Answer:
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Answer:
The absolute maximum is about -5.84 at x = -2.
And the absolute minimum is about -11.28 at x = -π/6.
Step-by-step explanation:
We want to find the absolute maximum and minimum values of the function:
[tex]\displaystyle f(x) = 5x-10\cos x\text{ for } -2\leq x\leq 0[/tex]
First, we should evaluate the endpoints of the interval:
[tex]\displaystyle f(-2) = 5(-2) - 10\cos (-2) \approx -5.8385[/tex]
And:
[tex]f(0) = 5(0) -10\cos (0) = -10[/tex]
Recall that extrema of a function occurs at its critical points. The critical points of a function are whenever its derivative is zero or undefined.
So, find the derivative of the function:
[tex]\displaystyle f'(x) = \frac{d}{dx}\left[ 5x - 10\cos x\right][/tex]
Differentiate:
[tex]\displaystyle f'(x) = 5 + 10\sin x[/tex]
Set the function equal to zero:
[tex]\displaystyle 0 = 5+10\sin x[/tex]
And solve for x:
[tex]\displaystyle \sin x = -\frac{1}{2}[/tex]
Using the unit circle, our solutions are:
[tex]\displaystyle x = \frac{7\pi}{6} + 2n\pi\text{ or } \frac{11\pi}{6} + 2n\pi \text{ where } n\in \mathbb{Z}[/tex]
There is only one solution in the interval [-2, 0]:
[tex]\displaystyle x = \frac{11\pi}{6} - 2\pi = -\frac{\pi}{6}\approx -0.5236[/tex]
Thus, we only have one critical point on the interval.
Substituting this back into the function yields:
[tex]\displaystyle\begin{aligned} f\left(-\frac{\pi}{6}\right) &= 5\left(-\frac{\pi}{6}\right) - 10\cos \left(-\frac{\pi}{6}\right) \\ \\ &=-\frac{5\pi}{6} - 5\sqrt{3}\\ \\ &\approx -11.2782 \end{aligned}[/tex]
In conclusion, the absolute maximum value of f on the interval [-2, 0] is about -5.8385 at x = -2 and the absolute minimum value of f is about -11.2782 at x = -π/6.
We can see this from the graph below as well.
which of the following tables represents an inverse variation between x and y
Answer:
I think that d is the answer
Question 7(Multiple Choice Worth 1 points)
(07.02 MC)
Jason has two bags with 6 tiles each. The files in each bag are shown below
1
2
3
4
5
6
Without looking, Jason draws a file from the first bag and then a file from the second bag What is the probability of Jason drawing the file numbered 5 from the first bag and an odd file from the second bag?
0
영
o
Answer:a.3/6
Step-by-step explanation:
Because there’s a total of 12 files in each bag which is 6 in each
A G.P is such that the 3rd term minus a first term is 48. The 4th term minus 2nd term 144. Find: (i) Common ratio ii) The first term (ii) 6th term of the sequence
Answer:
Step-by-step explanation:
r is the common ratio.
Third term minus first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
Fourth term minus second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
:::::
r²-1 = 48/a₁
a₁ = 6
:::::
a₆ = a₁r⁵ = 1458
(i) The common ratio for the given condition is 3.
ii) The first term of the sequence is 6.
iii) The 6th term of the sequence is 1458.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that a is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.
As the third term minus the first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
The fourth term minus the second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
r²-1 = 48/a₁
a₁ = 6
a₆ = a₁r⁵ = 1458
Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence is 1458.
Learn more about the sequence here:
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Which of the following describes an angle with a vertex at Z?
round 8 5/6 to the nearest whole number
Answer:
9
Step-by-step explanation:
8 5/6
5/6 is close to 1 so it will round up
8+1 = 9
8 5/6 rounds to 9
Answer:
[tex]9[/tex]
Step-by-step explanation:
Step 1: Round [tex]8\frac{5}{6}[/tex] to the nearest whole number
In order to round up, the fraction needs to be either 1/2 or greater than 1/2. In our case, it is greater than half therefore we will round up to 9.
Answer: [tex]9[/tex]
This is a list of the heights ( each nearest cm ) of 12 children
150 134 136 139 131 141
132 134 136 137 150 146
Select the type of the data.
Discrete
Continuous
Categorical
Qualitative
choose one
NO FAKE ANSWERS
FIRST MARKED BRAINLIST
qualitative
Step-by-step explanation:
b cos the question is in quality format
Answer:
cutee!
SUP???
Hiii friend :]
cuteee~!
prettyyy
I need help with this
Answer:
D. Rotation reflection is the right answer
Answer:
Rotation, reflection
Step-by-step explanation:
R and I are equal so if you rotate clockwise you'll see I is in the top left and R would be in the bottom left. By reflecting, it's like flipping a pancake. R will now be in the in the top left on top of I.
(It's kind of weird to explain) Sorry if that was confusing.
The temperature at 5 a.m. was −7.4°C. By 9 a.m., the temperature was −4.7°C. How much warmer was the temperature at 9 a.m.?
Answer:
2.7°C.
Step-by-step explanation:
If it was -7.4°C. at 5 am, then -4.7°C. at 9am, then the temperature rose by 2.7°C.
Proof:
-7.4
-4.7
--------
2.7
William's assembly unit has decided to use a p-Chart with 2-sigma control limits to monitor the proportion of defective castings produced by their production process. The quality control manager randomly samples 150 castings at 10 successively selected time periods and counts the number of defective castings in the sample.
Sample Defects
1 9
2 14
3 9
4 9
5 13
6 8
7 12
8 10
9 12
10 11
Required:
a. What is the Center Line of the control chart?
b. What value of z should be used to construct the control chart?
c. What is the Upper Control Limit?
d. What is the Lower Control Limit?
Answer: attached below is the missing p chart
a) 0.07133
b) 2
c) 0.098
d) 0.045
Step-by-step explanation:
sample size = 150 castings
number of periods = 10
a) Determine the center Line of the control chart
( 0.06 + 0.0933 + 0.06 + 0.06 + 0.0867 + 0.0533 + 0.08 + 0.067 + 0.08 + 0.073) / 10
mean = 0.07133
standard deviation = 0.01335
b) Determine the value of Z to be used
Given that we are using 2sigma limits .
the value of Z to be used = 2
c) Upper limit control
= mean value + z-value * std
= 0.0713 + 2*0.01335 = 0.098
d) Lower Control Limit
= mean value - z-value * std
= 0.0713 - 2*0.01335 = 0.045
please help
Find the missing side of this right
triangle.
X
7
12
X
= [?]
Answer:
13.9 (if x is the Hypotenuse)
Step-by-step explanation:
which one is the Hypotenuse (the side opposite of the 90 degree angle) ?
because that determines the calculation.
if x is the Hypotenuse then Pythagoras looks like this
x² = 7² + 12² = 49 + 144 = 193
x = sqrt(193) = 13.9
if 12 is the Hypotenuse, then it looks like this
12² = 7² + x²
144 = 49 + x²
95 = x²
x = sqrt(95) = 9.75
What is the area of the triangle formed from (0,-3), (0,4), and (4,-3)?
A. 24 square units
B. 48 square units
C. 14 square units
O D. 6 square units
find the area of a semicircle whose radius is 2.4 cm
Answer:
15.072
Step-by-step explanation:
Pls Mark Brainiest okay
Answer:
2.88 pi or approximately 9.0432 cm^2
Step-by-step explanation:
The area of a semicircle is 1/2 the area of a circle
A = 1/2 pi r^2
A = 1/2 pi ( 2.4)^2
A = 2.88 pi cm^2
If we use 3.14 as an approximation for pi
A = 2.88 * 3.14
A =9.0432 cm^2
Couldn’t figure this out, please help
(A)
Step-by-step explanation:
This system of equations will no solution if they have the same slope and only differ in the y-intercept values. So let's rewrite the two equations into their slope-intercept forms:
[tex]y = \frac{3}{h-2}x + 5[/tex]
[tex]y = \frac{8}{h}x + \frac{5}{h}[/tex]
For them to have no solution, their slopes must equal each other:
[tex]\dfrac{3}{h-2} = \dfrac{8}{h} \Rightarrow 3h=8h-16[/tex]
or
[tex]h = \dfrac{16}{5}[/tex]
Putting this value into our system of equations, we get
[tex]y = \frac{5}{2}x + 5[/tex]
[tex]y = \frac{5}{2}x + \frac{25}{16}[/tex]
This is a system of equations consisting of two parallel lines and as such, do not intersect and so, no solution.
URGENT PLZ HELP
Find the arc length of semi circle with diameter of 18
Answer:
Step-by-step explanation:
The formula to find arc length is
[tex]AL=\frac{\theta}{360}*\pi d[/tex] where theta is the measure of the central angle and d is the diameter. If we are dealing with a semicircle, the measure of the central angle is 180 degrees. Filling in:
[tex]AL=\frac{180}{360}*\pi (18)[/tex] which simplifies a bit to
[tex]AL=\frac{1}{2}*\pi (18)[/tex] and a bit more to
AL = 9π. That answer is obviously in terms of π; if you need it in terms of whatever your measurement is (feet, inches, cm, etc.) the answer would be, rounded to the nearest tenth, 28.3 units
its not telling me how to do this, please help
Step-by-step explanation:
Actually, it tells you exactly what to do.
First, translate, i.e., move over, the coordinates up by 3:
[tex](1, 4)\rightarrow (1+3, 4+3) = (4, 7)[/tex]
Then reflect this point about the x-axis and to do this,
[tex](x, y) \rightarrow (x, -y)[/tex]
[tex](4, 7) \rightarrow (4, -7)[/tex]
7/9 - 2/3 and 2/3 - 1/6
Answer:
The answer is 1/9 and 1/2
Im new and i need your help so please help me!!
Answer:
it's true
Step-by-step explanation:
To factorise you need to work out a number that add up to the number with a letter and multiply to the last number
someone please help asap
Answer:
(r/s)(6) = r(6)/s(6) = 3(6)-1 / 2(6)+1 = 18-1 / 12+1 = 17/3
So basically the first one is the correct answer.
Step-by-step explanation:
I hope this helped and please kindly mark Brainliest. Thank You <3
find the missing side lengths
Answer:
x = 11 * sqrt(2)
y = 11
Step-by-step explanation:
Use the ratios of the lengths of the sides of a 45-45-90 triangle.
y = 11
x = 11 * sqrt(2)
1/4 + 4/10 what is the answer plz give correct
Answer:
0.65 is the correct answer
Step-by-step explanation:
hopes it helps
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\boxed{\frac{13}{20}}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the answer...}}\\\\\frac{1}{4} +\frac{4}{10}\\------------\\LCM(4,10) = 20\\\\\rightarrow \frac{1}{4}=\frac{1*5}{4*5} = \frac{5}{20}\\\\\rightarrow \frac{4}{10}=\frac{4*2}{10*2}=\frac{8}{20}\\\\\\\rightarrow\frac{5}{20}+ \frac{8}{20} = \boxed{\frac{13}{20}}\\\\\\\text{The answer is in it's simplest form.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
To make concrete, the ratio of cement to sand is 1 : 3. If cement and sand are sold in bags of equal mass, how many bags of cement are required to make concrete using 15 bags of sand?
Answer:
5 bags of cement are required.
Step-by-step explanation:
Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:
Cement = 1
Sand = 3
3 = 15
1 = X
15/3 = X
5 = X
Therefore, 5 bags of cement are required.
For 0 less than or equal to theta less than 2(pi), what are thebsolutions to sin↑2(theta)=2(sin↑2)(theta/2)?
I assume the up arrows are supposed to indicate exponents, so that the equation is
sin²(θ) = 2 sin²(θ/2)
Recall the half-angle identity for sine,
sin²(θ/2) = (1 - cos(θ))/2,
as well as the Pythagorean identity,
sin²(θ) + cos²(θ) = 1
Rewrite the equation in terms of cosine and solve:
1 - cos²(θ) = 1 - cos(θ)
cos²(θ) - cos(θ) = 0
cos(θ) (cos(θ) - 1) = 0
cos(θ) = 0 or cos(θ) - 1 = 0
cos(θ) = 0 or cos(θ) = 1
[θ = arccos(0) + 2nπ or θ = arccos(0) - π + 2nπ] or
… … … [θ = arccos(1) + 2nπ]
(where n is any integer)
[θ = π/2 + 2nπ or θ = -π/2 + 2nπ] or [θ = 2nπ]
In the interval 0 ≤ θ < 2π, we get the solutions θ = 0, π/2, and 3π/2.
(That is, for n = 0 in the first and third solution families, and n = 1 in the second family.)
See above. okokokoookkokokokokkkkokokkokokkok
Answer:
B
Step-by-step explanation:
B is the correct answer
Which explains whether or not the graph represents a direct variation?
Answer:
The slope is 3 and equation of the line is y=3x. I think the answer is the 1st option
Step-by-step explanation:
Given:
y=3x
Direct variation equations have the form:
y=kx,
where
k is the constant of proportionality
so k=3
A half-century ago, the mean height of women in a particular country in their 20s was inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of of today's women in their 20s have mean heights of at least inches?
Answer:
0.26684
Step-by-step explanation:
Given that :
Mean, μ = 62.5
Standard deviation, σ = 1.96
P(Z ≥ 63.72)
The Zscore = (x - μ) / σ
P(Z ≥ (x - μ) / σ)
P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)
P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)
1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684
Which of the following pairs of functions are inverses of each other?
O A. f(x) = 8x? - 10 and g(x) = x +10
8
B. f(x) = {+8 and g(x) = 2x - 8
O C. f(x) = 18 - 9 and g(x) =
O D. f(x) = 3x2 +16 and g(x) = -
18
X+9
16
Answer:
A is the answer I guess so...
The functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function f(x)= 18/x - 9
Let us replace f(x) by y
y=18/x - 9
Now x=18/y-9
Add 9 on both sides
x+9=18/y
Apply cross multiplication
y(x+9)=18
Divide both sides by x+9
y=18/(x+9)
f⁻¹(x)=18/(x+9)
Hence, the functions f(x) = 18/x -9 and g(x) = 18/x+9 are inverse to each other.
To learn more on Functions click:
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Brendan has $65 worth of balloons and flowers delivered to his mother. He pays the bill plus an 8.5% sales tax and an 18% tip on the total cost including tax. He also pays a $10 delivery fee that is charged after the tax and tip. How much change does he receive if he pays with two $50 bills? Round to the nearest cent.
Answer:
its 6.78 i believe
Step-by-step explanation:
Help Please ASAP!!! Not sure how to solve this problem. Can someone help me please? Thank you for your help!
Answer:
This question is formatted incorrectly
Step-by-step explanation:
How
many solutions are there to the equation below?
4(x - 5) = 3x + 7
A. One solution
B. No solution
O C. Infinitely many solutions
SUB
Answer:
A one solution
Step-by-step explanation:
4(x - 5) = 3x + 7
Distribute
4x - 20 = 3x+7
Subtract 3x from each side
4x-3x-20 = 3x+7-3x
x -20 = 7
Add 20 to each side
x -20+20 = 7+20
x = 27
There is one solution
Answer:
Step-by-step explanation:
Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.
4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:
1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.
what is the quotient 3/8 ÷5/12
Answer:
9/10
Step-by-step explanation:
3/8 ÷5/12
Copy dot flip
3/8 * 12/5
Rewriting
3/5 * 12/8
3/5 * 3/2
9/10
