Answer:
Option C:The skaters path intersect twice, but only one of those points is inside the rink.
Step-by-step explanation:
Coordinates of center of ice rink: (0,0) Radius of ice rink circle = 35 m
We know that the equation of a circle with center coordinates (a,b) and radius of (r) is given as; (x - a)² + (y - b)² = r²
Thus, the total area on which the skaters are skating will be given by the equation;
x² + y² = 35²
Now, we are told the path along which Susan is skating is modeled by the equation: y = 6x - x² - 5
While Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9)
From equation of a parabola, the path along which like is skating can be modeled by;
(x - 8)² = 4a(y + 9)
To find a, we will substitute the coordinate started at to get;
(10 - 8)² = 4a(-21 + 9)
4 = 4a × -12
Divide both sides by 4 to get;
a = -1/12
Thus;
(x - 8)² = 4(-1/12)(y + 9)
(x - 8)² = (-1/3)(y + 9)
This gives: 3(x - 8)² = -(y + 9)
I've drawn the graph on demos and attached it.
From the graph we can see that the skaters points intersect twice but one is inside the rink circle while the other is outside the rink circle. The point at which they intersect outside the rink was slightly cropped out because of size. But it is clearly seen that they are both approaching point of intersection.
Thus, correct answer is Option C.
Answer:
C
Step-by-step explanation:
just took the quiz
On the beach boardwalk there are 20 different places to get food 20% of them are ice cream shops how many ice cream Shoppe’s are in the park
Answer:
( 4 )
Step-by-step explanation:
Hope this helps
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Herman is standing on a ladder that is partly in a hole. He starts out on a rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet. What is Herman’s final position, relative to ground level?
Answer:
Are there answers
Step-by-step explanation:
Answer:
answer
Herman is standing on a ladder that is partly in a hole. He starts out on a rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet. ...
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.
Suppose the paper is 7"-wide by 9"-long.
a. Estimate the maximum volume for this box?
b. What cutout length produces the maximum volume?
Answer:
B
Step-by-step explanation:
To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.
The solution is:
a) V (max) = 36.6 in³
b) x = 1.3 in
The volume of a cube is:
V(c) = w×L×h ( in³)
In this case, cutting the length "x" from each side, means:
wide of the box ( w - 2×x ) equal to ( 7 - 2×x )
Length of the box ( L - 2×x ) equal to ( 9 - 2×x )
The height is x
Then the volume of the box, as a function of x is:
V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x
V(x) = ( 63 - 14×x - 18×x + 4×x²)×x
V(x) = 4×x³ - 32×x² + 63×x
Tacking derivatives, on both sides of the equation
V´(x) = 12×x² - 64 ×x + 63
If V´(x) = 0 then 12×x² - 64 ×x + 63 = 0
This expression is a second-degree equation, solving for x
x₁,₂ = [ 64 ± √ (64)² - 4×12*63
x₁ = ( 64 + 32.74 )/ 24
x₁ = 4.03 this value will bring us an unfeasible solution, since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)
x₂ = ( 64 - 32.74)/24
x₂ = 1.30 in
The maximum volume of the box is:
V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3
V(max) = 4.4 × 6.4 × 1.3
V(max) = 36.60 in³
To chek for maximum value of V when x = 1.3
we find the second derivative of V V´´, and substitute the value of x = 1.3, if the relation is smaller than 0, we have a maximum value of V
V´´(x) = 24×x - 64 for x = 1.3
V´´(x) = 24× 1.3 - 64 ⇒ V´´(x) < 0
Then the value x = 1.3 will bring maximum value for V
Related Link: https://brainly.com/question/13581879
Daniel has 15 yards of fabric to make baby blankets. It takes 1 and 1/2 yards of fabric to make each blanket, and the expression that models the situation is 15 minus three-halves y. Which of the following are possible numbers of blankets that Daniel could make? Select all that apply.
Answer:
any number between 0 and 10
Step-by-step explanation:
15 - 3/2y
how many times can 3/2 go into 15?
10 times. The most blankets he can make is 10, so any number less than 10 and greater than zero would be a correct solution
can i get brainliest please?
Answer:
9 and 10
Step-by-step explanation:
Complete the point-slope equation of the line through (2,3)(7,4)
y-4=
What is the rate of return when 10 shares of Stock
A, purchased for 20 $/share, are sold for $310? The
commission on the sale is $6.
rate of return = [?] %
Give your answer as a percent rounded to the
nearest tenth.
Answer:
Rate of return = 52%
Step-by-step explanation:
Cost of Investment = 10 shares × $20 = $200
Gain on Investment = amount sold - commission on the sale
Gain on Investment = $310 - $6 = $304
Using the formula:
ROR = (Gain on investment - cost of Investment)/cost of Investment × 100
Plug in the values into the formula:
[tex] ROR = \frac{304 - 200}{200} * 100 [/tex]
[tex] = \frac{104}{200} * 100 [/tex]
[tex] = \frac{104*100}{200} [/tex]
[tex] = \frac{104}{2} = 52 [/tex]
Rate of return = 52%
How do you do this question?
Answer:
Diverges
Step-by-step explanation:
an = 7 / n^(1 + 1/n)
As n approaches infinity, an approaches 7 / n.
bn = 7 / n
Apply Limit Comparison Test.
lim(n→∞) an / bn
= lim(n→∞) [7 / n^(1 + 1/n)] / (7 / n)
= lim(n→∞) n / n^(1 + 1/n)
= lim(n→∞) 1 / n^(1/n)
= lim(n→∞) 1 / n⁰
= 1
The limit is greater than 0, and bn diverges, so an also diverges.
Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1 52 probability.
Required:
a. List the sample points in the event a jack is selected.
b. List the sample points in the event a club is selected.
c. List the sample points in the event a face card ( jack, queen, or king) is selected.
d. Find the probabilities associated with each of the events in parts (a), (b), and (c).
Answer:
Kindly check explanation
Step-by-step explanation:
A deck of card:
Number of hearts = 13
Diamond = 13
Spade = 13
Club = 13
Each of heart, club diamond and spade has is numbered from (2,3,4,5,6,7,8,9,10,Ace, queen, Jack, king)
Hence, a club, diamond, spade and heart has one of each of the above numbers.
a. List the sample points in the event a jack is selected.
Jack : ( heart, club, diamond, spade)
B.) club is selected :
Cub : (Ace, 2, 3,4,5,6,7,8,9,10,king,queen,jack)
C)
Jack : ( heart, club, diamond, spade)
Queen : (heart, club, diamond, spade)
King : (heart, club, diamond, spade)
D) probability = required outcome / Total possible outcomes
P(jack selected) = 4 /52 = 1/13
P(club selected). = 13/52 = 1/4
P(face card selected) = 12 / 52 = 3/13
Turn 2 1/8 into an improper fraction. Explain your steps
Answer:
17/8
Step-by-step explanation:
2 1/8 multiply 2 times 8 and 1 which equals to 17/8. The whole number times the denominator plus the numerator basically.
Answer:
17/8
Step-by-step explanation:
8 x 2 = 16
16 + 1 = 17
solve the following equation for a: -g + 3/4a = y
9514 1404 393
Answer:
a = (4/3)(y+g)
Step-by-step explanation:
Isolate 'a' term, then multiply by the reciprocal of its coefficient.
[tex]-g+\dfrac{3}{4}a=y\qquad\text{given}\\\\\dfrac{3}{4}a=y+g\qquad\text{add $g$}\\\\\boxed{a=\dfrac{4(y+g)}{3}}\qquad\text{multiply by $4/3$}[/tex]
which number is the same as 0.000 000 1: 10^7 or 10^-7
Answer:
= 1 × 10^-7
(scientific notation)
= 1e-7
(scientific e notation)
= 100 × 10^-9
(engineering notation)
(billionth; prefix nano- (n))
= 0.0000001
(real number)
Step-by-step explanation:
10^7 = 10000000
Six and forty-two ten-thousandths as a decimal
Please Help! :(
Six teams are out on the field playing soccer. The teams all have the same number of players. The head coach asks for 2 players from each team to come help him move some equipment. Now there are 78 players on the field. Write and solve an algebraic equation whose solution is the number of players, p, on each team.
Write the Equation and the answer please
Answer: there is 90 players in total
Step-by-step explanation:
6x 2= 12
78 + 12 = 90
Answer:
x=15
Step-by-step explanation:
6(x−2)=78 (or 6x−12=78), x=15
PLEASE ANSWER I WILL GIVE YOU BRAINLIEST!
Name the points which satisfy the conditions. In the second quadrant
9514 1404 393
Answer:
C, M
Step-by-step explanation:
The second quadrant is the upper left quadrant. There, x-values will be negative and y-values will be positive.
__
Point G is on the boundary with the 3rd quadrant, so is probably not considered to be in either of those quadrants.
Answer: C M
Step-by-step explanation:
I toss a coin 60 times. It lands on tails 24 times. What percent of the time does it land on tails?
Three times two less than a number is greater than or equal to five times the number. Find all of the numbers that satisfy the given conditions.
Let n = a number. Choose the inequality that represents the given relationship.
Answer:
D on edge
3(n – 2) ≥ 5n
Step-by-step explanation:
the next question's answer is B
Please help!!!- Find the measure of the angle in bold.
Need help to figure out to solve this.
Answer:
11x-6+(19x+6)=180°
11x+19x-6+6=180°
30x=180
x=180/30
x=6
it means that
19x+6=19*6+6=114+6=120°
What is the measure of angle F?
E. 20
D. 90
F.?
Answer:
the answer would be 70 because you take 90-20 and you get 70. you have a 90 degree angle is what you're working on right now
Step-by-step explanation:
HELPPPPP!! Is the expression 6 + 3 = 9 an equation ? Explain.
Answer:
No, because an expression is already solved and an equation is where you have to solve it
Step-by-step explanation:
Answer:
No as said you have to solve and equation yet an expression is already solved for your viewing.
Step-by-step explanation:
Two lines in the same plane that do not intersect are.
A.line segment
B.perpendicular
C.parallel
D.midpoint
What do I use to make a meat loaf?
Use the information to find the minimum sample size required to estimate an unknown population mean µ. Margin of error: $110, confidence level: 95%, σ = $500. Group of answer choices
Answer:
The minimum sample size required is 79.
Step-by-step explanation:
The following are given in the question:
e = Margin of error = 110
σ = Standard deviation = 500
Confidence level = 95%
n = Minimum sample size = ?
Therefore, we have:
Zσ = 1.96 at 95% confidence level
s.e. = Standard error = σ / [tex]\sqrt{n}[/tex] = 500 /
Alternatively, margin of error can be calculated as follows:
e = s.e. * Zσ = 110 ................... (1)
Substituting the other values into equation (1) and solve for n, we have:
500 / [tex]\sqrt{n}[/tex] * 1.96 = 110
500 / [tex]\sqrt{n}[/tex] = 110 / 1.96
500 / [tex]\sqrt{n}[/tex] = 56.1224489795918
500 = 56.1224489795918 * [tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex] = 500 / 56.1224489795918
[tex]\sqrt{n}[/tex] = 8.90909090909092
[tex]n^{\frac{1}{2}[/tex] = 8.90909090909092
Squaring both sides, we have:
([tex]n^{\frac{1}{2}[/tex])^2 = (8.90909090909092)^2
n = 79.3719008264465
Approximating to a whole number, we have:
n = 79
Therefore, the minimum sample size required is 79.
Find the product of (18k+ 2m)(m + k)
Answer:
18k^2+2m^2+20km
Step-by-step explanation:
PLEASE HELP IM TIMEZ) What is the value of the arithmetic series below? A. B. C. D.
Answer:
id say its C but I'm not sure
Find the selling price of each item original plate price of gold fish at $7.65 discount 10%
Answer:
6.88 is what I think you're looking for
Step-by-step explanation:
Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the question that follows, consider a sample of fifteen randomly selected people who recently booked a hotel.
What is the probability that at least fourteen out of fifteen people used an online travel website when they booked their hotel? Round to three decimal places.
A.0.028
B.0.025
C.0.323
D.0.978
Answer:
the answer is d because 0.978 cool number like yaaaa.
Step-by-step explanation:
Which one of these relationships is different than the other three?
Group of answer choices
A
B
C
D
help!!!1
Answer:
B
Step-by-step explanation:
I got this by looking at the graph and the numbers that I got vertically and horizontally I divided them .
x=4/9,y=1/2, and z=3/5 6wy-3z
Answer: The answer would be - 7/5 or (-0.46)
Plug in the numbers that each letter equals. So you get 6(4/9)(1/2) - 3(3/5). Then you just simplify.
Picture attached below. Please help
Answer:
饿着嘎嘎嘎嘎嘎嘎嘎嘎嘎嘎嘎;嘎嘎嘎嘎嘎嘎嘎嘎反反复复
From their location in the diagram, what are two possible values for n and m?
Answer:
n=7/5 m= 5
Step-by-step explanation: