Your aunt sells magazine subscriptions by telephone. If each call she makes takes about 1/16 of an hour, how many calls can she make in 1/8 hours?​

The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.

The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).

Now, multiplying both sides by dx we,

\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).

Dividing both sides by \(2^{\sqrt{x}}\) we have,

\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).

\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

learn more about differential equations here :

https://brainly.com/question/14620493

#SPJ9

Answer:

22° + m<C = 90°

Step-by-step explanation:

We are given that <A (which is equal to 22°) and <B are vertical angles, and that <B is complementary to <C.

We want to write an equation that will help us solve <C.

Recall that vertical angles are congruent by vertical angles theorem.

This means that <A ≅ <B; it also means that the measure of <B is also 22°.

Also recall that complementary angles add up to 90°.

This means that m<B + m<C = 90°.

Since we deduced that m<B is 22°, we can substitute that value into the equation.

Hence, an equation that can be used to solve for <C is:

22° + m<C = 90°

Answer:

then it's 34... sometimes I have a hard time understanding a math problem and I feel that... I suggest using Math*way without the (*) it helped me a lot through high school and college check it out see if you like it

Step-by-step explanation:

Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

<95141404393>

Answer:

9000

Step-by-step explanation:

Answer:

A) y<-2x-1

Step-by-step explanation:

The graph shows y as less than -2x-1, without including it.

Answer:

yes it did they are both the same if u put a reflection on it

Step-by-step explanation:

The length of the base of the triangle is 8 yards whose height is half of 28 yards.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

well.......................................3 cups are in a cup serving

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

C: 10.39 inches

Answer:

B(6, 5), C(1, -7)

Step-by-step explanation:

A(2, 5)

From A to B, there is translation x, (4, 0).

Add 4 to A's x-coordinate, and add 0 to A's y-coordinate.

B(2 + 4, 5 + 0) = B(6, 5)

From C to B there is the translation y, (5, 12).

Since we are going from B to C, we undo translation y.

The translation from B to C is (-5, -12).

C(6 - 5, 5 - 12) = C(1, -7)

The domain restrictions for (f/g)(x) are (c) x = 0, 6

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

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

Read more about domain at

https://brainly.com/question/27910766

#SPJ1

Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Answer:

His son present age is 20 years

His present age is 40 years

Step-by-step explanation:

Assume that this son's age now is x years

∵ His son's age now = x years

∵ Ankit age is twice as old as his son

→ Twice means × 2

∴ Ankit age = 2 × x = 2x years

→ In for years means after 4 years (add)

∵ His age in four years = 2x + 4

→ 9 years ago means before 9 years (subtract)

∵ His son 9 years ago = x - 9

∵ In 4 years he will be four times as old as what his son was 9 years ago

→ That means 2x + 4 = 4 × (x - 9)

∴ 2x + 4 = 4(x - 9)

→ Let us solve the equation to find x

∴ 2x + 4 = 4(x) - 4(9)

∴ 2x + 4 = 4x - 36

→ Subtract 4 from both sides

∵ 2x + 4 - 4 = 4x - 36 - 4

∴ 2x = 4x - 40

→ Subtract 4x from both sides

∵ 2x - 4x = 4x - 4x - 40

∴ -2x = -40

→ Divide both sides by -2

∵ \(\frac{-2x}{-2}\) = \(\frac{-40}{-2}\)

∴ x = 20

∵ x represents the present age of his son

∴ His son present age is 20 years

∵ 2x represents his present age

∵ 2(20) = 40

∴ His present age is 40 years

Answer:

Confidence Interval = (1.41, 1.59)

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.

The lengths of the sides of the triangle are as follows;

Short leg = 12 cm.

Longer leg = 16 cm.

Hypotenuse = 20 cm.

In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

Note: Let the variable x represent the smaller leg.

The hypotenuse is 8 cm longer than the longer leg: x + 8 = x + 8.

Substituting the given parameters into the Pythagorean's theorem formula, we have the following;

c² = a² + b²

(x + 8)² = x² + (x + 4)²

x² + 16x + 64 = x² + x² + 8x + 16

x² - 8x - 128 = 0

Adjacent leg, x = 12.

For the hypotenuse, we have:

Hypotenuse, c = x + 8

Hypotenuse, c = 12 + 8

Hypotenuse, c = 20 cm.

For opposite side, we have:

opposite side, b = 12 + 4

opposite side, b = 16 cm.

Read more on Pythagorean theorem here: brainly.com/question/15430861

#SPJ1

Complete Question:

The shorter leg of a right triangle is 4 cm shorter than the longer leg. The hypotenuse is 8 cm longer than the longer leg. Find the lengths of the sides of the triangle.

Answer:

from the graph we can see that

for 2 gallones - it can travell 70 miles

4 gallones - 140 miles

we will take the first case

2 gallones - 70 miles

17 gallones - ? miles

cross multiply

\( \frac{17 \times 70}{2} \)

= 595 miles

Answer:

8

Step-by-step explanation:

10-2 = 8 i think lol

Answer 1 1/4

Step-by-step explanation:

You can get this by finding 3/4 on the line plot and counting the x's. Then you must add the 3 x's which means 3 of 3/4 and sum is your answer. Be sure to change improper to proper fraction. 9/4 to 1 1/4.

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

The sentence best describes your temperature estimate is Your estimate is wrong, and it should be 75°F. Thus, option c is correct.

To convert temperature from one unit to another, you can use conversion formulas or conversion tables. Here are the conversion formulas for the most commonly used temperature units:

Celsius to Fahrenheit: °F = (°C × 1.8) + 32

Fahrenheit to Celsius: °C = (°F - 32) / 1.8

Celsius to Kelvin: K = °C + 273.15

Kelvin to Celsius: °C = K - 273.15

Temperature is a physical quantity that measures the degree of hotness or coldness of an object or environment. Different countries and regions use different units to measure temperature, with Celsius (°C) and Fahrenheit (°F) being two of the most commonly used units.

In this scenario, the thermometer reads a temperature of 24°C. If you want to convert this temperature to Fahrenheit, you can use the formula:

°F = (°C × 1.8) + 32

Substituting 24°C into the formula, we get:

°F = (24 × 1.8) + 32

°F = 43.2 + 32

°F = 75.2

Therefore, the temperature estimate in Fahrenheit is 75.2°F.

Hence, the sentence best describes your temperature estimate is "Your estimate is wrong, and it should be 75°F.

To learn more about temperature visit:

https://brainly.com/question/25677592

#SPJ1

\(\boldsymbol{\sf{6-\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}\)

Convert 6 to the fraction 18/3.

                       \(\boldsymbol{\sf{\dfrac{18}{3} -\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{y}x+5 }}\)

Since the fractions 18/3 and 1/3 have the same denominator, we add their numerators to calculate them.

                       \(\boldsymbol{\sf{\dfrac{18+1}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 \ \longmapsto \ \ [Add \ 18+1] }}\)

                              \(\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x=\dfrac{1}{2}x+5 }}\)

Subtract \(\bf{\frac{1}{2}x }\) on both sides.

                               \(\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{3}{4}x-\dfrac{1}{2}x=5 }}\)

Combine \(\bf{-\frac{3}{4}x}\) and \(\bf{-\frac{1}{2}x}\) to get \(\bf{-\frac{5}{4}x}\).

                                \(\boldsymbol{\sf{\dfrac{19}{3}-\dfrac{5}{4}x=5 }}\)

Subtract 19x from both sides.

                                       \(\boldsymbol{\sf{-\dfrac{5}{4}x=5-\dfrac{19}{3} }}\)

Convert 5 to the fraction 15/3.

                                      \(\boldsymbol{\sf{-\dfrac{4}{5}x=\dfrac{15}{3}-\dfrac{19}{3} }}\)

Since the fractions 15/3 and 19/3 have the same denominator, we add their numerators to calculate them.

                             \(\boldsymbol{\sf{-\dfrac{5}{4}x=\dfrac{15-19}{3} \ \longmapsto \ \ [Subtract \ 15-19] }}\)

                                 \(\boldsymbol{\sf{-\dfrac{5}{4}x=-\dfrac{4}{3} }}\)

Multiply both sides by -4/3, the reciprocal of -4/3.

                                    \(\boldsymbol{\sf{x=-\dfrac{4}{5}\left(-\dfrac{4}{5}\right) }}\)

Multiply -4/3 by -4/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

                   \(\boldsymbol{\sf{x=\dfrac{-4(-4)}{3\times5} \ \ \longmapsto \ \ Multiply, \ numerator \ and \ denominator. }}\)

                                 \(\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ \ \ x=\frac{16}{15} }}}}}\)

Answer:

Look at the attachment

Step-by-step explanation:

Answer: To find the derivative of the function h(x), we can use the quotient rule, which states that if f(x) = u(x) / v(x), then f'(x) = [v(x)u'(x) - u(x)v'(x)] / [v(x)]^2.

Using this rule, we can find the derivative of h(x) as follows:

h(x) = (x + 2) / (x - 2)

h'(x) = [(x - 2)(1) - (x + 2)(1)] / (x - 2)^2 // apply the quotient rule and differentiate numerator and denominator

h'(x) = (-2 - 2x) / (x - 2)^2

Therefore, the derivative of h(x) is h'(x) = (-2 - 2x) / (x - 2)^2.

Step-by-step explanation:

Answer:

y = \(\sqrt{55}\)

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(altitude)² = product of parts of hypotenuse

then

y² = 11 × 5 = 55 ( take square root of both sides )

y = \(\sqrt{55}\)

Answer:

The probability that the proportion of vegetarians in a sample of 471 Americans would be greater than 8% is P=0.776.

Step-by-step explanation:

We have to calculate a probability that a sample of n=471 has a proportion greater than 8%, given that the population proportion is 9%.

First, we have to calculate the parameters of the sampling distribution of the proportions:

\(\hat{p}=p=0.09\\\\\\\sigma_{\hat{p}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.09\cdot 0.91}{471}}=0.0132\)

Now, we can calculate the probability using the z-score:

\(z=\dfrac{p-\hat{p}}{\sigma_{\hat{p}}}=\dfrac{0.08-0.09}{0.0132}=\dfrac{-0.01}{0.0132}=-0.7576\)

Then, the probability is:

\(P(p>0.08)=P(z>-0.7576)=0.776\)

Answer:

x=4

or

x=36

Step-by-step explanation:

I am wondering if you mean 3x=12 or x/3=12

if 3x=12, then x=4

if x/3=12, then x=36

Geometry encompasses various topics such as angles, lines, triangles, circles, polygons, and more.

Whether you need help with a specific theorem, a geometric proof, or solving a particular problem, feel free to describe the problem or provide any relevant information.

You can also ask general questions about geometry concepts or seek clarification on any topic you find challenging. Remember to provide all the necessary details, such as given information, diagrams, or specific requirements of the problem, to help me understand and assist you better.

Geometry often involves visual representation, so if you can provide any diagrams or illustrations related to your question, it would be helpful. However, if you can only describe the problem or concept in words, that's perfectly fine too.

Rest assured that I'll do my best to provide clear explanations, step-by-step solutions, and any additional information or insights to help you understand and solve your geometry problem.

For more such questions on Geometry visit:

https://brainly.com/question/24375372

#SPJ8

Answer:

  No

Step-by-step explanation:

You want to know if -8 is irrational.

A number is irrational if it has a decimal fraction part that does not terminate and does not repeat.

If you can describe all of the digits of the number explicitly without resort to functions or symbols, the number is not irrational.

  -8 is not irrational