Answer:
Critical points of an equation are the zeroes of its first derivative. Since you have already provided me with the derivative (thanks for saving me the effort :) ), I am just going to start the process.
tan (x) + x(sec^2(x)) = 0
Solving this equation (using a graphing calculator set to radians), it is only true when x = 0.
So, 0 is a critical point of this function.
Hope this helped!
The derivative of tan(x) is sec^2(x) and the critical points for xtanx occur at x = π/2 + nπ.
Derivative of tan(x) can be found by using the formula: d/dx(tan(x)) = sec^2(x). Critical points for xtanx can be obtained by setting the derivative equal to zero and solving for x. In this case, the critical points are where sec^2(x) = 0, which occurs when x = π/2 + nπ, where n is an integer.
An elevator travels 110 feet in 10 seconds. At that speed, how fac can this elevator travel in 12 seconds?
Divide 110 by 10 to get a rate if 11 feet per second. Multiply 11 by 12 seconds to get 132 feet
The equation of a circle is x2+y2−12x+6y+20=0 .
What is the radius of the circle?
r = ?
Answer:
The radius is r=5 units
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center and r is the radius
we have
[tex]x^{2}+y^{2}-12x+6y+20=0[/tex]
Convert to standard form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](x^{2}-12x)+(y^{2}+6y)=-20[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side
[tex](x^{2}-12x+36)+(y^{2}+6y+9)=-20+36+9[/tex]
[tex](x^{2}-12x+36)+(y^{2}+6y+9)=25[/tex]
Rewrite as perfect squares
[tex](x-6)^{2}+(y+3)^{2}=5^{2}[/tex]
therefore
The center is the point (6,-3) and the radius is r=5 units
Approximately how much water does the average american use every day?
Answer: Estimates vary, but each person uses about 80-100 gallons of water per day
The range of which function includes –4?
Answer:
[tex]y=\sqrt{x} -5[/tex]
Answer:
The function [tex]f(x)=\sqrt{x-5}[/tex]
Step-by-step explanation:
The Range of any function is complete set of all possible resulting values of the dependent variable , after substituting the domain.
so, the function [tex]f(x)=\sqrt{x-5}[/tex] has range [tex]f(x)$\geq$ -5[/tex]
This includes - 4 .
Hence, the function is [tex]f(x)=\sqrt{x-5}[/tex] .
1. Find the phase shift of the function y = 5cos(2x + pi/2).
2. Which of the following functions has a maximum y value of 4?
y = 4cosx
y = cos4x
y = cosx + 4
y = cos(x + 4)
Answer:
see explanation
Step-by-step explanation:
1
The cosine function in standard form is
y = acos(bx + c)
where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and
phase shift = - [tex]\frac{c}{b}[/tex]
here b = 2 and c = [tex]\frac{\pi }{2}[/tex], thus
phase shift = - [tex]\frac{\frac{\pi }{2} }{2}[/tex] = - [tex]\frac{\pi }{4}[/tex]
2
the amplitude = | a |
which has a maximum of a and a minimum of - a
y = 4cosx ← has a maximum value of 4
Final answer:
The phase shift of the function y = 5cos(2x + π/2) is -π/4 radians. The functions y = 4cosx and y = cosx + 4 both have a maximum y value of 4.
Explanation:
To find the phase shift of the function y = 5cos(2x + π/2), we need to look at the argument of the cosine function. The general form is y = Acos(Bx - C) where C/B is the phase shift. In this case, the argument of the cosine is 2x + π/2, thus the phase shift is -π/2 divided by the coefficient of x, which is 2, giving us a phase shift of -π/4 or -0.785 radians.
To determine which of the provided functions has a maximum y value of 4, consider the amplitude of the cosine functions. For the functions y = 4cosx, y = cos4x, and y = cos(x + 4), the amplitude is 1, and thus the maximum y value is 1 for the latter two, and 4 for the first one. However, y = cosx + 4 is a cosine function shifted upward by 4 units, and hence its maximum y value is also 5. So, the functions with a maximum y value of 4 are y = 4cosx and y = cosx + 4.
A right regular pentagonal prism has a base edge length 14 cm, and height 12 cm. Identify the volume of the prism to the nearest tenth. HELP PLEASE!!
Answer:
4046.56 cm3
Step-by-step explanation:
The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of [tex] \frac{360} 5 = 72° [/tex]. Each of the other angle is [tex]\frac{180-72} {2} =54°[/tex]. From there, you can calculate the height of each base triangle as in [tex]\frac {h} 7 = tan54[/tex] or 9.634...cm.
Your volume will be [tex]5 * \frac {(14 * 9.634)} 2 * 12 = 4046.56 cm^3[/tex]
Identify the volume of the composite figure rounded to the nearest tenth. HELP PLEASE!!
Answer:
V = 115.3 ft³
Step-by-step explanation:
The left part of the figure shows a cube of side length 4.2 ft. The volume of a cube is V = s³, where s is the side length. Hence, the volume of this particular cube is V = (4.2 ft)³ = 74.088.
The volume of a pyramid is V = (1/3)(base area)(height).
Here V = (1/3)(4.2 ft)²(7 ft) = 41.16 ft³.
Summing up the two distinct areas, we get V = 41.16 ft³ + 74.088 ft³, or
V = 115.3 ft³ after rounding up to the nearest tenth.
The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.
What are Three Dimensional Figures ?Those figures that required x,y and z axis for their representation are three dimensional figures.
They have length , breadth and height.
All the object that we see around us can be categorized into Three Dimensional Figure.
In the given figure
It can be seen that it consists of a cube and a square pyramid
To determine the volume we have to determine the volume of each figure and then add
Volume of a cube = side * side * side
Side of the cube = 4.2 ft.
Substituting the values
Volume of cube = 4.2 * 4.2 * 4.2
Volume of cube = 74.088 cu.ft
Volume of a square pyramid is given by
(1/3) * a² * h
a is the area of the base
area of the base = area of the square = side * side
Area of the base = 4.2 * 4.2
Area of the base = 17.64 sq.ft
Height of the pyramid = 7 ft.
Volume of square pyramid = (1/3)* 17.64 *7
Volume of a square pyramid = 41.16 cu.ft
Total volume = 74.088 + 41.16
Total Volume = 115.2 cu.ft
Therefore , The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.
To know more about Three Dimensional Figures
https://brainly.com/question/24303419
#SPJ2
Sasha has a fever of 103°F. What is Sasha’s fever in degrees Celsius?
32°C
39.4°C
66.9°C
71°C
39.4 degrees Celsius
Hope this helps :)
Answer:
39.4°C
Step-by-step explanation:
The equation for fahrenheit to celsius is
(°F − 32) × 5/9 = °C
With our variable of 103 plugged in it is
(103°F − 32) × 5/9 = 39.444°C
Therefore, her fever is 39.4°c
Sketch the following in standard position.
Determine the quadrant the angle lies in (if it is on an axis, state which axis it is on and if it is + or - axis)
Then determine the reference angle.
Answer: 1) Quadrant: I, reference angle: [tex]\dfrac{2\pi}{5}[/tex]
2) Quadrant: III, reference angle: 85°
3) Quadrant: IV, reference angle: [tex]\dfrac{\pi}{4}[/tex]
Step-by-step explanation:
Reference angle is the angle closest to the x-axis
1) The given angle is (2/5)π. The first quadrantal (π/2) would be (2.5/5)π
Since (2/5)π < (2.5/5)π then it must be in Quadrant 1.
The angle closest to the x-axis is the same as the given angle.
2) The given angle is -95°. It is measured clockwise since it is a negative angle. Since it is greater than 90°, it is greater than the 270° quadrantal. So it must be in Quadrant III.
The angle closest to the x-axis is 85°.
3) The given angle is (23/4)π. Since (8/4)π is one rotation, this is greater than one rotation. (23/4)π - (8/4)π - (8/4)π = (7/4)π. So, it rotates two complete rotations and lands at coterminal angle (7/4)π.
The angle closest to the x-axis is π/4
BASIC MATH
Paul uses the expression 4.2 x 12.3 x 14.6 to determine the cost of tiling the floor of a room that measures 12.3 feet by 14.6 feet; each square foot of tile costs $4.20. How many decimal places will be in Paul’s final answer?
A. one
B. three
C. five
D. eight
B. Three. It is three because there is one decimal place in each factor.
Answer:
B. Three.
Explanation:
Three because there is one decimal place in each factor and there are 3 factors.
I need help
A rectangular shelf has a perimeter of 46 inches. Its area is 76 square inches. What are the dimensions of the shelf?
Answer:
19 in × 4 inStep-by-step explanation:
l - length
w - width
The formula of a perimeter of a rectangle: P = 2(l + w)
The formula of an area of a rectangle: A = lw
We have P = 46in and A = 76in² Substitute:
(1) 2(l + w) = 46
(2) lw = 76
2(l + w) = 46 divide both sides by 2
l + w = 23 subtract w from both sides
l = 23 - w
subtitute it to (2):
(23 - w)w = 76 use the distributive property
23w - w² = 76 subtract 76 from both sides
-w² + 23w - 76 = 0 change the signs
w² - 23w + 76 = 0
w² - 4w - 19w + 76 = 0
w(w - 4) - 19(w - 4) = 0
(w - 4)(w - 19) = 0 ⇔ w - 4 = 0 or w - 19 = 0
w - 4 = 0 add 4 to both sides
w = 4
w - 19 = 0 add 19 to both sides
w = 19
Put the values of w to (1):
l = 23 - 4 = 19 or l = 23 - 19 = 4
Investigation Circles: Investigation 2
I need help with the worksheet
Explanation:
1. In order for the idea of "perpendicular distance" to make any sense in this context, the number of sides of the polygon must be even. Then the "diameter" is the diameter of the inscribed circle. As the number of sides increases, the polygon differs less and less from a circle, so the relationship of perimeter and "diameter" becomes closer to the relationship in a circle.
"As the number of sides in a regular polygon increases, the ratio of perimeter to diameter for that polygon approaches pi."
__
2. We know from the first question that ...
circumference/diameter = π
And we know that ...
diameter = 2·radius
Then the following are true:
A. circumference = π · diameter
B. circumference = (2·radius) · π
__
3. The expressions in order evaluate to approximately ...
4.0, 3.45, 3.31, 3.24
Of these, the last is closest to pi (3.14....). The appropriate choice is ...
D. (10·5)/15.4
__
4. Pi cannot be expressed as a rational number, because pi is irrational. A number of lengthy proofs have been offered to demonstrate this fact. One of them makes use of the fact that the tangent of any rational number is irrational, and the tangent of π/4 is 1. Since 1 is a rational number, π/4 cannot be, so π cannot be expressed as a rational number.
In a bag there are 5 red marbles, 10 blue marbles, and 15 green marbles. What is the probability that you will draw a blue marble?
1/2
1/3
2/3
3/4
probability of drawing a blue marble is 1/3
Plot the points P(1, 0), Q(4, 0) and S(1, 3). Find the coordinates of the point R such that PQRS is a square. Also find the area of the square.
Answer:
the point r would be located at (4,3)
Step-by-step explanation:
granted that the quadralaterel is a square that would mean that all side lengths are equal and the distance between points x and q is 3 meaning that the same would have to be said about the distance between s and r
Marcus needs to rewrite f(x) = x2 + 6x + 4 in vertex form.
His answer is f(x) = (
)2 – 5.
Hm, it seems like his answer is off. The image is what I got.
Answers:
X+3
Step-by-step explanation:
I got it right
Please please help me..
The yellow and orange triangle is AA
It is AA because the orange triangle has two angles listed and, the yellow triangle has two angle listed.
Answer:
AA
Step-by-step explanation:
For the 2 triangles to be similar we require 2 corresponding angles to be congruent.
There are 2 angles of measure 30°
If we consider the yellow triangle the the third angle is
180° - ( 41 + 30)° = 180° - 71 = 109°
The 2 triangles have therefore 2 corresponding congruent angles
Hence the triangles are similar by the postulate AA
Tony is standing at sea level. From his location, the angle of elevation of the top of Blue Mountain is 23°. Staying at sea level, he walks 220 yards toward the mountain. The angle of elevation of the top is now 27°. Find the height of Blue Mountain. Round intermediate results to 3 decimal places and the final answer to 1 decimal place.
Answer:
559.2 yards.
Step-by-step explanation:
Let the height of the mountain be x yards and the distance from the second location to the base of the mountain be y yards.
Then we have the equations:
tan 27 = x/y
tan 23 = x / (220 + y)
From the first equation y = x/ tan27 so substituting in the second one we have:
tan 23 = x / (220 + x / tan 27)
Cross multiply:
x = 220 tan23 + x tan 23 / tan 27
x = 93.384 + 0.833 x
x - 0.833x = 93.384
x = 93.384 / 0.167
x = 559.2 yards to 1 dec place (answer).
PLEASE HELP ME OUT :) Independent or Dependent?
Also, is there an easier way to determine if these are independent or dependent other than working out the entire problem? (Not trying to be lazy. My school website uses common core learning which explains each problem in, seemingly, the most difficult way possible for most different types of algebra and geometry)
Answer:
Option 1.
[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex] Dependent
Option 2
[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex] Independent
Option 3
[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex] Dependent
Option 4
[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex] Independent
Step-by-step explanation:
Two events A and B are independent if the occurrence of A does not affect the probability of B.
On the other hand The probability of A given B is defined as:
[tex]P (A | B) = \frac{P (A\ and\ B)}{P (B)}[/tex]
When two events are independent then:
[tex]P (A\ and\ B) = P (A) * P (B)[/tex]
So if the two events A and B are independent this means that:
[tex]P (A | B) = \frac{P (A) * P (B)}{P (B)}[/tex]
[tex]P (A | B) = P (A)[/tex]
Which makes sense because if the events are independent then the probability of A not being affected by B.
So to solve this problem identify in what cases
[tex]P (A | B) = P (A)[/tex] or [tex]P (B | A) = P (B)[/tex]
When this happens those events are independent
Option 1.
[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex] Dependent
Option 2
[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex] Independent
Option 3
[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex] Dependent
Option 4
[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex] Independent
Joshua has a ladder that is 17 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 16.5 ft above the ground. For Safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. Will the ladder be safe at this height? show your work
Answer:
No, it is not safe
Answer:
Hello!
The answer is no, he will not be safe. I had a similar problem on a test and got the answer correct. The only difference was they used slightly different numbers, so I am pretty sure this is correct. I hope this helps!
Step-by-step explanation:
Okay, so you are looking for x.
sin x= [tex]\frac{16.5}{17}[/tex]
x=[tex]sin^{-1}[/tex]([tex]\frac{16.5}{17}[/tex])
x≈76.07
76.07>70
Please please help me
Answer: 5 Vertices
Step-by-step explanation: I believe if it had 4 faces and 8 edges it would have 5 vertices.
The pie store is having a 20% , percent off sale on all of its pies. If the pie you want regularly costs $18 dollar sign, 18, how much would you save with the discount?
20% off, means that 20% of the regular price is how much you would save.
Multiply the original price by 20%
18 x 0.20 = 3.6
The discount is $3.60
Please answer this correctly
Answer:8462
Step-by-step explanation:
Answer:
8862 feet
Explanation:
The formula for circumference is C=pi*diameter. So, by substitution we can use 26586=(3)d and solve by dividing 26586 by 3 which gives us d=8862 feet.
Find the area of the triangle.
Answer: 118.3 m^2
Step-by-step explanation:
Use Heron's formula: √s(s-a)(s-b)(s-c)
s= a+b+c/2
13+18.2+22.3/2 = 26.75
√26.75(26.75-13)(26.75-18.2)(26.75-22.3)
√26.75(13.75)(8.55)(4.45)
√13994.34609
118.297701 = 118.3 m^2
Sophie Ruth is eating a 505050-gram chocolate bar which contains 30\%30%30, percent cocoa. How many grams of cocoa are in the chocolate bar?
Answer:
15 g
Step-by-step explanation:
30% · 50 g = 30/100 · 50 g = 1500/100 g = 15 g
Answer:
15g
Step-by-step explanation:
Using the keys above, enter an expression equivalent to (3x^2-8x-24)-(9x+6) using the fewest possible terms.
Answer:
Final answer in simplified form is [tex]3x^2-17x-30[/tex]
Step-by-step explanation:
Given expression is [tex](3x^2-8x-24)-(9x+6)[/tex]
Now we need to find an equivalent expression for [tex](3x^2-8x-24)-(9x+6)[/tex]
First we can distribute the negative sign and remove the parenthesis the combine like terms
[tex](3x^2-8x-24)-(9x+6)[/tex]
[tex]=3x^2-8x-24-9x-6[/tex]
[tex]=3x^2-17x-30[/tex]
Hence final answer in simplified form is [tex]3x^2-17x-30[/tex]
(6Q) Find the domain and range.
Answer: Option a.
Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
We have the function [tex]f(x) = 2x + cosx[/tex]
Note that f(x) is the sum of two continuous functions [tex]h(x) = 2x[/tex] and [tex]g(x) = cosx[/tex]
The domain and range of h(x) are all real numbers
The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]
Then the domain of [tex]f(x) = h(x) + g(x)[/tex] will be the intersection of the domains of the function [tex]h(x) = 2x[/tex] and the function [tex]g(x) = cosx[/tex].
Therefore the domain of f(x) are all real numbers. x ∈ (-∞, ∞)
The range of f(x) will be equal to the union of the range of g(x) and h(x)
Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)
Thomas has a collection of CDs that he plays regularly. He has five rock CDs, three country CDs, and four movie sound track CDs. If Thomas chooses a CD at random, what are the odds that he chooses a country CD?
Answer:
The answer is 1/4.
Step-by-step explanation:
5 rock CDs, plus 3 country CDs, plus 4 movie sound track CDs, equal 12 CDs in total. To find the odds of choosing a country CD, you divide the total number of CDs, by the number of what you choose (3/12).
Answer:
The odds that he choose a country CD is 1/3
Step-by-step explanation:
12/12 ÷ 3 = 1/3
Solve x^2 +5x-10=0. How do you solve this
Answer:
(-5 +/- sqrt(65))/2
Step-by-step explanation:
To solve this, we can use the quadratic formula!
So,
x = (-b +/- sqrt(b^2-4ac))/2a
x = (-5 +/- sqrt(25+40))/2
x = (-5 +/- sqrt(65))/2
So (-5 +/- sqrt(65))/2 is our answer.
Frank and his family are going to the grand opening of a circus there is a special price on tickets this weekend tickets cost 36 each this is a 60% of the cost of a regular price ticket. What is the cost of a regular price ticket?
Answer:
60
Step-by-step explanation:
(This is not how teachers usually teach you)
First i divided 36 by 2 to get 30% = 18 then i multiplied 30% by 3.3333etc. to get 100% and i multiplied 18 by the same number (18*3.3333 = 60) and i got 60.
Answer:
The cost of a regular price ticket is $60.Step-by-step explanation:
Givens
Tickets cost $36 each, which represents 60% of the regular price.To find the regular price for tickets, we can use the rule of three.
If $36 represents 60%, how much would represents 100%?
[tex]x=100\% \frac{\$36}{60\%} = \$60[/tex]
Therefore, the cost of a regular price ticket is $60.
What is the area of triangle ABC? Round your final answer to the nearest cm.
Answer:
A = 21.65 cm squared
Step-by-step explanation:
The basic area formula for a triangle is
[tex]A= \frac{1}{2}bh[/tex]
We have our base as 5, so we can find the height using right triangle trig. Side BC is opposite the given angle, which is the height, and we are given side CD as 5 which is the base. Using the tangent ratio to find side BC:
[tex]tan(60) = \frac{x}{5}[/tex] which simplifies to
5 tan(60) = x so
x = 8.66
Filling in for the area:
[tex]A= \frac{1}{2}(5)(8.66)[/tex] so
A = 21.65 cm squared