The height of the blade of a wind turbine as it turns through an angle of is given by the function h()=8.5sin(+180⁰) + 40, with height measured in meters.

Find the maximum and minimum positions of the blade.

Explain what the value of 40 in the equation represents.

What is the amplitude? Explain what it represents.

Sketch the function over two cycles.

The formula of the parabola is y = 2/35(x + 7)(x - 5)

The parameters in the question are given as

These parameters can be represented as

x₁ = -7 and x₂ = 5

(x, y) = (0, -2)

The quadratic function can be represented as

y = a(x - x₁)(x - x₂)

Substitute the known values in the above equation So, we have the following equation

y = a(x + 7)(x - 5)

At (x, y) = (0, -2), we have

-2 = a(0 + 7)(0 - 5)

Evaluate

a = -2/-35

Divide

a = 2/35

So, we have

y = 2/35(x + 7)(x - 5)

Hence, the equation is y = 2/35(x + 7)(x - 5)

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[tex]-\frac{5}{2} (8a - 2b) = ...[/tex] the answer for this question is zero (0)

How can the answer is zero?

The first thing that we should do is simplify questions.

[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (- 2b)\\= - 20a + 5b[/tex]

After that, we will search for "a" and "b" to solve the question. For me, i will search for "b" first.

[tex]- 20a + 5b \\5b = 20a\\b = \frac{20}{5} a\\b = 4a[/tex]

Next step is find the "a" by enter the "b" into the same question.

[tex]- 20a + 5b =\\20a = 5b\\20a = 5 (4a)\\20a = 20a\\a = 1[/tex]

After we find the "a" and "b", the next step is to enter it into the main question to find the right answer.

[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a - 2[4a]) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (-8a)\\= - 4a + 4a\\= -4 (1) + 4 (1)\\= -4 + 4\\= 0[/tex]

So, the answer is zero (0).

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Answer:

[tex] - 20a + 5b[/tex]

Step-by-step explanation:

[tex] - \frac{5}{2} (8a - 2b)[/tex]

[tex] - \frac{5}{2} (8a) - \frac{5}{2} ( - 2b)[/tex]

[tex] - 20a + 5b[/tex]

The scalene right triangle RGH is given by the image shown at the end of the answer.

There are two classifications of triangles, either regarding the side lengths or the angles.

Regarding the side lengths, the classifications are given as follows:

Regarding the measure of the greatest angle, the classifications are given as follows:

In this problem, RGH is a scalene right triangle, hence:

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Answer:

$55.71

Step-by-step explanation:

$320/7=$45.71 per day

45.71/8=5.71 per hour

45.71+10=$55.71 for 9 hours of work

45.71+ 45.71+55.71 =$147.13 for 3days +1 hour overtime

By Computing the Logarithmic Relation, we calculate that the time between injections is 5.1 hours or 5 hours and 6 minutes.

The given formula is

[tex]D = 5e^{-0.1h}[/tex]

where D is the amount of drug in milligrams in the patient's bloodstream and h is the number of hours after the drug was administered.

So, it is given that D = 3 and we need to evaluate the number of hours it took between the injections,

So, We have,

[tex]D = 5e^{-0.1h}[/tex]

[tex]\frac{D}{5} = e^{-0.1h}[/tex]

Taking Natural log on both sides, we have :

[tex]ln\frac{D}{5} =ln e^{-0.1h}\\\\ln\frac{D}{5} = -0.1h\\[/tex]

We have D = 3, putting it in the formula, we get

[tex]\ln\frac{3}{5} = -0.1h\\\\ln(0.6) = -0.1h\\\\-0.5108 = -0.1 h\\\\h = \frac{0.5108}{0.1} = 5.1[/tex]

Hence, the time between injections is 5.1 hours or 5 hours and 6 minutes.

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Answer:

4.25 minutes

Step-by-step explanation:

[tex]\frac{32 \:copies}{1\:min} = \frac{136\: copies}{x \: min} \\\\x\: min = \frac{136 \: copies}{32 \: copies} \\\\x=4.25 \: min[/tex]

Answer: 4 mins 15 seconds (4.25 mins)

Step-by-step explanation:

136 copies/32 copies per minute = 4.25 minutes

So we know it will take 4.25 mins. 4.25 mins is equal to 4 mins and 15 seconds.

Answer:

75

Step-by-step explanation:

1 minute=15

2 minutes=30

3 minutes=45

4 minutes=60

5 minutes=75

Answer:

-8

Step-by-step explanation:

f(-3) = 2(-3)-2

f(-3) = -6 -2

f(-3) = -8

Answer:

[tex] \huge{f( - 3) = - 8}[/tex]

Step-by-step explanation:

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

In order to find f(-3) we substitute the value of x that's -3 into f(x) that's wherever we find x in f(x) we substitute it with -3 and solve for f(-3).

We have

[tex]f( - 3) = 2( - 3) - 2 \\ = - 6 - 2 \\ = - 8[/tex]

We have the final answer as

[tex] \bold{f( - 3) = - 8}[/tex]

Hope this helps you

Answer:

12 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

substitute the given values for p and q into the expression

p² + 3q²

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

= [tex]\frac{1}{4}[/tex] + 3(4)

= [tex]\frac{1}{4}[/tex] + 12

= 12 [tex]\frac{1}{4}[/tex]

If A is located at (3,4) and B is located at (7,6) , then the slope of BC is -2  .

In the question ,

it is given that ,

In the rectangle ABCD , the coordinate of the point A is (3,4) and the coordinate of the point B is (7,6) .

since the sides of the rectangle are at 90° , that means they are perpendicular .

which means AB⊥BC ,

the slope of AB = (6-4)/(7-3)

slope = 2/4

slope = 1/2

Since , AB⊥BC ,

(slope of AB)×(slope of BC) = -1

substituting the values , we get

(1/2)×(slope of BC) = -1

slope of BC = -1/(1/2)

slope of BC = -2 .

Therefore , If A is located at (3,4) and B is located at (7,6) , then the slope of BC is -2  .

The given question is incomplete , the complete question is

On rectangle ABCD, if A is located at (3,4) and B is located at (7, 6), what is the slope of BC ?

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Answer:  2(x+4) >3(x+7)-4

Step-by-step explanation:

Hope this helps

Answer:

2(n+4)≤3(n+7)-4

Step-by-step explanation:

The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.

We need to find the inequality of the statement given;

"Two times the sum of a number and four is no more; than three times the sum of the number and seven decreased by four"

Let n be the unknown number

Then it would be;

2(n+4) ≤ 3(n+ 7) - 4

Hence, The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4

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Total time taken by Bethany to make a round trip of NY to Pittsburgh as per  given conditions is equal to 1 (7/ 20)hours.

As given in the question,

Time taken by Bethany to flew from NY to Pittsburgh is equal to 3/4 hours

Now using jet stream ,

Time taken by airlines from Pittsburgh to NY is (4/5) th of (3/4) hours

= (4/5) × (3/4) hours

= 3/5 hours

Total time taken by airlines to make a round trip from NY to Pittsburgh is given by:

= [(3/4) + (3/5)] hours

= [(15 +12)/20] hours

= 27/20 hours

= 1 7/20 hours

Therefore, total time taken by Bethany to make a round trip of NY to Pittsburgh as per  given conditions is equal to  1 (7/ 20)hours.

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The F Test statistic is 1.58.

Given data is

Source       SS           df          MS

between   21,000.00       2        6,000.00

within  442,500.00  117        3,782.00

The SStotal is sometimes easier to calculate than SSbetween Since ......

SSwithin +SSbetween = SStotal you can use SStotal to calculate SSbetween.

= 442,500+21,000 =  463,500

In ANOVA, the F test statistic is the  ratio of the between - treatments variance and the within-treatments variance. The value of the F test statistic is 1.58 when the null hypothesis is true , the F test statistics is closer to 1, when the null hypothesis is false, the F test statistic is most likely large in general, you should reject null hypothesis for larger values of the F test statistic.

Hence the answer is the F Test statistic is 1.58.

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The Isosceles obtuse triangle in which the obtuse vertex is angle T is represented with the attached diagram.

An isosceles obtuse triangle is a type of triangle which is formed by two equal sides of the triangle.

As long as the measures of the angles add up to 180°, it is an isosceles obtuse triangle.

An obtuse angle is an angle greater than 90 degrees but less than 180 degrees.

A triangle is a polygon with three sides and three angles. There are different types of triangle, which includes:

So therefore, an isosceles obtuse triangle is formed by having two equal sides of a triangle.

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The surface area of a cube that has a width of 25 centimeters is 3750 cm².

It should be noted that surface area simply implies the measure of the total area that the surface of an object occupies.

In this case, the surface area of a cube is measured as 6a² where a = side

In this case, the side is 25. Therefore, the surface area will be:

= 6a²

= 6 × 25²

= 3750 cm²

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Answer:

11

Step-by-step explanation:

Find the difference using subtraction:

18 - 7 = 11

So, the numbers are 11 units apart.

Answer:

0.32

Step-by-step explanation:

[tex]\frac{780-532}{780}[/tex] = [tex]\frac{248}{780}[/tex] = 0.32 Rounded.

Answer:

They should pay AED 180 as interest.

Step-by-step explanation:

Simple interest:

        P = The amount borrowed = AED 3000

        R = rate of interest = 3% per year

       t = time = 24 months = 24 ÷ 12 = 2 years

          [tex]\sf \boxed{Interest = PRt}[/tex]

Substitute the values,

                            [tex]\sf = 3000 * \dfrac{3}{100}*2\\\\ = 30*3*2\\\\=AED \ 180[/tex]

The probability that the next number pointing north is between 2 and 7 is 13/18 .

1) The circle is divided into 9 parts.

Now the parts are uneven.

So the data about the spins is required to calculate the probability .

The total number of items in the box = 18

favorable outcomes (between 2 and 7) = 13 possible outcome.

Required probability

= favorable outcome / total outcome

= 13 / 18

2) Using the Venn diagram we can calculate the various parts of the problem:

Shoppers at big-box store or online or local store = sum of all the shoppers = 109+57+107+18+17+38+34 = 380 shoppers

3) Shoppers made purchase online or locally owned shop but not at a big box store = 107 + 38 + 34 = 179 shoppers.

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Answer: e) 6.7

Step-by-step explanation:

This is a Similarity of Triangles problem (geometry)

if x is the height of the lamp post, then:

x/5 = (3 + 9) / 9

x (9) = (12) (9)

x = 60/9 = 6.7

After 2 hours the plan needs to be changed, and purchase solar for the cost effect.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh.

Total cost = 6x100 = 600 pounds

Total cost for 2 hours = 200 pounds

Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW.

Total cost for this:

From 8 AM to 12 PM = Number of hours 4 hours

4.5 GW = 4500 MW

= 105 pounds/MWh

Total cost for  4 hours = 630 pounds for 4500 MW per hour

Thus, after 2 hours the plan needs to be changed, and purchase solar for the cost effect.

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The approximate of √59 is 7.7 when rounded off to the nearest tenth place.

Given,  √59

we are asked to determine the approximation without using a square root button.

√59 is a decimal number since it is not a perfect square. Therefore, rather than finding a precise value, we will need to obtain a near approximation of 59 in decimal form.

the square root of the number 59 is:

7.6811

You rounded to the nearest tenths place. The 6 in the tenths place rounds up to 7 because the digit to the right in the hundredths place is 8.

= 7.7

When the digit to the right is 5 or greater we round away from 0.

7.6811 was rounded up and away from zero to 7.7

Hence we get the required approximation.

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The solution of the composite function (f/g)(x) is [tex]\frac{-4x+3}{6+7x}[/tex]

Composite functions are when the output of one function is used as the input of another.

In other words, a composite function is generally a function that is written inside another function.

Composite function involves the composition of functions is combining two or more functions as a single function.

Therefore, let's solve the function below:

f(x) = -4x + 3

g(x) = 6 + 7x

Hence,

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

Therefore,

f(x) / g(x) = [tex]\frac{-4x+3}{6+7x}[/tex]

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A disadvantage of using a questionnaire is that B. The respondent controls the validity.

Questionnaires are a means of gathering data in research in order to find out more about a certain phenomenon. They involve writing questions and giving them to a respondent to fill out the answers.

Questionnaires are inexpensive to administer and can lead to confidential results which is good. However, they have the disadvantage that respondents control the validity of questionnaire results and can decide to lie if they feel it would make them look better, which would confuse the research results.

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The measure of the Largest angle using the angle sum property of a triangle is: 80°

What is the Angle sum property of a triangle?

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.

In the given figure, we have:

Measure of 1st angle = 64°

Measure of 2nd angle = (2x + 14)°

Measure of 3rd angle = (6x + 14)°

and we know the angle of the property,

using the  angle of property,

64° + (2x + 14)° + (6x + 14)° = 180°

⇒64° + 8x + 14° + 14° = 180°

⇒92°  + 8x = 180°

⇒ 8x = 180° - 92°

⇒8x = 88°

⇒ x = 11°

So,

Measure of 2nd angle = (2x11 + 14)°

Measure of 2nd angle = (36)°

Measure of 3rdangle = (6x11 + 14)°

Measure of 2nd angle = (80)°

Hence,

The measure of the Largest angle using the angle sum property of a triangle is: 80°

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The volume V of the water in the cone as a function of the height h of the water is,

V = (1/48)πh³

Given, water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches.

We have to express the volume V of the water in the cone as a function of the height h of the water.

Now, at any instant let the height of the water in the cone be h and radius of the water in the cone be r,

So, using the concept of similarity in triangles

we get, r/4 = h/16

r = h/4

Now, the volume of the water in the cone be,

V = (1/3)πr²h

V = (1/3)π(h/4)²h

V = (1/48)πh³

So, the function expressing the volume of the water in the cone be,

V = (1/48)πh³

Hence, the volume V of the water in the cone as a function of the height h of the water is,

V = (1/48)πh³

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Answer:

x=9 (9,25)

Step-by-step explanation:

9*7=27

27-2=25

The solutions of the equations are x = 1 and y = 2

The system of equations are

4x + 3y = 10

-4x + 5y = 6

Here we have to use the elimination method. Eliminate the x term and find the value of y term

Add both equation

3y + 5y = 10 +6

Add the like terms

8y = 16

y = 16 / 8

Divide  the terms

y = 2

Substitute the value of x in the first equation

4x + 3y = 10

4x + 3×2 =  10

Multiply the terms

4x + 6  = 10

4x = 10 - 6

4x = 4

x = 4 / 4

Divide the terms

x = 1

Hence, the solutions of the equations are x = 1 and y = 2

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