The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression of period of [tex]\pi/4[/tex]phase shift of [tex]\pi/4[/tex] to rightHow does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is [tex]y = f(x)[/tex], assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift): Left shift by c units: [tex]y = f(x+c)[/tex]earlier)Right shift by c units: [tex]y = f(x-c)[/tex]output, but c units late)Vertical shift:Up by d units: [tex]y = f(x) + d[/tex]Down by d units: [tex]y = f(x) - d[/tex]Stretching:Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]For this case, we're specified that:
y = cos(x) (the parent cosine function) was transformed to [tex]y = 0.35\cos(8(x-\pi/4))[/tex]
We can see its vertical stretch by 0.35, right shift by [tex]\pi/4[/tex]horizontal stretch by 1/8
Period of cos(x) is of [tex]2\pi[/tex] length. But 1.8 stretching makes its period shrink to [tex]2\pi/8 = \pi/4[/tex]
Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:
vertical stretch of 0.35horizontal compression to period of [tex]\pi/4[/tex] (which means period of cosine is shrunk to [tex]\pi/4[/tex] which originally was [tex]2\pi[/tex] )phase shift of [tex]\pi/4[/tex] to rightLearn more about transformation of functions here:
https://brainly.com/question/17006186
A rectangular flower bed measures 10 m by 6 m. It has a path 2 m wide around it. Find the area of the path.
Step-by-step explanation:
the easiest way to answer this is to calculate the area of the large rectangle (white) and subtract the area of the small rectangular (black).
we know the dimensions of the small rectangle : 10×6
and because of the 2m thick "frame" we know the dimensions of the large rectangle by adding 2×2 m to every small dimension : 14×10
(2 m on the top and the bottom, and 2 m left and right, so 4 m added in every direction).
the area of the large rectangle is
14 m × 10 m = 140 m²
the area of the small rectangle is
10 m × 6 m = 60 m²
so the area of the path is
140 - 60 = 80 m²
The question is below:
[tex]3(x - 2) + 7x = \frac{1}{2} (6x - 2) [/tex]
Solving It[tex]3(x - 2) + 7x = \frac{1}{2} (6x - 2) \\ \\ \implies3x - 6 + 7x = ([\frac{1}{2} \times 6 \: x] - [\frac{1}{2} \times 2]) \\ \\ \implies10x - 6 = ([\frac{1}{ \cancel2} \times \cancel 6 \: x] - [\frac{1}{ \cancel2} \times \cancel2]) \\ \\ \implies 10x - 6 = 3x - 1 \\ \\ \fbox{Bringing (3x )to left side whereas( - 6 )in right side} \\ \\ \implies10x - 3x = - 1 + 6 \\ \\ \implies7x = 5 \\ \\ \therefore x = \frac{5}{7} [/tex]
The Solution is = [tex] \frac{5}{7}[/tex]
[tex]\text\red{One Solution set is possible.}[/tex]
Hope This HelpsA triangle has two sides of length 1 and 8. What is the smallest possible whole-number length for the third side?
Answer:
8
Step-by-step explanation:
For the smallest possible length, this has to be one of the shorter sides. Let the length of this side be x.
So, by the triangle inequality theorem, 1+x>8, which means x>7.
So, the smallest possible whole number length is 8.
Find the area of the unshaded region.
Answer: 21
Step-by-step explanation:
find the simple interest on $6000 invested for 8 years at 4%
Answer:
$1920.00
Step-by-step explanation:
You want to calculate the interest on $6000 at 4% interest per year after 8
year(s).
The formula we'll use for this is the simple interest formula, or:
I= P * r * t
Where:
• P is the principal amount, $6000.00.
• r is the interest rate, 4% per year, or in decimal form, 4/100=0.04.
• t is the time involved, 8.…..year(s) time periods
So, t is 8...year time periods.
To find the simple interest, we multiply 6000 x 0.04 x 8 to get that:
The interest is: $1920.00
Please answer the question in the picture :) tysm
Answer:
a= 50
b=50
c=110
d=20
Answer:
Step-by-step explanation:
This is a kite. So the two triangles formed by the longest diagonal being drawn in form 2 congruent triangles.
Therefore c = 110 degrees.
d = 20 degrees.
a and b are found by noting that every triangle has 180 degrees.
110 + 20 + a = 180 Combine the left.
130 + a = 180 Subtract 130 from both sides
a = 180 - 130
a = 50 degrees
b also equals 50 degrees. Congruent triangles
Answer
a = 50b = 50c = 110d = 20A pitcher of water contains 1/4 liters of water. The water is poured equally among 5 glasses. How many liters of water are in each glass
Answer:
-3.86
Step-by-step explanation:
Please help as soon as possible
Answer:
[tex]9 \times 3 = 27 \\ 15 \times 6 = 90 \\ = 30.255 \\ 49 \times 3.14 = 153.86 \\ 153.86 + 30.255 + 27 = 211.115[/tex]
I WILL GIVE 100 PRECENT BRAINLIEST. PLS ANSWER THIS CORRECTLY,DUE IN A DAY.
[tex]x^{2} =3x-1 , x^{2} +\frac{1}{x^{2} }= what[/tex].
pls answer correctly,will mark brainliest for 100 percent real.
Answer:
7
Step-by-step explanation:
1. Solve for x in [tex]x^2 = 3x - 1[/tex].
[tex]x=\frac{3+ \sqrt{5}}{2} ,\frac{3- \sqrt{5}}{2}[/tex]
2. Substitute [tex]x=\frac{3+ \sqrt{5}}{2} ,\frac{3- \sqrt{5}}{2}[/tex] into [tex]x^2 + \frac{1}{x^2} = y[/tex].
[tex]\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2} = y[/tex]
3. Solve for y in [tex]\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2} = y[/tex]
[tex]y=\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2}[/tex]
4. Therefore,
[tex]x=\frac{3 + \sqrt{5} }{2}, \frac{3-\sqrt{5}}{2}\\y=\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2}[/tex]
............
[tex]x= \frac{3-\sqrt{5}}{2}[/tex]≈[tex]0.381966011, y=7[/tex]
[tex]x= \frac{\sqrt{5}+3}{2}[/tex]≈[tex]2.618033989, y=7[/tex]
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Please rate and click the Thanks button if it helped you out. Brainliest would be MUCH appreciated. Have a great day!
Stay Brainy!
−Kallmekrish
The best way to predict the future is to create it.
- Abraham Lincoln, Past U.S. President
Answer:
7
Step-by-step explanation:
Given equation: [tex]x^2=3x-1[/tex]
Rearrange so that it is equal to zero:
[tex]\implies x^2-3x+1=0[/tex]
Quadratic formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Using the quadratic formula to solve the given equation:
[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(1)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{5}}{2}[/tex]
[tex]\implies x^2=\dfrac{7 \pm 3\sqrt{5}}{2}[/tex]
Substituting this into [tex]x^2+\dfrac{1}{x^2}[/tex]
[tex]\implies \dfrac{7\pm3\sqrt{5}}{2}+\dfrac{1}{\dfrac{7\pm3\sqrt{5}}{2}}[/tex]
[tex]\implies \dfrac{7\pm3\sqrt{5}}{2}+\dfrac{2}{7\pm3\sqrt{5}}[/tex]
[tex]\implies \dfrac{(7\pm3\sqrt{5})(7\pm3\sqrt{5})}{2(7\pm3\sqrt{5})}+\dfrac{4}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{(7\pm3\sqrt{5})(7\pm3\sqrt{5})+4}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{49\pm42\sqrt{5}+45+4}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{98\pm42\sqrt{5}}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{14(7\pm3\sqrt{5})}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{14}{2}[/tex]
[tex]\implies 7[/tex]
help, asap, explain, thx
a^2-b^2=8
a+2=2
then a-b=?
Step-by-step explanation:
a + 2 = 2
a = 2 - 2
a = 0
a² - b² = 8
0 - b² = 8
b² = -8
This question is impossible.
A circular concrete patio has a circumference of about 53 yards. The patio has a diameter of d yards. Which expression best represents the value of pi?
The expression that best represents the value of pi is 53/d.
What is the expression that represents pi?Pi can be described as the ratio of the circumference of a circle to its diameter. The circumference of the patio is the distance round the patio. The formula that can be used to represent the circumference of the patio is πD
53 = πD
π = 53/d
To learn more about how to determine the circumference of a circle, please check: https://brainly.com/question/14351152
How do I prove if EFGH is a rhombus in this paragraph proof?
Explanation:
There are many approaches you can take. Perhaps one of the easiest is to show the sides of the rhombus are all the same length. This can be done several ways. Here are a couple of them.
__
1.A square has degree 4 rotational symmetry, so will map to itself when rotated by any multiple of 90°. This means the midpoints of adjacent sides will map to themselves, and any segment joining the midpoints of adjacent sides will map to itself. When segments map to themselves, they are congruent, hence the four sides of EFGH are congruent, and the figure is a rhombus.
__
2.The sides of a square are the same length and all corner angles are right angles. Midpoints of the sides divide the sides into congruent parts, so all of the segments PF, FQ, QG, GR, and so on are congruent. This means all of the triangles PFE, QGF, RHG, and SEH are congruent by the LL postulate. Corresponding sides of congruent triangles are congruent, so the sides of EFGH are congruent, and the figure is a rhombus.
FIND THE VOLUME OF EACH SNOWBALL)
Joshua and Isabella are having a snowball fight. Joshua has a snowball, shaped as a sphere, with a radius of 6 cm. Isabella also has a spherical snowball that is 6cm across the center of the sphere find the volume of each snowball use 3.14 for pi
Answer:
Step-by-step explanation:
The length of a square is 3x - 4 units. Find the area in terms of x.
Answer:
9x^2 - 24x + 16 is area in terms of x alternativly (3x-4)^2 is also true
Step-by-step explanation:
L * W = area length = width on a sqare so L * L = area too
(3x - 4) * (3x - 4)
use foil method
9x^2 - 24x + 16
Answer:
9x^2 − 24x + 16
Step-by-step explanation:
To find the area of a square, you use the formula
A = x^2
So we plug in 3x-4 for x
A = (3x-4)^2
A = 9x^2 − 24x + 16
what is the answer please i need help asap
Answer: a third
Step-by-step explanation: im simply a genius
Helppp meee please this one confuses me
Step-by-step explanation:
=[tex] =(3x + 2)(x + 1) \\ = 3x(x + 1) + 2(x + 1) \\ = {3x}^{2} + 3x + 2x + 2 \\ = {3x}^{2} + 5x + 2[/tex]
Answer:
Bro really?? Anyway it's
[tex]anyway \: its \: 3x { }^{2} + 3x + 2x + 2[/tex]
Which answers describe the shape below? Check all that apply.
A. Square
B. Trapezoid
C. Quadrilateral
D. Parallelogram
E. Rhombus
F. Rectangle
Answer:
The answers are C, D, and F
Step-by-step explanation:
the sum of a minutes and b seconds, expressed in minutes, is:
Answer:
(1+b/60) minutes
Step-by-step explanation:
A minute = 1minute
b seconds = b/60minutes =b/60 minutes
sum of a minute and b seconds= (1+ b/60) minutes
A survey stopped men and women at random to ask them where they purchased
groceries, at a local grocery store or online.
How many men surveyed shop at a local grocery store.
Tiles with numbers 1 through 9 are placed in a bag. What is the probability of choosing an even number that is greater than or equal to 4? 1/9, 2/9, 3/9 or 4/9
Answer:
3/9
Step-by-step explanation:
Okay, first let's list all the numbers between 1 and 9
1, 2, 3, 4, 5, 6, 7, 8, 9
Now let's list all of the even numbers from the previous list
2, 4, 6, 8
Now let's list all of the numbers from the previous list that are equal to, or greater than, 4
4, 6, 8
That's only three potential numbers, out of a total of nine numbers
So it's a 3/9 chance
A map shows a scale of 5cm = 40 miles. The distance from Los Angeles,
CA to San Francisco, CA is 400 miles. How far apart will the two cities be
on the map?
OA) 0.5 cm
OB) 5 cm
O C) 50 cm
OD 500 cm
Answer:
C
Step-by-step explanation:
It's 50 cm for sure
Answer:
C
Step-by-step explanation:
It's 50 cm for sure
What is the domain of function f?
Answer:
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set.
Answer:
B. -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞
Step-by-step explanation:
The domain of a graph is all the x-values it covers. Since this graph does not have any arrows at its end or beginning points, we can assume it goes on forever. Lines that go on forever always have an infinite domain.
What is the surface area? 5 cm 7 cm 4 cm square centimeters
Answer: 166 feet^2
Step-by-step explanation:
The equation for surface area is 2(wl+hl+hw). So that would be:
Surface Area = 2×(5×7 + 5×4 + 7×4) = 166 feet^2
Answer:16 square cm
Step-by-step explanation: Surface area = base, height (Side 1 + Side 2+ Side 3) H = Side 1 = 5 cm
Side 2 = 7cm
Side 3 = 4cm (add all these numbers ) = 16 Square cm
what is the surface area of the a cylinder with base radius 3 and height 8.
Bonjour,
πr² *h
3,14 * 3² *8
= 3,14 *9 *8
=>226, 08 ....²
Answer:
66π square units
Step-by-step explanation:
The density of apple juice is 1. 04 grams per cm^3
Answer:
1,040kg/m³
Step-by-step explanation:
1g/cm³ =1,000kg/m³
1.04g/cm³=?
= 1.04×1000
Density =1,040kg/m³
Show that among all rectangles with area a the square has the minimum perimeter
Answer:
Step-by-step explanation:
Find the measure of the arc or angle indicated
Answer:
D) 130
Step-by-step explanation:
So there are three arc sections in this problem,
The first one is given: 158
To find the arc between S and R, you can use the angle of point T and double it.
So:
36 * 2 = 72
The second arc is 72
Now for the one that they want you to find, you have to add the two arcs that you have and substract it from 360, which is the angle of a whole circle
Like so:
360 - (158 + 72) = 130
Answer:
130
Step-by-step explanation:
James has 3 blue candies and 3 green candies. 3 people come in and take 2 candies. What is the probability that they do not take 2 candies of the same color?
~ pls solve, i'm really confused
Answer:
33.3333333333
Step-by-step explanation:
we see that there are 6 candies in total
we also see that there is a 50% chance that someone will take out 3 candies of the same color,
50/3 = 16.66666666666667
so the chance of getting 2 marbles of the same color is 16.66666666666667 + 16.66666666666667 which is 33.3333333333
I hope I could help
At noon, the temperature outside was 25 degrees. By 8:00pm, the temperature had dropped 27 degrees. What was the temperature outside at 8:00pm, in degrees?
Answer:
-2
Step-by-step explanation:
25°-27°= -2°
At noon, the temperature outside was 25 degrees. By 8:00pm, the temperature had dropped 27 degrees. What was the temperature outside at 8:00pm, in degrees?
= 25 - 27
= - 2°
6 h −1=−3
what is the answer
Answer:
h=[tex]-\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]6h-1=-3\\6h=-2\\h=-\frac{2}{6} \\h=-\frac{1}{3}[/tex]
Answer:
[tex]\boxed{\sf{h=-\dfrac{1}{3}=-0.33 }}[/tex]Step-by-step explanation:
Isolate by the h from one side of the equation.
6h-1=-3
First, add by 1 from both sides.
[tex]\sf{6h-1+1=-3+1}[/tex]
Solve.
-3+1=-2
Rewrite the problem down.
6h=-2
Then, you divide by 6 from both sides.
[tex]\sf{\dfrac{6h}{6}=\dfrac{-2}{6} }[/tex]
Solve.
-2/2=-1
6/2=3
Rewrite as a fraction.
[tex]\boxed{\sf{h=-\dfrac{1}{3}=0.33}}[/tex]
Therefore, the correct answer is h=-1/3=0.33.I hope this helps you! Let me know if my answer is wrong or not.