Find all the roots of the given function on the given interval. Use pre-liminary analysis and graphing to find good initial approximations.
f(x) = cos (4x) - 4x2 + 9x
Answers
Answer:
The roots for [tex]f(x) = \cos 4x - 4\cdot x^{2} + 9\cdot x[/tex] are [tex]x_{1} = -0.098[/tex] and [tex]x_{2} = 2.166[/tex], respectively.
Step-by-step explanation:
A root is a value of [tex]x[/tex] so that [tex]f(x) = 0[/tex]. Let suppose that function is the consequence of the subtraction between two functions, that is:
[tex]f(x) = g(x) - h(x)[/tex] (1)
If we know that [tex]f(x) = 0[/tex], [tex]g(x) = \cos 4 x[/tex] and [tex]h(x) = 4\cdot x^{2}-9\cdot x[/tex], then we have the following identity:
[tex]g(x) = h(x)[/tex]
We can estimate graphically the roots of [tex]f(x)[/tex] by graphing the following system:
[tex]y = \cos 4x[/tex] (2)
[tex]y = 4\cdot x^{2}-9\cdot x[/tex] (3)
Where roots are the points in which functions find each other.
With the help of a graphing, we estimate two solutions:
[tex](x_{1}, y_{1}) = (-0.098, 0.924)[/tex], [tex](x_{2}, y_{2}) = (2.166, -0.725)[/tex]
Related Questions
Helpppppppppppppp:))))
Answers
Given:
Principal value = $1500
Rate of interest = 7% per annum compounded daily
Time = 2 years.
To find:
The amount after 2 years.
Solution:
Formula for amount:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is principal, r is the rate of interest in decimals, n is the number of time interest compounded in an year and t is the number of years.
We know that 1 year is equal to 365 days and the interest compounded daily. So, n=365.
Substituting [tex]P=1500,\ r=0.07,\ n=365,\ t=2[/tex] in the above formula, we get
[tex]A=1500\left(1+\dfrac{0.07}{365}\right)^{365(2)}[/tex]
[tex]A=1500\left(\dfrac{365+0.07}{365}\right)^{730}[/tex]
[tex]A=1500\left(\dfrac{365.07}{365}\right)^{730}[/tex]
Using calculator, we get
[tex]A\approx 1725.39[/tex]
The amount after two years is $1,725.39. Therefore, the correct option is (c).
mike is looking at the roof of a new house from the front. he notices that the roof is triangular in shape with a base 11.2m. the left side is 6.7m long and makes an angle of 72 degree with the base of the roof. if this is the only known information, determine the angle the right side of the roof makes with the base of the roof to the nearest degree. be sure to first make a sketch
Answers
Answer:
35°
Step-by-step explanation:
From the sketch made, to obtain B we use the cosine angle formula :
We have 2 so des and an included angle
Cos B = (a² + c² - b²) / 2ac
First we obtain the side c
c² = a² + b² - 2ab CosC
c² = 11.2² + 6.7² - 2(11.7 * 6.7) * cos 72
c = 11.13
Using the value of c
Cos B = (a² + c² - b²) / 2ac
CosB = (11.2² + 11.13² - 6.7²) / (2*11.2*11.13)
Cos B = 204.4269 / 249.312
B = Cos^-1(204.4269 / 249.312)
B = 34.9°
my last question 30 pts plzzzzzzzzz help
An expression is shown below:
4(m + 3 + 5m)
Part A: Write two expressions that are equivalent to the given expression. (3 points)
Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)
Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)
Answers
Answer:
A) 48m + 12 and 3(2m + 4 + 14m)
B) 48m + 12 is equivalent to 6(m + 2 + 7m) because if you distribute the 6 to everything inside the parentheses, you get 6m + 12 + 42m. This can be simplified further by adding 6m and 42m together, leaving you with 48m + 12.
C) m = 2
6(m + 2 + 7m)
6[2 + 2 + 7(2)]
6(4 + 14)
6(18) 1
108
3(2m + 4 + 14m)
3[2(2) + 4 + 14(2)]
3(4 + 4 + 28)
3(8 + 28) 3
(36) 108
108 = 108
Which statement is true about the graphed function?
O Fx) < 0 over the interval (-0, 4)
OFx) < 0 over the interval (-0, -3)
O F(x) > 0 over the interval (-00, -3)
O F(x) > 0 over the interval (-0, 4)
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Answer:
D is the answer to the question
Please help quickly I really don’t understand this question and i’m freaking out.
Answers
Answer:
[tex] \frac{4 \sqrt{3x} }{9} [/tex]Step-by-step explanation:
[tex] \frac{4 \sqrt{ {21x}^{2} } }{3 \sqrt{63x} } [/tex][tex] \frac{4 \sqrt{ \frac{21 {x}^{2} }{63x} } }{3} [/tex][tex] \frac{4 \sqrt{ \frac{x}{3} } }{3} [/tex][tex] \frac{4 \sqrt{ \frac{x \times 3}{3} } }{3} [/tex][tex] \frac{\frac{4 \sqrt{3x} }{3} }{3} [/tex][tex] \frac{4 \sqrt{3x} }{3} \times \frac{1}{3} [/tex][tex] \frac{4 \sqrt{3x} }{9} [/tex]Hope it is helpful...HELP EDCITEE !! PLEASE !!!
Answers
Answer:
75.3074525 dgrees
Step-by-step explanation:
law of sines
29/sin(115 degrees) = 13/sin(B)
==> B = 0.418374736 rad
or 75.3074525 dgrees
A bicycle wheel has a diameter of 26 inches. What is the circumference?
Answers
Answer:
81.64 Inches
Step-by-step explanation:
Given :
Diameter of wheel =26 inches
Radius of wheel (r)=26/2=13 inches
Circumference (C) of wheel can be calculated as :
C= 2πr
C=6.28(13)
C=81.64 Inches
Giving out brainliestttt answer !!! help me out?!!!
Answers
Answer:
F= 60.256
D = 29.744
Step-by-step explanation:
This is a completely different from the way usually I do it
B = arcsin(b·sin(A)a)
= 1.05166 rad = 60.256°
180-60.256-90 = 29.744°
A point particle with charge q is at the center of a Gaussian surface in the form of a cube. The electric flux through any one face of the cube is: _________.
i. q/E0
ii. q/E4Ï€E0
iii. q/4E0
iv. q/6E0
v. q/16E0
Answers
Answer:
iv. q/6E0
Step-by-step explanation:
Electric flux formula:
The electic flux formula, of a charge q is given by, through an entire cube, is given by:
[tex]E = \frac{q}{E_o}[/tex]
In which [tex]E_o[/tex] is a constant related to the material.
The electric flux through any one face of the cube is:
Key-word is face, and a cube has 6 faces, with the force distributed evenly throughout it. Thus
[tex]E_f = \frac{1}{6} \times \frac{q}{E_o} = \frac{q}{6E_o}[/tex]
And the correct answer is given by option iv.
What is the x-intercept of the line y = 2x – 10?
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
(5,0)
»»————- ★ ————-««
Here’s why:
I have graphed the equation in a program. When graphed, the point crosses through the point (5,0). This means that (5,0) is the x-intercept. See the graph attached below.»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
What is the horizontal distance between (−5/3, -2) and (4, -2)?
ANSWER QUICK GIVING BRAIN LEST
Answers
Answer:
-2?
Step-by-step explanation:
use y2-y1 over x2-x1 to find the answer. So you would do -2--5/3 over 4--2. The two negitives turn into a positive. SO it is now -2+5/3 over 4+2. -2+5/3= -1/3 over 4+2=6 it is now -1/3/6 which equals -2. So I think the answer is -2. I do not know if you should trust me on this but I tried.
Which table represents a linear function?
c
2
0
1
2
y
0
-1
4
-9
0
1
2
3
y
3
1
1
-3
2
0
y
0
1
4
9
y
1
3
0
1
2
3
1
--3
2
3
-1
Answers
Answer:
Table C is the answer
Step-by-step explanation:
how are they the same
Answers
Answer:
Step-by-step explanation:
The ways that they are the same are.
The slope is the same.Since the slope is the same for both of them, there is no possible solution meant for both of them. The slope is 1/4They are both written in slope y intercept form.The only difference is the y intercept is different. y intercept for y = 1/4 x is 0,0y intercept for y = 1/4 x is 0,5Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ= 7. Compute the probability.
Answers
Complete question is;
Assume the random variable X is normally distributed with mean μ = 50 and standard deviation σ = 7. What is the probability P (X > 42)?
Answer:
P(X > 42) = 0.1271
Step-by-step explanation:
We are given;
mean; μ = 50
Standard deviation; σ = 7
Formula for the z-score is;
z = (x - μ)/σ
Thus;
z = (42 - 50)/7
z = -1.14
Since we are looking for P (X > 42), then let's look up this z-value from the z-distribution table attached.
We have;
P(X > 42) = 0.1271
Which system of equations represents the matrix shown below?
Answers
Answer:
c
Step-by-step explanation:
Suppose we are interested in bidding on a piece of land and we know one other bidder isinterested. The seller announced that the highest bid in excess of $10,000 will be accepted.Assume that the competitor’s bid x is a random variable that is uniformly distributedbetween $10,000 and $15,000.a. Suppose you bid $12,000. What is the probability that your bid will be accepted?b. Suppose you bid $14,000. What is the probability that your bid will be accepted?c. What amount should you bid to maximize the probability that you get theproperty?d. Suppose you know someone who is willing to pay you $16,000 for the property. Wouldyou consider bidding less than the amount in part (c)? Why or why not?
Answers
Answer:
a. 0.4 = 40% probability that your bid will be accepted
b. 0.8 = 80% probability that your bid will be accepted.
c. $15,000.
d. Bidding $15,000 guarantees you a profit of $1,000, while trying to bid less than $15,000, you can end up without a profit, thus, you should not consider bidding less than the amount in part (c).
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
Assume that the competitor’s bid x is a random variable that is uniformly distributed between $10,000 and $15,000.
This means that [tex]a = 10, b = 15[/tex], considering the measures in thousands of dollars.
a. Suppose you bid $12,000. What is the probability that your bid will be accepted?
Probability that the other bidder's bid is less than 12000(X < 12). So
[tex]P(X < 12) = \frac{12 - 10}{15 - 10} = \frac{2}{5} = 0.4[/tex]
0.4 = 40% probability that your bid will be accepted.
b. Suppose you bid $14,000. What is the probability that your bid will be accepted?
Probability that the other bidder's bid is less than 14000(X < 14). So
[tex]P(X < 14) = \frac{14 - 10}{15 - 10} = \frac{4}{5} = 0.8[/tex]
0.8 = 80% probability that your bid will be accepted.
c. What amount should you bid to maximize the probability that you get the property?
The upper bound of the uniform distribution, that is, $15,000.
d. Suppose you know someone who is willing to pay you $16,000 for the property. Would you consider bidding less than the amount in part (c)? Why or why not?
Bidding $15,000 guarantees you a profit of $1,000, while trying to bid less than $15,000, you can end up without a profit, thus, you should not consider bidding less than the amount in part (c).
A balloon is 4 ft above the ground. It is released and floats up 3 ft
every second. Write an equation to model the height of the balloon
as a function of time in seconds. Write your answers in the blanks.
Answers
Answer:
4+(3 times x)= height of balloon. x = seconds
Step-by-step explanation:
I hope this helps you! :D
Shine has some money in his account.Every Month, he used the same amount of money from his account to pay for his music classes. The table below shows the amount of money left in his account after a certain amount of time, in months:
Option 4) -$45 per month; the amount of money withdrawn per month
Answers
Answer:
Option 4) -$45 per month; the amount of money withdrawn per month.
Step-by-step explanation:
The rate of change is 45. Before he began taking money out to pay for his classes[month 0], he had $190. Since then, every month, $45 have been withdrawn.
What is an opposite number?
Answers
Answer:
The opposite of a number is the number on the other side of 0 number line, and the same distance from 0.
Ordena de mayor a menor el siguiente grupo de fracciones y decimales
-2,14; 7/50; -2,41; -11/8; -2,1
Answers
Answer:
-2.41: -2.14: -2.1: -11/8: 7/50
In ATUV, the measure of _V=90°, VU = 84, TV = 13, and UT = 85. What ratio
represents the cotangent of _T?
U
85
84
T
13
Answers
A company's mean salary is $65,000 with a standard deviation of $6,000. If a sample of
40 employees is taken, determine the standard error.
948.68
325.25
9328.71
none of these
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Answer:
umm not sure on this one either 9328.71
Step-by-step explanation:
Can you help me please
Answers
Answer:
no solution
Step-by-step explanation:
[tex]\dfrac{2x - 6}{4} > \dfrac{x - 3}{2}[/tex]
The LCD is 4, so multiply both sides of the inequality by 4.
[tex]4 \times \dfrac{2x - 6}{4} > 4 \times \dfrac{x - 3}{2}[/tex]
[tex]2x - 6 > 2 \times (x - 3)[/tex]
[tex]2x - 6 > 2x - 6[/tex]
Subtract 2x from both sides.
[tex]-6 > -6[/tex]
Since -6 = -6, the above statement is false, so there are no solutions.
Answer: no solution
Ali surveyed his classmates to see who liked tennis. In all, 32 males liked tennis, and 6 males did not like tennis; 13 females liked tennis, and 4 females did not like tennis. How many females did Ali survey
Answers
Answer:
Ali surveyed 17 females.
Step-by-step explanation:
From Ali's survey:
13 females liked tennis, while 4 did not.
This means that Ali's surveyed 13 + 4 = 17 females.
How many females did Ali survey?
Ali surveyed 17 females.
2) What is the probability you roll an odd number on a six-
sided die ?
Answers
Answer:
1/2 or 0.5
Step-by-step explanation:
All possible odd values on a 6-sided die include 1, 3, and 5; that is 3 values out of 6 total values. 3/6 or 1/2 is a 0.5 probability.
In how many ways can 10 people be seated in 10badjacenr seats in a theater
Answers
Which point on the x-axis lies on the line that passes point C and is parallel to line AB
Answers
Answer:
(2,0)
Step-by-step explanation:
find the value of x and y in the parallelogram
Answers
Answer:
x=14
y=40
Step-by-step explanation:
A parallelogram is like a rectangle 2 parallel sides are equal.
so x+3=17 and y-2=38
x+3=17
x=17-3
x=14
y-2=38
y=38+2
y=40
The sum of two numbers is 67. The difference of the two numbers is 41. What are the two numbers.
Let 3 be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 67."
Write an equation that expresses the information in the sentence "The difference of the two numbers is 41."
Solve the system you have written above.
The larger number, 2 is
The smaller number, y is
Answers
Answer:
32
Step-by-step explanation:
a) Two thirds of the class are freshman
Is it parameter or statistic
Answers
Answer:
parameter
Step-by-step explanation:
