(4 - x² - y²)

To find the critical points, we need to find where the partial derivatives of f(x, y) equal zero. Since we are restricted to the boundary of D, we can use Lagrange multipliers to consider the constraint x² + y² = 4.

Let's set up the Lagrange multiplier equation:

∇f(x, y) = λ∇g(x, y)

where g(x, y) = x² + y² - 4 and ∇ denotes the gradient.

Calculating the gradients:

∇f(x, y) = <-x/√(4 - x² - y²), -y/√(4 - x² - y²)>

∇g(x, y) = <2x, 2y>

Setting the components equal, we have:

-x/√(4 - x² - y²) = 2xλ

-y/√(4 - x² - y²) = 2yλ

x² + y² = 4

We can simplify the equations by canceling out the x and y terms (assuming they are not zero):

1/√(4 - x² - y²) = 2λ

x² + y² = 4

From the second equation, we know that x² + y² = 4. Substituting this into the first equation, we get:

1/√(4 - 4) = 2λ

1/√0 = 2λ

0 = 2λ

Since λ cannot equal zero, we can conclude that there are no critical points within the interior of D.

However, we need to check the boundary of D for critical points. The boundary is defined as x² + y² = 4.

Let's find the critical points on the boundary:

Substituting x² + y² = 4 into f(x, y):

f(x, y) = √(4 - x² - y²)

To find the absolute minimum and maximum on the boundary, we need to find the extremum points by analyzing the function along the boundary.

Using techniques such as Lagrange multipliers or parameterization, we can find that the absolute minimum occurs at (x, y) = (-2, 0), and the absolute maximum occurs at (x, y) = (2, 0).

Therefore:

a = -2

b = 0

The absolute minimum of f(x, y) is 0, and the absolute maximum is 2.

Please note that this solution assumes that the question is asking for critical points and extrema on the boundary of D, not at corner points. If the question intends to ask for extrema at corner points as well, further analysis would be needed.

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