A road running north to south crosses a road going east to west at the point P. car A is driving north along the first road, and an airplane is flying east above the second road. At a particular time the car is 15 kilometers to the north of P and traveling at 55 km/hr, while the airplane is flying at speed 185 km/hr 10 kilometers east of P at an altitude of 2 km. How fast is the distance between the car and the airplane changing? 148.38 km/hr Draw a sketch that shows the roads intersecting at point P, Car A, and the airplane. Label the horizontal distance from P to the airplane x and the vertical distance from P to Car A as y, and let z represent the altitude of the plane. What equation relates the distance from Car A to the plane with x, y and z? Using implicit differentiation, solve for the appropriate derivative that answers the "how fast" question.

Answers

Answer 1

The distance between car A and the airplane is changing at a rate of 148.38 km/hr.

To better understand this answer, we can draw a sketch of the scenario and label the variables accordingly.

Let x represent the horizontal distance from P to the airplane, y the vertical distance from P to car A, and z the altitude of the airplane. The equation that relates the distance from car A to the plane can be written as:

[tex]d^2 = (x^2 + y^2 + z^2)[/tex]

We can use implicit differentiation to solve for the derivative of this equation with respect to time, which answers the “how fast” question. The derivative of the equation is:

x = 185t (horizontal distance from P to airplane)

y = 15 - 55t (vertical distance from P to car)

z = 2 (altitude of airplane)

Now we can substitute these expressions into our equation for the distance between the car and the airplane, and take the derivative with respect to time:

distance between car and airplane = sqrt((185t)^2 + (15 - 55t)^2 + 2^2)

d/dt(distance between car and airplane) = d/dt(sqrt((185t)^2 + (15 - 55t)^2 + 2^2))

= 1/2 * (185^2 * 2t + (15 - 55t)(-55)) / sqrt((185t)^2 + (15 - 55t)^2 + 2^2)

Evaluating this expression at t = 0 (the time when the car is at its closest point to the airplane), we get:

d/dt(distance between car and airplane) = 1/2 * (185^2 * 2(0) + (15 - 55(0))(-55)) / sqrt((185(0))^2 + (15 - 55(0))^2 + 2^2)

= 1/2 * (-825) / sqrt(15^2 + 2^2)

= -412.5 / sqrt (229)

The negative sign indicates that the distance between the car and the airplane is decreasing, as expected. Finally, we can take the absolute value of this expression to get the speed at which the distance is changing:

d/dt (distance between car and airplane)| = 412.5 / sqrt (229) ≈ 148.38 km/hr.

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Related Questions

Can anyone help me please

Answers

Answer:

a) 44 children can safely play in the playground of area 154 m^2.

b) The smallest playground area in which 24 children can play is 84 m^2.

Step-by-step explanation:

We have the ratio 210m^2 : 60.

a) 154/210 is 11/15. Multiplying this scale factor gives the ratio 154 m^2 : 44.

44 is found by multiplying 11/15 by 60.

44 children can safely play in the playground of area 154 m^2.

b) 24/60 is 2/5. Multiplying this scale factor gives the ratio 84 m^2 : 24

84 is found by multiplying 2/5 by 210.

The smallest playground area in which 24 children can play is 84 m^2.

Hope this helps!

Pls read ss

PLS HELPP

Answers

The slopes are,

1) 7/6

2)7/2

3) -1

4) -2

5) 10/9

What is slope?

Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.

1) The given points , [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (6,8)[/tex] then,

=> slope  = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{8-1}{6-0} = \frac{7}{6}[/tex]

2) The given points [tex](x_1,y_1) =(-1,10)[/tex] and [tex](x_2,y_2) = (-5,-4)[/tex] then,

=> Slope = [tex]\frac{-4-10}{-5+1} = \frac{-14}{-4}=\frac{7}{2}[/tex]

3)  The given points [tex](x_1,y_1) =(-10,2)[/tex] and [tex](x_2,y_2) = (-3,-5)[/tex] then,

=> slope = [tex]\frac{-5-2}{-3+10} = \frac{-7}{7}=-1[/tex]

4)  The given points [tex](x_1,y_1) =(-3,-4)[/tex] and [tex](x_2,y_2) = (-1,-8)[/tex] then,

=> slope = [tex]\frac{-8+4}{-1+3} = \frac{-4}{2}=-2[/tex]

5)The given points [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (-9,-9)[/tex] then,

=> slope = [tex]\frac{-9-1}{-9+0} = \frac{-10}{-9}=\frac{10}{9}[/tex]

Hence the slopes are,

1) 7/6

2)7/2

3) -1

4) -2

5) 10/9

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A triangle has an area of 42 cm. The height of the triangle is 14 centimeters. What is the length of the base of the triangle?

Answers

The answer is going to be 3

if you have four cards and were to bet based upon suits while flipping them one at a time while trying to minimize variance, how would you do it?

Answers

The steps which can help in minimizing the variance in the four cards are correct selection of the suit with maximum number of cards.

How to minimize variance?

If you have four cards and were to bet based upon suits while flipping them one at a time while trying to minimize variance, you should follow the below steps:

First, you need to check the suits of the four cards you have.

Now, you need to select the suit that has a maximum number of cards. For instance, if the four cards are 5 of hearts, 7 of spades, 2 of diamonds, and 10 of hearts, you need to select hearts as it has two cards.

After selecting the suit with the maximum number of cards, you need to start flipping the cards one at a time.

Keep a count of the number of times you get the chosen suit. For instance, if you chose hearts, you will count the number of times you get hearts after flipping each card.

Once you get the chosen suit, you can place your bet. The amount of your bet can depend on the number of times you have gotten the chosen suit so far.

So, this process doesn't guarantee that you will win every time.

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Imagine your friend missed class today. How would you explain to them how you would solve the problem below to them? Use complete sentences for full written communication points.

Problem:
(4x+3)(5x-2)

Answers

To solve the problem, first you use distributive property by multiplying 4x to 5x and -2 then you multiply 3 to 5x and -6 which gives you 20x^2 - 8x + 15x -6. then you add all the variables together and all the numbers together which gives you 20x^2 + 7x - 6.

Answer:

[tex]=20x^{2} +2x-6[/tex]

Step-by-step explanation:

First step: you're going to multiply each variable from the first bracket to the first and second variable from the second bracket:

=4x(5x)+4x(-2)

=[tex]20x^{2} -8x[/tex]

Second step: now you're going to do the same thing but for the second variable:

=2(5x)+3(-2)

=10x-6

we're going to add the answers that we got from the first two steps to get the final answer:

[tex]=(20x^{2} -8x)+(10x-6)\\[/tex]

[tex]=20x^{2} +(-8x+10x)+(-6)\\=20x^{2} +2x-6[/tex]

HELPP PLEASE




Try going backwards!




Use the digits `9`, `8`, `7`, `6`, `5`, `4`, `3`, `2`, and `1` in that order to create `100`

Answers

Using the digits 9, 8, 7, 6, 5, 4, 3, 2, and 1 in that order to create 100 by using the mathematical operations, (9 + 8 + 7) x (6 - 5) x (4 + 3 + 2) - 1 = 100

It is not possible to create 100 using the digits 9, 8, 7, 6, 5, 4, 3, 2, and 1 in that order without using any mathematical operations.

However, it is possible to create 100 by using mathematical operations like addition, subtraction, multiplication, division, and parentheses. One possible way to do this is:

(9 + 8 + 7) x (6 - 5) x (4 + 3 + 2) - 1 = 100

Here, we first add the first three digits (9 + 8 + 7 = 24), subtract the fourth and fifth digits (6 - 5 = 1), add the next three digits (4 + 3 + 2 = 9), and finally multiply all three results and subtract the last digit (24 x 1 x 9 - 1 = 215 - 1 = 100).

So, using this sequence of digits and mathematical operations, we can create 100.

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Mary runs 600m every day.
Work out how far Mary runs in one week.
Give your answer in kilometres.

Answers

Answer:

Mary runs 600 meters per day, so in one week, she runs:

600 meters/day x 7 days/week = 4200 meters/week

To convert meters to kilometers, we need to divide by 1000:

4200 meters/week ÷ 1000 meters/kilometer = 4.2 kilometers/week

Therefore, Mary runs 4.2 kilometers in one week.

Answer: 4.2 km per week

Step-by-step explanation:

Can someone help me please? I'm literally dying, I don't understand how to graph this because the x-axis has the numbers this way?? Help omg

Answers

This inequality will intersect x axis at -2 and y axis at 100.

Inequalities Definition

An inequality in the algebra is called mathematical statement that employs the inequality symbol to represent how two expressions relate to one another. The data on each side of an inequality symbol are nonequal. Relation  between two algebraic expressions that are represented by the inequality symbols are known as literal inequalities.

"A limk is referred an inequality if two real numbers  are connected by the symbols ">," "," "," or "."

Example: 3≤x<8 ( x is greater than or equal to 3 and less than 8)

Given Inequality

y<50x+100

For x=0;

y<100

For y=0;

x>-2

The graph of the inequality is attached below:

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The supplement of an angle measures 25° more than twice its complement. Find the measure of the angle. ​

Answers

The measure of the angle is x = 25°.

What is angle?

An angle is a geometric figure formed by two rays that share a common endpoint called the vertex. The two rays are called the sides or arms of the angle. Angles are typically measured in degrees, with a full rotation around a point being 360 degrees.

Let the angle be x.

The supplement of the angle is 180° - x.

The complement of the angle is 90° - x.

According to the problem, we have:

180° - x = 2(90° - x) + 25°

Simplifying and solving for x, we get:

180° - x = 180° - 2x + 25°

x = 25°

Therefore, the measure of the angle is x = 25°.

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this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. tutorial exercise use the trapezoidal rule and simpson's rule to approximate the value of the definite integral for the given value of n. round your answers to four decimal places and compare the results with the exact value of the definite integral. integral 0 - 4 for x2 dx, n=4

Answers

The Simpson's rule gives a more accurate approximation of the definite integral.

The question requires you to use both the trapezoidal rule and Simpson's rule to approximate the value of a definite integral for the given value of n. Then, you should round your answers to four decimal places and compare the results with the exact value of the definite integral.Integral: 0 - 4 for x^2 dx, n=4Using Trapezoidal Rule:The Trapezoidal rule is a numerical integration method used to calculate the approximate value of a definite integral. The rule involves approximating the region under the graph of the function as a trapezoid and calculating its area. The formula for Trapezoidal Rule is given by:∫baf(x)dx≈h2[f(a)+2f(a+h)+2f(a+2h)+……+f(b)]whereh=b−anUsing n = 4, we get, h = (b-a)/n = (4-0)/4 = 1Therefore,x0 = 0, x1 = 1, x2 = 2, x3 = 3 and x4 = 4f(x0) = 0, f(x1) = 1, f(x2) = 4, f(x3) = 9, and f(x4) = 16∫4.0x^2 dx = (1/2)[f(x0) + 2f(x1) + 2f(x2) + 2f(x3) + f(x4)](1/2)[0 + 2(1) + 2(4) + 2(9) + 16] = 37

Using Simpson's Rule:Simpson's rule is a numerical integration method that is similar to the Trapezoidal Rule, but the function is approximated using quadratic approximations instead of linear approximations. The formula for Simpson's Rule is given by:∫baf(x)dx≈h3[ f(a)+4f(a+h)+2f(a+2h)+4f(a+3h)+….+f(b)]whereh=b−an, and n is even.Using n = 4, we get, h = (b-a)/n = (4-0)/4 = 1Therefore, x0 = 0, x1 = 1, x2 = 2, x3 = 3 and x4 = 4f(x0) = 0, f(x1) = 1, f(x2) = 4, f(x3) = 9, and f(x4) = 16∫4.0x^2 dx = (1/3)[f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + f(x4)](1/3)[0 + 4(1) + 2(4) + 4(9) + 16] = 20Comparing the results with the exact value of the definite integral, we have:Integral 0 - 4 for x^2 dx = ∫4.0x^2 dx = [x^3/3]4.0 - [x^3/3]0 = 64/3 ≈ 21.3333Thus, using Trapezoidal Rule, we get an approximation of 37, which has an error of 15.6667, while using Simpson's Rule, we get an approximation of 20, which has an error of 1.3333. Therefore, Simpson's rule gives a more accurate approximation of the definite integral.

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Function g is a transformation of the parent function f(x) = x². The graph of g is a
translation right 2 units and up 3 units of the graph of f. Write the equation for g in
the form y = ax² + bx+c.

Answers

Answer:

g(x) = x² - 4x + 7

Apply De Morgan's law repeatedly to each Boolean expression until the complement operations in the expression only operate on a single variable. For example, there should be no xy¯ or x+y¯ in the expression. Then apply the double complement law to any variable where the complement operation is applied twice. That is, replace x¯¯ with x.
a. 1/ x + yz + u b. 1/x(y + 2)u c. 1/(x + y)(uv + x y) d. 1/xy + yz + xz

Answers

The simplified expression using De Morgan's law are  a)x'y'z'u  b)x'y'u c): x'y'u and d)x'y'z'+xy'z'+xyz.

The main idea is to simplify each Boolean expression by repeatedly applying De Morgan's law until each complement operation operates on a single variable.

Then, apply the double complement law to simplify the expression further. In the end, the simplified expression should contain only AND and OR operations without any complement operators acting on multiple variables.

a. 1/ x + yz + u can be simplified using De Morgan's law to: (x'y'z')u'. Then, applying the double complement law, we get the simplified expression as: x'y'z'u.

b. 1/x(y + 2)u can be simplified using De Morgan's law to: x'(y'+2')u'. Then, applying the double complement law, we get the simplified expression as: x'y'u.

c. 1/(x + y)(uv + xy) can be simplified using De Morgan's law to: (x'y')(u' + x'y'). Then, applying the double complement law, we get the simplified expression as: x'y'u.

d. 1/xy + yz + xz can be simplified using De Morgan's law to: (x'+y')(y'+z')(x'+z'). Then, applying the double complement law, we get the simplified expression as: x'y'z'+xy'z'+xyz.

In summary, to simplify Boolean expressions, we can apply De Morgan's law repeatedly and then use the double complement law to remove complement operators acting on a single variable twice.

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janelle fills two buckets with water the blue bucket holds 5 quarter of water which bucket holds more water how many cups more does it hold 1 quart= 2pints 1 pint = 2 cups

Answers

the blue bucket holds 5 x 4 = 20 cups of water.

what is a probability?

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is represented as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

Since 1 quart of water is equivalent to 2 pints of water and 1 pint of water is equivalent to 2 cups of water, then 1 quart of water is equivalent to 4 cups of water (2 pints x 2 cups per pint = 4 cups).

To determine which bucket holds more water, we need to know the amount of water in the other bucket. Without that information, we cannot compare the two buckets.

Assuming that Janelle filled the other bucket with water as well, we would need to know how many cups of water it holds in order to compare the two buckets.

Therefore, the blue bucket holds 5 x 4 = 20 cups of water.

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A $2,000 investment was made 16 years ago into an account that earned quarterly
compounded interest. If the investment is currently worth $6,883.55, what is the
annual rate of interest?

Answers

Answer:

We can use the formula for compound interest to solve the problem:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, we know that P = $2,000, A = $6,883.55, n = 4 (quarterly compounding), and t = 16. We can solve for r by rearranging the formula as follows:

r = n[(A/P)^(1/nt) - 1]

Substituting the values, we get:

r = 4[(6,883.55/2,000)^(1/(4*16)) - 1] = 0.0522 or 5.22%

Therefore, the annual interest rate is approximately 5.22%

Assume that X is normally distributed with a mean of 7 and a standard deviation of 4. Determine the value for x that solves each of the following equations. (a) P(X>x) 0.5 (b) P(X>x) 0.95 (c) P(x< X<9)= 0.2 (d) P(3< X

Answers

For (a), the value for x is 11, as P(X>x) = 0.5 when the mean is 7 and the standard deviation is 4. This can be found using the standard normal table.

For (b), the value for x is 19, as P(X>x) = 0.95 when the mean is 7 and the standard deviation is 4. This can also be found using the standard normal table.

For (c), the value for x is 9, as P(x< X<9) = 0.2 when the mean is 7 and the standard deviation is 4. This is found by subtracting the z-scores of x and 9 from each other, and then finding the area of the z-score between those two numbers using the standard normal table.

For (d), the value for x is 4, as P(3< X) = 0.2 when the mean is 7 and the standard deviation is 4. This is found by subtracting the z-score of 3 from the mean and then finding the area of the z-score to the left of that number using the standard normal table.

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A quadrilateral has two angles that measure 291° and 17°. The other two angles are in a
ratio of 4:9. What are the measures of those two angles?

Answers

Answer:

The sum of all four angles of a quadrilateral is 360 degrees.

Let's denote the two unknown angles as 4x and 9x, where x is a constant.

We can set up an equation using the given information:

291 + 17 + 4x + 9x = 360

Simplifying the equation:

308 + 13x = 360

13x = 52

x = 4

So, the two unknown angles are:

4x = 16 degrees

9x = 36 degrees

Therefore, the measures of the two angles in a ratio of 4:9 are 16° and 36°.

A particle is traveling on the curve, R, where R = {(x, y) = x² +9y² = 25} At time, t(o), the particle is at (-2,1); given that X' (to) = -1/2, what is y'(to) ?​

Answers

so is in essence implicit differentiation

[tex]R(x,y)\implies x^2+9y^2=25\implies \stackrel{ chain~rule }{2x\cdot \cfrac{dx}{dt}}+9\cdot \stackrel{ chain~rule }{2y\cdot \cfrac{dy}{dt}}=0 \\\\\\ x\cdot \cfrac{dx}{dt}+9y\cdot \cfrac{dy}{dt}=0\implies 9y\cdot \cfrac{dy}{dt}=-x\cdot \cfrac{dx}{dt}\implies \cfrac{dy}{dt}=-x\cdot \cfrac{dx}{dt}\cdot \cfrac{1}{9y} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{we also know that at t(0)}\hspace{5em} x'(t(0))=-\cfrac{1}{2}\hspace{5em}(\stackrel{x}{-2}~~,~~\stackrel{y}{1}) \\\\[-0.35em] ~\dotfill\\\\ \left. \cfrac{dy}{dt}=-x\cdot \cfrac{dx}{dt}\cdot \cfrac{1}{9y}\right|_{(-2,1)}\implies -(-2)\left( -\cfrac{1}{2} \right)\cdot \cfrac{1}{9(1)}\implies \boxed{-\cfrac{1}{9}}[/tex]

You are given the following information obtained from a random sample of 6 observations. Assume the population has a normal distribution. 14 20 21 16 18 19 a. What is the point estimate of u? b. Construct an 80% confidence interval for u. Construct a 98% confidence interval for u. d. Discuss why the 80% and 98% confidence intervals are different.

Answers

A higher confidence level is associated with a wider confidence interval.

a. The point estimate of µ = (14 + 20 + 21 + 16 + 18 + 19) / 6 = 108 / 6 = 18.

b. For 80% confidence interval for µ, the confidence coefficient is 1 - α = 0.8, so α = 0.2 / 2 = 0.1. From the z-table, we can find the corresponding value of z to be 1.28. The confidence interval can be calculated as follows:

Upper Bound: µ + z*σ / √n = 18 + (1.28)(2.3) / √6 = 21.35

Lower Bound: µ - z*σ / √n = 18 - (1.28)(2.3) / √6 = 14.65

The 80% confidence interval is (14.65, 21.35). For 98% confidence interval for µ, the confidence coefficient is 1 - α = 0.98, so α = 0.01. From the z-table, we can find the corresponding value of z to be 2.33. The confidence interval can be calculated as follows:

Upper Bound: µ + z*σ / √n = 18 + (2.33)(2.3) / √6 = 23.88

Lower Bound: µ - z*σ / √n = 18 - (2.33)(2.3) / √6 = 12.12

The 98% confidence interval is (12.12, 23.88). The 80% and 98% confidence intervals are different because as we move to higher confidence levels, the z-values become larger, which in turn causes the confidence intervals to become wider. Therefore, a higher confidence level is associated with a wider confidence interval.

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Una pintura incluyendo su marco tiene 25 cm de largo y 10 cm de ancho cuánto es el area del marco, si este tiene 4cm de ancho?

Answers

216 cm2 is the size of the rectangle border.

the translation of the question is

A painting including its frame is 25 cm long and 10 cm wide, what is the area of ​​the frame if it is 4 cm wide?

What is a rectangle's area?

When the dimensions of a rectangle with length and width are multiplied, the area of the rectangle is determined as follows:

A = lw.

The total area is therefore given by:

A = 25 x 10 = 250 cm².

The white region's size is shown by:

A = (25 - 2 x 4) x (10 - 2 x 4) is equal to 17x 2 and 34 cm2.

Hence, the border's area is as follows:

216 cm2 = 250 cm2 - 34 cm2.

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suppose that two people standing 2 miles apart both see the burst from a fireworks display. after a period of time, the first person standing at point a hears the burst. one second later, the second person standing at point b hears the burst. if the person at point b is due west of the person at point a and if the display is known to occur due north of the person at point a , where did the fireworks display occur?

Answers

The fireworks display occurred due north of the person at point A. This can be determined by calculating the direction and speed of sound. Assuming the speed of sound is approximately 343 meters per second, the fireworks display must have occurred approximately 0.58 seconds away from point A, which is approximately 343 meters due north of point A. This means that the fireworks display occurred somewhere between the two points.


To double-check the calculations, we can look at the two points and the direction in which the sound traveled. Point A is due north of the fireworks display, and point B is due west. This means that the sound traveled both north and west, which is consistent with the calculations.


Therefore, we can conclude that the fireworks display occurred due north of point A.

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Given that sec n - tan n = ¼ , find sec n + tan n

Answers

Given, [tex]$$(\sec n - \tan n) = \frac{1}{4}[/tex], so, using Trigonometry we can obtain [tex]$$\sec n + \tan n = 0$$[/tex].

Trigonometry is a branch of mathematics that deals with the study of relationships between the sides and angles of triangles. It involves the study of trigonometric functions such as sine, cosine, and tangent, and their applications to various fields such as engineering, physics, and navigation. Trigonometry helps in solving problems related to triangles, circles, and periodic phenomena such as waves and oscillations.

To find sec n + tan n using the given equation, we can use the following identity:

[tex]$$\sec^2 n - \tan^2 n = 1$$[/tex]

Multiplying both sides of the given equation by sec n + tan n, we get:

[tex]$$(\sec n - \tan n)(\sec n + \tan n) = \frac{1}{4}(\sec n + \tan n)$$[/tex]

Using the identity above, we can simplify the left-hand side of the equation as:

[tex]$$\sec^2 n - \tan^2 n = 1$$[/tex]

Therefore, we can substitute 1 for [tex]sec^2 n - tan^2[/tex] n in the equation above to get:

[tex]$$(\sec n - \tan n)(\sec n + \tan n) = \frac{1}{4}(\sec n + \tan n)$$[/tex]

[tex]$$1(\sec n + \tan n) = \frac{1}{4}(\sec n + \tan n)$$[/tex]

Simplifying further, we get:

[tex]\frac{3}{4} * $$(\sec n + \tan n) = 0[/tex]

Therefore, we can solve for sec n + tan n as:

[tex]$$\sec n + \tan n = \frac{0}{\frac{3}{4}}$$[/tex]

[tex]$$\sec n + \tan n = 0$$[/tex]

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Complete the table for the given rule.

Rule: y=\dfrac{x}{2}y=

2

x



y, equals, start fraction, x, divided by, 2, end fraction

xxx yyy

111

2. 52. 52, point, 5

3. 53. 53, point, 5

Answers

The proportionate relationship is used to determine that:

Y=0.5 when x = 1.

Y Equals 1.25 when x = 2.5.

Y = Y = 1.75 when x = 3.5.

What does "proportional relationship" mean?

In a proportional connection, the output variable is determined by the input variable multiplied by a proportionality constant, as in the equation: y = kx.

where k is the proportionality constant.

The relationship in this issue is provided by:

y = x/2

Hence, y = 1/2 = 0.5 when x = 1.

Y = 2.5/2 = 1.25 when x = 2.5.

When x = 3.5:

y = 3.5/2 = 1.75

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T.6 Converse of the Pythagorean theorem: is it a right triangle? EQZ
A triangle has sides with lengths of 3 feet, 4 feet, and 5 feet. Is it a right triangle?
yes
no

Answers

A triangle has sides with lengths of 3 feet, 4 feet, and 5 feet which is a right triangle.

What is right triangle?

A right triangle is a type of triangle that has one angle measuring exactly 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.

According to question:

The converse of the Pythagorean theorem states that if a triangle has sides of lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

In this case, the triangle has sides of lengths 3 feet, 4 feet, and 5 feet. To determine whether it is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse  is the same as the total of the squares formed by the other two sides' lengths.

If the triangle is a right triangle, then the longest side (the hypotenuse) must satisfy this equation. Thus, we have:

5² = 3² + 4²

25 = 9 + 16

25 = 25

Since this equation is true, we can conclude that the triangle is a right triangle.

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In the morning 134 books were checked out from the library.in the afternoon 254 books were checked out and 188 books were checked out in the evening.how many books were checked out in the library that day?

Answers

Answer:

576 books.

Step-by-step explanation:

134+254+188=576 books in total.

Hopefully this helps!

Write the following series in sigma notation. 2 + 12 + 22 + 32 + 42

Answers

The given series in the sigma notation can be written as [tex]\sum_{n = 1} ^ 5 10n - 8[/tex].

What are arithmetic series?

An arithmetic series is a set of integers where each term is made up of the common difference, a fixed amount, and the sum of the terms before it. In other words, the terms of the series may be represented as follows if the first term of an arithmetic series is a and the common difference is d:

a, a + d, a + 2d, a + 3d, ...

The given series is 2 + 12 + 22 + 32 + 42.

The total number of terms are 5.

The first term is 2, and the common difference is:

d = 12 - 2 = 10

Now, using the nth term of sequence we have:

an = 2 + (n - 1) 10

= 10n - 8

= [tex]\sum_{n = 1} ^ 5 10n - 8[/tex]

Hence, the given series in the sigma notation can be written as [tex]\sum_{n = 1} ^ 5 10n - 8[/tex].

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help me i have a test tmmr

Answers

Answer:

Step-by-step explanation:

[tex]\frac{2}{x} -3=\frac{1}{2}[/tex]

      [tex]\frac{2}{x}=\frac{1}{2}+3[/tex]      (-3 both sides)

      [tex]\frac{2}{x}=\frac{7}{2}[/tex]            (added fraction)

      [tex]2=\frac{7x}{2}[/tex]           (×[tex]x[/tex] both sides)

      [tex]4=7x[/tex]           (×2 both sides)

      [tex]x=\frac{4}{7}[/tex]             (÷7 both sides)

A landowner wishes to use 12 miles of fencing to enclose an isosceles triangular region of as large an area as possible. What should be the lengths of the sides of the triangle?
Let x be the length of the base of the triangle. Write the area as a function of x.
What is A(x)?
Length of base?
and length of remaining sides?

Answers

The area of a triangle is given by the formula A = 1/2 * b * h, where b is the base and h is the height.

The sides of an isosceles triangle are two equal sides and one unequal side. Therefore, to maximize the area of the triangle, we can set the two equal sides equal to x and the remaining side equal to 2x.

The area as a function of x is then:
A(x) = 1/2 * x * 2x = x2.
Therefore, the length of the base of the triangle is x, and the length of the remaining sides is 2x.

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Prove that the commutator is bilinear: [cA+dB. C]=c[A. C]+d[B. C]

Answers

As we proved that the commutator  [cA+dB. C]=c[A. C]+d[B. C] is bilinear

Let us start with the left-hand side of the equation: [cA + dB, C]. By definition, this is equal to (cA + dB)C - C(cA + dB).

Using the distributive property of multiplication, we can expand this expression to get

=> cAC + dBC - cCA - dBC.

Now let us consider the right-hand side of the equation:

=> c[A,C] + d[B,C].

By definition,

=> [A,C] = AC - CA and [B,C] = BC - CB.

Substituting these expressions into the right-hand side of the equation, we get

=> c(AC - CA) + d(BC - CB).

Using the distributive property of multiplication, we can expand this expression to get

=> cAC - cCA + dBC - dCB.

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PLEASE HELP WITH NUMBERS 9 and 10!!!
Pythagorean theorem (triangles)

Answers

Answer:

9. 6.32

10. 4.12

Step-by-step explanation:

9. c^2 = 2^2 + 6^2 = 4 + 36 = 40

c = √40 = 6.32

10. c^2 = 1^2 + 4^2 = 17

c = √17 = 4.12

The table shows the weights of 10 newborn pygmy marmosets meke a line plot to display the data. How many pygmy marmosets weigh more than 1/2 ounce ?

Answers

After closely analyzing the line graph, it can be seen that the number of pygmy marmosets weighing more than 1/2 ounce are 8.

To create a line plot, we plot each weight of the each pygmy marmosets on the y-axis and the pygmy marmoset number on the x-axis, which will be ultimately being connected using the points with a line.

After ploting the each mentioned weights (in ounces ) and taking a close study of the plotted line graph,  we can see that there are total 8 pygmy marmosets which are weighing more than 1/2 ounce.

Therefore, the total number of pygmy marmosets with weight more than 1/2 ounces are 8.

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The complete question is :

The table shows the weights of 10 newborn pygmy marmosets make a line plot to display the data. How many pygmy marmosets weigh more than 1/2 ounce ?

Pygmy Marmoset      Weight (ounces)

1                                 0.4

2                                 0.5

3                                 0.6

4                                 0.7

5                                 0.8

6                                 0.9

7                                 1.0

8                                 1.1

9                                 1.2

10                                 1.3

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