Answer:
Step-by-step explanation:
Maximum value is when cos x = 1
So it is -2 + 4(1) = 2.
Minimum value, when cos x = -1:
= -2 + 4(-1) = -6.
Answer:
The maximum 2 is reached when x=2pi,4pi, and 6pi.
The minimum -6 is reached when x=pi, 3pi,and 5pi.
Step-by-step explanation:
So let's first look at cos(x) on interval (0,21].
How many rotations is that? Does it at least contain 1 full rotation? If it contains one full rotation that means all the values from -1 to 1 (inclusive) are tagged? If it doesn't contain a full rotation, we might have to dig a little deeper.
So we know x=0 isn't included and that's when cosine is first 1,but this doesn't mean 1 won't be hit later.
Let's figure out the number of rotations:
21/(2pi)=3.3 approximately
This means we make at least 3 rotations.
So this means we definitely will have all the values from -1 to 1 tagged (inclusive).
Now let's look at whole function.
f(x) = -2 + 4 cos x
-2+(-4) to -2+4 will be the range of the function
So the minimum is -6 and the maximum is 2.
So the min occurs when cos(x)=-1 and the max occurs when cos(x)=1.
We have a little over three rotations and remember we can't include x=0.
cos(x)=1
when x=2pi (one full rotation)
when x=4pi (two full rotations)
when x=6pi (three full rotations)
We will stop here because cosine won't be 1 again until a fourth full rotation
cos(x)=-1
when x=pi (half rotation)
When x=3pi (one + half rotation)
When x=5pi (two+half rotation)
We can't include x=7pi (three+half rotation)
because this one is actually not in the interval because 3.5 is more than 3.3 .
The maximum 2 is reached when x=2pi,4pi, and 6pi.
The minimum -6 is reached when x=pi, 3pi,and 5pi.
the recipe for pumpking pie instructs you to bake the pie at 425∘F, for 15 minutes and then reduce the oven temperature to 350∘F. What is the change in temperature in degrees Celsius?
Answer:
ΔT = -75°F
Step-by-step explanation:
ΔT = T₁ - T₀ = 350 - 425 = -75°F
which of the following
is not
a fraction equivalent to 3/4?
a) 6/8
b) 9/12
c) 12/18
d) 21/28
e) 27/36
Answer:
c
Step-by-step explanation:
12/18 = 2/3
Answer:c
Step-y-step explanat:c
PLEASE ANSWER THIS !!!!
Answer:
option D
Step-by-step explanation:
Area of the square is 100 m² so each side is √100 = 10 m and half the area is 50 m²
Area of one quarter of the circle is ¼πr² = ¼π(10²) = 25π
The shaded area is thus (25π - 50) m²
In a colony, there are 55 members. Every member posts a greeting card to all the
members. How many greeting cards were posted by them?
Answer:
55*54
=2970
Step-by-step explanation:
Find the area of the following figure. Explain how you found your answer.
HELP ASAP WILL GIVE BRIANLYEST
Answer:
Below
Step-by-step explanation:
Let's say that each square on the grid represents 1 cm
First find the area of the two triangles
For the larger one: A = bh/2
A = 3 x 3 / 2
= 4.5 cm^2
For the smaller one : A = bh/2
A = 2 x 2 / 2
= 2 cm^2
For the rectangle : A = lw
A = 4 x 5
= 20 cm^2
Add them all up to get the area
4.5 + 2 + 20 = 26.5 cm^2
Hope this helps!
Answer:
26 1/2 units
Step-by-step explanation:
First find the area of the rectangle at the bottom
A = l*w
A = 5 *4 = 20
Then find the area of the left triangle
A =1/2 bh = 1/2 (3 * 3) = 9/2
Then find the area of the right triangle
A = 1/2 bh = 1/2 ( 2*2) = 4/2 =2
Add the areas together
20 + 9/2+2 = 22 +9/2 = 22+4 1/2= 26 1/2
Find the slope of the line passing through the points (-1, 7) and (-5, 1)
Answer:
3/2
Step-by-step explanation:
y2 - y1 / x2 - x1
1 - 7 / -5 - (-1)
-6 / -4
= 3/2
Answer:
m=3/2
Step-by-step explanation:
m=y2-y1/x2-x1
m=1-7/-5-(-1)
m=-6/-4
m=3/2
Find the focus and directrix of the parabola y = .5(x + 2)2 – 3
Answer:
comparing equation with standard equation x 2 =4aya=2/5co-ordinates of focus =(o,a) i.e. (0, 2/5)equation of directrix=y=-a i.e. y=-(2/5)length of latus rectum= 4a i.e. 8/5co-ordinates of latus rectum=(-2a,a) and (2a,a) i.e. (-4/5,2/5) and (4/5,2/5)..Step-by-step explanation:
And please marks me as brainliests..please and follow me...If the lengths of the legs of a right triangle are 5 and 12, what is the length of the hypotenuse?
Answer:
13
Step-by-step explanation:
If we have a right triangle, we can use the Pythagorean theorem to find the hypotenuse
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2 + 12^2 = c^2
25+144= c^2
169 = c^2
Take the square root of each side
sqrt(169) = sqrt(c^2)
13= c
Answer:
The length of the hypotenuse is 13.
Step-by-step explanation:
[tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex]
[tex]a^2 = 12^2 + 5^2[/tex]
[tex]a^2 = 144 + 25[/tex]
[tex]a^2 = 169[/tex]
a=[tex]\sqrt{169}[/tex]
a= 13
Here we use the idea of the Pythagoras' theorem. Which suggests that [tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex] in which [tex]a^{2}[/tex] is the hypotenuse of the triangle and [tex]b^2[/tex] and [tex]c^{2}[/tex] are the two other lengths of the triangle.
HOPE THIS HELPED
The length of a picture is 14.25 inches shorter than twice the width period if the perimeter of the picture is 133.5 inches, find its dimensions
Answer: Dimension = 27 inches by 39.75 inches
Concept:
A perimeter is a path that encompasses/surrounds/outlines a shape.
Perimeter (rectangle) = 2 (l + w)
l = length
w = width
Solve:
l = 2w - 14.25
w = w
P = 133.5
Given equation
P = 2 (l + w)
Substitute values into the equation
133.5 = 2 (2w - 14.25 + w)
Combine like terms
133.5 = 2 (3w - 14.25)
Distributive property
133.5 = 6w - 28.5
Add 28.5 on both sides
133.5 + 28.5 = 6w - 28.5 + 28.5
162 = 6w
Divide 6 on both sides
162 / 6 = 6w / 6
w = 27 in
l = 2w - 14.25 = 2 (27) - 14.25 = 39.75 in
Hope this helps!! :)
Please let me know if you have any questions
Charla has six segments with which to make two triangles. The segments lengths are 2 in., 3 in., 4 in., 5 in., 6 in., and 7 in. Which are possible side lengths of her two triangles?
2 in., 4 in., 6 in. and 3 in., 5 in., 7 in.
2 in., 5 in., 6 in. and 3 in., 4 in., 7 in.
2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.
2 in., 3 in., 6 in. and 4 in., 5 in., 7 in.
Answer:
The answer is option C
2 in., 3 in., 4 in. and 5 in., 6 in., 7 in.
Step-by-step explanation:
i need help figuring it out
Complete the equation: x2 + 8x + __ = (__)^2
Answer:
B
Step-by-step explanation:
16,x+4
by completing square formula
Solve this inequality: 4x-8>-40
Answer:
x > - 8
Step-by-step explanation:
4x - 8 > - 40
4x > - 40 + 8
4x > - 32
Divide 4 on both sides,
4x / 4 > - 32 / 4
x > - 8
please help, my course ends tonight and all im getting are spammers
Research some terms for parts of a circle and find examples of them in fields such as engineering or architecture. Describe in detail how these terms are used and how these uses relate to what you’ve learned in class.
Answer:
parts of a circle = tangent, chord, arc, segment, sector, diameter, radius, circumference.
A lot of jobs use area and perimeter such as; Surveying, flooring estimates architecture, mechanical engineering,
Typically, a land surveyor conducts and records a perimeter survey and part of this includes the transverse
Surveyors typically measure positions in series. Starting at control points, they measure angles and distances to new locations and use trigonometry to calculate positions in a plane coordinate system. Measuring a series of positions in this way is known as "running a traverse." A traverse that begins and ends at different locations is called an open traverse.
Here they create segments as seen below attached.
Engineers Drawing Circles: Begins by defining the radius, diameter and circumference and asking students to draw circles with a given radius, circumference or area. and when requiring they draw two circles with the same centre, one property of each circle being given in example with bridges, or arc of a circle working with calculating precise length for material lists.
The Annulus: the shape formed between two circles. They use the properties of the annulus by completing a table with values of pertaining to the properties of the inner circle, the outer circle and the annulus.
With sectors, engineers, can defining major and minor sector, they calculate the arc length and the area of a sector of a circle. They have learnt how to complete a table of values of properties of a circle and a sector of that circle given different properties from which to start with.
Architecture typically used series of circles in gothic architecture, but also art deco and earlier historic arches, use of semi-circular arches in architecture, and tangents are used as a .function to compute a building's height if they know their distance from the structure and the angle between their eyes and the building's top; clinometers can help them measure those angles.
Metal fabricators and product design workers use spring dividers help them inscribe an arc or create a circle pattern.
I would then write a little more about chords and radius
The number of hearing aids that needs to be produced and sold is??
Answer:
14.36 AND 9.89 ===> 14 or 10
Step-by-step explanation:
Y = Ax2 Bx C
Enter coefficients here >>> -4 97 -568
Standard Form: y = -4x²+97x-568
-24.25 -12.125 147.015625 -588.0625 20.0625
Grouped Form: No valid Grouping
Graphing Form: y = -4(x-12.13)²+20.06
Factored Form: PRIME
Solution/X-Intercepts: 14.36 AND 9.89
Discriminate =321 is positive, two real solutions
VERTEX: (12.13,20.06) Directrix: Y=20.13
12345 are divisible by 15 with exlpin
Answer:
hfwhww45 5h wahdaw 5656 adshjdawh bh4 54
Step-by-step explanation:
5767
12345
Sum of digits = 1+2+3+4+5
= 15
Which means divisible by 3
Ends with 0 or 5 = Yes ends with 5
Therefore the number is divisible by 15
12345÷15 = 823
Divisiblity rule of 15 = Any number is divisible by 15 if the sum of the digits is divisible by 3 and the number ends with a 0 or 5.
Must click thanks and mark brainliest
Help!!
A.) find f^-1 and use it to evaluate: f^-1(12)
B.) write a formula for the function g(x) that results when the parent function: f(x) = x^3 is vertically stretched by a factor of three, shifted to the left by 4 units and shifted down by 5 units
Answer:
Step-by-step explanation:
y = x³
x = ∛y
Switch x and y:
y = ∛x
f⁻¹(x) = ∛x
f⁻¹(12) = ∛12 ≅ 2.29
check:
x = 2.29
f(x) = 2.29³ ≅ 12
In the figure, ΔABC and ΔDEF are similar. What’s the scale factor from ΔABC to ΔDEF?
translate this into an expression: the quotient of a number, x, and 8, could you please explain it to me?
Answer:
x/8
Step-by-step explanation:
First, we are given "the quotient of...". This means that we are dividing something/something else. If two numbers are given in the phrase "something and something else", the first number given will be the something, and the second number will be the something else.
The first number listed is x. Therefore, we have
x/something else.
Next, we are given "and 8", so we have x/8 as our expression
I need help completing this answer are you available
Answer:
Step-by-step explanation:
find the greatest number than divides 45 60 75 without leaving remainder
Answer:
15
Step-by-step explanation:
15 is the greatest number that divides 45 60 75 without leaving remainder
Answer:
15
Step-by-step explanation:
Let write the factors of each number:
45: (1,3,5,9,15,45)
60:(1,2,3,4,5,6,10,12,15,20,30,60)
75:(1,3,5,15,15,75).
The greatest common factor is 15. So the answer is 15.
Prove that if (c, f(c)) is a point of inflection of the graph of f and f'' exists in an open interval that contains c, then f''(c)=0 Hint: Apply the First Derivative Test and Fermat's Theorem to the function g=f'
We can conclude that if (c, f(c)) is a point of inflection of the graph of f and f'' exists in an open interval that contains c, then f''(c)=0.
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
We can prove this statement using the First Derivative Test and Fermat's Theorem.
First, we know from the First Derivative Test that at a point of inflection, the first derivative of the function (in this case, f') must equal 0. Therefore, at the point (c, f(c)), f'(c) = 0.
Next, we can apply Fermat's Theorem. This theorem states that if a function f has a local maximum or minimum at c, then f'(c) = 0. Since the point (c, f(c)) is a point of inflection, we can apply Fermat's Theorem to say that f'(c) = 0.
Now, since f'' exists in an open interval that contains c, we can use the fact that if f'(c) = 0, then f''(c) = 0.
Therefore, we can conclude that if (c, f(c)) is a point of inflection of the graph of f and f'' exists in an open interval that contains c, then f''(c)=0.
To learn more about the differentiation of an equations visit:
https://brainly.com/question/25731911.
#SPJ2
Need help so confused thankssss
Given the graph below select the factors that comprise the function.
f(x) = ____ * ____ * ____ * ____
a.) (x - 2)
b.) (x + 1)
c.) (x - 1)
d.) x
e.) 1
f.) (x + 3)
h.) (x + 2)
i.) (x - 3)
Answer:
Below.
Step-by-step explanation:
The zeroes are at x = -2, 0, 1 and 3 so the factors are
(x +2)
x
(x - 1)
(x - 3)
Find an upper bound for E(h) the error of the machine approximation of the two-point forward difference formula for the first derivative and then find the h corresponding to the minimum of E(h).
The two-point forward difference formula for f'(x) is:_________
Answer:
I doubt it is not going to be a great
Find the minimum turning point of y = x^2 + x - 12
Answer:
(x+4)(x-3)
Step-by-step explanation:
x^2+x-12
=x^2+(4-3)x-12
=x^2+4x-3x-12
=x (x+4)-3 (x+4)
=(x+4)(x-3)
Answer:x=6
Step-by-step explanation:
If(a²-1) x²+(a-1)x+a²-4a+3=0 is an identity in x, then find the value of a
Answer:
Step-by-step explanation:
[tex](a^2-1)x^2+(a-1)x+a^2-4a+3=0\\\\Calculate\ and\ identify\ the\ polynomials\\\\\Longleftrightarrow\ a^2x^2-x^2+ax-x+a^2-4a+3=0\\\\\Longleftrightarrow\ a^2x^2+ax+a^2-4a+3=x^2+x+0\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}a^2&=&1\\a&=&1\\a^2-4a+3&=&0\\\end{array} \right.\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}(a-1)(a+1)&=&0\\a-1&=&0\\(a-1)(a-3)&=&0\\\end{array} \right.\\\\\\We\ must\ exclude\ a=-1\ and\ a=3\ (not\ solution)\\\Longrightarrow\ a=1\\[/tex]
Find the area of each shaded region.
What is the slope of the line passing through the points (6,1) and (-3,-4)?
Answer:
5/9
Step-by-step explanation:
y2-y1/x2-x1 = 5/9
Dia is 10 years old. How many years have to add with twice of her age to get 24?
Answer:
4
Step-by-step explanation:
twice her age:
10*2 = 20
24-20 = 4
Answer:
4 i believe that's the answer
