Answer:
B. s = 0.85r
Step-by-step explanation:
The sale price is 15% off the regular price. In equation form, that is ...
s = r - 15%×r
s = r(1 - 0.15) = 0.85r
The equation that can be used to calculate the sale price is s = 0.85r.
If you have 14 1/2 dozen boxes of envelopes, and you order 3 1/4 dozen more, how many dozen boxes will you have in all?
The answere is 213 boxes
If you add 3 dozens to 14 dozens of boxes of envilopes , then you get 17 dozens of boxes of envilopes.Then of you sum up the 1/2 (2/4 ) with the 1/4.You get 3/4. Finally, you add 17 dozens to 3/4 of a dozen you get 17 3/4 dozens( wich is 213 boxes )
a cylindrical barrel has a height of 8 feet and a diameter of 6 feet. what is the volume of the barrel?
Answer: The volume is about 226 feet squared
Step-by-step explanation:
Find the volume of a cylinder with a diameter of 19km and height of 5 km. Label your answer
Answer:
1,417.64 km³
Step-by-step explanation:
The formula for the volume of a cylinder in terms of its diameter is ...
V = (π/4)d²·h
Fill in the given numbers and do the arithmetic.
V = π/4×(19 km)²×(5 km) ≈ 1,417.64 km³
The volume of a cylinder is found using the formula V = πR²h. To find the radius, we divide the diameter by 2, giving us 9.5 km. The volume is therefore approximately 1413.716 km³.
Explanation:To find the volume of a cylinder, we use the formula: V = πR²h. In this case, we are given the diameter and height of the cylinder. The diameter is double the radius, so to find the radius, we divide the diameter (19km) by 2, which gives us 9.5km. Substitute the radius and height into the formula, we get: V = π * (9.5 km)² * 5 km.
Now, we can calculate it. π is approximately 3.14159, (9.5 km)² equals 90.25 km², and multiply it all together with the height (5 km), we get approximately 1413.716 km³.
This is the volume of the cylinder.
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Use this formula to find the value of a house with appreciation: A = V (1+r)Y
When Henry bought his house for $135,700, he was told that it would appreciate at a rate of five percent per year. If this remains true, how much will his house be worth in four years?
Answer:
[tex]A=\$164,944.20[/tex]
Step-by-step explanation:
we know that
[tex]A=V(1+r)^{Y}[/tex]
In this problem we have
[tex]r=5\%=0.05[/tex]
[tex]V=\$135,700[/tex]
[tex]Y=4\ years[/tex]
substitute in the formula and solve for A
[tex]A=\$135,700(1+0.05)^{4}=\$164,944.20[/tex]
Geometry Worksheet 11.1-11.2 Angles and Arcs in a Circle Name______________________________________ What is the difference between a minor arc and a major arc?____________________________________________________ How many letters do we use to name a MINOR arc?_______________ How many letters to name a MAJOR arc? __________________ How many degrees are in a semi-circle? ____________ How many letters to name a SEMI CIRCLE ? __________________ NAME the arc shown in bold, then state if it is a MINOR arc, MAJOR arc, or a SEMICIRCLE. 1. 2. 3. Name of arc: ________ Type of arc: _________ Name of arc: ________ Type of arc: _________ Name of arc: ________ Type of arc: _________ Determine whether the given arc is a MINOR arc, MAJOR arc, or SEMICIRCLE. 4. ______________ 5. ______________ 6. ______________ 7. ______________ 8. ______________ 9. ______________ 10. ______________ 11. ______________ Name the following for the circle at the right. 12. Two DIFFERENT minor arcs. __________ and ___________ 13. Two DIFFERENT major arcs. __________ and ___________ 14. Two DIFFERENT semi-circles.__________ and ___________ 15. There are ____________ degrees in a circle. 16. There are ____________ degrees in a semi-circle. 17. The measure of the arc is ____________________________ to the measure of the central angle. Find the measure of each arc. 18. m = _______ 19. m = ________ 20. m = ________ m = __________ m = ______ m = ______ 21. m = _______ 22. m = ________ 23. m = ________
Answer:
In the figures attached, the complete question is shown.
What is the difference between a minor arc and a major arc?
the measure of a minor arc is less than 180°
the measure of a major arc is greater than 180°
How many letters do we use to name a MINOR arc? 2
How many letters do we use to name a MAJOR arc? 3
How many degrees are in a semi-circle? 180°
How many letters to name a SEMI CIRCLE? 3
1. Name of arc: AB Type of arc: minor
2. Name of arc: ADB Type of arc: major
3. Name of arc: PSQ Type of arc: semi-circle
4. AE: minor
5. AEB: semi-circle
6. FDE: semi-circle
7. DFB: major
8. FA: minor
9. BE: minor
10. BDA: semi-circle
11. FBD: major
12. PQ and ST
13. QPT and PUS
14. PUT and QPU
15. There are 360° degrees in a circle.
16. There are 180° degrees in a semi-circle.
17. The measure of the arc is equal to the measure of the central angle.
18. mPQ: 50°, mPXQ: 310°
19. mPQ: 90° , mPRQ: 270°
20. mPQ: 150° , mPXQ: 210°
21. mQS: 45°, mQRS: 315°
22. mGH: 30°, mGFH: 330°
23. mAB: 75°, mADB: 285°
Solve for x.
1/10(x - 3) = -40
A) -403
B) -397
C) -7
D) -1
Answer:
-397Step-by-step explanation:
This may look daunting, but let us approach it step by step.
Step 1: Remove the Parenthesesmultiply 1/10 by x - 3
0.1x - 0.3 = -40
Step 2: Add 0.3In algebra, the goal is always to undo all the operations and get back to the original problem so that the mystery value can be determined. In this case since 0.3 was removed, we must add it back.
0.1x = -39.7
Step 3. Divide by 0.10.1x/0.1 = x
39.7/0.1 = -397
Step 4. Preliminary AnswerAnswer seems to be B. -397, but we should still check it.
Step 5: Check0.1(-397) - 0.3 = -40
-39.7 - 0.3 = -40
-40 = -40 Correct
If the answer was incorrect, this would show that there had been a flaw in our calculations. But everything checks out, so we are done!
Step 6: Final AnswerOur final answer is B. -397.
PLEASE MARK BRAINLIEST
Answer:
The answer is -397
Step-by-step explanation:
4.) What is the exact value of sinθ when θ lies in Quadrant II and cosθ=−513
Fill in the blanks.
___/___
10.) Suppose that a laser light, positioned 100 ft from the base of a flag pole, illuminates a flag that is 85 ft above the ground.
What is the angle of inclination (angle of elevation) of the light beam?
Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.
11.)
Suppose that a man standing at the edge of a cliff near the North Rim of the Grand Canyon is looking downward towards a campground inside the canyon. The elevation of the North Rim is 5389 ft and the elevation of the campground is 2405 ft. The man's range finder indicates that his line of sight distance to the campground is 3044 ft.
What is the angle of depression of the man's line of sight to the campground?
Express your answer in degrees rounded to the nearest hundredth.
Enter your answer in the box.
12.) What is the exact value of arcsin(0.5)?
Determine the value in degrees.
13.) Determine the exact value in degrees:
What is the exact value of arcsin−2√2
Answer:
Part 4) [tex]sin(\theta)=\frac{12}{13}[/tex]
Part 10) The angle of elevation is [tex]40.36\°[/tex]
Part 11) The angle of depression is [tex]78.61\°[/tex]
Part 12) [tex]arcsin(0.5)=30\°[/tex] or [tex]arcsin(0.5)=150\°[/tex]
Part 13) [tex]-45\°[/tex] or [tex]225\°[/tex]
Step-by-step explanation:
Part 4) we have that
[tex]cos(\theta)=-\frac{5}{13}[/tex]
The angle theta lies in Quadrant II
so
The sine of angle theta is positive
Remember that
[tex]sin^{2}(\theta)+ cos^{2}(\theta)=1[/tex]
substitute the given value
[tex]sin^{2}(\theta)+(-\frac{5}{13})^{2}=1[/tex]
[tex]sin^{2}(\theta)+(\frac{25}{169})=1[/tex]
[tex]sin^{2}(\theta)=1-(\frac{25}{169})[/tex]
[tex]sin^{2}(\theta)=(\frac{144}{169})[/tex]
[tex]sin(\theta)=\frac{12}{13}[/tex]
Part 10)
Let
[tex]\theta[/tex] ----> angle of elevation
we know that
[tex]tan(\theta)=\frac{85}{100}[/tex] ----> opposite side angle theta divided by adjacent side angle theta
[tex]\theta=arctan(\frac{85}{100})=40.36\°[/tex]
Part 11)
Let
[tex]\theta[/tex] ----> angle of depression
we know that
[tex]sin(\theta)=\frac{5,389-2,405}{3,044}[/tex] ----> opposite side angle theta divided by hypotenuse
[tex]sin(\theta)=\frac{2,984}{3,044}[/tex]
[tex]\theta=arcsin(\frac{2,984}{3,044})=78.61\°[/tex]
Part 12) What is the exact value of arcsin(0.5)?
Remember that
[tex]sin(30\°)=0.5[/tex]
therefore
[tex]arcsin(0.5)[/tex] -----> has two solutions
[tex]arcsin(0.5)=30\°[/tex] ----> I Quadrant
or
[tex]arcsin(0.5)=180\°-30\°=150\°[/tex] ----> II Quadrant
Part 13) What is the exact value of [tex]arcsin(-\frac{\sqrt{2}}{2})[/tex]
The sine is negative
so
The angle lies in Quadrant III or Quadrant IV
Remember that
[tex]sin(45\°)=\frac{\sqrt{2}}{2}[/tex]
therefore
[tex]arcsin(-\frac{\sqrt{2}}{2})[/tex] ----> has two solutions
[tex]arcsin(-\frac{\sqrt{2}}{2})=-45\°[/tex] ----> IV Quadrant
or
[tex]arcsin(-\frac{\sqrt{2}}{2})=180\°+45\°=225\°[/tex] ----> III Quadrant
Which members are in the sample
Answer:
20, 26, 35, 18
Step-by-step explanation:
So starting at row 129, we look at the sequence two-digits at a time without overlapping. If that number is between 01 and 43, then they get selected.
The first two digits are 20. That fits between 01 and 43, so that member gets selected.
Next, we have 26. That also fits.
After that we have 64. Nope, too high.
98 and 44 are also too high.
35 fits though. So does 18.
So the members that get selected are 20, 26, 35, 18.
(10.02)
The point (−3, 1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
Answer:
Part 1) [tex]sin(\theta)=\frac{\sqrt{10}}{10}[/tex]
Part 2) [tex]cos(\theta)=-3\frac{\sqrt{10}}{10}[/tex]
Part 3) [tex]tan(\theta)=-1/3[/tex]
Step-by-step explanation:
we know that
The angle is in the second quadrant so the sine is positive, the cosine is negative and the tangent is negative
step 1
Find the radius r applying the Pythagoras theorem
[tex]r^{2}=x^{2} +y^{2}[/tex]
substitute the given values
[tex]r^{2}=(-3)^{2} +(1)^{2}[/tex]
[tex]r^{2}=10[/tex]
[tex]r=\sqrt{10}\ units[/tex]
step 2
Find the value of [tex]sin(\theta)[/tex]
[tex]sin(\theta)=y/r[/tex]
substitute values
[tex]sin(\theta)=1/\sqrt{10}[/tex]
Simplify
[tex]sin(\theta)=\frac{\sqrt{10}}{10}[/tex]
step 3
Find the value of [tex]cos(\theta)[/tex]
[tex]cos(\theta)=x/r[/tex]
substitute values
[tex]cos(\theta)=-3/\sqrt{10}[/tex]
Simplify
[tex]cos(\theta)=-3\frac{\sqrt{10}}{10}[/tex]
step 4
Find the value of [tex]tan(\theta)[/tex]
[tex]tan(\theta)=y/x[/tex]
substitute values
[tex]tan(\theta)=-1/3[/tex]
Please please help me
Answer:
x = 8.3
Step-by-step explanation:
Given a tangent and 2 secants drawn to the circle from an external point then
The square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant.
Using the secant with measure 4 + x, then
4(4 +x) = 7²
16 + 4x = 49 ( subtract 16 from both sides )
4x = 33 ( divide both sides by 4 )
x = 33 ÷ 4 = 8.25 ≈ 8.3 ( nearest tenth )
if UVWX is a parallelogram, what is the value of y?
Answer:
B. 60
Step-by-step explanation:
The opposite sides of a parallelogram are parallel and congruent.
This implies that:
|UV|=|XW|
From the diagram; |UV|=15
and [tex]|XW|=\frac{1}{4}y[/tex]
We equate the two side lengths to get:
[tex]15=\frac{1}{4}y[/tex]
We multiply both sides by 4 to obtain:
[tex]4\times 15=4\times \frac{1}{4}y[/tex]
This implies that:
y=60
Answer:
B!
Step-by-step explanation:
Anyone mind helping me out?:)
The answer is does matter.
Please please help me out
Answer:
The measure of angle y is [tex]m\angle y=54\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle is half that of the arc it comprises.
[tex]m\angle y=\frac{1}{2}(108\°)=54\°[/tex]
Please help me with this :)
Answer:
x = 74°
Step-by-step explanation:
The angle whose vertex lies on the circle, that is angle x is one- half the measure of it's intercepted arc, that is
x = 0.5 × 148° = 74°
simplify this expression
5*sqrt(x^22) where x<0
Answer:
[tex]\boxed{5x^{11}, x < 0}[/tex]
Step-by-step explanation:
[tex]5\sqrt{x^{22}}[/tex]
Remember that we evaluate the term under the radical first.
Even though x < 0, x²² > 0
So,
[tex] 5\sqrt{x^{22}} = 5x^{11}[/tex]
The simplified expression is
[tex]\boxed{5x^{11}, x < 0}[/tex]
at certain time of day , a 30 meter high building cast a shadow that is 31 meters long . what is the angle of the elevation of the sun? round to the nearest degree.
A. 46 degree
B. 16 degree
C.44 degree
D.75 degree
Answer:
Option C. 44 degree
Step-by-step explanation:
Let
A-----> the angle of the elevation of the sun
we know that
The tangent of angle A is equal to divide the opposite side angle A by the adjacent side angle A
In this problem
The opposite side is 30 meters
The adjacent side is 31 meters
[tex]tan(A)=\frac{30}{31}[/tex]
[tex]A=arctan(\frac{30}{31})=44\°[/tex]
Can someone find x (the height) for me please!!
Answer:
x = √5
Step-by-step explanation:
The Pythagorean theorem tells you the square of the diagonal is the sum of the squares of the two sides:
(√7)² = (√2)² + x²
7 = 2 + x² . . . . . . simplify
5 = x² . . . . . . . . . subtract 2
√5 = x . . . . . . . . . take the square root
Is the relationship shown by the data linear? If so, model the data with an equation. x y 1 5 5 10 9 15 13 20 The relationship is linear; y – 5 = (x – 1). The relationship is not linear. The relationship is linear; y – 5 = (x – 1).
Answer:
The relationship is linear; y – 5 = 5/4*(x – 1)
Step-by-step explanation:
We have been given the following data set;
x: 1, 5, 9, 13
y: 5, 10, 15, 20
The values of x increase by 4 while those of y increase by 5. This would imply that the average rate of change between any pair of points is a constant and thus the relationship exhibited by the data is linear.
The average rate of change is equivalent to the slope;
(change in y) / (change in x)
Using the first two pair of points we have;
(10-5) / ( 5-1) = 5/4
The point-slope form of equation of the line is thus;
y - 5 = 5/4 (x - 1)
Find the zeros of the function. Write the smaller solution first, and the larger solution second. G(x)=4x^2-484
Answer:
-11, 11
Step-by-step explanation:
You have to find when the function crosses the x-axis. You could find this using algebra by solving for x in the equation but I prefer to simply graph it using something like desmos and see when it crosses the x-axis. Doing that I can see the answers would be -11 and 11
Answer:
x = -11,11
Step-by-step explanation:
G(x)=4x^2-484
To find the zero's, set the function equal to zero
0 = 4x^2 - 484
Add 484 to each side
484 = 4x^2 -484+484
484 = 4x^2
Divide each side by 4
484/4 = 4x^2/4
121 = x^2
Take the square root of each side
sqrt(121) = sqrt(x^2)
±11 =x
x = -11,11
Ms. Ling and Mr Marshal have the same ratio of boys to girls in their classes. Ms. Ling has 6 boys and 14 girls. Mr. Marshal has 21 girls in his class. How many boys are in Mr. Marshals class?
Answer:
There are 13 boys in Mr. Marshals class
Step-by-step explanation:
Hello there! Mr. Marshal has 9 boys.
To find the number of boys Mr. Marshal has, start by finding the ratio. If there are 6 boys and 14 girls, the boys to girls ratio is 6:14. Simplified, the ratio is 3:7. So, if there are 21 girls, you want to find how many boys there are. To find this, find what you need to multiply 7 by to get 21 by and multiply 3 by that number.
21/7 = 3.
So, now we multiply 3 by 3 to get the number of boys.
3 x 3 = 9.
This means there are 9 boys, with a ratio of 9:21. If we simplify this, we get 3:7, making this answer correct.
I hope this helps and have a great day!
What should the balance be in Diane's register?
Will give BRAINLIEST
Answer:
The balance of Dianne's register should be $359.41
Step-by-step explanation:
We can begin at the ending balance on the bank statement at $578.30
Then a check is written for $219.25, so a debit
Next a deposit is made for $140.36, so a credit
Then a withdrawal is made for $140.00, so a debit
This means we can make the equation
[tex]578.30-219.25+140.36-140.00=359.41[/tex]
Please use the information below to complete this assignment.
y = 4
(1) What is the slope of this line?
(2) What is the x-intercept?
(3) What is the y-intercept?
Answer:
y = 4
That's a straight line.
The slope is 0.
There is no x-intercept.
The y-intercept is 4.
I'm only a few Brainliests away from ranking up, so one would be much appreciated. Thank you, and good luck!
Answer:
the slope is 0
the x intercept is 0
the y intercept is 4
HELP PLEASE!!
Question 1 (2 points)
Generalize the pattern by finding the nth term.
6, 10, 14, 18, 22,
A. 4n
B. 4n + 2
C. 4n + 10
D. 6n + 4
Answer:
B. 4n+2
Step-by-step explanation:
You are given the pattern 6, 10, 14, 18, 22
Rewrite it as
[tex]a_1=6\\ \\a_2=10\\ \\a_3=14\\ \\a_4=18\\ \\a_5=22[/tex]
Note that
[tex]a_2-a_1=a_3-a_2=a_4-a_3=a_5-a_4=4[/tex]
This means that given pattern is a part of arithmetic sequence with
[tex]a_1=6\\ \\d=4[/tex]
So, the nth term of this arithmetic sequence is
[tex]a_n=a_1+(n-1)d\\ \\a_n=6+4(n-1)\\ \\a_n=6+4n-4\\ \\a_n=4n+2[/tex]
Hotdogs and corndogs were sold at last night’s football game. Use the information below to write equations to help you determine how many corndogs were sold.
The number of hotdogs sold was three fewer than twice the number of corndogs sold. Write an equation relating the number of hotdogs and corndogs. Let h represent the number of hotdogs and c represent the number of corndogs. A hotdog costs $3 and a corndog costs $1.50. If $201 was collected, write an equation to represent this information. How many corndogs were sold? Show how you calculated your answer.
Answer:
28
Step-by-step explanation:
If we set up our equation using the unknown number of hot dogs and corn dogs with their individual prices attached to them, we can set the sum of them equal to $201. We know that a hot dog costs $3, so we can represent hot dogs monetarily by attaching the cost of a single hot dog to the h. For example, if a hot dog costs $3, and we represent the expression as 3h, with h being the number of hot dogs sold, if we sell 4 hot dogs at $3 apiece, we make $12. If we sell 6 hot dogs we will make $18. The same goes for the corn dogs. We don't know how many corn dogs or hot dogs we sold, but we do know that the sales of both made $201. So our expression for that is
3h + 1.50c = 201
That's great, but we have too many unknowns, and that's a problem. So let's look back up to where we are told that the number of hot dogs is 3 less than 2 times the number of corn dogs. "3 less than" is -3 algebraically. "Twice the number" is 2times and the words "is" and "was" represent the = sign. So putting those words into an algebraic equation looks like this:
h = 2c - 3
That says "the number of hot dogs was twice the number of corn dogs less 3". Now that we have an expression for hot dogs we can sub it into our money equation in place of h:
3h + 1.5c = 201 becomes 3(2c - 3) + 1.5c = 201
Now we have an equation with only c's in it.
Distribute through the parenthesis to get
6c - 9 + 1.5c = 201
Simplify to 7.5c = 210
Now divide by 7.5 to get that c = 28.
Now that we know that, we go back with that number and sub it in for c in
h = 2c - 3 --> h = 2(28) - 3 gives us that the number of hot dogs sold was 53
The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53
let
h = number of hotdogs
c = number of corndogs.
cost of hotdog = $3
corn dog = $1.50
The equation:
3h + 1.50c = 201 (1)
h = 2c - 3 (2)
substitute (2) into (1)
3(2c - 3) + 1.50c = 201
6c - 9 + 1.50c = 201
7.50c - 9 = 201
7.50c = 201 + 9
7.50c = 210
c = 210/7.50
c = 28
Therefore,
h = 2c - 3
= 2(28) - 3
= 56 - 3
= 53
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Please help me out please
What we have here is called INTERSECTING CHORDS IN A CIRCLE.
The equation is:
10 times x = 7 times 7
10x = 49
x = 49/10
x = 4.9
answer 4.9cm
10times x=7times7(multiple it)
10x=49
x=49/10
x=4.9
Assume that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year. Find when the sale of cars will be more then the sale of motorcycles.
Answer:
Final answer is approx 6.644 years.
Step-by-step explanation:
Given that a company sold 5.75 million motorcycles and 3.5 million cars in the year 2010. The growth in the sale of motorcycles is 16% every year and that of cars is 25% every year.
So we can use growth formula:
[tex]A=P\left(1+r\right)^t[/tex]
Then we get equation for motorcycles and cars as:
[tex]A=5.75\left(1+0.16\right)^t[/tex]
[tex]A=3.5\left(1+0.25\right)^t[/tex]
Now we need to find about when the sale of cars will be more than the sale of motorcycles. So we get:
[tex]3.5\left(1+0.25\right)^t>5.75\left(1+0.16\right)^t[/tex]
[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]
[tex]3.5\left(1.25\right)^t>5.75\left(1.16\right)^t[/tex]
[tex]\frac{\left(1.25\right)^t}{\left(1.16\right)^t}>\frac{5.75}{3.5}[/tex]
[tex]\left(\frac{1.25}{1.16}\right)^t>1.64285714286[/tex]
[tex]t\cdot\ln\left(\frac{1.25}{1.16}\right)>\ln\left(1.64285714286\right)[/tex]
[tex]t>\frac{\ln\left(1.64285714286\right)}{\ln\left(\frac{1.25}{1.16}\right)}[/tex]
[tex]t>6.6436473051[/tex]
Hence final answer is approx 6.644 years.
Final answer:
To determine when car sales will surpass motorcycle sales given their growth rates, we use exponential growth formulas for both, set them equal to find the crossover point, and solve for the time required.
Explanation:
To find when the sale of cars will be more than the sale of motorcycles given their respective annual growth rates, we'll use the concept of exponential growth.
The initial sale of motorcycles is 5.75 million with an annual growth rate of 16%, and the initial sale of cars is 3.5 million with an annual growth rate of 25%. We will set up an equation where the sales of cars equals the sales of motorcycles and solve for the number of years it takes for this to occur.
The formula for exponential growth is:
Final Amount = Initial Amount × (1 + Growth Rate) ^ Years
For motorcycles, the formula becomes:
M = 5.75 × (1 + 0.16)^t
For cars, the formula becomes:
C = 3.5 × (1 + 0.25)^t
We want to find when C > M, so we set the formulas equal to each other and solve for t:
5.75 × (1 + 0.16)^t = 3.5 × (1 + 0.25)^t
After finding a common base and applying logarithms, we can solve for t, the number of years until the sale of cars surpasses that of motorcycles.
[Trigonometric Graphs]
Use the following information to write an equation of the graph described:
10. sin; Amp = 4, per = 2π/3; phase shift = right π/4; vertical shift = up 3; reflect over x-axis.
12. cos; Amp = 2, period of 10π/3, reflect over x-axis.
Explain.
Answer:
Here's what I get.
Step-by-step explanation:
Question 10
The general equation for a sine function is
y = a sin[b(x - h)] + k
Here's what the parameters control:
a = amplitude
k = vertical shift
b = the period (period = 2π/b; If period = 2π/3, b = 3)
h = horizontal shift
Reflect across y-axis (x ⟶ -x)
Your sine function will be:
[tex]\begin{array}{rllll}y = & a \text{ sin}[ & b(x- & h)] + & k)\\& \downarrow & \downarrow & \downarrow & \downarrow\\& 4 & 3 & \frac{\pi}{4} & 3\\\end{array}[/tex]
Here are the effects of each parameter.
(a) Amp = 4
Increases the amplitude by a factor of 4 (Fig. 1)
(b) Up 3
k = 3. The graph shifts up three units (Fig. 2).
(c) Period = 2π/3
Set k = 3. The period changes from 2π to 2π/3 (Fig. 3).
Notice that you now hav3 three waves between 0 and 2π, where originally you had one.
(d) Right π/4.
Set h = 4. The graph shifts right by π/4.
notice how the trough at ½π shifts to ¾π.
(e) Reflect about y-axis
Set x equal to -x. Notice how the trough at (¾π, -1) is transformed to the trough at (-¾π, -1) (Fig. 5).
Question 12
y = a cos[b(x - h)] + k
a = 2
Per = 10π/3 ⟶ b = 3/5
h = 0
k = 0
Reflect over x-axis: y ⟶ -y
(a) a = 2
The amplitude is doubled.
(b) Per = 10π/3 ⟶ b = 3/5
The period (peak-to-peak distance) lengthens to 10π/3.
(c) Reflect about x-axis (y ⟶ -y)
All peaks are transformed into troughs and vice-versa.
If the radius is 10 inches , in square inches, what is the circumference of the circle?
A. 15.7
B. 31.4
C. 47.1
D. 62.8
[tex]C=2\pi r =2\pi10=20\pi\approx\boxed{62.8}[/tex]
The answer is D.
The circumference of a circle with a radius of 10 inches is approximately 62.8 inches, calculated using the formula C = 2πr, resulting in the answer choice D. 62.8.
To calculate the circumference of a circle when the radius is given, we use the formula C = 2πr. Given that the radius (r) of the circle is 10 inches, we can calculate the diameter (d) as 2×10 inches, which equals 20 inches. Now, we multiply the diameter by π (approximately 3.1416) to find the circumference:
C = πd = 3.1416 × 20 inches = 62.832 inches.
Based on standard rounding rules, this is approximately 62.8 inches. Thus, the correct answer is D. 62.8 square inches.
If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?
Answer:
3x^2+2x-1
Step-by-step explanation:
Start by plugging in the 2 equations into their assigned places then simplify.
Answer:14
Step-by-step explanation:( 3X2+1)-(1-X)
=3X2+1 -1+X
=3X2+X
ANY WHERE WE SEE X WE PLACE 2
=3(2)(2)+2
3*4+2
=12+2
14
Can someone help me¿
Answer:
Step-by-step explanation:
number3