A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.
What is meant by Quartic polynomial?A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.
Quartic in mathematics refers to something that is of the "fourth order," such as a function. One of the following is possible: Quartic function, a fourth-degree polynomial function. Quartic polynomial, a polynomial equation of degree 4, where an is a nonzero polynomial that defines the quartic equation.
A quartic equation, also known as an equation of the fourth degree, is an equation of the form that reduces a quartic polynomial to zero. A quartic function's derivative is a cubic function.
Therefore, the correct answer is option a) quartic.
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Find
d93 /dx93 *(cos x)
by taking the first few derivatives and observing the pattern that occurs.
d93 /dx93 *(cos x) = - sin x
Now,
d/dx (cos x ) = -Sin x
d2/dx2 (cos x) = - cos x
d3/dx3 (cos x) = sin x
d4/dx4 (cos x) = cos x
d5/dx5 (cos x) = - sin x
d6/dx6 (cos x) = -cos x
The same pattern will repeat for every 6th derivative so ,
Now,
93 = (4 x 23) + 1
Therefore,
d93 /dx93 *(cos x) = - sin x
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11. Algebra The total cost of the Fatigato
family's two cars was $71,482. The cost of
one car was $38,295. Write an equation
using a variable to represent the cost of
the family's other car.
Answer:
$33,187
Step-by-step explanation:
Our total is 71,482 so let's set our equation to 71482=_________
Now we have $38,295 for one car, and we will subtract it from the total to find the other car, as there are 2 cars.
Equation:
71482-38295=x OR 71482=38295+x
X is the cost of the second car.
what is the slope of the line that passes through the points (-7,-8) and (-5,-6)? Write your answer in simplest form.
Answer:
m=1
Step-by-step explanation:
a=460 rounded to the nearest 10 b=11.9 rounded to 1 dp find the minimum (to 2 dp) of a / b
The minimum result (to 2 dp) of a / b is 38.66
What is rounding decimals?The term "rounding decimals" refers to the accurate rounding of decimal figures. When rounding a decimal number, certain principles must be followed. Simply put, if the last digit is less than 5, round down the previous digit. However, if it is 5 or greater, round the previous digit up.Given:
a=460 rounded to the nearest 10
b=11.9
Now, substitute the values of a and b in a/b,
a/b = 460/11.9
Multiply the same integer(10) by both the numerator and denominator,
a/b = 4600/119
Round the number obtained
a/b ≅ 38.66
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Arc Length S. Central Angle 0 82 miles. 135°Find the radius and radians r of a circle with an arc length s and a central angle 0.
Central angle of 135 degrees = 135 (Pi/180) = (3/4)Pi = 2.356 radians
First answer:
Central angle = 2.356 radians
Arc lenght = 2 Pi r (angle/360), in this case:
82 = 2 Pi r (135/360) = 2 Pi r (3/8) = (3/4) Pi r
82 = (3/4) Pi r
r = 82/(3/4)Pi = 82/2.35619449
r = 34.80188089
Second answer:
Radius = 34.8 miles
Evaluate the expression below using the properties of operations. -36 ÷ 1/4 • (-1/8) • (-3) ÷ 6
Answer:
-9
Step-by-step explanation:
We are working with multiplications and divisions, which have no precedence over each other. So we can do the operations in order. It is important to remind that in these operations, if two numbers have different signals, the result of the operation is negative, otherwise, positive.
-36 ÷ 1/4
Different signals, so the result will be negative
[tex]\frac{-36}{\frac{1}{4}}=-36\ast\frac{4}{1}=-36\ast4=-144[/tex]-36 ÷ 1/4 • (-1/8) = -144 * (-1/8)
Same signal, so positive
[tex]-144\ast(-\frac{1}{8})=\frac{144}{8}=18[/tex]-36 ÷ 1/4 • (-1/8) • (-3) = 18 * (-3) = -54
-36 ÷ 1/4 • (-1/8) • (-3) ÷ 6 = -54 ÷ 6 = -9
Which expression is equivalent to (sin 2θ)(sec2θ)? 2sin θ sin θ tan θ 2tan θ
Answer:
Explanation:
Here, we want to get the expression that is equivalent to the given expression
We have this as follows:
[tex]\begin{gathered} \text{ sec 2}\theta=\text{ }\frac{\sec^2\theta}{2-\sec^2\theta} \\ \\ \sin 2\theta\text{ = 2sin}\theta\cos \theta \end{gathered}[/tex]Now, we can rewrite the overall expression as:
[tex]undefined[/tex]
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that
each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 18 couples.
Find the expected number of girls in groups of 18 births
Answer:
since the method is deemed to have no effect
which means probability of having a girl child is same as having a boy child which is 0.5
Total births = 18
Therefore, expected number of girls in groups should be equal to = 0.5 × 18 = 9
I hope this is helpful
What value of x makes this equation true?x+7------7A. 6B. 8C. 35 D. 42
We have
[tex]\begin{gathered} \frac{x+7}{7}=6 \\ x+7=6\times7 \\ x+7=42 \\ x=42-7 \\ x=35 \end{gathered}[/tex]Option C
Find the largest of three consecutive odd integers whose sum is 111.
The largest of three consecutive odd integers whose sum is 111 is 39
What is an integer?Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.
Odd integers that follow each other grow (or shrink) by a factor of 2. Consider the numbers 1, 3, and 5. Add two to the preceding number to move from one to the following. You don't know where to begin, and that is the issue here. In actuality, you are searching for the least of the three integers, therefore this is your unknown.
x + (x + 2) + (x + 4) = 111
x + x + 2 + x + 4 = 111
3x + 6 = 111
3x = 105
x =[tex]\frac{105}{3}[/tex]
x = 35
35 ,37,39
The largest of three consecutive odd integers whose sum is 111 is 39
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In the diagram below, the circle has a radius of 25 inches. the area of the unshaded is 500pi in^2Determine and state the degree measure of angle Q, the central angle of the shaded sect
1) In this question, we are going to make use of the formula for the area of that sector, to find the central angle.
2) So, let's write it out an expression involving the area of a circle, the unshaded area, and the shaded one and then plug into that the given data:
[tex]\begin{gathered} A=\frac{\alpha}{360^{\circ}}\times\pi r^2 \\ A_{Unshaded}+A_{shaded}=A_{Circle} \\ 500\pi+\frac{\alpha}{360}\times\pi r^2=\pi r^2 \\ \\ 500\pi+\frac{α}{360}\pi25^2=25^2\pi \\ \\ 500\pi+\frac{125\piα}{72}=625\pi \\ \\ 500\pi +\frac{125\pi α}{72}-500\pi =625\pi -500\pi \\ \\ \frac{125\pi α}{72}=125\pi \\ \\ \frac{72\times \:125\pi α}{72}=72\times \:125\pi \\ \\ \frac{125\pi α}{125\pi }=\frac{9000\pi }{125\pi } \\ \\ α=72^{\circ} \\ \\ \end{gathered}[/tex]Thus, the centra angle of that shaded area is 72º
For what values of m does the graph of y = 3x² + 7x + m have two x-intercepts?
0 m> 25
O
Om<25
3
49
Om 12
49
m> 12
The graph of y = 3x² + 7x + m will have two x-intercepts if m < 49/12.
The given function is,
y = 3x² + 7x + m
Having two x-intercepts means that the value of y should be 0.
So, we can write,
3x² + 7x + m = 0
Now, this has become a quadratic equation and it will have two zeroes according to the question,
As we know, the condition of quadratic to have two different values of x is,
0 < √(b²-4ac)
Where,
a = 3
b = 7
c =m
Putting all the values,
√(7²-4(3)(m)) > 0
Squaring both sides,
7²-4(3)(m) > 0
49-12m > 0
49/12 > m.
So, the graph will have two intercepts if m < 49/12.
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Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
h(x) = x−1⁄3 (x − 12)
The critical value of the given function is = -11/2
The x values for which f'(x) = 0 are the crucial values of a function f(x).
The function in this quandary is:
h(x) = x−1⁄3 (x − 12)
The derivative is discovered using the quotient rule as follows:
[tex]h(x) = \frac{x - 1}{3(x - 12)} \\\\h'(x) = \frac{ (x-1) (3x - 36)' - (x - 1)'(3x - 36)}{(3x - 36)^{2} }\\\\h'(x) = \frac{ (x-1) (3) - (-1)(3x - 36)}{(3x - 36)^{2} }\\\\On equating it to 0\\\\\frac{ (x-1) (3) + 1(3x - 36)}{(3x - 36)^{2} } = 0\\\\3x - 3 + 3x + 36 = 0\\\\6x + 33 = 0\\\\x = \frac{-11}{2}[/tex]
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How many solutions does this system of equations have?
y = x2 + x + 3
y = -2x - 5
Answer: (x, y) = (-8/5, -9/5)
Assume the annual day care cost per child is normally distributed with a mean of $8000 and a standard deviation of $1500. In a random sample of 300 familles, how many pay morethan $6440 annually for day care per child?Of the 300 families, approximately pay more than 56440 annually for day care per child(Round to the nearest whole number as needed.)
Let's begin by listing out the information given to us:
Mean = $8,000, SD = $1,500
In a sample of 300, how many pay more than $6440?
A circle has a diameter of 24 centimeters. Central angle FOG is drawn, determining an arc FG. The radian measure of angle FOG is 3/4 What is the length of arc FG in centimeters?16 cm9 cm32 cm18 cm
Answer:
9 cm
Explanation:
We are given the following information:
Diameter = 24 cm
Angle FOG = 3/4 rad
The formula for calculating arc length is written below:
[tex]\begin{gathered} L=\theta\times r \\ where\colon \\ \theta=central\text{ angle of }arc,\text{ in }rad \\ r=radius \\ r=\frac{\text{Diameter}}{2}=\frac{24}{2}=12cm \\ \theta=\frac{3}{4}rad \\ \text{Substitute these into the formula, we have:} \\ L=\frac{3}{4}\times12 \\ L=\frac{3\times12}{4} \\ L=9cm \\ \\ \therefore L=9cm \end{gathered}[/tex]Therefore, the arc length is 9 cm
Describe the shape, orientation, and vertex of
each parabola relative to the graph of y=x².
Sketch each graph.
a) y=-0.5x² + 2
c) y = -0.1x² - 6
e) y=-3x²-5
g)y=8x²+4
b) y = 2x²
d)y=x²+4
f) y=0,1x² +2
h) y=-0.7x²-3
The parabola y = - 0.5x² + 2 opens downwards and the vertex is at (0,2) .
A parabola is a mirror-symmetric planar curve with a rough U-shape. It can be defined by many seemingly unrelated mathematical descriptions that all relate to the same curves.
One way to interpret a parabola is with a line and a point (the focus) (the directrix). The directrix is less significant. The parabola lies between the directrix or the focus and the endpoints in this plane that are uniformly spaced apart.
a) y=-0.5x² + 2 vertex is at (0,2)
c) y = -0.1x² - 6 vertex at (0,6)
d)y=x²+4 vertex at (0,-4)
e) y=-3x²-5 vertex at (0,5)
g)y=8x²+4 vertex at (0,-4)
h) y=-0.7x²-3 vertex at (0,3)
A parabola can also be thought of as a conic section formed by joining a right circular conical area with a plane perpendicular to another axis.
The graph of the parabola is attached below.
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Write the quadratic function in vertex form. Then identify the vertex.
g(x)=x^2+12x+37
The vertex form is y= (x+ 6)²+1.
What is Vertex form?The vertex form of a quadratic equation is y = a (x- h)² + k as opposed to the regular quadratic form, which is an x² + bx + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.
a=1
b=12
c=37
Consider the vertex form of a parabola.
a(x+ d)²+e
Now, d= b/2a
d=12/ 2
d=6
and, e= c-b²-4a
e= 37 - (12)²/4x1
e= 37 - 36
e= 1
Then, the vertex form is
y = a(x+ d)²+e
y= 1(x+ 6)²+1
y= (x+ 6)²+1
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Point P(-3, 4) is a point on the terminal side of 0 in standard form. Find the exact value ofsine, cosine, and tangent for 0.
Solution
Step 1
The terminal side, containing point (-3, 4) is located in Quadrant 2.
sine is positive
cosine and tangent are both negative.
Step 2
Draw a diagram to illustrate the information
Step 3
[tex]\begin{gathered} Find\text{ d using the Pythagoras theorem} \\ d^2\text{ = 3}^2+\text{ 4}^2 \\ d^2\text{ = 9 + 16} \\ d^2\text{ = 25} \\ d\text{ = }\sqrt{25} \\ \text{d = 5} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} sine\text{ = }\frac{Opposite}{Hypotenuse} \\ Sin\theta\text{ = }\frac{4}{5} \end{gathered}[/tex][tex]\begin{gathered} Cosine\text{ = }\frac{Adjacent}{Hypotenuse}\text{ = }\frac{x}{d} \\ Cos\theta\text{ = }\frac{-3}{5} \end{gathered}[/tex][tex]\begin{gathered} tangent\text{ = }\frac{Opposite}{Adjacent}\text{ = }\frac{y}{x} \\ tan\theta\text{ = }\frac{-4}{3} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} sin\theta\text{ = }\frac{4}{5} \\ cos\theta\text{ = }\frac{-3}{5} \\ tan\theta=\frac{-4}{3} \end{gathered}[/tex]12+212+25,432*5,000+
Answer:
127160224
or use a calculator
Solve for brainliest and 20 points
Answer:
x = 50
Step-by-step explanation:
50 x 3 - 15 = 135
an octagon has 8 sides & 8 angles. 135 x 8 = 1,080 which is the amount of degrees an octagon equals.
Answer:
50
Step-by-step explanation:
Total angles in an octagon is 1080
Because there are 8 sides you must divide 1080/8 to find the angle of one side ... 1080/8 = 135
3x-15=135
1) 135+15 = 150
2)150/3=50
Hope this helps, have a great day!
2(y−1)+6y = −10 please help fastest answer gets 37 points
Need help with absolute value please
Answer:
let's say you need to find the absolute value of -5 the answer would be 5.
Step-by-step explanation:
Since the distance between -5 and 0 in a number line is 5. This would also be applied If you you were trying to find the absolute value of 5. it would also be 5.
When in math, I figured out negative number's absolute value will always be positive. absolute value numbers of positive numbers will stay the same.
Find X. Circumscribed Angles
The value of of angle x of the circumscribing circle is x° = 140°
In the above question, the following figure is given, where
The angle inside the circle made by the intersection of two line segments is = 40°
We need to find the angle x made by the angle made by the tangents outside the circle
A line that touches a curve or a circle at one point is said to be tangent.
The point of tangency is the intersection of the tangent line and the curve.
We'll find the value of of angle x using the theorems of the circumscribing circle.
The sum of opposite angles of a circumscribing quadrilateral is always 180°
Using this property we can write,
40° + x° = 180°
x° = 180° - 40°
x° = 140°
Hence, the value of of angle x using the theorems of the circumscribing circle is x° = 140°
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How long do people typically spend traveling to work? The answer may depend on where they live. Here are the travel times in minutes of 20 randomly chosen workers in New York state
Based on the information given, the standard deviation for the observation is: 23.802698 or approximately 24.
The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
The formula for Standard deviation is given as:
σ[tex]= \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} .[/tex]
Where
σ = population standard deviation
[tex]\bar x[/tex] = mean
x = each value of the population
n = number of observation
Note that mean ([tex]\bar x[/tex]) = [tex]\( \frac{1}{n} \sum_{i=i}^{n} x_{i} \),[/tex]
[tex]\bar x[/tex] = (5+10+10+10+10+12+15+20+20+25+30+30+40+40+60+60+65+70+70+70)/20
= 33.6
Hence the standard deviation for travel times for these 20 New York workers is:
Standard Deviation = [tex]\sqrt{\frac{\sum(x_{1} - {\bar x})^{2} }{n-1} }[/tex]
= √ [(5-33.6)²+ (10 - 33.6)² + .... + (70 - 33.6)²]/(20-1)]
Standard Deviation = √(10764.8)/(20-1)
SD = √(10764.8/19)
SD = √566.56842
SD = 23.802698
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Full Question:
How long do people spend traveling to work? The answer may depend on where they live here are the travel times in minutes for 20 workers in New York chosen at random by the census bureau:
5 10 10 10 10 12 15 20 20 25 30 30 40 40 60 60 65 70 70 70
What is the standard deviation for travel time for these 20 New York state workers?
(2tanθ-3cosθ) Expand
what is the value of a in the equation 5a – 10b = 45, when b =3?a)3b)15c)21d)39
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]5a-10b=45[/tex]STEP 2: Substitute 3 for b in the equation
[tex]5a-10(3)=45[/tex]STEP 3: Simplify the equation to solve for a
[tex]\begin{gathered} 5a-30=45 \\ 5a=45+30 \\ 5a=75 \\ a=\frac{75}{5} \\ a=15 \end{gathered}[/tex]Hence, the value of a is 15
please help me solve. I have the answer in yellow, but it's not correct.
Remember that
27=(3)(3)(3)=3^3
so
[tex]\sqrt[]{3\cdot}\sqrt[\square]{27}=\sqrt[]{3\cdot}\sqrt[\square]{3^3}=\sqrt[]{3^4}=3^2=9[/tex]answer is 9
so
9 NA
blank 1 ------> 9
blank 2 ------> NA
Brittany has 34,011 in a savings account that earns 6% annually. the interest is not compounded. How much interest will she earn in 4 years? use the formula I = PRT, where I is the interest earned, p is the principal, r as the interest rate expressed as a decimal, and T is the time in years.
Notice that we are dealing with simple interest, and therefore given by the formula:
I = P * R * T
where P = $34,011
R = 6% in "decimal" form (0.06)
T = 4 (for 4 years)
Then, we have:
I = 34011 * 0.06 * 4 = $8162.64
This is the interest Brittany earned in 4 years.
If one of the flights is randomly selected find the probability that the flight silicon Rosa United Airlines flight given that it was on time.
Total of flights on time: 22 + 53 = 75
probability that the flight selected was silicon Rosa United Airlines:
53/75 = 0.71 = 71%