if dydx=ysec2x and y = 5 when x = 0, then y =

Answer:

7x^2+15x+31

Step-by-step explanation:

(3x+5)(x+5)

FOIL

3x^2+15x+5x+25

(3x^2+20x+25)+(4x^2-5x+6) = 7x^2+15x+31

Step-by-step explanation:

The distance from one corner of a rectangle to the opposite corner is sometimes called the diagonal and is given by (w2+h2)1/2

Parameterize S by the vector function

\(\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle\)

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

\(\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle\)

The integral of the field over S is then

\(\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv\)

\(\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv\)

\(\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}\)

Answer:

Step-by-step explanation:

Let the price for children and adults package be represented with x and y respectively.

For the first week the sum of the package will be as follows:

3x+8y = 126

For the two weeks after:

6x+4y= 108

So, we will be having two equations

3x+8y = 126..... (1)

6x+4y= 108.......(2)

These are simultaneous equations

From equation 1

3x+8y = 126

3x = 126-8y

X = 126-8y/3 ............. (3)

Put equation 3 into 2

6 ( 126-8y)/3 +4y = 108

756-48y/3 +4y = 108

756-48y+12y/3 = 108

Cross multiplying

756-48y+12y= 108×3

756-48y+ 12y = 324

Collecting like terms

756-324 = 48y-12y

432= 36y

Divide both sides by 36

432/36 = 36y/36

y= 12

Substituting y into equation 1

3x+8= 126

3x+96=126

3x= 126-96

3x= 30

Divide both sides by 3

3x/3 = 30/3

x = 10

Hence for each of the packages for children and adults. It will be 10 and 12 respectively.

The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

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The first derivative of y² = x² + 2x is dy/dx = x + 1/y, and the second derivative is d²y/dx² = 1/y - x/y².

The given equation is:\(y² = x² + 2x\)

To find the first derivative of the given equation, we need to take the derivative with respect to y and x and then divide the resulting terms.

So we get:

(d/dx) y²

= (d/dx) (x² + 2x)2y(dy/dx)

= 2x + 2dy/dx

= (2x + 2)/2ydy/dx

= x + 1/y

To find the second derivative of the given equation, we need to take the derivative of dy/dx with respect to x, so we get:(d/dx) dy/dx = (d/dx) (x + 1/y)(d²y/dx²) = 1/y - x/y²

Thus, the first derivative of y² = x² + 2x is dy/dx = x + 1/y, and the second derivative is d²y/dx² = 1/y - x/y².

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Let me = the minutes we are searching for.

(-2.5)/11_1/4 = 1/m

Rewrite 11_1/4 as 45/4.

(-2 5)/(45/4) = 1/m

Cross-multiply to find m.

45/4 = -2.5m

Divide both sides by -2.5.

45/4 ÷ -2.5 = m

Use your calculator and good luck.

Answer:

2x-(3y +4)=2x-3y+4

Nothing is wrong with it

Answer:

Nothing

Step-by-step explanation:

2x-(3y+4)=2x-3y+4

The parenthesis didnt change anything.

this is a infinite solution problem.

The number of candy bars Clarissa had left are 55

Given,

In the question:

Clarissa had 72 candy bars to sell. She sold 4 per day for 8 days. She ordered 15 more candy bars to share with her 3 friends.

To find the number of candy bars Clarissa had left.

Now, According to the question:

Total candy sells is 72

Sold candy = 4 per day for 8 days

Sharing candy is 15

Based on the given conditions,

Formulate:

15 + 72 - 8 x 4

Calculate the product or quotient:

15 + 72 - 32

calculate the sum or difference

87 - 32

= 55

Hence,  the number of candy bars Clarissa had left are 55.

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Answer: 35

Step-by-step explanation:

Answer:

Median: 20

first quartile: 9.75

third quartile: 28.75

interquartile range: 19

Explanation:

First we arrange the data from least to greatest

INDUCTIVE REASONING uses sample results to make generalization about the population.

The reasoning method that uses sample results to attempt to make generalizations about the population is called "inductive reasoning." In this method, you gather data from a sample and then use it to draw conclusions about the entire population. The steps involved in this process are:
1. Collect a sample from the population.
2. Analyze the sample data to find trends or patterns.
3. Use the trends or patterns observed in the sample to make generalizations about the entire population.

Inductive reasoning is a powerful tool in many fields, including science, statistics, and social sciences, as it allows us to make informed decisions based on limited data. However, it is important to remember that the accuracy of the generalization depends on the quality of the sample and the size of the sample.

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In conclusion for part A  it would take T - 32.5 minutes to cook a 1.5 kg joint. For part B w is given by the formula w = (T - 25) / (-35). For part C 6.6 kg of beef needs to be cooked for 207 minutes. For part D  5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.

How to solve?

a) To find how long it would take to cook a 1.5 kg joint, we can substitute w = 1.5 into the formula:

T - 35w + 25 = T - 35(1.5) + 25 = T - 32.5

So, it would take T - 32.5 minutes to cook a 1.5 kg joint.

b) To make w the subject of the formula, we need to isolate w on one side of the equation. We can start by subtracting 25 from both sides:

T - 35w = T - 25

Next, we can divide both sides by -35:

w = (T - 25) / (-35)

Therefore, w is given by the formula w = (T - 25) / (-35).

c) To find the weight of beef that needs to be cooked for 207 minutes, we can substitute T = 207 into the original formula:

T - 35w + 25 = 207

Simplifying this equation, we get:

-35w = -232

Dividing both sides by -35, we get:

w = 6.6 kg

Therefore, 6.6 kg of beef needs to be cooked for 207 minutes.

d) To find the weight of beef that needs to be cooked for 3 hours and 48 minutes (which is equivalent to 3 × 60 + 48 = 228 minutes), we can substitute T = 228 into the original formula:

T - 35w + 25 = 228

Simplifying this equation, we get:

-35w = -207

Dividing both sides by -35, we get:

w = 5.91 kg

Therefore, 5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.

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As a result, the right triangle's hypotenuse measures about 43.3 units in length.

The Pythagorean theorem, which asserts that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides, can be used to determine the length of the hypotenuse of a right triangle.

In this instance, we are aware of the right triangle's one angle's value of 55 degrees and the base's length of 27 units. The sine function, which links the ratio of the height to the hypotenuse to the sine of the angle, can be used in trigonometry to get the length of the other side (the height):

height/hypotenuse equals sin(55)

We can find the hypotenuse by rearranging this equation:

Height / sin is the hypotenuse (55)

When we enter this height expression into the first equation, we obtain:

(Base) / cos = hypotenuse (55)

By entering the specified values, we obtain:

Hypotenuse = 27/Cos(55), which is 43.3

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Answer:

1) y = -1/6x + 0

5) y = 1x - 9

I can’t answer all of them for you because there’s too many for me and my phone is about to go dead, but I did the first of the two types of problems and under I explain how to solve them.

Step-by-step explanation:

For numbers 1 through 4, you just need to remember that slope is the same as rise over the run, which is the same as the change in y divided by the change in x. Knowing this, create a table like shown in the first picture to find the slope and y intercept for your equation. After filling in what you know, find the change in x. Now you know the change in x, make something like the second picture. Fill in what you know. Now use what you learned about equivalent fractions in elementary school to find the change in y. Now that you know the change in y, go back to the table and fill in the ?. You can see the erased ? in one of the boxes in my graph in the third picture(my example using question 1). Now, create an equation with the info you now know.

For questions 5 through 8, use the equation in picture four to find the slope. When you know the slope, follow off the instructions for 1-4.

Answer:

Step-by-step explanation:

Sample Space

off  even numbers

= {2,4,6,8,10}.

There are 5 outcomes in the sample space,

Answer:

The answer is A. 31,250.

Step-by-step explanation:

To solve for the 7th term in the geometric sequence, start by plugging 7 into the explicit formula, and the formula will look like \(a_{7}=2*5^{(7-1)}\).

Next, subtract 1 from 7, and the formula will look like \(a_{7}=2*5^{6}\).

Then, raise 5 to the power of 6, which will look like \(2*15625\).

Finally, multiply 2 by 15,625, and the answer will be 31,250.

Answer:

4 in²

Step-by-step explanation:

A triangular prism is a polyhedron made of a triangular base, a copy of the base at the top, and 3 rectangular/square faces joining corresponding sides.

The area of each of the triangle = (1/2) * base * height = (1/2) * 1 in * 1 in = 1/2 in²

Area of each of the square faces = length * breadth = 1 in * 1 in = 1 in²

The surface area of the prism = (2 * area of each triangle) + (3 area of each square face)

The surface area of the prism = (2 * 1/2 in²) + (3 * 1 in²) = 1 in² + 3 in² = 4 in²

The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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The vertical asymptotes for the given function are x = 4 and x = -4.`Therefore, Student A is correct in their approach and final answer.

Given the rational function is `f(x) = (x + 3) / (x² - 16)`.To find the vertical asymptote for the given rational function `f(x) = (x + 3) / (x² - 16)` for four students and to identify who is correct in their approach and final answer, first, we have to find the vertical asymptote of the given function. We know that the vertical asymptotes occur at the zeroes of the denominator when the numerator is not zero. Thus, the denominator must equal zero at `x = -4` and `x = 4`. So, the vertical asymptotes occur at `x = -4` and `x = 4`.Hence, the correct approach and final answer for vertical asymptote of the given rational function is Student A.  Student A: `The vertical asymptotes are the vertical lines that indicate where the function becomes unbounded. These lines occur when the denominator of the rational function is zero and the numerator is not zero.

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The question asks for four students determined the vertical asymptote for this rational function. The correct approach and answer is needed.

Therefore, the correct student's answer is (D) which indicates there are three vertical asymptotes at x = –2,

x = 1, and

x = 4.

Let's find the answer to the question: To find the vertical asymptote of the rational function, we need to find out when the denominator is equal to zero. We can factor the denominator, so we have (x + 2) (x – 1) (x – 4). The denominator will be equal to zero when any of the three factors are equal to zero:

(x + 2) = 0

(x – 1) = 0,

or (x – 4) = 0.

Solving each equation, we find the following values for x:

x = –2,

x = 1,

and x = 4

Therefore, the correct student's answer is (D) which indicates there are three vertical asymptotes at x = –2,

x = 1, and

x = 4.

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Answer:299 cm

Step-by-step explanation: you have to find the area of square and rectangle. 33*6.5 = 214.5 plus 13 * 6.5 = 84.5 then add together

214.5 + 84.5 = 299cm

The average change in the volume of water per day is obtained as 0.625  litres.

The rate change of volume is the change of volume with respect to time.

For instantaneous change the derivative of the expression of volume can be taken.

The average change in the volume of water can be obtained as follows,

Average change = Volume of water ÷ Number of days

                            = 2.5 ÷ 4 = 0.625

Hence, the average change in water volume is given as  0.625 liters per day.

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Answer:

43,560 sq ft

Step-by-step explanation:

The amount of candle burn after 6 hours is 4.95 inches.

What is the total amount?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total.

Here, we have

Given that the 9-inch candle burns in 6 hours.

We know that we first have to calculate how 1 hour how much candles will burn.

Candle burn in 1 hour is :

= 9 / 10

= 0.9 inch

Now,

To find out how far the candle burnt after 6 hours we need to multiply the part of the candle burned by one hour by 11/2 hours.

= 11/2 × 0.9

= 4.95 inches

Hence, the amount of candle burn after 6 hours is 4.95 inches.

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Answer:

128

Step-by-step explanation:

Let's start by figuring out the last side of the triangle

we can use the pathagoryous theroem and get

11.9²+x²=16.9²

Solve this and get x=12

Let's now compute the area of the triangle

b*h*.5

12*11.9*.5=71.4

So 71.4 is the area of the triangle

we now need to find the area of the semi circle.

to do this we are going to find the area and then divide it by 2

We know that the length is equal to 12 which means that the radius is 6

so we have

π6²/2

which is 56.55

We add the 71.4+56.55= 127.94 which rounds to 128

Answer:

212.758

Step-by-step explanation:

Find the semi-circle first, the diameter is 16.9 ft.

To find area:

Formula:

pi x radius x radius x 1/2

16.9 ÷ 2 = 8.45 (radius)

22/7 x 8.45 x 8.45 = 224.407 (Circle)

224.407 ÷ 2 = 112.203 (Semi circle)

Find the triangle:

1/2 x base x height or length x base x height

But for now, we will use the first one.

1/2 x 16.9 x 11.9 = 100.555

Now add them up.

100.555 + 112.203 = 212.758

(I don't know what units you to put for your answer since I don't learn American mathematics, so it's up to you)

The value of result in the following expression will be 0 if x has the value of 12:

result = x > 100 ? 0 : 1.

The expression given is known as a ternary operator.

It's a short form of if-else.

The ternary operator is written with three arguments separated by a question mark and a colon:

`variable = (condition) ? value_if_true : value_if_false`.

Here, `result = x > 100 ? 0 : 1;` is a ternary operator, and its meaning is the same as below if-else block.if (x > 100)  {  result = 0; }  else {  result = 1; }

As per the question, we know that if the value of `x` is `12`, then the value of `result` will be `0`.

Hence, the answer is `0`.

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The expression that does not represent  "four more than one-third x" is \(\frac{1}{4}x + 3\)

Expressions are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Therefore, let's write out the expression and know the options that does not represent it.

Hence, four more than one-third x is represented as follows:

\(\frac{1}{3}x + 4\) or \(\frac{x}{3}+4\)

Therefore, the value that does not represent the expression is \(\frac{1}{4}x + 3\)

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Answer:

125 + 25h

Step-by-step explanation:

(a) The probability that a randomly selected package weighs between 48 and 50 grams is 0.5596.

(b) The probability that a randomly selected package weighs more than 51 grams is 0.1587.

(c) we can solve for k using the formula z = (k - μ) / σ: 1.645 = (k - 49.8) / 1.2

What is probability?

Probability is a measure of the likelihood of an event occurring.

a. To find the probability that a randomly selected package weighs between 48 and 50 grams, we need to calculate the area under the normal curve between these two values.

We can standardize the values using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

For x = 48, z = (48 - 49.8) / 1.2 = -1.5

For x = 50, z = (50 - 49.8) / 1.2 = 0.1667

Using a standard normal distribution table or a calculator, we can find the area under the curve between z = -1.5 and z = 0.1667 to be approximately 0.5596.

Therefore, the probability that a randomly selected package weighs between 48 and 50 grams is 0.5596.

b. To find the probability that a randomly selected package weighs more than 51 grams, we need to calculate the area under the normal curve to the right of 51.

Again, we can standardize using z = (x - μ) / σ, where x = 51, μ = 49.8, and σ = 1.2.

z = (51 - 49.8) / 1.2 = 1

Using a standard normal distribution table or a calculator, we can find the area under the curve to the right of z = 1 to be approximately 0.1587.

Therefore, the probability that a randomly selected package weighs more than 51 grams is 0.1587.

c. To find the value of k for which the probability that a randomly selected package weighs more than k grams is 0.05, we need to find the z-score that corresponds to the area to the right of k being 0.05.

Using a standard normal distribution table or a calculator, we can find that the z-score for an area of 0.05 to the right of it is approximately 1.645.

Therefore, we can solve for k using the formula z = (k - μ) / σ:

1.645 = (k - 49.8) / 1.2

Solving for k, we get:

k = 1.645(1.2) + 49.8 ≈ 51.02

So the value of k for which the probability that a randomly selected package weighs more than k grams is 0.05 is approximately 51.02 grams.

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Answer:

D

Step-by-step explanation:

We have the two linear equations:

\(\text{ Line 1: }y=3x+3\)

\(\text{ Line 2: }y=-3x-5\)

And we want to determine the relationship between them.

Let's go through each of the answer choices.

Parallel?

Remember that parallel lines have the same slopes.

The slope of Line 1 is 3, while the slope is Line 2 is -3.

Since they have different slopes, they are not parallel.

Perpendicular?

Perpendicular lines have slopes who are negative reciprocals of each other.

For example, the negative reciprocal of 2 will be -1/2. And the negative reciprocal of -1/2 is 2.

The slope of Line 1 is 3. The negative reciprocal of 3 is -1/3. This is not the slope of Line 2.

We can do it for Line 2 just to confirm. The slope of Line 2 is -3. The negative reciprocal of -3 is 1/3.

So, because their slopes are not negative reciprocals of each other, the two lines are not congruent.

Both?

No two lines can be both parallel and perpendicular simultaneously, so this is out of the question.

[N]either?

Yes indeed. They lines are neither parallel nor perpendicular, so this is our only choice.

And we're done!