Answer:
Dα/dt = 0.079 degree/sec
Step-by-step explanation:
From problem statement, is easy to see, that if point A is ubicated at the top of the telescope, the shoreline is directly below the woman ( point B), and the point where the boat is, which is at distance x from shoreline is point C. These three point shape a right triangle with angle α (the angle of the telescope).
So we have
tan α = x/250
Differentiating both sides of the equation we get
D (tan α)/dt = ( 1/250)* Dx/dt
sec² α Dα/dt = ( 1/250)* Dx/dt
we already know that Dx/dt = 20 feet/sec
sec² α Dα/dt = 20/250 ⇒ sec² α Dα/dt = 0.08
Dα/dt = 0.08 / sec² α
Then
tan α = 20/250 = 0,08 α = arctan 0.08 α ≈ 5⁰
Dα/dt = 0.08/ sec² α
From tables we get cos 5⁰ = 0.9961 then
1/ 0.9961 = 1.003
sec α = 1.003 and sec² α = 1.0078
Dα/dt = 0.08/ sec² α ⇒ Dα/dt = 0.08/1.0078
Dα/dt = 0.079 degree/sec
The change of position of the boat results in a change of the angle of the telescope, which can be calculated using related rates. With known factors such as the speed of the boat and its distance from shore, the rate of change of the telescope's angle can be found using the principles of trigonometry and calculus.
Explanation:This question is about related rates in calculus. Related rates describe the relationship between different rates of change that are connected to each other. In this case, the changing position of the boat creates a change in the angle of the telescope.
We know the woman is watching a boat that is approaching a shoreline directly below her at 20 feet per second, and we are asked to find the rate that the angle of the telescope is changing when the boat is 250 feet from shore. Here is a way of visualizing it:
Let D be the distance of the boat from the base of the cliff and θ the angle that the telescope makes with the horizontal. We are given that D(t) decreases at 20 feet per second and that when D(t) = 250, we want to know what is dθ/dt.
By using trigonometry, we can find a relationship between D and θ. Specifically, tan(θ) = 250/D, so by implicit differentiation, (sec^2(θ)) * dθ/dt = -250/D^2 * dD/dt. From the given data, dD/dt = -20 and D = 250, so substitute them into the equation and evaluate θ using the tan–1(1) to obtain dθ/dt.
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A(n) is a typical, highly representative example of a concept. It is often described as an "average" or an "ideal member."
Answer:
Prototype
Step-by-step explanation:
Before a product is made, an original model of the product is first formulated. This is called a prototype. It is not simply a part of the design, but a very important part that the process of creating the final product solely depends on it. It is largely described as a highly representative example of a concept or product.
A prototype is a typical, highly representative example of a concept. It is often described as an "average" or an "ideal member."
What is a prototype?In Engineering, a prototype can be defined as a rudimentary (early) model, release, or sample of a particular product, so as to avail the developers and manufacturers an opportunity and ability to test a concept, functionality, or process within it.
For instance, the main purpose of the prototype of a robot is to determine and show whether or not the robot and all of its features are in tandem with the design specifications and market requirements.
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Suppose you can work at most a total of 25 hours per week. Baby-sitting, x, pays $6 per hour and working at the grocery store, y, pays $9 per hour. You need to earn $171 a week to pay for your expenses.
Answer:
y=7 number of hours at grocery store
x=18 number of hours at baby- sitting
Step-by-step explanation:
According to the information provided.
x is number of hours at baby- sitting
y is number of hours at grocery store
total number of hours worked
1) x+y =25
total earn in a week
2) x*$6 + y* $9 = $171
from equation 1
x+y=25
x= 25-y
we place the above derived equation in equation 2
x*$6 + y* $9 = $171
(25-y)*$6 + y* $9 = $171
(25*6) -6y +9y =171
150+3y=171
3y=171-150
3y=21
y=7 number of hours at grocery store
x= 25-y
x= 25-7
x=18 number of hours at baby- sitting
Two chess players, A and B, are going to play 7 games. Each game has three possible
outcomes: a win for A (which is a loss for B), a draw (tie), and a loss for A (which is
a win for B). A win is worth 1 point, a draw is worth 0.5 points, and a loss is worth 0
points.
(A) How many possible outcomes for the individual games are there, such that overall
player A ends up with 3 wins, 2 draws, and 2 losses?
(B) How many possible outcomes for the individual games are there, such that A ends
up with 4 points and B ends up with 3 points?
(C) Now assume that they are playing a best-of-7 match, where the match will end as
soon as either player has 4 points. For example, if after 6 games the score is 4 to 2 in
favor of A, then A wins the match and they don’t play a 7th game. How many possible
outcomes for the individual games are there, such that the match lasts for 7 games and
A wins by a score of 4 to 3?
Answer:
A) 210
B) 357
C) 267
Step-by-step explanation:
A) Among 7 games, we can first choose 3 wins, and then among remaining 4 games, we can choose 2.
To calculate the possibility, we will use Combination.
[tex]C(7,3)*C(4,2) = 35 *6 = 210[/tex]
B) Player A can get 4 points with the following cases:
4 wins and 3 loses
3 wins, 2 draws and 2 loses
2 wins, 4 draws and 1 lose
1 win and 6 draws
Indeed, these cases matches for Player B too to get 3 points.
So again, we will use Combination to calculate the possibility.
[tex]C(7,4) + C(7,3)*C(4,2) + C(7,2)*C(5,4) + C(7,1) = 357[/tex]
C) Here, we need to find two possibilities after 6 games and add them, while Player A has 3 points and wins the 7th game, and Player A has 3.5 points and draws the 7th game.
[tex][C(6,3)+C(6,2)C(4,2)+C(6,1)C(5,4)+C(6,6)] + [C(6,3)C(3,1)+C(6,2)C(4,3)+C(6,1)] =[20+90+30+1]+[60+60+6]=141+126=267[/tex]
What is the first speed at which the ratio of stopping distance to speed is greater than 3 to 1
50 mph
40 mph
20 mph
Answer:
40 mph
Step-by-step explanation:
3 times the speed in mph will be ...
3 × 20 = 60 . . . . . more than 43
3 × 40 = 120 . . . . less than 126
The stopping distance in feet is more than 3 times the speed in mph for a speed of 40 mph.
_____
The answer will depend on the units of the ratio. Here, we are apparently to use units of feet per (mile per hour), that is, (ft·h/mi). The answer would be different for distance in meters and speed in km/h, for example.
The reflector of a flashlight is in the shape of a parabolic surface. The casting has a diameter of 8 inches and a depth of 4 inches.
How far should The light bulb should be placed from the vertex?
Answer:
1 in
Step-by-step explanation:
We are given that
Diameter of casting=8 in
Radius of casting=[tex]\frac{Diameter}{2}=4 in[/tex]
Depth of casting=4 in
We have to find the distance of light bulb should be from the vertex
It means the reflector passing through the point (4,4).
Equation of parabola along y-axis is given by
[tex]x^2=4ay[/tex]
Using the equation substitute x=4 and y=4
[tex]16=16a[/tex]
[tex]a=\frac{16}{16}=1[/tex]
The focus of parabola is at (0,a).
Therefore, the focus of reflector=(0,1)
Hence, the light bulb should be placed 1 in far from the vertex.
The distance of light bulb can be calculated using equation of parabola. The parabola is a plane curve which is U-shaped.
The distance of light bulb is [tex]1\:\rm in[/tex].
Given:
The diameter is [tex]8\:\rm in[/tex].
The radius is [tex]=\frac{d}{2}=\frac{8}{2}=4 \:\rm in[/tex].
The depth is [tex]4\:\rm in[/tex].
Since the depth is [tex]4\:\rm in[/tex] and radius is [tex]4\:\rm in[/tex] so reflector passes through the point [tex](4,4)[/tex].
Write the equation of parabola for y-axis.
[tex]x^2=4ay[/tex]
Putting [tex]4[/tex] for [tex]x[/tex] and [tex]4[/tex] for [tex]y[/tex].
[tex]4^2=4\times a\times 4\\a=\frac{16}{16}\\a=1[/tex]
The focus of a parabola is [tex](0,1)[/tex].
The distance of light bulb is [tex]1\:\rm in[/tex].
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Worldwide quarterly sales of a brand of cell phones were approximately q = −p + 126 million phones when the wholesale price was $p. (a) If the cellphone company was prepared to supply q = 9p − 354 million phones per quarter at a wholesale price of $p, what would have been the equilibrium price? $ 48 Correct: Your answer is correct. (b) The actual wholesale price was $43 in the fourth quarter of 2004. Estimate the projected shortage or surplus at that price. HINT [See Example 4.] There is an estimated Correct: Your answer is correct. of Incorrect: Your answer is incorrect. million phones.
Answer:
a) equilibrium price = $48
b) shortage of 50 million phones
Step-by-step explanation:
Quarterly sales of a brand/quantity demanded (q) =
-p+126 million phones
a) if supply(q) = 9p - 354 million phones, at equilibrium quantity demanded = quantity supplied
-p + 126 = 9p - 354
-p - 9p = -354 - 126
-10p = -480
p = -480/-10
p = $48
The price at equilibrium = $48
b) actual wholesale price in the fourth quarter of 2004= $43
Quantity demanded = -p + 126
= -43 + 126
= 83 million phones
Quantity supplied = 9p - 354
= 9(43) - 354
= 387 - 354
= 33 million phones
Since quantity supplied is less than quantity demanded, there will be a shortage.
Shortage = 83 -33
= 50 million phones
The equilibrium price is determined to be $48 by equating the demand and supply. At an actual price of $43, there is a shortage of 50 million phones. This is found by comparing the quantities demanded and supplied at that price.
Equilibrium Price and Surplus/Shortage Estimation
We are given the demand and supply functions for cell phones, where the demand function is q = −p + 126 and the supply function is q = 9p − 354. To find the equilibrium price, we set the demand function equal to the supply function:
−p + 126 = 9p − 354Solving for p:
126 + 354 = 9p + p480 = 10pp = 48Hence, the equilibrium price is $48.
For part (b), we need to estimate the shortage or surplus at an actual wholesale price of $43. We substitute p = 43 into both demand and supply functions:
Demand: qd = −43 + 126 = 83 million phonesSupply: qs = 9(43) − 354 = 387 − 354 = 33 million phonesTherefore, there is a shortage of 83 - 33 = 50 million phones at the price of $43.
Mark wants to use a grid like the ones in exercises 1 and 2 to model the percent equivalent of the fraction 2/3.How many grid squares should he shade? What percent would his model show?
Answer:
67 squares or 66.66 squares.
2/3 turned into a decimal is 66.66 or rounded, 67 squares.
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If there were 400 foreclosures this year and 500 last year what is the percent of change?
Answer:
-20% ?
Step-by-step explanation:
I'm not sure but 2% of 5 is 1 so 20% of 500 is 100. so minus 20% would give you 400.
To find the percent of change in foreclosures, subtract the new number from the old number, divide by the old number, and multiply by 100. The foreclosures went from 500 to 400, resulting in a 20 percent decrease.
To calculate the percent of change in the number of foreclosures from one year to the next, you take the difference in the numbers (new number - old number), divide by the old number (the number from the earlier year), and then multiply the result by 100 to obtain a percentage. In this case, there were 500 foreclosures last year and 400 this year. Therefore, the calculation is as follows:
(Old Number - New Number) / Old Number × 100 = Percent Change
(500 - 400) / 500 × 100 = 100 / 500 × 100
0.2 × 100 = 20%
There has been a 20 percent decrease in foreclosures from last year to this year.
Hasn't worked two jobs last summer to start saving for a car he mowed lawns during the day and work at a pizza place in the evening with my cousin earn a total of $1400 if you earn 360 more at the pizza place the mowing one how much did he earn each job
Answer:
Hudson earned $520 in moving lawns and $880 by working in Pizza place.
Step-by-step explanation:
Given:
Total Money Earned = $1400
Let Money earned in moving lawns be 'x'
Also Given:
he earned $360 more at the pizza place than mowing lawns
Money Earned working at pizza place = [tex]x+360[/tex]
we need to find money earned in each job.
Now Total money earned is equal to sum of Money earned moving lawns and money earned working at pizza place.
Framing the equation we get;
[tex]x+x+360=1400[/tex]
Solving the equation we get;
[tex]2x+360 =1400\\\\2x = 1400-360\\\\2x =1040\\\\x=\frac{1040}{2}=\$520[/tex]
Money Earned working at pizza place = [tex]x+360 = 520 +360 = \$880[/tex]
Hence Hudson earned $520 in moving lawns and $880 by working in Pizza place.
Final answer:
To determine the earnings from each job, equations were set up using the total amount earned and the difference between the two earnings. The student earned $520 mowing lawns and $880 at the pizza place.
Explanation:
The student has provided information indicating that he worked two jobs and earned a combined total of $1400 over the summer. He earned $360 more at the pizza place than he did mowing lawns. To solve for how much he earned at each job, we need to set up two equations based on the given information. Let the amount earned mowing lawns be x and the amount earned at the pizza place be y.
From the information given, we have two equations:
x + y = $1400 (The total combined earnings) y = x + $360 (Earned $360 more at the pizza place than mowing lawns)Now we can substitute the second equation into the first to find how much he earned from each job. From the second equation, we have y = x + $360. Substituting this into the first equation gives us:
x + (x + $360) = $1400
Combining like terms gives us:
2x + $360 = $1400
Subtract $360 from both sides yields:
2x = $1040
Dividing both sides by 2 gives us:
x = $520
Therefore, the student earned $520 mowing lawns. To find how much was earned at the pizza place, we substitute x back into the second equation:
y = $520 + $360
So, the student earned $880 at the pizza place.
Melissa wants to purchase a digital camera.The listed price of the camera is $195.99.The camera is no sale for 10% off and Melissa has a coupon for 5% off the sales tax is 7%. How much money will the 10% off sale save Melissa
Answer:
The 10% off sale will save Melissa $10.49.
Step-by-step explanation:
Given:
The listed price of the camera is $195.99.
The camera is no sale for 10% off and Melissa has a coupon for 5% off the sales tax is 7%.
Now, to find the money Melissa will save of the 10% off sale.
So, to get the price of camera of the 5% off sale:
[tex](195.99-5\%\ of\ 195.99)[/tex]
[tex]=(195.99-\frac{5}{100}\times 195.99)[/tex]
[tex]=(195.99-9.80)[/tex]
[tex]=186.19[/tex]
Now, adding the sales tax:
[tex]186.19+7\%\ of\ 186.19[/tex]
[tex]=186.19+\frac{7}{100} \times 186.19[/tex]
[tex]=186.19+13.03[/tex]
[tex]=199.22[/tex]
Thus, the price is $199.22.
Now, to get the price of 10% off sale:
[tex]195.99-10\%\ of\ 195.99[/tex]
[tex]=195.99-\frac{10}{100} \times 195.99[/tex]
[tex]=176.39[/tex]
So, adding sales tax:
[tex]176.39+7\%\ of\ 176.39[/tex]
[tex]=176.39+\frac{7}{100} \times 176.39[/tex]
[tex]=188.73[/tex]
Hence, the price is $188.73.
Now, to get the money 10% off sale will save Melissa:
[tex]199.22-188.73[/tex]
[tex]=10.49[/tex]
Therefore, the 10% off sale will save Melissa $10.49.
Final Answer:
The 10% off sale will save Melissa approximately $19.60.
Explantion:
To calculate the savings from the 10% off sale on the listed price of the digital camera, follow these steps:
1. Determine the listed price of the camera. In this case, the listed price is $195.99.
2. Calculate the discount amount by multiplying the listed price by the discount percentage (expressed as a decimal). For a 10% discount, you would convert that percentage to a decimal by dividing by 100:
10% = 10/100 = 0.10.
3. Multiply the listed price by the decimal form of the discount percentage to find the savings:
Savings = Listed Price × Discount Percentage
Savings = $195.99 × 0.10
4. Calculate the actual savings:
Savings = $195.99 × 0.10 = $19.599
5. Since savings are typically represented in dollar format (rounded to two decimal places), we round the savings to the nearest cent:
Savings ≈ $19.60
So, the 10% off sale will save Melissa approximately $19.60.
2918+49
Which numbers should be used?
The estimated quotient is?
Answer: Use all numbers to add.
2918+49=2967
Estimated.... 2918+49 ≈ 3050
Hope this helps you out.
Answer:use all the numbers
Step-by-step explanation:
2918+49 ≈ 3050
Brayden has math and reading homework tonight. Brayden can solve each math problem in 4 minutes and he can read each page in 2.5 minutes. The number of pages Brayden read is twice the number of math problems he solved. And it took him 45 minutes to complete all of his homework. Determine the number of math problems Brayden solved and the number of pages he read.
Answer:
Brayden Solved 5 math problem and read 10 pages.
Step-by-step explanation:
Let the number of Math Problem solved be x.
Also Let the Number of Pages he read be y.
Given:
The number of pages Brayden read is twice the number of math problems he solved.
Hence equation can be framed as;
[tex]y =2x[/tex]
Also Given:
Ayden can solve each math problem in 3 minutes and he can read each page in 1 minute and it took him 50 minutes to complete all of his homework.
Hence the equation can be framed as;
[tex]4x+2.5y =45[/tex]
Now Substituting the value of y in above equation we get;
[tex]4x+2.5(2x) =45\\\\4x+5x=45\\\\9x=45\\\\x=\frac{45}{9}=5[/tex]
Now Substituting the value of x to find the value of y we get;
[tex]y =2x =2\times5 =10[/tex]
Hence Brayden Solved 5 math problem and read 10 pages.
The second hand on a clock is 8 \text{ cm}8 cm8, start text, space, c, m, end text long. What is the distance the tip of the second hand travels in 101010 minutes?
The second hand of a clock is 8 cm long what is the distance of the tip of the second hand travel in 10 minutes
Answer:
The distance travelled by tip of second hand in 10 minutes is 502.4 cm
Solution:
Length of second hand = 8 cm long
In one revolution it travels a circumference of a circle of which radius is 8 cm
The circumference of circle = [tex]2 \pi r[/tex]
[tex]c = 2 \times \pi \times 8 = 16\pi[/tex]
We are aksed to find the distance of the tip of the second hand travel in 10 minutes
Second hand complete 1 revolution in 1 minute.
Therefore, in 10 minutes it revolves 10 revolution,
In 1 revolution tip of second covers = 16π
Hence distance travelled is given as:
[tex]\rightarrow 16 \pi \times10 = 160 \pi[/tex]
We know that π is a constant equals to 3.14
[tex]\rightarrow 160 \pi = 160 \times 3.14 = 502.4[/tex]
Thus the distance travelled by tip of second hand in 10 minutes is 502.4 cm
Answer:
502.4
Step-by-step explanation:
Describe how to use the vertical line test to determine if a graph is a function.
Using a ruler/straight edge to draw a vertical line for any values of x.If the curve is cut more than once, the graph is not for a function.
Step-by-step explanation:
Use a ruler to draw a line parallel to the y-axis for the taken values of x.When the vertical line is drawn, observe how the line intersect the graph. If the line intersects the graph more than once for nay value of x then that is not a graph of a function.
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Keywords: vertical line test, function, graph
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HELP PLZZZ ASAPP!!! (Plz answer em right!)
Answer:
1) B, C, and D
2) plane BFD
Step-by-step explanation:
1) Collinear points are points on the same line. There are two lines shown. One of them shows points A, C, and E on it. The other line shows points B, D, and D on it. The latter set of points is listed among the answer choices.
__
2) A plane can be named by three points in the plane that are not on the same line. The points shown as being in the plane are B, C, D, F, with points B, C, and D being on the same line (see question 1). So, the plane can be named with point F and any two of B, C, and D. Plane BFD is an appropriate name.
Let f(x) be a polynomial such that f(cos θ) = cos(4) θ for all θ. Find f(x). (This is essentially the same as finding cos(4) θ in terms of cos θ we structure the problem this way so that you can answer as a polynomial. Be sure to write your polynomial with the terms in order of decreasing degree.)
Answer:
f(x) = 8x⁴-8x²+1
Step-by-step explanation:
I will assume that f(cos θ) = cos(4θ). Otherwise, f would not be a polynomial. lets divide cos(4θ) in an expression depending on cos(θ). We use this properties
cos(2a) = cos²(a) - sin²(b)sin(2a) = 2sin(a)cos(a)sin²(a) = 1-cos²(a)cos(4θ) = cos(2 * (2θ) ) = cos²(2θ) - sin²(2θ) = [ cos²(θ)-sin²(θ) ]² - [2cos(θ)sin(θ)]² = [cos²(θ) - ( 1 - cos²(θ) ) ]² - 4cos²(θ)sin²(θ) = [2cos²(θ)-1]² - 4cos²(θ) (1 - cos²(θ) ) = 4 cos⁴(θ) - 4 cos²(θ) + 1 - 4 cos²(θ) + 4 cos⁴(θ) = 8cos⁴(θ) - 8 cos²(θ) + 1
Thus f(cos(θ)) = 8 cos⁴(θ) - 8 cos²(θ) + 1, and, as a result
f(x) = 8x⁴-8x²+1.
what is the difference between Compound Interest and simple interest???
Answer:
Simple interest is calculated using initial principle while compound interest is calculated considering the interest also .
Step-by-step explanation:
Interest is the cost of borrowing money, where the borrower pays a fee to the lender for using his money. The interest, typically expressed as a percentage, can either be compounded or simple .
Simple interest is based on the principal amount , while compound interest is based on the principal amount and the interest that adds onto it in every period and the final principle is used for calculating the interest.
Simple interest is calculated on the principal amount of a loan and it's easier to find out than compound interest.
In the triangle below, what ratio is sin θ?
Answer:
[tex]\displaystyle \frac{12}{13} = sin\:θ\:[0,3743340836π ≈ θ][/tex]
Step-by-step explanation:
Remember this?!
Extended Information on Trigonometric Ratios
[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ[/tex]
I am joyous to assist you anytime.
Maggie graphed the image of a 90° counterclockwise rotation about vertex A of △ABC. Coordinates B and C of △ABC are (2, 6) and (4, 3) and coordinates B’ and C’ of it’s image are (–2, 2) and (1, 4). What is the coordinate of vertex A?
Answer:
A(2, 2)
Step-by-step explanation:
I find it useful to graph the given points. The center of rotation is at the place where the perpendicular bisectors of BB' and CC' meet. That point is ...
A = (2, 2).
__
The graph shows you the slope of BB' is 1, so its perpendicular bisector will have a slope of -1. The midpoint of BB' is (2-2, 6+2)/2 = (0, 4). This is the y-intercept of the line, so the perpendicular bisector of BB' has equation ...
y = -x +4
The slope of CC' is -1/3, so its perpendicular will have a slope of -1/(-1/3) = 3. The midpoint of CC' is (4+1, 3+4)/2 = (5/2, 7/2). In point-slope form the equation of the perpendicular bisector of CC' is ...
y -7/2 = 3(x -5/2)
2y -7 = 3(2x -5) . . . . multiply by 2
2(-x+4) -7 = 3(2x -5) . . . substitute for y
-2x +1 = 6x -15 . . . . .eliminate parentheses
16 = 8x . . . . . . . . . . add 2x+15
x = 2 . . . . . . divide by 8
y = -2+4 = 2 . . . . from the equation for y
The intersection of the perpendicular bisectors of BB' and CC' is the center of rotation:
A = (2, 2)
Final answer:
The coordinate of vertex A is (2, 2), found by equating B' to (y, x) and using the given B' coordinates.
Explanation:
To find the coordinates of vertex A, we can use the properties of a rotation. A 90° counterclockwise rotation about a point involves switching the coordinates and negating the y-coordinate. Let's denote the coordinates of A as (x, y). After the rotation, A becomes B', so we have:
B' = (y, x)
From the given coordinates of B' (–2, 2), we can equate:
y = 2
-2 = -x
Solving these equations, we find that x = 2. Therefore, the coordinates of vertex A are (2, 2). So, Maggie's image graph depicts a 90° counterclockwise rotation about vertex A (2, 2) of triangle ABC.
*trigonometry and area.*
Find the area of a regular octagon with a side length of 8cm. Round to the nearest tenth.
Answer:
The correct answer is that the area of the regular octagon is 309 cm²
Step-by-step explanation:
There are several formulas for calculating the area of a regular octagon. We will use this one for solving this question because it does not require additional information .
Area = (2 * s²)/tan 22,5°
s = 8 cm
Replacing with the real values, we have:
Area = (2 * 8²)/tan 22,5°
Area = 2 * 64/0.4142
Area = 128/0.4142
Area = 309 cm² (Rounding to the nearest tenth)
Need help please!!! Just the numbers 4-7!
All 231 students in the Math Club went on a field trip. Some students rode in vans which hold 7 students and some students rode in buses which hold 25 students each. How many of each type of vehicle did they use if there were 15 vehicles in total?
answer : 8 vans and 7 buses
The height of a curved support can be modeled by
f(x) = x^2/256 + 16
Find the width of the beam
Answer:
128
Step-by-step explanation:
I assume there's a negative sign missing, since the image is a downwards parabola.
f(x) = -x²/256 + 16
The width of the beam is the distance between the x-intercepts.
0 = -x²/256 + 16
x²/256 = 16
x² = 4096
x = ±64
So the width is:
64 − (-64) = 128
One pound of tomatoes costs $1.59.One pound of bananas costs $1.87. How much more do 5 pounds of tomatoes costs than 2 pounds of bananas? Show your work
when you multiply $1.59 by 5 you get $7.95
when you multiply $1.87 by 2 you get $4.74
so when you subtract them you get $3.21
If m arc CD = 143°, and m arc AB = 39°, what is m∠ DEC ?
Answer:
[tex]m\angle DEC=91^o[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite
so
[tex]m\angle DEC=\frac{1}{2}[arc\ AB+arc\ DC][/tex]
substitute the given values
[tex]m\angle DEC=\frac{1}{2}[39^o+143^o][/tex]
[tex]m\angle DEC=\frac{1}{2}[182^o][/tex]
[tex]m\angle DEC=91^o[/tex]
Chris has 7/8 yards of purple ribbon and 1 1/6 yards of green ribbon. Chris has a total of 3 2/3 yards of ribbon. How many yards of Chris's ribbon are neither purple nor green.
Answer:The number of yards of Chris's ribbon are neither purple nor green is 1.625 yards
Step-by-step explanation:
Chris has a total of 3 2/3 yards of ribbon. Converting 3 2/3 yards to improper fraction, it becomes 11/3 yards. Chris has 7/8 yards of purple ribbon. He also has 1 1/6 yards of green ribbon. Converting to improper fraction, it becomes 7/6 yards of green ribbon.
The total length of purple and green ribbon that Chris has would be 7/8 + 7/6 = (21+28)/24 = 49/24
The number of yards of Chris's ribbon are neither purple nor green is 11/3 - 49/24 = (88 - 49)/24
= 39/24 = 1.625 yards
To estimate the length of the lake, caleb starts at one end of the lake and walk 95m. He then turns a 60° angle and walks on a new path and walks 8m more then arrives at the other end of the lake. Approximately how long is the lake?
Answer:
Length of the lake is 97.30 m
Step-by-step explanation:
We have given Caleb starts at one end of the lake and walk 95 m
So [tex]d_1=95m[/tex]
And then he turns at an angle of 60°
So [tex]\Theta =60^{\circ}[/tex] and then again walk 8 m
So [tex]d_2=8m[/tex]
We have to fond the total length of the lake , that is d
Total length of the lake is given by [tex]d=\sqrt{d_1^2+d_2^2+2d_1d_2cos\Theta }=\sqrt{95^2+8^2+2\times 95\times 8\times cos60^{\circ}}=97.30m[/tex]
So length of the lake is 97.30 m
Final answer:
Using the Law of Cosines with Caleb's path measurements of 95 meters and 103 meters at a 60-degree angle, the length of the lake is found to be approximately 104 meters.
Explanation:
To estimate the length of the lake, we can represent Caleb's path as a triangle, where the length of the lake forms one side of the triangle. Caleb starts by walking 95 meters along one side, then makes a 60° angle and walks 8 meters more than the length of the first path, forming the second side of the triangle. The length of the lake, which is the final side, can be calculated using the Law of Cosines.
The Law of Cosines is given by c² = a² + b² - 2ab×cos(γ), where γ is the enclosed angle and a, b, and c are the lengths of the sides of the triangle.
In this case, a = 95m, b = 95m + 8m = 103m, and γ = 60°. Plugging these values into the Law of Cosines, we will find the length of the lake (c).
c² = 95² + 103² - 2×95×103×cos(60°)
c² = 9025 + 10609 - 19570×0.5
c² = 9025 + 10609 - 9785
c² = 10849
c ≈ √10849
c ≈ 104.16 meters
Therefore, the length of the lake is approximately 104 meters long.
In the rectangular coordinate system, points (4,0) and (–4,0) both lie on circle C. What is the maximum possible value of the radius of C ?
Answer:
There is no finite maximum value of the radius of C.
Step-by-step explanation:
We have been given that in the rectangular coordinate system, points (4,0) and (–4,0) both lie on circle C. We are asked to find the maximum possible value of the radius of C.
If the center of the circle C would have been at origin (0,0), then the radius of the circle C would be 4 units.
Since there is no information given about center of circle, so radius can be infinitely long. Therefore, there is no finite maximum value of the radius of C.
What is the equation of the line which
includes the points (2, 4) and (14, –2)?
A. y=5x−12
B. y=−12x−5
C. y=−12x+5
D. y=−2x+5
Answer:
The equation of the line is y = (-1/2)x + 5
Step-by-step explanation:
[tex]m = \frac{y2 - y1}{x2 - x1 } [/tex]
First of all, have to find gradient using the formula above :
(2,4) & (14,-2)
m = (-2-4) / (14-2)
= -6 / 12
= -1/2
Second, using y = mx + b as b is a constant and is a y-intercept. Using any of these 2 coordinates to find the value of b with given gradient :
y = mx + b
Let y=4 & x=2
4 = (-1/2)(2) + b
b = 4 + 1
= 5
Lastly, put the value of gradient and y-intercept into the equation :
y = mx + b
Let m=-1/2 & b=5
y = (-1/2)x + 5
Which correlation coefficient best represents a moderate relationship showing fewer anxiety symptoms in people who report higher life satisfaction? –0.5 +0.7 –0.2 +0.4
Answer:
-0.5
Step-by-step explanation:
The correlation coefficient represents the relationship between two variables and here two variables are anxiety symptoms and life satisfaction. As it is mentioned in the statement that less anxiety symptoms are present in the individuals who have higher life satisfaction, so there is negative/ inverse relationship between anxiety symptoms and life satisfaction. Just to be clear the inverse relationship means that increase in one variable lead to decrease in second variable and vice versa. Also according to rule of thumb 0.5 represents the moderation correlation because correlation coefficient ranges from -1 to +1 and 0.5 is a middle value. So the correlation coefficient in the given scenario is -0.5.