Consider y=h(θ) described in the table. When comparing h(θ) to the parent function f(θ)=cos(θ), which statements are true? Select all that apply.
Answers
2 Answers:
Choice AChoice E=====================================================
Explanation:
Let's go through the answer choices
---------------------------------
A)
The lowest point is y = 1, and the highest point is y = 27. Computing the midpoint gets us (yMin+yMax)/2 = (1+27)/2 = 28/2 = 14.
The midline of [tex]h(\theta)[/tex] is y = 14.
Consider that the parent function [tex]\cos(\theta)[/tex] has a midline of y = 0. The jump from y = 0 to y = 14 must mean [tex]h(\theta)[/tex] has a vertical shift of 14.
Choice A is true
---------------------------------
B)
The period is the length of the cycle. For the function [tex]h(\theta)[/tex], the function starts at [tex]\theta = 0[/tex] and repeats when it gets to [tex]\theta = \frac{\pi}{2}[/tex]. This is a difference of pi/2 units which is the period.
Choice B is false. It contradicts with choice E.
---------------------------------
C)
Choice C is false. The max for [tex]h(\theta)[/tex] is at y = 27
---------------------------------
D)
To figure out the amplitude, we can note the vertical distance from the midline y = 14 to the max is 27-14 = 13 units.
Or we can note the distance from the midline to the min is 14-1 = 13 units.
Or we subtract the min and max, and divide by 2: (yMax-yMin)/2 = (27-1)/2 = 26/2 = 13
Either way, the amplitude is 13 units
Choice D is false.
---------------------------------
E)
Choice E is true. Refer to choice B to see why this is the case.
---------------------------------
Side note: one possible function is [tex]h(\theta) = 13\cos(4\theta+\pi) + 14[/tex]. The various pieces of that function (in)directly lead to the amplitude, period, and vertical shift.
The correct two options are h(Ф) has vertical shift of 14 and Choice E
The period of a fuction is x/2
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
Let's go through the answer choices
A)
The lowest point is y = 1, and the highest point is y = 27. Computing the midpoint gets us (yMin+yMax)/2 = (1+27)/2 = 28/2 = 14.
The midline of is y = 14.
Consider that the parent function has a midline of y = 0. The jump from y = 0 to y = 14 must mean has a vertical shift of 14.
Choice A is true
B)
The period is the length of the cycle. For the function , the function starts at and repeats when it gets to . This is a difference of pi/2 units which is the period.
Choice B is false. It contradicts with choice E.
C)
Choice C is false. The max for is at y = 27
D)
To figure out the amplitude, we can note the vertical distance from the midline y = 14 to the max is 27-14 = 13 units.
Or we can note the distance from the midline to the min is 14-1 = 13 units.
Or we subtract the min and max, and divide by 2: (yMax-yMin)/2 = (27-1)/2 = 26/2 = 13
Either way, the amplitude is 13 units
Choice D is false.
E)
Choice E is true. Refer to choice B to see why this is the case.
Side note: one possible function is h(Ф) = 13 Cos(4Ф + π) + 14 . The various pieces of that function (in)directly lead to the amplitude, period, and vertical shift.
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Related Questions
Find the distance between the two points in simplest radical form.
(-8, -2) and (-6,2)
Answers
Answer: [tex]2\sqrt{5}\\\\[/tex]
To get that answer, we apply the distance formula
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-8-(-6))^2 + (-2-2)^2}\\\\d = \sqrt{(-8+6)^2 + (-2-2)^2}\\\\d = \sqrt{(-2)^2 + (-4)^2}\\\\d = \sqrt{4 + 16}\\\\d = \sqrt{20}\\\\d = \sqrt{4*5}\\\\d = \sqrt{4}*\sqrt{5}\\\\d = 2\sqrt{5}\\\\d \approx 4.472136\\\\[/tex]
As an alternative, you could plot the two points on the same xy grid, and then form a right triangle. Afterward, apply the pythagorean theorem and you should get the same result as shown above.
The container of orange juice held 53 cups of juice. If a serving of orange juice is ã of a cup of orange juice, to the
nearest whole serving, how many servings were in the container?
05 servings
O 6 servings
15 servings
19 servings
Mark this and return
Save and Exit
Next
Submit
Answers
Answer:
5 servings = 265 cups of orange juices
5 servings = 318 cups of orange juices
5 servings = 795 cups of orange juices
5 servings = 1,007 cups of orange juices
Step-by-step explanation:
Given:
1 serving contain = 53 cups of orange juices
Find:
Serving in;
5 servings
6 servings
15 servings
19 servings
Computation:
5 servings = 53 x 5
5 servings = 265 cups of orange juices
5 servings = 53 x 6
5 servings = 318 cups of orange juices
5 servings = 53 x 15
5 servings = 795 cups of orange juices
5 servings = 53 x 19
5 servings = 1,007 cups of orange juices
Can someone help me plz
Answers
Step-by-step explanation:
the answer is in the image above
what is the definition of risk ?
Answers
Answer: DOING SOMETHING THAT HAS THE POSOBILITY OF IT BEING BAD
Step-by-step explanation: BECAUSE
Answer:
D
Step-by-step explanation:
just got it right on edge
Show √7 , √5 on a number line.
please hurry up my cissy and oppa
Answers
Answer:
Draw the number line like in the picture.
Step-by-step explanation:
√5 is about 2.236, meaning it's kind of close to 2.25.
√7 is about 2.646, meaning it's very close to 2.625.
D equals f plus fx, solve the equation for x
Answers
Answer:
question says D = f + fx,
then,
D = 2fx
so,
D/2f = x
how do you find the area of a rectangle
Answers
Answer:
You multiply length by width.
Step-by-step explanation:
To find the area of a rectangle you multiply length and width together.
For example if a rectangle has length 2 and width 3 the area of the rectangle would be 6, since 2 * 3 is 6.
Answer:area =length x width
Step-by-step explanation:
which of the following is true?
Answers
Answer:
the right ones are a c and d maybe
Step-by-step explanation:
these are probably wrong but I need my points so figure it out.
which step in the construction of coping a lin segment ensures that the new line segment has the same length as the original line segment
Answers
Step-by-step explanation:
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
Here are the steps I think you probably will go through.
1. Draw a line that is longer than the segment but shorter than the width of the page.
1a. Make sure this line is at least 1/2 inch from the left hand side.
2. Use a compass to measure the length of the original segment. Never use a ruler. Rulers do not exist in pure geometry.
3. Measure out the distance on the line you just drew with the compass. One end is on the left hand edge and the other end (the pencil end) is marking the segment so it is the same length as the compass. You are done.
The key step either two or three.The steps to copy a line segment are given below:
1. Lets start with a line segment AB that we have to copy.
2. Now mark a point C. below or above AB, that will be one endpoint of the new line segment.
3. Now, put the compass tip on point A of the line segment AB.
4. Spread the compass up to point B, so as the compass width is equal to length of AB.
5. Without changing the compass width, now place the compass tip on the point C that you made in step 2.
6. Now, draw an arc roughly without changing the compass settings. Mark that point D. This will form the new line segment.
7. Draw a line from C to D.
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
The solutions to the equation -4|x + 9| = -8 are:
7, 11
7, -11
-7, 11
-7, -11
Answers
Answer:
option 4
Step-by-step explanation:
Given Equation :-
=> -4| x + 9 | = -8
To FinD :-
=> Solution of the equation .
Solving it :-
=> -4| x + 9 | = -8
=> | x + 9 | = -8/-4
=> |x + 9| = 2
=> ( | x + 9 | )² = 2²
=> x + 9 = ±2
=> x = -9 +2 , -9-2
=> x = - 7 , -11
Option 4 is correct.
Answer:
x = - 7 , - 11
Step-by-step explanation:
[tex]-4 | x +9| = - 8\\\\\frac{-4}{-4} |x+9| = \frac{-8}{-4}\\\\1 | x+9| = 2\\\\x+9 = - 2\ , x + 9 = 2\\\\x + 9 - 9 = - 2 - 9 , \ x + 9 - 9 = 2 - 9\\\\x + 0 = - 1 1 \ , \ x + 0 = - 7\\\\x = -11 \ , \ x = - 7[/tex]
A skateboard that is originally $107 is on sale for 90% off!! How much does the skateboard cost?
Answers
90% off means is is selling for 10% of the original price.
Multiply original price by 10%
107 x 0.01 = $10.70
It is selling for $10.70
Triangle ACB is the pre-image and triangle DFE is the image. What is the scale factor of the dilation?
Answers
Answer:
½
Step-by-step explanation:
the scale factor of dilation = 6/12 = ½
Please show your working too
1. Five men takes 3 hours and 20 minutes paint a house. How long would it take four men to paint a similar house? Give your answer in hours and minutes.
2. If 24 houses can be built by 6 builders in one year, how many builders would it take to build 52 houses in the same amount of time?
3. Two people can build four identical walls in three days. At this rate, how many of these walls could ten people build in 3.75 days?
4. Two toy makers can make eight toy soldiers in two weeks. How many toy soldiers could seven toy makers make in three weeks if they work at the same rate?
Answers
Answer:
1. 4hrs and 10mnts
2. 13 builders
3. 25 walls
4. 52 toy soldiers
Step-by-step explanation:
1. then, one man can do it in 16hrs and 40mnts, so, 4 men would take 4hrs and 10mnts
2. one builder can build 4 houses in a year, so 13 builders are needed to build 52 houses
3. they can do it at a rate of 2 walls per person for 3 days, so 10 ppl can make 25 walls in 3.75 days
4. 4 toys per person for 2 weeks, so 7 makers can make 52 toys for 3 weeks
Consider the equations:
y=|x-1| and y=3x+2
What is the approximate solution of this system of equations?
Answers
Answer:
ans: (-3/2, -5/2), (-1/2, -5/4)
Step-by-step explanation:
here;
y =| x - 1| can be any of form I.e
y = x - 1 say equation••••1
OR
y = -( x - 1) say equation •••2
our next equation is,
y = 3x + 2 say equation ••••3
substituting 'y' from equation 1 and 2 to 3
we got
x - 1 = 3x + 2 -( x - 1) = 3x +2
- 3 = 2x -1 = 4x
hence
x= -3/2 and -1/4
substituting x in equation 3 we got
y = -5/2 and -5/4
OR ,
can be solve by iterative method which is quite long
Answer:
(-0.2,1.2)substitute 3x+2 for y and set them equal to eachother then plug in x for y
Step-by-step explanation:
NEED HELP ASAP
The length of a rectangular parking lot at the airport is 2/3 mile.if the area is 1/2 square mile, what is the width of the parking lot?
Answers
Answer:
3/4 mile
Step-by-step explanation:
[tex]A = l *w\\\frac{1}{2} = \frac{2}{3} * w\\w = \frac{3}{2} * \frac{1}{2}\\w = 3/4 mile[/tex]
Confused on how to solve this problem, please help and offer a step by step explanation
Answers
Answer:
7x+5=180
7x=175
x=25
Hope This Helps!!!
pls help I'll mark brainliest
Answers
Answer:
305°
Step-by-step explanation:
The angle between the north line at L and the line connecting PL is
125° (75° + 50° ) ← alternate angle between parallel lines
Then
bearing of P from L is 180° + 125° = 305°
What’s the answers to this one
Answers
Answer:
g(- 2) = 0, g(4) = - 4
Step-by-step explanation:
x = - 2 in the interval - 2 ≤ x ≤ 4 , then
g(- 2) = 0
x = 4 in the interval 4 ≤ x < 10 , then
g(4) = - 4
The height of a seat on a Ferris wheel can be modeled as H (t) = 48 sin (pi/30 t+ 3pi/2) + 53, where tis time in seconds and H(t) is height in feet How far off the ground is a seat when it is at the top of the Ferris wheel?
Answers
Answer:
101ft
Step-by-step explanation:
the answer is in the above image
Which expression correctly represents the perimeter of a rectangle that is 12 centimeters long and 7 centimeters wide?
Answers
Answer:
The expression for the perimeter of the rectangle is:
P = 2*(12 cm) + 2*(7 cm)
And the perimeter is:
P = 38cm
Step-by-step explanation:
We know that for a rectangle of length L and width W, the perimeter is given by:
P = 2*L + 2*W
So, if we have a rectangle that is 12 cm long, we have L = 12cm
and if the rectangle is 7cm wide, we have W = 7cm
Now we can replace these in the perimeter equation to get:
P = 2*(12 cm) + 2*(7 cm)
P = 24cm + 14cm
P = 38cm
Which inequality is true?
A) |−6| > −6
B) |12| < |−5|
C) |−8| < 8
D) 7 > |−10|
Answers
Answer:
A) |−6| > −6
Step-by-step explanation:
Absolute value means take the non negative number
A) |−6| > −6 = 6> -6 true
B) |12| < |−5| 12 < 5 false
C) |−8| < 8 8 < 8 false
D) 7 > |−10| 7 > 10 false
Why is addition used to represent the submarine’s position changing from －8
feet to 0 feet below sea level?
What integer represents a submarine 8 feet below sea level?
What integer represents a submarine rising 8 feet?
Answers
-8ft (below from sea level)
8ft (above from sea level)
Please mark brainliest!!
x2+ y2 − 8x + 12y + 27 = 0
Using the standard form of the equation in question 1, what are the length of the radius and the coordinates of the center for this particular circle? Watch your signs for the variables h and k.
Answers
Central (4,–6)
Radius 5
Answer:
this was the answer from edmentum
Step-by-step explanation:
What is the length of EF in the right triangle below?
E
19
12
F
Answers
Answer:
F
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
EF² + 12² = 19²
EF² + 144 = 361 ( subtract 144 from both sides )
EF² = 217 ( take the square root of both sides )
EF = [tex]\sqrt{217}[/tex] → F
The length of EF in the right triangle below is √217.
Option F is the correct answer.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Using the Pythagorean theorem,
DE² = EF² + DF²
19² = 12² + EF²
EF² = 361 - 144
EF = √217
Thus,
The length of EF in the right triangle below is √217.
Learn more about the Pythagorean theorem here:
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Can someone
Please
Help
Me
Find the surface area of this sphere.
Round to the nearest tenth.
16 ft
Formulas for Spheres
S.A. = 4nr?
V = rer
[?] ft?
Answers
[tex]804.2\:ft^{2}[/tex]
Step-by-step explanation:
[tex]A=4 \pi r^{2}[/tex]
We are given D = 16 ft, which means that r = (1/2)D = 8 ft. Therefore, the surface area of the sphere is
[tex]A=4 \pi (8 ft)^{2} = 804.2\:ft^{2}[/tex]
The surface area of the sphere is approximately 804.2 square feet.
What is a sphere?It is a three-dimensional figure where the volume is given as:
The volume of a sphere = 4/3 πr³
We have,
The surface area of a sphere with diameter d is given by the formula:
SA = 4πr²
where r is the radius of the sphere, which is half the diameter. In this case, the diameter is 16 feet, so the radius is 8 feet.
Plugging in the value of r, we get:
SA = 4π(8²)
SA = 4π(64)
SA = 256π
Rounding to the nearest tenth gives:
SA ≈ 804.2 square feet
Therefore,
The surface area of the sphere is approximately 804.2 square feet.
Learn more about sphere here:
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Find the slope of the line below. Enter your answer as a fraction or decimal. Use a slash mark (/) as the fraction bar if necessary.
Answers
Answer:
1/4
Step-by-step explanation:
We can use the slope formula to find the slope
m = (y2-y1)/(x2-x1)
= (2-0)/(4 - -4)
= (2-0)/( 4+4)
= ( 2/8)
= 1/4
2.) z varies jointly as x and y. If z = 26 when x = 4 and y = 6, find the constant of variation and the equation of the relation.
Answers
2.) z varies jointly as x and y. If z = 26 when x = 4 and y = 6, find the constant of variation and the equation of the relation.
Solution:-[tex]\sf{z = kxy}[/tex]
[tex]\sf\rightarrow{16=k(4)(6)}[/tex]
[tex]\sf\rightarrow{K= \frac{16}{24} }[/tex]
[tex]\sf\rightarrow{K={\color{magenta}{ \frac{2}{3} }}}[/tex]
Answer:-The equation of variation is,
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \color{red}\sf{z = \frac{2}{3} \: xy.}[/tex]
[tex]{\large{——————————————————}}[/tex]
#CarryOnMath⸙
2.) z varies jointly as x and y. If z = 26 when x = 4 and y = 6, find the constant of variation and the equation of the relation.
Answer:[tex]\large \rightarrow \bf {The \: answer \:is \: {\green{z = \frac{3}{2} \: xy}}}[/tex]
What is the period of the graph of…
Answers
The +3 translates the whole curve up 3 units
The period tells you the space between repetitions of the curve.
When x = 0, y = 2 x 1 + 3 = 5
This next happens when pi/3 x = 2pi so x would = 6
The period of the curve = 6
Math help please show work thanks
Answers
Answer:
The curve surface area(CSA) of a cylinder is 2πrh.
Since diameter=1.5 in.
radius=diameter/2
=1.5/2 in.
=0.75 in.
And, the height of the bottle is 5 in.
Now,
CSA=2πrh
=2π*0.75*5 in^2
=15π/2 or 23.56 in^2
The size of the label needed to cover the entire bottle is 15π/2 or 23.56 in^2.
How many bacteria are in generation 9?
O A. 1,180,980
O B. 393,660
C. 1440
O D. 6561
Answers
Answer:
B. 393,660
Step-by-step explanation:
lemme get Brainliest please
Answer:
B. 393,660
Step-by-step explanation:
I plugged it into the symbolab calculator and attached the steps below! Hope this helps!