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A ferris wheel is 30 meters in diameter and boarded from a platform that is 5 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).
Answers
Answer:
h = f(t) = -15cos((π/5)t) +20
Step-by-step explanation:
If you like, you can make a little table of positions:
(t, h) = (0, 5), (5, 35)
Since the wheel is at an extreme position at t=0, a cosine function is an appropriate model:
h = Acos(kt) +C
The amplitude A of the function is half the difference between the t=0 value and the t=5 value:
A = (1/2)(5 -35) = -15
The midline value C is the average of the maximum and minimum:
C = (1/2)(5 + 35) = 20
The factor k satisfies the relation ...
k = 2π/period = 2π/10 = π/5
So, the function can be written as ...
h = f(t) = -15cos((π/5)t) +20
The equation of the function of the height in meters above the ground t minutes after the wheel begins to turn, is presented as follows;
[tex]\mathbf{h = f(t) = 15 \cdot sin\left[ \left(\dfrac{\pi}{5} \right) \cdot (t - 2.5)\right] + 20}[/tex]
The process for finding the above function is as follows;
The given parameters of the Ferris wheel are;
The diameter of the Ferris wheel, D = 30 meters
The height of the Ferris wheel above the ground, d = 5 meters
The level of loading the platform = The six o'clock position
The time it takes the wheel to make one full revolution, T = 10 minutes
The required parameter;
The function which gives the height, h, of the Ferris wheel = f(t)
Method;
The equation that can be used to model the height of the Ferris wheel is the sine function which is presented as follows;
y = A·sin[k·(t - b)] + c
Where;
A = The amplitude = (highest point - Lowest point)/2
∴ A = (35 - 5)/2 = 15
The period, T = 2·π/k
∴ 10 minutes = 2·π/k
k = 2·π/10 = π/5
k = π/5
At the starting point, the Ferris wheel is at the lowest point, and t = 0, we have;
The sine function is at the lowest point when k·(t - b) = -π/2
Therefore, we get;
π/5·(0 - b) = -π/2
-b = -π/2 × (5/π) = -5/2 = -2.5
b = 2.5
The vertical shift, c = (Max - Min)/2 + Min = (Max + Min)/2
∴ c = (35 + 5)/2 = 20
c = 20
The equation of the Ferris wheel of the form, y = A·sin[k·(t - b)] + c, is therefore;
[tex]\mathbf{h = f(t) = 15 \cdot sin\left[ \left(\dfrac{\pi}{5} \right) \cdot (t - 2.5)\right] + 20}[/tex]
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Related Questions
Evaluate 14 - 2xy when x = -6 and y = 2.
Answers
Answer: 38
Step-by-step explanation:
14 - 2xy
(substitute x and y)
14 - 2 (-6) (2)
14 + 24
38
Answer:
its 38
Step-by-step explanation:
Do xy first and you get -24 and 14-(-28) would be a double negative so you add them together.
Let × represent th he number of television show episodes that are taped in a season. Write an expression for the number of episodes taped in 4 seasons.
Answers
Answer:
y=4x
Step-by-step explanation:
Given : x represent the number of television show episodes that are taped in each seasons
To Find : write an expression for the number of episodes taped in 4 seasons
Solution:
Let number of episodes taped in 4 seasons be y
Number of the episodes taped in 1 season = x
So, number of episodes taped in 4 seasons :
y= 4x
Hence the required expression for the numder of episodes taped in 4 seasons :y= 4x
In January 2011 the rate of a VAT increased from 17.5% to 20% Work out the difference in price of a car worth £15000 + VAT due to the increase of VAT
Answers
Answer:
£375
Step-by-step explanation:
The tax changed from 17.5% of the car's price to 20% of the car's price, an increase of 2.5% of the car's price.
The increased tax amount is ...
0.025 × £15000 = £375
The price of the car went up by £375 due to the increase in VAT.
A customer wants rhombus-shaped tiles for his countertops. The height is 3 inches and the length of each side is 6.5 inches. What is the area of each tile?
Answers
Answer:
Area of each tile = 19.5 inches^2
Step-by-step explanation:
Rhombus:-
A rhombus is a type of quadrilateral whose opposite sides are parallel and equal.Also, the opposite angles of a rhombus are equal and the diagonal intersect each other perpendicularly.
To find the area of a rhombus when the measures of its height and side length are given, use the formula
A = Base X height
Area of a rhombus = 6.5 X 3
A = 19.5 inches^2
The area of each rhombus-shaped tile is 19.5 square inches for the given dimensions. Thus, each tile has an area of 19.5 square inches.
To find the area of a rhombus, you can use the formula
⇒ Area = base × height
In this case, the height is given as 3 inches and the length of each side is 6.5 inches, but the length of the sides is not needed, as we are working with the base and height directly.
So, the area can be calculated as follows:
Identify the base and height:⇒ Base = 6.5 inches
⇒ Height = 3 inches.
Use the formula for the area of a rhombus:⇒ Area = base × height.
Calculate:⇒ Area = 6.5 inches × 3 inches
= 19.5 square inches.
Therefore, the area of each rhombus-shaped tile is 19.5 square inches.
Determine whether the value given below is from a discrete or continuous data set.
In an election poll comma Derek received 17 comma 551 comma 093 votes.In an election poll, Derek received 17,551,093 votes.
A. A continuouscontinuous data set because there are infinitely many possible values and thosethere are infinitely many possible values and those values can be counted.values can be counted.
B. A discretediscrete data set because there are a finite number of possible values.there are a finite number of possible values. nothing
C. A continuouscontinuous data set because there are infinitely many possible values and those values cannot be counted.values cannot be counted.
D. The data set is neither continuous nor discrete.
Answers
Answer:
B
Step-by-step explanation:
The discrete type of data contains observations that can be counted and consists of finite set of data. In the given problem the votes received by Derek consists of finite set of value and votes received by Derek are countable.
Hence the votes received by Derek is discrete data set because there is finite number of values.
2/xy^2 Give the equivalent numerator if the denominator is x³y².
x²y
2x²
2x³y²
Need this Asap, the fastest correct answer will be marked Brainliest.
Answers
Answer:
2x^2.
Step-by-step explanation:
2x^2 / x^3y^2
= 2/xy^2
Answer:
I'm pretty sure if there's two answers you can mark them brainliest.
Step-by-step explanation:
Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. She bought seven total shirts. How many fancy and plain shirts did Kristin buy? Write two equations.
Answers
Answer:
2 fancy shirts and 5 plain shirts
Step-by-step explanation:
28x + 15x = 131
28(2) + 15(5) = 131
56 + 72 = 131
(there are no other equation i could find)
Identify the equations below that are true. You may wish to watch the video Powers of 10, Part 3 for a review of operations (adding, subtracting, multiplying, dividing) with powers of 10.a. (10^5)^3=10^5×3b. 10^5÷10^3=10^5−3c. 10^5×10^3=10^5+3d. 10^5/10^3=10^5−3
Answers
The equations that are true according to the exponent rules for powers of 10 include: [tex]10^5 / 10^3 = 10^5-3, 10^5 * 10^3 = 10^5+3,[/tex] and [tex]10^5 / 10^3 = 10^5-3.[/tex]
Explanation:The subject in question deals with exponent rules for powers of 10. Here, we'll identify which equations are true based on these rules:
a. (10^5)^3 = 10^5×3. This is not correct. According to the power of a power rule, we should multiply the exponents, so the answer should be 10^15.
b. [tex]10^5 / 10^3 = 10^5-3.[/tex] This is correct. When dividing bases that are the same, we subtract the exponent of the denominator from the exponent of the numerator, hence 10^(5-3) = 10^2.
c. 10^5 × 10^3 = 10^5+3. This is correct. When multiplying bases that are the same, we add the exponents, hence 10^(5+3) = 10^8.
d. [tex]10^5 / 10^3 = 10^5-3[/tex]. This is correct, as explained in point b. The answer is 10^2.
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Final answer:
Equation c [tex](10^5*10^3 = 10^{(5+3)})[/tex] and equations b and d [tex](10^5/10^3 = 10^{(5-3)})[/tex] are correct. To multiply or divide numbers in scientific notation, multiply or divide the coefficients and add or subtract the exponents, respectively. This method can be used to calculate without converting to standard form.
Explanation:
The equations that are true out of the ones provided are as follows:
[tex](10^5)^3 = 10^{(5*3)}[/tex]or 10^15, so option a is not correct since it incorrectly states that [tex](10^5)^3 = 10^(5+3).[/tex][tex]10^5/10^3 = 10^{(5+3) }or 10^8[/tex], so option c is correct.[tex]10^5/10^3 = 10^{(5-3)} or 10^2[/tex], so options b and d, being the same, are both correct.To evaluate (4.506 × 10^4) × (1.003 × 10^2) without entering scientific notation into your calculator, first multiply the coefficients (4.506 × 1.003) and then add the exponents for the powers of 10 (10^4 × 10^2 = 10^(4+2) or 10^6). The result is 4.514518 × 10^6.To evaluate (8.552 × 10^6) ÷ (3.129 × 10^3) without entering scientific notation into your calculator, first divide the coefficients (8.552 ÷ 3.129) and then subtract the exponents for the powers of 10 (10^6 ÷ 10^3 = 10^(6-3) or 10^3). The result is approximately 2.73189 × 10^3.
The population of Bigville increased from 387,480 to 571,533 in the last 7 years. During the same time period, Smallville increased its population by 53.67%. Compare the towns to determine which is growing at the greatest rate and by what factor? (round to nearest hundredth)
Answers
Answer:
Smallville is growing at a greater rate
Step-by-step explanation:
use the formula for percentage increase to find what percentage the population of Bigville increased.
(Increase ÷ original number) * 100 = % of increase
increase = 571,533 - 387,480 = 184,053
(184,053 ÷ 387,480) * 100 = 47.5
Bigville percent of increase is 47.5%
Smallville percent of increase is 53.67%
since, smallville has a bigger percentage, it is growing at the greater rate
Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2 Monday Tuesday Wednesday Thursday
Answers
Answer:
Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2
(i) Monday
(ii) Tuesday
(iii) Wednesday
(iv) Thursday
Ans
(iv)Thursday
Step-by-step explanation:
Forecast for
Monday +4 Abs |+4| = 4
Tuesday –6 Abs |-6| = 6
Wednesday +7 Abs |+7| = 7
Thursday –2 Abs |-2| = 2
The most accurate is the day closest the temperature forecast is closest to observed temperature, which is
Thursday (-2)
Answer:
it is thursday
Step-by-step explanation:
hope it helps
Evaluate \dfrac jk -0.2k k j −0.2kstart fraction, j, divided by, k, end fraction, minus, 0, point, 2, k when j=25j=25j, equals, 25 and k=5k=5k, equals, 5.
Answers
Answer:
After evaluating the given expression we get the value as 4.
Step-by-step explanation:
Given:
[tex]\frac{j}{k}-0.2k[/tex]
We need to evaluate the expression when j =25 and k =5
Solution:
On substituting the values of k and j in the expression we get;
[tex]\frac{25}{5}-0.2\times5[/tex]
We will use PEDMAS which means first operation performed will be division.
So we can say that;
[tex]5-0.2\times5[/tex]
Now next Operation to be performed is multiplication.
So we can say that;
[tex]5-1[/tex]
Finally we will use subtraction operation and then we will get;
[tex]4[/tex]
Hence After evaluating the given expression we get the value as 4.
A baseball player got 52 hits one season. He got h of the hits in one game. What expression represents the number of hits he got in the rest of the games?
Answers
Answer:
The expression that represents the number of hits he got in the rest of the games is [tex]t=52-h[/tex].
Step-by-step explanation:
Given:
Number of hits in one season = 52 hits
Number of hits in one game = 'h'
We need to write expression that represents the number of hits he got in the rest of the games.
Solution:
Let the number of hits he got in the rest of the games be 't'.
Now we can say that;
The number of hits he got in the rest of the games is equal to Number of hits in one season minus Number of hits in one game.
framing in equation form we get;
[tex]t=52-h[/tex]
Hence expression that represents the number of hits he got in the rest of the games is [tex]t=52-h[/tex].
Answer:
52 - h
Step-by-step explanation:
Simplify: 52 - h
Which is the graph of 3x – 2y = 6? A coordinate plane with a line passing through (negative 2, 0) and (0, 3). A coordinate plane with a line passing through (0, negative 3) and (2, 0). A coordinate plane with a line passing through (0, negative 2) and (3, 0). A coordinate plane with a line passing through (negative 3, 0) and (0, 2).
Answers
Answer:
The answer to your question is A coordinate plane with a line passing through (0, -3) and (2,0)
Step-by-step explanation:
Line
3x - 2y = 6
Solve for y
-2y = -3x + 6
y = 3/2 x - 3
Find "y" when x = 0
y = 3/2(0) - 3
y = -3 Point (0, -3)
Find "x" when y = 0
0 = 3/2x - 3
3 = 3/2 x
x = 6/3
x = 2 Point (2, 0)
The graph of the equation 3x - 2y = 6 passes through the points (0, -3) and (2, 0). This conclusion is reached after rearranging the equation into the slope-intercept form and comparing the slope and the y-intercept with coordinates of the given lines.
Explanation:To find the correct graph for the equation 3x - 2y = 6, we first need to rearrange the equation in the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.
We rearrange our equation as follows: 3x - 6 = 2y. Simplifying, we get y = 1.5x - 3.
This equation tells us that the y-intercept (where the line crosses y-axis) is -3, and the slope is 1.5, in other words, for each step in positive x-direction, y increases by 1.5 steps.
Now looking at our coordinate plane options, the graph that fits this description is the one with a line passing through the points (0, -3) and (2, 0). Hence, this is the graph of the given equation.
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Here you guys go!
attached screenshot whoever is first gets brainliest!
Answers
PLEASE MARK BRAINLIEST!
Answer:
Honestly, if you think about it, the answer is right in front of you!
Step-by-step explanation:
The y- intercept is 3, and the x-intercept is 1. This means that the curve should have coordinate plots of (0,3) and (1,0).
The other information is not really needed if you know the x-and-y-intercepts!
There is only 1 curve that has the included intercepts, and that is the curve on option A)'s graph.
So your answer is option A)I hope this helps and wasn't too confusing!
- sincerelynini
2560 divided by 50 Thank you I gotta be an extra for me to get this stuff out to the shop I have so little money was my first place I gotta I love I'm glad I had my hair cut ♂️ this is my life so I'm happy I am a new day in a dream that you are truly amazing I wanna I loved you all my love I've got a good night
Answers
Answer:
51.2
Step-by-step explanation:
To divide 2560 by 50, you can use long division. The answer is 51.
Explanation:To divide 2560 by 50, you can use long division. Here's how:
Start by dividing 25 into 256. The quotient is 10.Multiply 10 by 50, which equals 500.Subtract 500 from 2560 to get 2060.Bring down the next digit, which is 0.Divide 25 into 206, which gives you a quotient of 8.Multiply 8 by 50, which equals 400.Subtract 400 from 206 to get 60.Bring down the next digit, which is 0.Divide 25 into 600 to get a quotient of 24.Multiply 24 by 50, which equals 1200.Subtract 1200 from 600 to get 0.Therefore, 2560 divided by 50 equals 51.
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A motorboat left a harbor and traveled to an island at an average rate of 10 knots. The average speed on the return trip was 10 knots. If the total trip took 4.0 hours, how far is the harbor from the island?
Answers
The distance between the harbor and the island is 20 nautical miles.
Explanation:To find the distance between the harbor and the island, we need to calculate the average speed of the motorboat for the entire trip. Since the average speed on the outbound trip was 10 knots and the average speed on the return trip was also 10 knots, we can conclude that the boat traveled at a constant speed throughout the trip. Let's assume the distance between the harbor and the island is 'd'.
Since speed = distance / time, we can calculate the time taken for each leg of the trip using the average speeds and the total time of 4.0 hours:
Time taken for the outbound trip = d / 10 knots
Time taken for the return trip = d / 10 knots
Since the total time is 4.0 hours, we can write the equation: d / 10 + d / 10 = 4.0
Simplifying the equation, we get: 2d / 10 = 4.0
Multiplying both sides by 10, we get: 2d = 40
Dividing both sides by 2, we get: d = 20
Therefore, the distance between the harbor and the island is 20 nautical miles.
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Consider the function f(x) = -2x + 5 what is f(5)
Answers
Answer:
[tex]\displaystyle -5 = f(5)[/tex]
Step-by-step explanation:
[tex]\displaystyle -2[5] + 5 = -10 + 5 = -5[/tex]
I am joyous to assist you anytime.
Answer: -5
Explanation: In this problem, we're given the function f(x) = -2x + 5 and we are asked to find f(5).
To find f(5) or the value of the function when x = 5, we simply substitute 5 in for x in our function.
So we have f(x) = -2(5) + 5 or -10 + 5 which equals -5.
So f(5) or the value of the function when x = 5 is -5.
Company A charges $70.50 and 18 cents per mile. Company B charges $30.50 and 11 cents per mile. How much more does company A charge for x miles than company B?
Answers
Answer:
Step-by-step explanation:
Let x represent the number of miles with either company A or company B.
Company A charges $70.50 and 18 cents per mile. Converting 18 cents to dollars, it becomes
18/100 = $0.18
Total cost of x miles with company A would be
0.18x + 70.50
Company B charges $30.50 and 11 cents per mile. Converting 11 cents to dollars, it becomes
11/100 = $0.11
Total cost of x miles with company B would be
0.11x + 30.50
For the amount that company A charges more than company B, it becomes
0.18x + 70.50 - 0.11x + 30.50
0.18x - 0.11x + 70.5 - 30.5
0.07x + 40
Company A charges 0.07x + 40 more than company B
What is the total cost of a $720 ipad that is on sale at 15% off if the local sales tax is 6%
Answers
Answer:
$828
Step-by-step explanation:
15% = 0.15
0.15 x 720 = 108
total cost = $720 + $108 = $828
Final answer:
To find the total cost of an iPad that is on sale at 15% off with a 6% sales tax, calculate the discount, subtract it from the original price, determine the sales tax, and add it to the discounted price.
Explanation:
To find the total cost of the iPad:
Calculate the discount: $720 * 15% = $108 discount
Subtract the discount from the original price: $720 - $108 = $612
Calculate the sales tax: $612 * 6% = $36.72
Add the sales tax to the discounted price: $612 + $36.72 = $648.72
The perimeter of a rectangle is 48 in the length of 6 in greater than the width Define a variable and write an equation to represent the situation solve the system by using substitution
Answers
Answer:
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
The perimeter of a rectangle is 48 in. It means that
48 = 2(L + W)
L + W = 48/2
L + W = 24 - - - - - - - - - 1
the length of the rectangle is 6 in greater than the width. It means that
L = W + 6
Substituting L = W + 6 into equation 1, it becomes
W + 6 + W = 24
2W + 6 = 24
2W = 24 - 6 = 18
W = 18/2 = 9
L = W + 6 = 9 + 6 = 15
Final answer:
The student's problem involves finding the length and width of a rectangle given its perimeter and the fact that the length is 6 inches greater than the width. To solve it, we defined the width as a variable, set up an equation based on the perimeter, and used substitution to find that the width is 9 inches and the length is 15 inches.
Explanation:
The perimeter of a rectangle is given by the formula 2(length + width). In the stated problem, we are given the total perimeter (48 inches) and told that the length is 6 inches greater than the width. We can define the width as w and the length as w + 6. So, the perimeter equation is:
2(w + (w + 6)) = 48
Simplify the equation: 2(2w + 6) = 48.Distribute the 2: 4w + 12 = 48.Subtract 12 from both sides: 4w = 36.Divide by 4 to find w: w = 9.Now that we have the width, we can find the length using substitution:
w + 6 = 9 + 6 = 15
Therefore, the width is 9 inches and the length is 15 inches.
Claire is cyclingcling at a speed of 12 miles per hour. If she starts at a position chosen zero point what will her positon be after 45 minutes. 7th grade math
Answers
plz, help ASAP!!!!!!
Answers
Answer:
The answer is C
Step-by-step explanation:
The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. Example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (5,-4)
A truck skids for a distance of 25\,\text m25m25, start text, m, end text with the road pushing on its tires with force of 1500\,\text N1500N1500, start text, N, end text as its brakes are applied.
Answers
The truck, experiencing a force of 1500 N, skids a distance of 25 meters, resulting in a change in kinetic energy of 37,500 J. Now, let's break down the concept of kinetic energy and the given data:
Definition of Kinetic Energy:
Kinetic energy, in physics, is the energy possessed by a moving object.
It represents the effort required to accelerate an object of a specific mass from rest to a particular velocity.
The body retains its kinetic energy even with slight speed variations, maintaining the energy acquired during acceleration.
Kinetic Energy Conservation:
When the body decelerates from its current velocity to a state of rest, the same amount of energy is expended.
Formal Definition:
Kinetic energy is formally described as any quantity exhibiting a gradient with respect to time in the Lagrangian of a system.
Given Data:
Force (F) = 1500 N
Distance (d) = 25 m
Calculation of Change in Kinetic Energy:
Utilize the formula for change in kinetic energy: ΔK.E = F × d
Substitute the values: ΔK.E = 1500 × 25
This results in ΔK.E = 37,500 J.
Therefore, the observed change in kinetic energy for the truck, moving a distance of 25 meters with a force of 1500 N, is precisely 37,500 J.
Complete questions
A truck skids for a distance of 25 m with the road pushing on its tires with force of 1500 N as its brakes are applied. What is the change in kinetic energy for the truck? Round the answer to two significant digits.J
what is the midpoint of the segment shown below?
Answers
Answer:
i say its c or b
Step-by-step explanation:
The first term is 1 in the geometric sequence 1, −3, 9, −27, . . . What is the SEVENTH term of the geometric sequence? Select your answer.
A. −243
B. −30
C. 81
D. 189
E. 729
Answers
Answer:
729
Step-by-step explanation:
The first term is 1 in the geometric sequence 1, −3, 9, −27, . .
First find out the nth term formula for the geometric sequence
[tex]a_n=a_1(r)^{n-1}[/tex]
where a_1 is the first term =1
r is the common ratio,
[tex]\frac{-3}{1}=-3[/tex]
[tex]\frac{9}{-3}=-3[/tex]
[tex]\frac{-27}{9}=-3[/tex]
r=-3, a_1=1
[tex]a_n=a_1(r)^{n-1}[/tex]
[tex]a_n=1(-3)^{n-1}[/tex]
Now find out the seventh term, n=7
[tex]a_7=1(-3)^{7-1}=729[/tex]
To find the seventh term of the geometric sequence 1, −3, 9, −27, ..., we calculate the common ratio and use it in the formula for the n-th term. The common ratio is −3 and the seventh term turns out to be 729. So the correct option is E.
Explanation:Calculating the SEVENTH Term of a Geometric Sequence
The given geometric sequence is 1, −3, 9, −27, ... and we are asked to find the seventh term. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio (r). To find the common ratio, we can divide the second term by the first term, or the third term by the second term, and so on.
Common ratio (r) calculation:
Divide the second term (−3) by the first term (1), which gives us r = −3.
To find the seventh term, we use the formula for the n-th term of a geometric sequence, which is:
a_n = a_1 × r^(n-1), where a_n is the n-th term, a_1 is the first term, and n is the term number.
Seventh term calculation:
a_7 = 1 × (−3)^(7-1) = 1 × (−3)^6. Since −3 to an even power is positive, the answer is 1 × 3^6 = 729.
Therefore, the seventh term of the geometric sequence is 729.
Suppose x is directly proportional to y but inversely proportional to z. If x =3 when y = 6 and z =4, then what is z when y=3?
Answers
When y = 3, the value of z is 2.
Since x is directly proportional to y and inversely proportional to z, we can write this relationship as:
[tex]x = k \frac{y}{z}[/tex]
where k is a constant of proportionality.
We are given the values x = 3, y = 6, and z = 4. Let's use these values to find k.
[tex]3 = k \frac{6}{4}[/tex]
Simplifying this, we get:
[tex]3 = k \cdot 1.5[/tex]
Solving for k:
[tex]k = \frac{3}{1.5} = 2[/tex]
Now we know the constant k. We can use it to find z when y = 3.
We know the relationship:
[tex]x = 2 \frac{y}{z}[/tex]
We need to find z when x = 3 and y = 3.
[tex]3 = 2 \frac{3}{z}[/tex]
Rearranging to solve for z:
[tex]3 = 6 \div z[/tex]
[tex]z = 2[/tex]
PLZ HELP, GIVING BRAINLIEST!!
If the endpoints of the diameter of a circle are (3, 10) and (-1, 6), what are the coordinates of its center?
A. (-2,-2)
B. (2, 2)
C. (1, 8)
D. (2, 16)
Answers
The slope of the line below is -
Write the point-slope equation for the
line using the coordinates of the
labeled point.
Answers
Answer:the point slope form is
y + 1 = - 1/2(x - 6)
Step-by-step explanation:
The point slope form of a line is expressed as
y - y1 = m(x - x1)
Where
m represents the slope of the line.
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
From the information given,
slope, m = - 1/2
y1 = - 1
x1 = 6
Therefore, the point slope eqy would be
y - - 1 = - 1/2(x - 6)
y + 1 = - 1/2(x - 6)
Answer:
y - - 1 = - 1/2(x - 6)
y + 1 = - 1/2(x - 6)
Step-by-step explanation:
Olivia is making baggies of cookies for a bake sale. She wants to put nine cookies in each bag. She made 41 oatmeal cookies and 13 chocolate chip cookies. How many baggies of cookies can Olivia make?
Answers
Answer:
6
Step-by-step explanation:
Mai tutors history. For each hour that she tutors, she earns 20 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H . Then use this equation to find Mai's earnings after tutoring for 17 hours.
Answers
Answer:the equation relating E to H is
E = 20H
Step-by-step explanation:
Let E represent her earnings (in dollars) after tutoring for H hours.
For each hour that she tutors, she earns 20 dollars. This means that in H hours, her total earnings would be
E = 20H
To find Mai's earnings after tutoring for 17 hours, we would substitute H = 17 into the equation. It becomes
E = 20 × 17
E = $340
Mai's earnings [tex](\(E\))[/tex] after tutoring for 17 hours would be $340, calculated as [tex]\(E = 20 \times 17\).[/tex]
To relate Mai's earnings [tex](\(E\))[/tex] to the number of hours she tutors [tex](\(H\))[/tex], we can use the following equation:
[tex]\[E = 20H\][/tex]
This equation represents that Mai earns $20 for each hour she tutors. By multiplying the number of hours [tex](\(H\))[/tex] by the rate of $20 per hour, we get her total earnings [tex](\(E\))[/tex].
Now, to find Mai's earnings after tutoring for 17 hours, we can plug in [tex]\(H = 17\)[/tex] into the equation:
[tex]\[E = 20 \times 17\][/tex]
[tex]\[E = 340\][/tex]
So, Mai's earnings after tutoring for 17 hours would be $340.