Find the domain of the vector function. (Enter your answer in interval notation.) r(t) = t − 2 t + 2 i + sin(t)j + ln(36 − t2)k

Matching of the functions domain and range are as follows:

f(x)   = 4-4x ;

Domain:{0,1,3,5,6}

Range;{-20,-16,-8,0,4}

f(x) = 5x - 3

Domain:{-2,-1,0,3,4}

Range:{-13,-8,-3,12,4}

f(x) = -10x

Domain:{-4,-2,0,2,4}

Range:{-40,-20,0,20,40}

f(x) = (3/x) + 1.5

Domain:{-3,-2,-1,2,6}

Range:{0.5,0,-1.5,3,2}.

1) The function f(x) = 4 - 4x

Take Domain:{0,1,3,5,6}

If, we take x=0 and put in the function then we get

f(x)=4-0

f(x)=4

put x=1

f(x) = 4 - 4 =0

put x=3 then we get

f(x)=4-12=--8

put x=5 them we get

f(x)=4-20=-16

put x=6 then we get

f(x)=4-24=-20

Therefore ,range:[-20,-16,-8,0,4}

2) The function f(x)=5x-3

Take domain{-2,-1,0,3,4}

Now, put x=-2 in the function then we get

f(x) = -13

now put x=-1 then we get

f(x)=-5-3=-8

Put x=0 then we get

f(x)=0-3=-3

Put x=3 then we get

f(x)=15-3=12

Put x=4 then we get

f(x)=20-3=17

Therefore , range:{-13,-8,-3,12,17}

3) The function f(x)=-10x

Take domain:{-4,-2,0,2,4}

Put x=-4 in the function then we get

f(x)=40

Put x= -2 then we get

f(x)=20

Put x=0 then we get

f(x)=0

Put x=2 then we get

f(x)=-20

Put x=4 then we get

f(x)=-40

Therefore , range :{-40,-20,0,20,40}

4) The function f(x)= (3/x) + 1.5

Take domain:{-3,-2,-1,2,6}

Put x= -3 in the taken function then we get

f(x)=-1+1.5=0.5

put x=-2 then  we get

f(x)= -1.5+1.5=0

Put x=-1 then we get

f(x)=-3+1.5=-1.5

Put x= 2 then we get

f(x)=1.5+1.5=3

Put x= 6 then we get

f(x)=0.5+1.5=2

Therefore, range : {0.5,0,-1.5,3,2}.

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Answer:

82 units.

Step-by-step explanation:

The Pythagorean Theorem is a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the legs.

In this case, 18 and 80 are the legs.

18^2 + 80^2 = c^2

324 + 6,400 = c^2

6,724 = c^2

c^2 = 6,724

c^2 = 82^2

c = plus or minus 82

Since measurements cannot be negative, the length of the hypotenuse is 82 units.

Hope this helps!

Answer:

82 units   indeed!

Step-by-step explanation:

c = \(\sqrt{ 18^{2} + 80^{2} }\)

c = 82

Answer:

i think its 116

Step-by-step explanation:

\(x^4\) - 8x³ + 16x² - 3x³ + 24x² - 48x is the polynomial P(x).

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

P(x) is a polynomial of degree 4.

It has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at

x = 0 and x = -3.

This means,

x = 0 ____(1)

x = -3

(x - 3) = 0 _____(2)

x = 4 with multiplicity 2

(x - 4)² = 0 ______(3)

So,

From (1), (2), and (3).

P(x) = x (x - 3) (x - 4)²

= (x² - 3x) (x² - 8x + 16)

= \(x^4\) - 8x³ + 16x² - 3x³ + 24x² - 48x

We see that the degree is 4.

Thus,

\(x^4\) - 8x³ + 16x² - 3x³ + 24x² - 48x is the polynomial.

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The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

Given that:

Total surface area of the rectangular box or cuboid = 100 cm²

A rectangular box with largest volume is a cube.

The total surface area of a cube = 6 times square of one edge length.

Let the edge length = given dimensions; x, y, z

So,

x = y = z

6x^2 = 100

x^2 = 100 / 6

x = √ 100 / 6

x = 10 / √ 6 cm

x = 2.449 cm

Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

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Answer:

x=73

Step-by-step explanation:

The two angles are equivalent, therefore x=73

The slopes are best approximated as: The slopes are approximately -1.7, 0, and 1.7.

The formula to find the slope between two coordinates is expressed as:

Slope = (y₂ - y₁)/(x₂ - x₁)

The slope of each line above the x-axis are:

Slope 1 = (5 - 0)/(5 - 8)

Slope 1 = -1.7

Slope 2 = (5 - 5)/(5 - (-2))

Slope 2 = 0

Slope 3 = (5 - 0)/(-2 - (-5))

Slope 3 = 5/3 = 1.7

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The amount Siya will spend on tiles is given by the expression (1.1 x T / 6) x R234, where T represents the required number of tiles. To calculate the amount Siya will spend on tiles, we need to determine the number of boxes of tiles he needs to purchase and then multiply it by the price per box.

First, we need to determine the number of tiles required. Let's assume the required number of tiles is represented by the variable "T."

Since the builder recommends buying 10% more tiles in case of breakages, Siya needs to purchase 110 percentage of the required number of tiles. This can be calculated as:

110% of T = 1.1 x T

Next, we need to convert the number of tiles into the number of boxes required. We know that one box contains 6 tiles, so the number of boxes Siya needs to purchase is:

Number of boxes = (1.1 x T) / 6

Finally, we can calculate the total cost by multiplying the number of boxes by the price per box:

Total cost = (1.1 x T / 6) x R234

Please note that without knowing the specific number of tiles required (T), we cannot provide an exact amount Siya will spend.

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Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer:

Step-by-step explanation:

the consecutive are 39,40,41 and the smallest here is 39

Hope this helped

Answer:

64°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the third angle be x , then

x + 90° + 26° = 180°

x + 116° = 180° ( subtract 116° from both sides )

x = 64°

the other angle is 64°

Answer: its D because Jews (Hebrew: יְהוּדִים, ISO 259-2: Yehudim, Israeli pronunciation: [jehuˈdim]) or Jewish people are an ethnoreligious group,[10] nation or ethnos[11][12] originating from the ancient Israelites[13][14][15] and Hebrews[16][17][18] of historical Israel and Judah. Jewish ethnicity, nationhood, and religion are strongly interrelated,[19][20] as Judaism is the ethnic religion of the Jewish people, although its observance varies from strict to none.[21][22]

Jews originated as an ethnic and religious group in the Middle East during the second millennium BCE,[9] in a part of the Levant known as the Land of Israel.[23] The Merneptah Stele of ancient Egypt appears to confirm the existence of a people of Israel somewhere in Canaan as far back as the 13th century BCE (Late Bronze Age).[24][25] The Israelites, as an outgrowth of the Canaanite population,[26] consolidated their hold in the region with the emergence of the kingdoms of Israel and Judah. Some consider that these Canaan-sedentary Israelites melded with incoming nomadic groups known as the "Hebrews".[27] The experience of life in the Jewish diaspora, from the Babylonian captivity and exile (though few sources mention this period in detail[28]) to the Roman occupation and exile, and the historical relations between Jews and their homeland in the Levant thereafter became a major feature of Jewish history, identity, culture, and memory.[29]

In the following millennia, Jewish diaspora communities coalesced into three major ethnic subdivisions according to where their ancestors settled: the Ashkenazim (Central and Eastern Europe), the Sephardim (initially in the Iberian Peninsula), and the Mizrahim (Middle East and North Africa).[30][31] Prior to World War II, the global Jewish population reached a peak of 16.7 million,[32] representing around 0.7 percent of the world population at that time. During World War II, approximately 6 million Jews throughout Europe were systematically murdered by Nazi Germany during the Holocaust.[33][34] Since then, the population has slowly risen again, and as of 2018, was estimated to be at 14.6–17.8 million by the Berman Jewish DataBank,[1] comprising less than 0.2 percent of the total world population.[35][note 1] The modern State of Israel is the only country where Jews form a majority of the population.

Step-by-step explanation: Hitler + jew=bad

Answer:

Step-by-step explanation:

hope this helps...

have a nice day

Answer:

this is a really long paragrah 0-0

Step-by-step explanation:

very long paragraph

Answer:

x = 11 | Scale factor = 2

Step-by-step explanation:

As you can see, the 3 turns into a six meaning it multiplied by 2. Apply this to 5.5 to get 11. The 2 is your scale factor.

Hope this helps,

If you like my answer please give brainliest

Happy Holidays to everyone!

The solution of the expression is,

a) 3,724

b) 2,784

We have to given that,

a) Divide 70,756 by 19.

b) Subtract 940 from your answer to part a).​

Now, We can simplify as,

a) Divide 70,756 by 19.

⇒ 70,756 ÷ 19

⇒ 3,724

And, Subtract 940 from your answer to part a).​ that is, 3724

⇒ 3724 - 940

⇒ 2,784

Therefore, The solution of the expression is,

a) 3,724

b) 2,784

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To modify a function in R to also determine if the R-squared is significant based on a given threshold, you can add an additional step to the function that calculates the p-value for the R-squared using the summary function.

Here is an example of how you might modify a function to do this:

modifyFunction <- function(data, threshold) {

 # Fit the model and get the summary

 model <- lm(y ~ x, data = data)

 summary <- summary(model)

 # Calculate the p-value for the R-squared

 rsquared <- summary$r.squared

 n <- nrow(data)

 pvalue <- 1 - pf(rsquared * (n - 2) / (1 - rsquared), 1, n - 2)

 # Determine if the R-squared is significant based on the threshold

 if (pvalue < threshold) {

   result <- "R-squared is significant"

 } else {

   result <- "R-squared is not significant"

 }

 return(result)

}

# Test the function

modifyFunction(data = mydata, threshold = 0.05)

In this example, the function takes two arguments: data and threshold. The data argument is the data frame containing the data, and the threshold argument is the level of significance that you want to use to determine if the R-squared is significant.

The function first fits a linear model using the lm function, and then gets the summary using the summary function. It then calculates the p-value for the R-squared using the pf function and compares it to the threshold. If the p-value is less than the threshold, the function returns the result "R-squared is significant". If the p-value is greater than the threshold, the function returns the result "R-squared is not significant".

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The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

The Mean is defined as the ratio of sum of numbers present in the data to the total numbers present in the data. Median is defined as the ratio of sum of middle numbers present in the data. Mode is defined as the most recurring number present in the data. Midrange is the ratio of the largest and smallest number in the data to 2.

Let's see how to calculate Mean, Median, Mode and Midrange.

Mean = 13 + 15 + 18 + 18 + 21 / 5

Mean = 85 / 5

Mean = 17

Median = 18 (as it is the middle term of the data)

Mode = 18 (as it is most recurring number)

Midrange = 21 + 13 / 2

Midrange = 34 / 2

Midrange = 17

Therefore, The Mean is 17, Median is 18, Mode is 18 and, Midrange is 17.

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Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

Answer:

$215.92

Step-by-step explanation:

Answer:

correct order=

Step-by-step explanation:

Answer: The slope of the line = 4.

Step-by-step explanation:

We know that ,

Slope of a line passes through \((x_1,y_1)\) and \((x_2,y_2)\)  = \(\dfrac{y_2-y_1}{x_2-x_1}\)

Here , the line passes through points (2,18) and (8,42).

Then the slope of the given line = \(\dfrac{42-18}{8-2}\)

\(=\dfrac{24}{6}=4\)

Hence, the slope of the line = 4.

Answer:

4

Step-by-step explanation:

i took the test and got it right

An expression for the length of the hypotenuse z is \(\sqrt{x^2 + y^2}\) = z.

What is Pythagoras' theorem?

A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

Here, we have

Given: A right triangle with legs of lengths x and y has a hypotenuse of length z.

We have to write an expression for the length of the hypotenuse z.

By Pythagoras' theorem

x²+y² = z²

\(\sqrt{x^2 + y^2}\) = z

Hence, an expression for the length of the hypotenuse z is \(\sqrt{x^2 + y^2}\) = z.

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Answer:

-12y^10

Step-by-step explanation:

First let's rewrite the equation using the commutative property of multiplication
3 x (-4)y^8y^2

Multiply y^8 by y^2 by adding the exponents
y^8+y^2= y^10

3 x (-4)y^10

Now multiply 3 by -4
3 x -4= -12

Finally put them together
-12 + y^10= -12y^10

Answer:

\( - 12 {y}^{10} \)

Step-by-step explanation:

We are to simplify:

\((3 {y}^{8} )( - 4 {y}^{2} )\)

3 multiplies -4 to get -12, as shown below

\(3 \times - 4 = - 12\)

Now, to multiply the exponents which are 8 and 2, we have to use the exponential rule of multiplication: \( {a}^{b} \times {a}^{c} = {a}^{b + c} \)

Therefore:

\( {y}^{8} \times {y}^{2} = = > {y}^{8 + 2} = {y}^{10} \)

Now, combine -12 and \( {y}^{10} \) to get your final answer.

Final answer \( = - 12 {y}^{10} \)

1 year insurance policy covering its equipment was purchased for 6,144. The date purchased was June 14 but it doesn't go into effect until June 16th, the amount paid for the month of June is approximately $252.75, and the amount paid for the entire year is approximately $6,144.

To calculate the amount paid for the month and the year, we need to consider the number of days covered by the insurance policy. Let's break it down step by step:

Step 1: Determine the number of days covered in June.

Since the policy doesn't go into effect until June 16th, there are 15 days remaining in June that will be covered by the insurance policy.

Step 2: Calculate the daily rate.

To find the daily rate, we divide the total cost of the insurance policy by the number of days in a year:

Daily rate = 6,144 / 365

Step 3: Calculate the amount paid for June.

The amount paid for June can be found by multiplying the daily rate by the number of days covered:

Amount paid for June = Daily rate * Number of days covered in June

Step 4: Calculate the amount paid for the year.

To calculate the amount paid for the year, we simply multiply the daily rate by 365 (the total number of days in a year):

Amount paid for the year = Daily rate * 365

Now let's perform the calculations:

Step 2: Daily rate

Daily rate = 6,144 / 365 ≈ 16.85 (rounded to two decimal places)

Step 3: Amount paid for June

Amount paid for June = 16.85 * 15 ≈ 252.75 (rounded to two decimal places)

Step 4: Amount paid for the year

Amount paid for the year = 16.85 * 365 ≈ 6,144 (rounded to two decimal places)

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Answer: 160

Step-by-step explanation:

160 is the answer trust me

Answer:

i think 6.4

Step-by-step explanation:

because at first i I thought you needed to multiply but i divided  

Answer:

5x^2 + x + 10

Step-by-step explanation:

you appear to have a typo. I'd say

(f+g)(x) = f(x) + g(x) = 9-x + 5x^2+2x+1 = 5x^2 + x + 10

Answer:

300

Step-by-step explanation:

Neptune is approximately 33 times farther from the sun that earth.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Distance of Earth from the Sun  = 9 × 10⁷

Distance of Neptune from the Sun = 3 × 10⁹

Now,

Since, Distance of Earth from the Sun  = 9 × 10⁷

Distance of Neptune from the Sun = 3 × 10⁹

Hence, The times of distance between the Earth and Sun from Neptune; = 9 /3 × 10⁷×10²

=  100/3  × 9× 10^7        

=  100/3   times of distance between Earth & Sun

Hence, Neptune is approximately 33 times farther from the sun that earth.

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