What is the longest side of a right angled triangle called?

Answer:

216

Step-by-step explanation:

y=k÷x

k=xy

k=9×24

k=216

The tangent to the curve at a point P (x, y) has slope dy/dx at that point. By the chain rule,

dy/dx = (dy/dθ) / (dx/dθ)

We're in polar coordinates, so

y (θ) = r (θ) sin(θ)   ==>   dy/dθ = dr/dθ sin(θ) + r (θ) cos(θ)

x (θ) = r (θ) cos(θ)   ==>   dx/dθ = dr/dθ cos(θ) - r (θ) sin(θ)

We're given r (θ) = 1 - sin(θ), so that

dr/dθ = -cos(θ)

Then the slope of the tangent to the curve at P is

dy/dx = (dr/dθ sin(θ) + r (θ) cos(θ)) / (dr/dθ cos(θ) - r (θ) sin(θ))

dy/dx = (-cos(θ) sin(θ) + (1 - sin(θ)) cos(θ)) / (-cos²(θ) - (1 - sin(θ)) sin(θ))

dy/dx = - (cos(θ) - sin(2θ)) / (sin(θ) + cos(2θ))

The tangent is horizontal if dy/dx = 0 (or when the numerator vanishes):

cos(θ) - sin(2θ) = 0

cos(θ) - 2 sin(θ) cos(θ) = 0

cos(θ) (1 - 2 sin(θ)) = 0

cos(θ) = 0   or   1 - 2 sin(θ) = 0

cos(θ) = 0   or   sin(θ) = 1/2

[θ = π/2 + 2nπ   or   θ = 3π/2 + 2nπ]   or   [θ = π/6 + 2nπ   or   θ = 5π/6 + 2nπ]

where n is any integer.

In the interval 0 ≤ θ ≤ 2π, we get solutions of θ = π/6, θ = 5π/6, and θ = 3π/2. (We omit π/2 because the denominator is zero at that point and makes dy/dx undefined.) So the points where the tangent is horizontal are themselves (√3/4, 1/4), (-√3/4, 1/4), and (0, -2), respectively.

The tangent is vertical if 1/(dy/dx) = 0 (or when the denominator vanishes):

sin(θ) + cos(2θ) = 0

sin(θ) + (1 - 2 sin²(θ)) = 0

2 sin²(θ) - sin(θ) - 1 = 0

(2 sin(θ) + 1) (sin(θ) - 1) = 0

2 sin(θ) + 1 = 0   or   sin(θ) - 1 = 0

sin(θ) = -1/2   or   sin(θ) = 1

[θ = 7π/6 + 2nπ   or   θ = 11π/6 + 2nπ]   or   [θ = π/2 + 2nπ]

Then for 0 ≤ θ ≤ 2π, the tangent will be vertical for θ = 7π/6 and θ = 11π/6, which correspond respectively to the points (-3√3/4, -3/4) and (3√3/4, -3/4). (Again, we omit π/2 because this makes dy/dx non-existent.)

Answer:

y = -2(x + 3)² + 2

y = 2{ -(x + 3)²+ 1}

y = 2{ -(x² + 6x + 9) + 1}

y = 2{ -x² - 6x - 9 + 1}

y = 2{ -x² - 6x - 8 }

y = -2 { x² + 6x + 8}

OR

y = -2{(x + 4)(x + 2)}

Answer:

The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces

Step-by-step explanation:

To find the sample mean, we can find the mean of the confidence interval.

(15.875 + 16.595)/2 = 16.235

To find the margin of error, that is the difference between the mean and one of the edges of the confidence interval. 16.595 - 16.235 = 0.36

The sample mean weight is 16.235 ounces, and the margin of error is 0.360 ounces

Answer:

C. We are 90% confident that the interval from 15.875 ounces to 16.595 ounces captures the true mean weight of bags of grapes.

Step-by-step explanation:

Answer:

Relative minimum: [tex]\left(-\frac{5}{2}, -\frac{33}{4}\right)[/tex], Relative maximum: [tex]DNE[/tex]

Step-by-step explanation:

First, we obtain the First and Second Derivatives of the polynomic function:

First Derivative

[tex]f'(x) = 2\cdot x + 5[/tex] (1)

Second Derivative

[tex]f''(x) = 2[/tex] (2)

Now, we proceed with the First Derivative Test on (1):

[tex]2\cdot x + 5 = 0[/tex]

[tex]x = -\frac{5}{2}[/tex]

The critical point is [tex]-\frac{5}{2}[/tex].

As the second derivative is a constant function, we know that critical point leads to a minimum by Second Derivative Test, since [tex]f\left(-\frac{5}{2}\right) > 0[/tex].

Lastly, we find the remaining component associated with the critical point by direct evaluation of the function:

[tex]f\left(-\frac{5}{2} \right) = \left(-\frac{5}{2} \right)^{2} + 5\cdot \left(-\frac{5}{2} \right) - 2[/tex]

[tex]f\left(-\frac{5}{2} \right) = -\frac{33}{4}[/tex]

There are relative maxima.

Answer:

The total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

Step-by-step explanation:

Given that last year, Manuel deposited $ 7000 into an account that paid 11% interest per year and $ 1000 into an account that paid 5% interest per year, and no withdrawals were made from the accounts, to determine what was the total interest earned at the end of year and what was the percent interest for the total deposited, the following calculations must be performed:

7000 x 0.11 + 1000 x 0.05 = X

770 + 50 = X

820 = X

8000 = 100

820 = X

820 x 100/8000 = X

82,000 / 8,000 = X

10.25 = X

Therefore, the total interest earned at the end of the year was $ 820, and the interest generated by the total deposited was 10.25%.

Answer:

Take a look of the image below, we can think on this problem as a problem of two triangle rectangles.

We can see that both triangles share the adjacent cathetus, then the height of the flagpole is just the difference between the opposite cathetus.

Remember the relation:

Tan(a) = (opposite cathetus)/(adjacent cathetus)

So, if we define H as the height of the cliff

X as the distance between the observer and the cliff

and h as the height of the flagopole

we can write:

tan(40°) = H/X

tan(45°) = (H + h)/X

Notice that we have two equations and 3 variables (we should have the same number of equations than variables) then here is missing information, and we can't get an exact solution for the height of the flagpole.

But we can write it in terms of the height of the cliff H, or in terms of the distance between the observer and the cliff.

We want to find the value of h.

If we take the quotient between both equations, we get:

Tan(45°)/Tan(40°) = (H + h)/H

1.192 = (H + h)/H

1.192*H = H + h

1.192*H - H = h

0.192*H = h

So the height of the flagpole is 0.192 times the height of the cliff.

In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:

4x-5

Answer:

Solution given:

B.g(x)=[tex]\frac{x+5}{4}[/tex]

let

g(x)=y

y=[tex]\frac{x+5}{4}[/tex]

Interchanging role of x and y

we get:

x=[tex]\frac{y+5}{4}[/tex]

doing crisscrossed multiplication

4x=y+5

y=4x-5

So

g-¹(x)=4x-5

Given that,

→ g(x) = x+5/4

Then g(x)=y,

→ y = x+5/4

Now we can interchange role of x and y,

→ x = y+5/4

Then use the cross multiplication,

→ 4x = y+5

→ y = 4x-5

Hence, g-¹(x) = 4x-5 is the solution.

Answer:

1. False 2. True

Step-by-step explanation:

For a geometric sequence,

[tex]\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}[/tex]

1. The sequence is :

3, 13, 23, 33,...

[tex]\dfrac{13}{3}\ne \dfrac{23}{13}[/tex]

It is not geometric. It is false

2. The sequence is :

5, -25, 125, -625

[tex]\dfrac{-25}{5}=\dfrac{125}{-25}\\\\-5=-5[/tex]

So, the sequence is geometric as the common ratio is same. It is true.

Answer:

Take the picture you uploaded.

Click the rotate button twice.

Done

Answer:

81

Step-by-step explanation:

Given data:

mean μ = 70.

standard deviation σ, 9.6.

P(Z < 1.123) = 0.13

z = 1.13

Use the z-score formula,

x = z×σ +μ

Substitute the values in the above equation.

x = 1.13 9.6 + 70 = 81

The minimum score required for an A grade is = 81

Answer:

ghthtf

Step-by-step explanation:

tygtgg

Answer:

Guessing at least one incorrect answer

Step-by-step explanation:

The complement of guessing 5 correct answers on a 5-question true/false exam is-

Guessing at least one incorrect answer because, when 1 or more questions are incorrectly guessed, the event of 5 correct answers can not occur.

Complete Question

Assisted-Living Facility Rent.Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increased 17% over the last five years to $3486 (the Wall Street Journal, October 27, 2012). Assume this cost estimate is based on a sample of 120 facilities and, from past studies, it can be assumed that the population standard deviation is s = $650. a. Develop a 90% confidence interval estimate of the population mean monthly rent.

Answer:

[tex]CI: 3388.39<X<3583.61[/tex]

Step-by-step explanation:

Sample Size n=120

Mean \=x =3486

Standard Deviation \sigma=650

Confidence interval CI=0.9

Therefore

Level of sig [tex]\alpha=0.1[/tex]

Therfore

The Critical Value from table is

Z_c=1.645

Generally the equation for Standard error is mathematically given by

[tex]S.E=\frac{\sigma}{\sqrt{n}}[/tex]

[tex]S.E=\frac{650}{\sqrt{120}}[/tex]

[tex]S.E=59.3366[/tex]

Generally the equation for Margin error is mathematically given by

[tex]M.E= = Z_c * SE[/tex]

[tex]M.E=1.65 * 59.34[/tex]

[tex]M.E= 97.61[/tex]

Therefore

[tex]CI= \=x \pm M.E[/tex]

[tex]CI= 3486 \pm 97.61[/tex]

Lower limit

[tex]LL= \=x-M.E=3486-97.6087[/tex]

[tex]LL= 3388.39[/tex]

Upper limit:

[tex]UL= \=x+E=3486+97.6087[/tex]

[tex]UL= 3583.61[/tex]

Therefore The  90% confidence interval estimate of the population mean monthly rent.

[tex]CI: 3388.39<X<3583.61[/tex]

Answer:

12

Step-by-step explanation:

Answer:

8 * 8 * 8 * 8 * 8

Step-by-step explanation:

8^5 is basically 8 times itself five times.

Answers:

Choice 2) Angle ABC is bisected by ray BD.

Choice 3) BC = 1/2 AC

Choice 5) 2*(angle DBC) = angle ABC

================================================

Explanation:

Since B is the midpoint of AC, this means that AC is cut in half to form the smaller equal pieces AB and BC

We can then say

AB+BC = AC

BC+BC = AC

2BC = AC

BC = (1/2)*AC

which shows why choice 3 is one of the answers

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

Angle ABD is shown to be 90 degrees. Let's say we didn't know angle DBC is also 90. Lets call it x

(angle ABD) + (angle DBC) = 180

90 + x = 180

x = 180 - 90

x = 90

So angle DBC is also 90.

We can see that the 180 degree angle (ABC) is cut in half into two smaller 90 degree angles (ABD and DBC). Therefore, angle ABC has been cut in half and that's why choice 2 is another answer.

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

Using the angle addition postulate, we know that,

(angle ABD) + (angle DBC) = angle ABC

(angle DBC) + (angle DBC) = angle ABC

2*(angle DBC) = angle ABC

Showing why choice 5 is the third answer.

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

Choice 1 isn't true since ray BD helps form angle DBC.

Choice 4 isn't true because there isn't a tickmark on segment BD to indicate it's the same length as BC.

Answer:

Step-by-step explanation:

Answer to question 1:

On average do part-time students spend less than 20 hours per work on academic work and assignments ?

Answer to question 2:

On average do students work greater than 50 hours a week ?

Answer:

a

Step-by-step explanation:

square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8

Answer:

y = -x.

Step-by-step explanation:

The slope of the line (m) = -1.  ( because of the -x in y = -x - 5)

y - y1 = m (x - x1)    where (x1, y1) is a point on the line, so we get;

y - 2 = -1(x - (-2))

y - 2 = -x + -1 * +2

y - 2 = -x - 2

y = -x.

Answer:

567000000

Step-by-step explanation:

Standard is the actual number. Multiply 5.67 and 10^8.

9514 1404 393

Explanation:

Your question covers a good bit of the material in an algebra course. The short answer is, "the same way you solve a numerical equation." The point of algebra is that literals can stand for numbers, and so be manipulated the same way numbers are.

Expressions are evaluated according to the Order of Operations. For equations involving a single variable, the equation specifies what operations are being performed on that variable. To find the vale of the variable (solve for that literal), you need to "undo" the operations that are performed on it. As with many problems that have layers, you work down through the layers from the outside in. Generally, that means working through the list of operations "backwards," undoing the last one first.

Simple example

  y = mx + b . . . . . . solve for x

In this equation, the operations performed on x are ...

In accordance with the above, the first thing we do is "undo" the addition of b. (Note that this could be a number or literal--or even a complicated expression--and the process would be exactly the same.) To "undo" addition, we add the opposite.

  y -b = mx +b -b   ⇒   y -b = mx

Next, we "undo" the multiplication by m. That is, we divide by m, or multiply by the reciprocal of m. Either is the same as the other.

  (y -b)(1/m) = (mx)(1/m)   ⇒   (y -b)/m = x

Now, we have solved this literal equation for x.

_____

Throughout this process you must adhere strictly to the properties of equality. That is, anything you do to one side of the equation must also be done to the other side.

The reason you study inverses and identity elements is so you understand that addition of an additive inverse produces the additive identity element:

  x + (-x) = 0

Similarly, multiplication by the multiplicative inverse (reciprocal) produces the multiplicative identity element.

  x · (1/x) = 1

When other operations are involved, such as raising to a power, trig functions, roots, logs, exponentiation, each of these has an associated inverse function that produces an identity:

  (x^a)^(1/a) = x^1 = x

  arcsin(sin(x)) = x

  (√x)^2 = x

  10^(log(x)) = x   or   log(10^x) = x

Some of these inverse functions have restricted domains, so care must be used when solving equations involving them.

When a variable of interest appears on both sides of the equal sign, then you must figure a way to rearrange the equation so the terms with the variable can be combined.

Example:

  ax + b = cx +d . . . . . solve for x

  ax -cx = d -b . . . . . . subtract (cx+b). (Of course, this is subtracted from both sides of the equation.)

  x(a -c) = d -b . . . . . combine x-terms

  x = (d -b)/(a -c) . . . . divide by the coefficient of x

Note that we had to divide the entire right-side expression by the x-coefficient, so had to enclose it in parentheses.

More Complicated Example:

A recent Brainly problem asked for the solution to ...

  T = 2π√(L/g) . . . . solve for L

Here, L is divided by g, a root taken, and that multiplied by 2π. Undoing these in reverse order, we first divide by 2π, square both sides to undo the root, then multiply by g to undo the division:

  [tex]T=2\pi\sqrt{\dfrac{L}{g}}\\\\\dfrac{T}{2\pi}=\sqrt{\dfrac{L}{g}}\\\\\left(\dfrac{T}{2\pi}\right)^2=\dfrac{L}{g}\\\\\boxed{L=g\left(\dfrac{T}{2\pi}\right)^2}[/tex]

The problem posted on Brainly had numbers where some of these variables are. That does not affect the solution method, except that sometimes numerical values can be combined where literal values cannot.

_____

Key Points

I believe your answer is D.) $900

204 + 96 = 300

300 x 3 = 900

I hope this is correct and helps!

Answer:true

Step-by-step explanation:

i dont know

Answer:

20 participants

Step-by-step explanation:

Given

[tex]Conditions = 2[/tex]

[tex]Scores = 20[/tex]

Type: Repeated design

Required

The number of participants (n)

The repeated measure design implies that the test was conducted repeatedly on the same sample size.

Since the score in each test is 20; then:

[tex]n = 20[/tex] --- the number of participants

Answer:

Price per bottle is 1.5 or $1.50

Step-by-step explanation:

To get price per unit, you just divide the amount of money spent by the items purchased. 9/6 = 1.5

Answer:

Perimeter: 30 Area: 30

Step-by-step explanation:

Perimeter of a triangle= Add all sides = 5+12+13 = 30

Area of a triangle= (B*H)/2 = (5*12)/2 = 60/2 = 30

Hope this helps! :)

9514 1404 393

Answer:

  y = x^2 +10x -9

Step-by-step explanation:

Quadratic regression generally requires the use of "technology" to aid in finding the equation of the curve of best fit. Use the technology you've been introduced to.

__

When only a few data points are provided, I prefer to use the Desmos graphing calculator. It shows the equation to be ...

  y = x^2 +10x -9

Step-by-step explanation:

If

[tex]V=\dfrac{4\pi}{3}r^3[/tex]

then we can solve for r as

[tex]r = \sqrt[3]{\dfrac{3V}{4\pi}}[/tex]

If the volume of the sphere is 150 ft^3, then the radius is

[tex]r = \sqrt[3]{\dfrac{3(150\:\text{ft}^3)}{4\pi}} = 3.30\:\text{ft}[/tex]

The radius of the given sphere with a volume of 150 cubic feet is 2.29 feet, correct to two decimal places.

Given that

the volume of a sphere = 150 cubic feet.

the radius of the sphere=????

a round solid figure, or its surface, with every point on its surface equidistant from its center.

as we know,

the volume of a sphere

[tex]V=\frac{4}{3} *\pi *r^3[/tex]

[tex]r = \sqrt[3]{\frac{3V}{4\pi } }[/tex][tex]r = \sqrt[3]{\frac{3*150}{4\pi } }[/tex][tex]=2.29 feet[/tex]

therefore, the radius of the given sphere is 2.29feet

to get more about sphere refer to the link,

https://brainly.com/question/22807400

Answer:

It could be a solution

Step-by-step explanation:

This depends on what equation you are solving. It could be a solution for a quadratic or even a transformation problem.