Identify two statements that contradict each other.
I. ZM is an obtuse angle.
II. m ZM +mZP= 90
III. 180 – mZM = 25
IV. mZP= 120

The partial sum for the power series of arctan\((x^2)\) consisting of the first four non-zero terms can be written as: arctan\((x^2) ≈ x^2 - (1/3)x^6 + (1/5)x^10 - (1/7)x^14\)

The power series representation of the function f(x) = arctan\((x^2)\) is given by:

\(f(x) = ∑n=0^∞ (-1)^n x^(2n+1) / (2n+1)\)

To find the partial sum consisting of the first four non-zero terms, we can simply substitute n = 0, 1, 2, and 3 into the above expression, and add up the resulting terms:

\(f(x) ≈ x - x^3/3 + x^5/5 - x^7/7\)

This is the desired partial sum for the power series representation of arctan\((x^2)\), consisting of the first four non-zero terms. Note that as we add more terms to this sum, we get a better and better approximation to the function f(x) over a wider range of x values.

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The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

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Answer:

Step-by-step explanation:  i think the answer is A

Answer:

The family of lines that are parallel to \(2\cdot x + y = 6\) is of the form \(2\cdot x + y = k, \,k\neq 6\). A possible solution is \(2\cdot x + y = -2\).

Step-by-step explanation:

Let be \(2\cdot x + y = 6\) the equation of a line, another line is parallel to it if and only if it is of the form:

\(2\cdot x + y = k, \,k\neq 6\)  (1)

Then, a possible solution is \(2\cdot x + y = -2\).

The maximum value of the function y = 8(x^2+1)^(1/2) - x on the interval [0,4] is approximately 29.658, which occurs at x = 4  and The minimum value of y is approximately 3.605, which occurs at x = 1/√15.

To find the maximum and minimum values of the function y = 8(x^2+1)^(1/2) - x on the interval [0,4], we will first take the derivative of the function and set it equal to zero to find the critical points. Then we will evaluate the function at those critical points and at the endpoints of the interval to find the maximum and minimum values.

First, we take the derivative of y with respect to x:

y' = 8(1/2)(x^2+1)^(-1/2)(2x) - 1

Simplifying, we get

y' = 4x(x^2+1)^(-1/2) - 1

Setting y' equal to zero and solving for x, we get

4x(x^2+1)^(-1/2) - 1 = 0

4x(x^2+1)^(-1/2) = 1

16x^2 = (x^2+1)

15x^2 = 1

x = ±(1/√15)

We check these critical points as well as the endpoints of the interval [0,4] to find the maximum and minimum values of y

y(0) = 8(0^2+1)^(1/2) - 0 = 8(1)^(1/2) = 8

y(4) = 8(4^2+1)^(1/2) - 4 ≈ 29.658

y(1/√15) = 8((1/√15)^2+1)^(1/2) - (1/√15) ≈ 3.605

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Find the maximum and minimum values of the function y = 8(x^2+1)^(1/2)-x on the interval [0,4]. (Round your answers to three decimal places.)

The first term of the arithmetic progression is 5

An arithmetic sequence can simply be defined as a sequence of numbers or terms in which the differences between successive or consecutive terms are always equal.

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + (n-1)d

Where;

Given that the first term of the sequence is a, the 43rd term is 26 and the common difference is 1/2

Substitute the values into the formula

26 = a + (43 -1)1/2

expand the bracket

26 = a + (42)1/2

Multiply through

26 = a + 21

collect like terms

a = 26 - 21

a = 5

Thus, the value is 5

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Step-by-step explanation:

18x²-8

= 2(9x²-4)

= 2(3x+2)(3x-2)

18x² - 8

Common factor is 2.

=》18x² - 8

=》2 (9x²- 4) [option C].

_____

RainbowSalt2222 ☔

Answer: Angle 2: 45°

Step-by-step explanation:

All triangles add up to 180, so all you would so is take both of those angles and subtract them from 180, so basically 180 - 135

Answer:

Step-by-step explanation:

to find the y intercept of AB, first find the slope of AB: m=(1-(-1))/(2-14)=-1/6

the equation of line AB is y=-(1/6)x+b

use either of the given two points to find out b: 1=(-1/6)*2+b => b=4/3

BC is perpendicular to AB, so the slope of BC is the negative reciprocal of the slope of AB, therefore, the slope of BC is 6

Equation of BC is y=6x+b

find out b by using the coordinates of point B: 1=6*2+b => b=-11

the equation of BC is: y=6x-11

the x coordinate of point C: 13=6*x -11 =>x=4

Answer:

yes

Step-by-step explanation:

it has a 90 degree angle

Attached is the pedigree. I found this exercise on the Internet.

The probability that both john and sue are carriers is:

The missing characters are: II-5, II-6, II-8, III-10, III-11, III-12, III-13.

Individual II-5 will have half black/half white squares. It's a square because it shows in the book that John's grandmother (I-2) fell ill.

Half black/half white transmits an allele that requires the disease allele because his mother has the disease, and his father does not carry or show the disease, so from him, John's father (II-5) only got one. normal allele.

The person will ask II-6 questions in a circle. A circle because John's mother once father is Example II-5. Since she has a daughter (John's Sister) with the disease, it means that John's sister inherited both alleles for the disease.

The Personal II-8 will have a half-black/half-white circle.

Circle because Sue's mother and father Probability Example II-7 (square). Half black/half white transmits an allele that requires the disease allele because her father has the disease, and her mother does not carry or show the disease, meaning she is from her, Sue's mother (II-8). take an old allele.

The person will ask the III-10 questions in a circle. The circle is because she is John's sister mentioned in the text. The question mark is that we can't be sure if this is an allele.

We know from the records that he has no symptoms of the disease, but if his mother is infected with only one allele, he may have inherited an allele from his father or mother, or he will inherit the disease allele. The disease allele comes from the mother, not from the father if the mother has the disease.

John, There will be questions in the People III-11 box. Square because John is a man. The question mark is that we can't be sure if this is an allele. We know from the literature that he has no symptoms of the disease, but if his mother is a carrier of only one of the disease alleles, he may have inherited the disease allele from his father. disease allele. If her mother has a disease, it is not from her father, but from her mother.

SU will have questions in the Humans III-12 circle. Circle it because she's Sue, the woman. The question mark is that we can't be sure if this is an allele. From the instructions, we learn that he has no symptoms of the disease, but that he may have inherited the disease allele from his mother, and that after his mother has the disease allele, he too can be a carrier or transmit the disease to others. The disease allele has inherited the normal allele from its mother. He inherited only one normal allele from his father.

III-13 individuals will have questions in the square. A square because according to the guide, he is Su's brother. The question mark is that we can't be sure if this is a disease allele. We know from the records that she did not show any signs of the disease, but she probably inherited the disease allele from her mother, and when her mother has the disease allele, she will also be a carrier or inherited. original allele from its mother. He inherited only one normal allele from his father.

Complete Question:

John and sue are expecting a child, but are concerned about a rare autosomal recessive disease that is present in both of their families. in the pedigree below, john is represented as individual iii-11 and sue is represented as individual iii-12. john\'s sister, iii-10, and sue\'s brother, iii-13, both do not show evidence of the disease, but john\'s paternal grandmother and sue\'s maternal grandfather both had the disease. assign the appropriate symbol to each individual in the pedigree. what is the probability that john is a carrier? probability: 66.7 % what is the probability that both john and sue are carriers?

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The equation of line parallel to y = -3 passing through (2,6) is y = 6

The slope-intercept form of straight line is used to find the equation of line. It is given as y =mx + b

where m is a slope of line

b is y-intercept

According to the question,

The required line is parallel to line y = -3

Slope of given line : m₁

m₁ = 0

When two lines are parallel to each other then their slopes are equal

Therefore , slope of required line is m₂ =  m₁ = 0

Also , given that the line is passing through the coordinate (2,6)

So , 6 = 0(2) + b

=> b = 6

Substituting the values of slope and intercept

y = 6 is required equation of line

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The formula of the nth term in the arithmetic sequence is a(n) = 3 + (n-1)9.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed constant, called the common difference, to the preceding term.

The sequence can be represented by the general term an = a1 + (n-1)d, where a1 is the first term and d is the common difference

In an arithmetic sequence, the difference between consecutive terms is constant. Therefore, if a(1) = 3 and a(2) = 12, the common difference (d) is 12 - 3 = 9.

The nth term of an arithmetic sequence is given by the formula:

a(n) = a(1) + (n-1)d

where:

a(n) is the nth term of the sequence

a(1) is the first term of the sequence

d is the common difference

n is the position of the term in the sequence

So, for the given sequence, the nth term a(n) of the arithmetic sequence is:

a(n) = a(1) + (n-1)d = 3 + (n-1)9

This means that the nth term of the arithmetic sequence is found by adding the common difference (9) to the first term (3), and then multiplying the result by (n-1) which indicates the position of the term in the sequence.

Therefore, a(n) = 3 + (n-1)9 is the formula of the nth term in the arithmetic sequence.

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Answer:

75m

Step-by-step explanation:

Answer:

18 miles per gallon

90/5=18

Step-by-step explanation:

Answer:

18 miles per gallon of gas

Step-by-step explanation:

because \(18*5=90\)

The coordinate is (2√2 , 0).

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

If you rotate the point (2,-2) positive 45 around the origin.

To find the coordinates:

the formula;

X = xcosФ - ysinФ

And Y = xsinФ + ycosФ

and here Ф = 45° and x = 2 and y = -2

Now, X = 2/√2 + 2/√2 = 2√2

Y = 2/√2 - 2/√2 = 0

Therefore, the coordinate is  (2√2 , 0).

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I don't see a table lol, link it and I'll solve it

Answer

8 More minutes

Step-by-step explanation:

15+ 17 = 32

32/.8 = 40

40 - 32 = 8

Answer:

Its C.

Step-by-step explanation:

I had this and its C. trust me

The inequality given by (x/3) + 5 ≥ 1/6 has the solution x ≥ -29/2 or [-29/2 , +∞).

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

To solve an inequality is to find the values of x such that when we substitute that number for x we have a true statement.

Given the inequality (x/3) + 5 ≥ 1/6, subtract 5 from both sides.

(x/3) + 5 - 5 ≥ 1/6 - 5

x/3 ≥ -29/6

Multiply both sides by 3.

3(x/3) ≥ 3(-29/6)

x ≥ -29/2

To check, let x = -29/2

x = -29/2 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

(-29/2)/3 + 5 ≥ 1/6

1/6 ≥ 1/6

let x = -14,

x = -14 ≥ -29/2

Substitute this value to the inequality.

(x/3) + 5 ≥ 1/6

-14/3 + 5 ≥ 1/6

1/3 ≥ 1/6

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The time complexity is O(1) as the recurrence reduces to a constant.

T(n) = 2T(n/2) + n/log n

T(1) = 1

T(2) = 2T(1) + 2/log 2

= 2 + 2/log 2

T(4) = 2T(2) + 4/log 4

= 2(2 + 2/log 2) + 4/log 4

T(8) = 2T(4) + 8/log 8

= 2(2(2 + 2/log 2) + 4/log 4) + 8/log 8

T(n) = 2^k T(1) + (2^k + 2^(k-1) + ... + 2 + 1)*n/log n

= 2^k + (2^k + 2^(k-1) + ... + 2 + 1)*n/log n

= 2^k + n*Σ_(i=1)^k▒2^i/log n

= 2^k + n/log n*(2^(k+1) - 1)

= 2^k + n/log n*(n/2 - 1)

= (2^k + n/2 - n/log n)*n/log n

= (2n - n/log n)*(log n/n)

= 2 - 1/log n

The time complexity is O(1) as the recurrence reduces to a constant.

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Answer:

8.2 units

Step-by-step explanation:

The formula for this type of problem is [ d = √(x2-x1)²+(y2-y1)² ]

d = √(-1-(-9))²+(0-)-2))²

d = √8²+2²

d = √64+4

d = √68

d ≈ 8.2

Best of Luck!

I would say its the second one.

the student shouldve distributed the 2^3x+3 into 2^3x+9

Answer:

Very top one

Step-by-step explanation:

the dot is in between -34 and -35 so 34.5

and the arrow is pointing left which means less than

DOL = ($76,000 / $38,000) = 2 , This means that for every 1% increase in sales, operating income will increase by 2%.

The degree of operating leverage (DOL) measures the percentage change in operating income resulting from a percentage change in sales. To calculate DOL for Bristo Corporation, we need to first calculate the contribution margin per unit. Contribution margin is the difference between the selling price and variable expenses. In this case, the contribution margin per unit is $40 (i.e., $50 - 20% of $50).
Next, we can calculate the total contribution margin by multiplying the contribution margin per unit by the number of units sold:
Total contribution margin = 1900 units x $40 per unit = $76,000
Finally, we can calculate the DOL using the following formula:
DOL = (contribution margin / operating income)
Operating income is the difference between total revenue and total expenses (fixed and variable):
Operating income = total revenue - total expenses
Operating income = (1900 units x $50 per unit) - (20% x 1900 units x $50 per unit + $66000)
Operating income = $38,000
Therefore, DOL = ($76,000 / $38,000) = 2
This means that for every 1% increase in sales, operating income will increase by 2%.

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\(B=\frac{h+D^{2}5g}{D^{2} }\)

h = D²(B - 5g)

h = D²B - D²5g

h + D²5g = D²B

B = (h + D²5g)/D²

Answer:

The scale in the ratio given considers the case that there are 9 sweets (2 + 3 + 4), however, to answer our question, we need to scale up the ratio, so that we can work out the share when we have 36 sweets

Step-by-step explanation:

Ratios are a way of displaying the proportional split of a value and they are very similar to fractions. In the example above, we see that for every 2 sweets Amy has, Beth gets 3 and, Colin will get 4. Like fractions, this proportion will stay the same regardless of the scale of the ratio. The scale in the ratio given considers the case that there are 9 sweets (2 + 3 + 4), however, to answer our question, we need to scale up the ratio, so that we can work out the share when we have 36 sweets. So, what scale factor do we need to get it from a total of 9 sweets to a sum of 36 sweets? We know that 9 multiplied by 4 gives us 36, therefore, we can use a scale factor of 4. Remember how whatever is done to the denominator of a fraction has to be done to the numerator? Ratios like to behave the same way, so now that we have scaled up the sum of the ratio, we need to scale up the individual values by 4 – (2x4) : 3x4 : 4x4. Once we work it out we get the new ratio 8:12:16. You can check if you’re right by adding up the new values and you will see that 8 + 12 + 16 = 36, which is the value that the 9 was initially scaled up to. So we now know that when sharing the 36 sweets, Amy will get 8 sweets, Beth will get 12 sweets and Colin will get 16.

Answer:

Because every outcome is equally likely, and the probability of the sample space must be 1, we can prove that each outcome must have probability: P ( an outcome ) = 1 | S | Where |S| is the size of the sample space, or, put in other words, the total number of outcomes of the experiment.

Step-by-step explanation:

Answer:

b because I am close to being done it's completely correct