In need of help for answers

In Need Of Help For Answers

Answers

Answer 1

The piecewise equation for the function shown in the diagram is [tex]f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.[/tex]

What is an equation?

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

From the diagram using the point (-6, 0.5) and (-1, 5):

y - 0.5 = [(5 - 0.5)/(-1 - (-6))](x - (-6))

y = (9/10)x + 5.9

Also, using the point (2, 1) and (4, -4):

y - 1 = [(-4 - 1)/(4 - 2)](x - 2)

y = -(5/2)x + 6

The piecewise equation for the function shown in the diagram is [tex]f(x)=\left \{ {{{[\frac{9}{10}x+5.9\ \ \ -6 \leq x\leq -1 } \atop {[2\ \ \ \ \ \ \ \ \ \ \ -1 < x\leq 2}} \atop {[-\frac{5}{2}x+6\ \ \ 2 < x\leq 6 }} \right.[/tex]

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Related Questions

does someone mind helping me with this question? Thank you!

Answers

Answer:

[tex]\frac{263}{999}[/tex]

Step-by-step explanation:

Find the local maximum and minimum values of f using both the first and second derivative tests. f(x) = 6 9x2 − 6x3 local maximum value local minimum value

Answers

The local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.

For given question,

We have been given a function f(x) = 6 + 9x² - 6x³

We need to find the local maximum and local minimum of the function  f(x)

First we find the first derivative of the function.

⇒ f'(x) = 0 + 18x - 18x²

⇒ f'(x) = - 18x² + 18x

Putting the first derivative of the function equal to zero, we get

⇒ f'(x) = 0

⇒ - 18x² + 18x = 0

⇒ 18(-x² + x) = 0

⇒ x (-x + 1) = 0

⇒ x = 0    or    -x + 1 = 0

⇒ x = 0     or    x = 1

Now we find the second derivative of the function.

⇒ f"(x) = - 36x + 18

At x = 0 the value of second derivative of function f(x),

⇒ f"(0) = - 36(0) + 18

⇒ f"(0) = 0 + 18

⇒ f"(0) = 18

Here, at x=0, f"(x) > 0

This means, the function f(x) has the local minimum value at x = 0,  which is given by

⇒ f(0) = 6 + 9(0)² - 6(0)³

⇒ f(0) = 6 + 0 - 0

⇒ f(0) = 6

At x = 1 the value of second derivative of function f(x),

⇒ f"(1) = - 36(1) + 18

⇒ f"(1) = - 18

Here, at x = 1, f"(x) < 0

This means, the function f(x) has the local maximum value at x = 1,  which is given by

⇒ f(1) = 6 + 9(1)² - 6(1)³

⇒ f(1) = 6 + 9 - 6

⇒ f(1) = 9

So, the function f(x) = 6 + 9x² - 6x³ has local minimum at x = 0 and local maximum at x = 1.

Therefore, the local minimum value of the function f(x) = 6 + 9x² - 6x³ is 6 and the local maximum value of the function f(x) = 6 + 9x² - 6x³ is 9.

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Use the figure to the right to find the value of PT. T is the midpoint of PQ
PT=3x+3 TQ=7x-9

Answers

If T is the midpoint of PQ and PT = 3x+3, TQ = 7x-9, then PT = 12 units.

Determining the Value of PT

It is given that,

T is the midpoint of PQ ........ (1)

PT=3x+3 ......... (2)

TQ=7x-9 .......... (3)

From (1), the distance from P to T and the distance from T to Q will be equal.

⇒ PT = TQ [Since, a midpoint divides a line into two equal segments]

Hence, equating the equations of PT and TQ given in (2) and (3) respectively, equal, we get the following,

3x + 3 = 7x - 9

or 7x - 9 = 3x + 3

or 7x - 3x = 9 + 3

or 4x = 12

or x = 12/4

⇒ x = 3

Substitute this obtained value of x in equation (2)

PT = 3(3) + 3

PT = 9 + 3

PT = 12 units

Thus, if T is the midpoint of PQ, then the measure of PT and TQ is equal to 12 units.

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if a + b is equals to 5 and a x b is equal to 6 then what is the value of a and b​

Answers

Answer: 2 and 3, or 3 and 2

Step-by-step explanation:

a + b = 5 so a = 5 - b

Substitute a = 5 - b into ab = 6; (5 - b)b =  6

5b - [tex]b^{2}[/tex] = 6

[tex]b^{2}[/tex] - 5b + 6 = 0

(b - 2)(b - 3) = 0

So b is either 2 or 3

So a is either 3 or 2 depending on what b is

Anna wanted to buy a camera. The first discount store sold her favorite camera for $95. The second store sold the same camera for $115, but it was on sale for 20% off. The third store carried the camera for $105 but offered it at 10% off with a coupon. which store had the better buy?

Answers

The second store offered the better buy at the price of $92.00.

What is better buy?

Better buy refers to the lowest price out of the prices offered by the three stores.

In order to determine the lowest price, the no discount price of the first store needs to be compared to the prices of  two other stores, bearing that after-discount price is the pre-discount price multiplied by 1 minus the discount rate.

First store price=$95.00

Second store after-discount price=pre-tax discount price*(1-discount rate)

pre-discount price=$115

discount rate=20%

Second store after-discount price=$115*(1-20%)

Second store after-discount price=$92.00

Third store after-discount price=pre-tax discount price*(1-discount rate)

pre-discount price=$105

discount rate=10%

Third store after-discount price=$105*(1-10%)

Third store after-discount price=$94.50

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Find the number of ways of delivering five letters to five houses so that no house gets
a correct letter.

Answers

Using the Fundamental Counting Theorem, it is found that there are 1024 ways of delivering the letters.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this problem, each house has a correct letter, however the letter cannot be used for the house, hence the parameters are given as follows:

n1 = n2 = n3 = n4 = n5 = 5 - 1 = 4.

Thus the number of ways is:

N = 4 x 4 x 4 x 4 x 4 = 4^5 = 1024.

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Sims waist is 30 inches. He wants to put on more weight and is hoping to gain enough weight to increase his waist size by 8%. How many inches does he want his waist to be?

Answers

Answer:

  32.4 inches

Step-by-step explanation:

Sam wants the increase to be 8% of 30 inches.

Increase

The amount of increase Sam wants in his waist size is ...

  8% × 30 in = 0.08×30 in = 2.4 in

Waist size

Adding the wanted increase to his present size would make Sam's waist size be ...

  30 in + 2.4 in = 32.4 in

Sam wants his waist size to be 32.4 inches.

__

Additional comment

The larger size can also be computed from ...

  30 +8%×30 = (1 +8%)×30 = 1.08×30 = 32.4 . . . inches

Analysis and observations in these two graphs

Answers

By critically observing the graph, we can infer and logically deduce the following points:

The linear function is given by y = 0.0169x + 32.485.The initial temperature for both data is greater than 32°C.The final temperature for both data is less than 33.5°C.Between 1980 and 2020, the temperature for graph 2 (thick-continuous line)  was constant.Graph 1 (thin-dashed line) is essentially a linear graph.

What is a graph?

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

What is a linear function?

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

This ultimately implies that, the data of a linear graph are directly proportional and as such, as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.

By critically observing the graph which models the changes in temperature over a specific period of time (in years), we can infer and logically deduce the following points:

The linear function is given by y = 0.0169x + 32.485.The initial temperature for both data is greater than 32°C.The final temperature for both data is less than 33.5°C.Between 1980 and 2020, the temperature for graph 2 (thick-continuous line)  was constant.Graph 1 (thin-dashed line) is essentially a linear graph.

In conclusion, there are four (4) points of intersection on this graph.

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(FIRST PERSON TO ANSWER GETS BRAINLIEST!!!) A student earned $2500.75 at his summer job making $12.50 per hour. Let h represent the number of hours the student worked. Which of the following equations could be used to determine how many hours the student worked at his summer job? (answer choices and question is below)

Answers

Answer:

[tex]12.50 \space\ h = 2500.75[/tex]

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

∴ Therefore, we can set up the following equation:

[tex]\boxed {12.50 \times h = 2500.75}[/tex]

From here, if we want to, we can find the number of hours worked by simply making h the subject of the equation and evaluating:

h = [tex]\frac{2500.75}{12.50}[/tex]

  = 200.6 hours

Answer: 12.50h = 2500.75

Step-by-step explanation:

We know from the question that the student earned $12.50 per hour.

Using this information, we can say that if the student worked for h hours, they would make a total of 12.50 × h dollars.

We also know that the total money they earned is $2500.75.

factorise completely
2x²+8+6

Answers

Use GCF
2( x^2 +4 +3)
Combine like terms
2 ( x^2 +7)
Can’t simplify further
Answer:: 2 ( x^2 +7)

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

⨠ add 8 and 6

[tex]\sf{2x^2+14}[/tex]

⨠ factor the 2 out

[tex]\sf{2(x^2+7)}[/tex]

Since we cannot simplify this more, we know that we've simplified completely.                                                                                   [tex]\small\pmb{\sf{Frozen \ melody}}[/tex]

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

Area=
Help me please!! Thanks so much :)
Asap

Answers

Answer:

16u²

Step-by-step explanation:

It is a regular parallelogram

we have points (3, 4) and (4, 0).

we also have the origin which is (0, 0) and the difference between (0, 0) and (4, 0) on the x axis is 4 and since it is a regular shape, that means the top right corner = (3, 4) + (4, 0), so it is (7, 4). we know the base is 4 now. the vertical height = (7, 4) - (1, 0) which is (6, 4). now we are looking at difference in y. which is between (4, 0) and (6, 4), so the difference is 4.

now we just do 4 x 4 since it is bh and you get 16 units ²

In one game, the final score was Falcons 3, Hawks 1. What fraction and
percent of the total goals did the Falcons score? Show your work in the space
below. Remember to check your solution.

Answers

Step-by-step explanation:

3over4 which is 75percent

What is the volume of the rectangular prism?
2 cm
2 cm
2 cm

Answers

Answer:

Step-by-step explanation:

The navy reports that the distribution of waist sizes among male sailors is approximately normal, with a mean of 32.6 inches and a standard deviation of 1.3 inches. part a: a male sailor whose waist is 34.1 inches is at what percentile? explain your reasoning and justify your work mathematically. (5 points) part b: the navy uniform supplier regularly stocks uniform pants between sizes 30 and 36. anyone with a waist circumference outside that interval requires a customized order. describe what this interval looks like if displayed visually. what percent of male sailors requires custom uniform pants? show your work and justify your reasoning mathematically. (5 points) (10 points)

Answers

Using the normal distribution, it is found that:

a. A male sailor whose waist is 34.1 inches is at the 87.5th percentile.

b. 5.7% of male sailors requires custom uniform pants.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 32.6, \sigma = 1.3[/tex]

For item a, the percentile is the p-value of Z when X = 34.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (34.1 - 32.6)/1.3

Z = 1.15

Z = 1.15 has a p-value of 0.875.

Hence 87.5th percentile.

For item b, the proportion who does not require an special order is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 30, hence:

X = 36:

Z = (36 - 32.6)/1.3

Z = 2.62

Z = 2.62 has a p-value of 0.996.

X = 30:

Z = (30 - 32.6)/1.3

Z = -2

Z = -2 has a p-value of 0.023.

0.996 - 0.023 = 0.943.

Hence the proportion who requires an special order is:

1 - 0.943 = 0.057.

5.7% of male sailors requires custom uniform pants.

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can someone help? will award brainliest​

Answers

Answer:

B

Step-by-step explanation:

The beginning temperature is -12 and then it rises 5 degrees each hour at the end of the game it is 32 degrees.

The answer is B

The temperature at the beginning of the hockey tournament is -12
degrees and rises five degrees each hour. At the end of the hockey
tournament the temperature is 32 degrees.

18. A tennis player uses up 800 calories every hour. In 1 hour and 15 minutes, how many calories does this player use? (A) 900 (B) 1000 (C) 1100 (D) 1200​

Answers

(C) 1000,
An hour = 60 minutes,
60/4= 15 minutes
The tennis player uses 800 calories, so 800/4 =200 calories
1 hour 15 minutes= 60 minutes + 15 min.
= 800 cal. + 200 cal.
=1000calories

To conduct a test of hypothesis with a small sample, we make an assumption that?

Answers

To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The normal distribution appears as a "bell curve" on a graph.

A probability bell curve is more properly described as the normal distribution.The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the usual distribution.

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Assume that thermometer readings are normally distributed with a mean of 0 C and a standard deviation of 1.00 C. A thermometer is randomly selected and tested. For the case​ below, draw a​ sketch, and find the probability of the reading.​ (The given values are in Celsius​ degrees.)

Between 1.50 and 2.25

1. Choose the correct graph
2.the probability of getting a reading between 1.50 and 2.25

Answers

The probability of getting a reading between 1.50 and 2.25 is; 0.00546

How to find the probability from z-score?

We are given the following information in the question:

Mean; μ = 0 °C

Standard Deviation; σ = 1 °C

We are given that the distribution of thermometer readings is a bell shaped distribution that is a normal distribution.

Formula for z-score is;

z = (x' - μ)/σ

P(Between 1.50 degrees and 2.25 degrees) is expressed as;

P(1.5 ≤ x ≤ 2.25)

= P((1.5 - 0)/1 ≤ z ≤ (2.25 - 0)/1))

= P(z ≤ 2.25) -  P(z < 1.5)

= 0.0546 = 5.46%

The graph that correctly describes this is the first graph

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Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference
2. Also, let b1, b2, b3, ... be a sequence of positive integers in geometric progression with common
ratio 2. If a1 = b1 = c, then the number of all possible values of c, for which the equality

2(a1 + a2 + ⋯ + an

) = b1 + b2 + ⋯ + bn

holds for some positive integer n, is _____

Answers

Since [tex]a_1,a_2,a_3,\cdots[/tex] are in arithmetic progression,

[tex]a_2 = a_1 + 2[/tex]

[tex]a_3 = a_2 + 2 = a_1 + 2\cdot2[/tex]

[tex]a_4 = a_3+2 = a_1+3\cdot2[/tex]

[tex]\cdots \implies a_n = a_1 + 2(n-1)[/tex]

and since [tex]b_1,b_2,b_3,\cdots[/tex] are in geometric progression,

[tex]b_2 = 2b_1[/tex]

[tex]b_3=2b_2 = 2^2 b_1[/tex]

[tex]b_4=2b_3=2^3b_1[/tex]

[tex]\cdots\implies b_n=2^{n-1}b_1[/tex]

Recall that

[tex]\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n[/tex]

[tex]\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]

It follows that

[tex]a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n +  n(n-1)[/tex]

so the left side is

[tex]2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n[/tex]

Also recall that

[tex]\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}[/tex]

so that the right side is

[tex]b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)[/tex]

Solve for [tex]c[/tex].

[tex]2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}[/tex]

Now, the numerator increases more slowly than the denominator, since

[tex]\dfrac{d}{dn}(2n(n-1)) = 4n - 2[/tex]

[tex]\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2[/tex]

and for [tex]n\ge5[/tex],

[tex]2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2[/tex]

This means we only need to check if the claim is true for any [tex]n\in\{1,2,3,4\}[/tex].

[tex]n=1[/tex] doesn't work, since that makes [tex]c=0[/tex].

If [tex]n=2[/tex], then

[tex]c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0[/tex]

If [tex]n=3[/tex], then

[tex]c = \dfrac{12}{2^3 - 6 - 1} = 12[/tex]

If [tex]n=4[/tex], then

[tex]c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N[/tex]

There is only one value for which the claim is true, [tex]c=12[/tex].

The length of plot is 8 meters more than its breath. If its perimeter is 80 metres, find its length and breath.

Answers

Answer:

length = 24 meters
breadth = 16 meters

Step-by-step explanation:

Let L be length and B be breadth

From the first fact we get the equation
L = B + 8         (1)

We know that perimeter = 2(L+B) and this is given as 80

So 2(L+B) = 80

L + B = 80/2 = 40
or
L = 40 - B              (2)

If we add equations (1) and (2) we can eliminate B

We get 2L = B + 8 + 40 - B =48

L = 48/2 = 24

Substituting for L in equation (1) we get

24 = B + 8  ==>

B = 24-8 =16

Cross-check

Perimeter = 2 (L+B) = 2(24 + 16) = 2(40) = 80

Hence check OK

all common factors of 24

Answers

Answer:

The all common Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24

An equilateral is shown inside a square inside a regular pentagon inside a regular hexagon. The square and regular hexagon are shaded.

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. Write an expression for the area of the shaded regions.

Shaded area = area of the
– area of the + area of the – area of the

Answers

Shaded area = area of the hexagon – area of the pentagon + area of the square – area of the equilateral triangle. This can be obtained by finding each shaded area and then adding them.

Find the expression for the area of the shaded regions:

From the question we can say that the Hexagon has three shapes inside it,

PentagonSquareTriangle

Also it is given that,

An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon.

From this we know that equilateral triangle is the smallest, then square, then regular pentagon and then a regular hexagon.

A pentagon is shown inside a regular hexagon.

Area of first shaded region = Area of the hexagon - Area of pentagon

An equilateral triangle is shown inside a square.

Area of second shaded region = Area of the square - Area of equilateral triangle  

The expression for total shaded region would be written as,

Shaded area = Area of first shaded region + Area of second shaded region

Hence,        

⇒ Shaded area  = area of the hexagon – area of the pentagon + area of the  square – area of the equilateral triangle.

 

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Answer:

Regular Hexagon

Regular Pentagon

Square

Equilateral Triangle

Step-by-step explanation:

E2020 Geometry B!! :3

HELP WANTED!!!!! NEED HELP ASAP!!!!! (02.06; 02.07 MC)

Part A: Michael bought vegetables that weighs 4 and 1 over 8 pounds. How many ounces does the vegetables weigh? Show your work. (5 points)

[16 ounces = 1 pound]

Part B: A running tap dispenses 0.16 gallons of water every second. How many pints of water is dispensed after 25 seconds? Show your work. (5 points)

[1 gallon = 4 quarts, 1 quart = 2 pints]

if you are every so kind.. PLS SHOW ME HOW TO DO THIS PLS!!!!!!!

Answers

Using proportions, it is found that:

A. The vegetables weigh 66 pounds.

B. 0.5 pints are dispensed after 25 seconds.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

4 and 1/8 pounds is equivalent to 4.125 pounds. Since each pound has 16 ounces, the weight of the vegetable is of:

W = 16 x 4.125 = 66 pounds.

Every second, 0.16 gallons are dispensed. Hence the amount dispensed in 25 seconds is:

A = 25 x 0.16 = 4 gallons.

Each gallon has 8 pints, hence the number of pints dispensed is:

4/8 = 0.5 pints.

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Shira's math test included a survey question asking how many hours students spent studying for the test. The scatter plot below shows the relationship between how many hours students spent studying and their score on the test. A line was fit to the data to model the relationship.

Which of these linear equations best describes the given model?

Answers

Answer:

Part 1) Option B. y = 10x + 45

Part 2) The score is 95

Step-by-step explanation:

Linear equation that best describes the given model

Let

x ---> number of hours students spent studying

y ---> their score on the test

Looking at the line that was fit to the data to model the relationship

The slope is positive

The y-intercept is the point (0,45)

For x=1, y=55 ----> point (1,55)

Find the slope

The formula to calculate the slope between two points is equal to

substitute the points (0,45) and (1,55)

Find the equation of the line in slope intercept form

we have

substitute

Part 2) Estimate the score for a student that spent 5 hours studying.

For x=5 hours

substitute in the linear equation and solve for y

PLEASE HELP FAST!

A cylinder and a cone have the same volume. The cylinder has radius x
and height y. The cone has radius 1/2x. Find the height of the cone in terms of y.

Answers

The height of the cone in terms of y is h = 12x⁴y

How to find the volume of a cone and cylinder?

The cylinder and the cone have the same volume.

Volume of a cylinder = πr²h

where

r = radiush = height

Therefore,

Volume of a cylinder = πx²y

volume of a cone = 1 / 3 πr²h

where

r = radius of the coneh = height of the cone

Therefore,

πx²y = 1 / 3 × π × (1 / 2x)² × h

πx²y = πh / 12x²

πx²y × 12x² / π = h

h = 12x⁴y

Therefore, the height of the cone in terms of y is h = 12x⁴y

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Prove the identity.
tan^5x = tan x (sec² x - 2 sec² x + 1)

Answers

goal:tan^5x=tanx(sec²x-2sec²x+1)

proof: from l.h.s to r.h.s

tan^5x=(tanx)^5=((tanx)(tan²x)(tan²x))

from trigonometry identity

(tan²x)=sec²x-1

tan^5x=(tanx(sec²x-1)(sec²x-1))

=(tanx(sec^4x-sec²x-sec²x+1))

=(tanx(sec^4x-2sec²x+1))

proved

Solve the following quadratic equation for all values of a in simplest form.
5(x − 6)² — 29 = −19

Answers

Answer:

[tex]X1 = 6-\sqrt{2} , X2 = 6+\sqrt{2}[/tex]

Step-by-step explanation:

Answer: x= √2 + 6, - √2 + 6

Step-by-step explanation:

Graduate management aptitude test (gmat) scores are widely used by graduate schools of business as an entrance requirement. suppose that in one particular year, the mean score for the gmat was 473, with a standard deviation of 104. what values are three standard deviations within the mean?

Answers

The values that exist two standard deviations above and below the mean are 681 and 265.

How to determine the values?

The given parameters exist:

Mean = 473

Standard deviation =104

The values above and below the mean exist calculated utilizing:

[tex]$x=\bar{x} \pm n \sigma$[/tex]

In this case n = 2.

So, we have, [tex]$x=\bar{x} \pm 2 \sigma$[/tex]

The value above is:

x = 473 + 2 [tex]*[/tex] 104 = 681

The value below is:

x = 473 - 2 [tex]*[/tex] 104 = 265

Therefore, the values that exist two standard deviations above and below the mean are 681 and 265.

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An interior designer is sketching a rough outline of a
corner room of an office building, as shown above.
If the area of the triangular-shaped room is 1,728
square feet, what is the value of sin(x)?

Answers

4 squares of feet and feet of squares 4..

The measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

The area of triangle A = 1728 square feet

The base length of the triangle b = 72 feet

Let h be the height of the triangle

Area = (1/2)b×h

1728 = (1/2)72×h

h = 48 feet

Half of the 72 is 72/2 = 36

As we know,

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

Applying trigonometric ratio:

tan(x) = 48/36

tan(x) = 1.333

x = 53.13 degrees

Thus, the measure of the angle x or the value of the x is 53.13 degrees if an interior designer is sketching a rough outline of a corner room of an office building.

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A farmer with 1200 meters of fencing wishes to enclose a rectangular field and then divide it into two plots with a fence parallel to one of the sides. What are the dimensions of the field that produce the largest area

Answers

The perimeter of a given figure is a measure of the addition of each individual length of the sides of the figure. Thus the dimensions that would produce the largest area of the field are; length = 300 m, and width = 200 meters.

The perimeter of a given figure is a measure of the addition of each length of the sides of the figure. It always has the unit as that of the given sides of the figure.

So in the given question, the perimeter of the fence required = 1200 meters.

Thus, let the length of the enclosed rectangle be represented by l and its width by w. Thus,

Perimeter = 2l + 3w

1200 = 2l + 3w

Thus, let l be equal to 300, we have;

1200 = 2(300) + 3w

1200 - 600 = 3w

w = 200

Thus the dimensions of the field that would produce the largest area are; length = 300 m and width = 200 m.

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