The path of a prairie dog as it burrows underground is modeled by the equation
y22
= x2 – 2.4x , where x is the linear distance in meters from where the prairie dog
went underground. The graph shows the path of a prairie dog after burrowing under
the ground at (0, 0). At which distance, x, from (0, 0) does the prairie dog reach to
ground level?
2.4 meters separate the prairie dog from (0,0) and the ground level.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
To find the distance x from (0,0) where the prairie dog reaches ground level, we need to find the point on the graph where y=0.
Substitute y=0 into the equation:
0 = x^2 - 2.4x
Factor out x:
0 = x(x - 2.4)
So either x = 0 or x - 2.4 = 0.
If x = 0, the prairie dog is still underground, so we take x = 2.4 as the distance from (0,0) where the prairie dog reaches ground level.
Therefore, the prairie dog reaches the ground level at a distance of 2.4 meters from (0,0).
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The Sea Dragon, a pendulum ride at an amusement park, moves from its central position at rest according to the trigonometric function P(t)=−10sin(pi/3t), where t represents time, in seconds. How many seconds does it take the pendulum to complete one full cycle?
A= 3
B= 5
C= 6
D= 10
Answer:T = 2*Pi / (Pi / 3) = 6 seconds
Step-by-step explanation:
The time (in seconds) that it take the pendulum to complete one full cycle is given by: Option C: 6 (seconds)
What is the period of sine function?Trigonometric functions are periodic. They repeat their values after some specific constant input interval (constant depends on the trigonometric function chosen).
For sine function, its period is 2π
Thus, we get:
[tex]y = \sin(x) = \sin(x+2\pi) = \sin(x + 2\pi n) ; n \in \mathbb Z[/tex] integer, and y is some constant at some constant value of x)
For this case, the pendulum's motion is modeled by:
[tex]P(t) = -10\sin\left(\dfrac{\pi}{3} t\right)[/tex]
Let it takes 'd' seconds to do one full cycle, then we get:
[tex]P(t) = P(t+d) = P(t+2d) = P(t + nd); n \in \mathbb Z - \mathbb Z^{-}[/tex] (n is non-negative integer).
Using the formula, we get:
[tex]-10\sin\left(\dfrac{\pi}{3} t\right) = -10\sin\left(\dfrac{\pi}{3} (t + nd)\right)\\\sin\left(\dfrac{\pi}{3} t\right) =\sin\left(\dfrac{\pi}{3}t + \dfrac{\pi}{3}nd\right)[/tex]
But we know that:
[tex]\sin\left(\dfrac{\pi}{3} t\right) =\sin\left(\dfrac{\pi}{3}t +2\pi n\right)[/tex]
Thus, we get:
[tex]2\pi n = \dfrac{\pi}{3}nd\\[/tex] (compared for non-negative values of n)
This gives:
[tex]d = \dfrac{2\pi n \times 3}{\pi n} = 6[/tex] (in seconds)
Thus, the time (in seconds) that it take the pendulum to complete one full cycle is given by: Option C: 6 (seconds)
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The graph of line p represents = x-1. If the slope of line p is multiplied by (-10)
to create liner, which statement about the graphs of the two lines is true?
A
Line r intersects line p.
B Line ris parallel to line 2.
CLine ris 10 units above line p.
D
Line ris 10 units below line p.
Answer:
A. Line r intersects line p
Step-by-step explanation:
to find the second graph multiply the slope of line p by -10
slope is 1/5 or 0.2
So,
0.2 * -10 = -2
slope of second line is -2
Graph shown
Altered line shown in blue
Line p shown in green
As you can see, they intersect and meet no other answers
Please help me I’m not smart
and this test is due in one hour.
Answer:
the pitch of the sound
Step-by-step explanation:
because the speed stays the same and the echo has the same variables so i believe it is the pitch
who wants to be friends? and what is the square root of a decimal
Answer:
Mee
Step-by-step explanation:
brad buys a pack of 12 energy drinks for £9.25
he sells all 12 for £1
work out the percentage profit
give your answer correct to 2 significant figures
Answer:
I dont I know i want points
6 out of 18 in a fraction
Answer:1/3
Step-by-step explanation:1/3 is the simplified fraction for 6/18 by using the GCD or HCF method. Thus, 1/3 is the simplified fraction for 6/18 by using the prime factorization method.
Answer:
6/18=1/3
Step-by-step explanation:
here so the 6 is common with 18 and so that is 3
Solve the following polynomial equation. Identify all solutions.
x^(3)+54x^(2)+53x=0
Brainlest + Thanks :)
help asap
I do not understand this question
Answer:
B
Step-by-step explanation:
24 miles / 4 hours = 6 miles per hour
.
and answer B is showing a graph with slope of 6 miles per hour
Please anwser fast it’s due in 5 minutes
Answer:30000 just 5000+ six time
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
B they equations i are múltiple
Find the area of a circle with a circumference of 31.4 units.
Answer:
area = 78.46
Step-by-step explanation:
31.4 = 2pi * r
divide 31.4 by 2 and get 15.7
15.7 = pi * r
divide 15.7 by pi and get
4.997 = r
(4.997^2) * pi = 78.46
Answer:
I agree with you. that is what I got too
Tell whether the events are independent or dependent. Explain PLEASE HELP I WILL GIVE BRAINLIEST!!!
Answer:
5: independent, 6:independent, 7:independent, 8:dependent, 9:dependent
Step-by-step explanation:
5 is independent because the first roll of the die does nothing to affect the second.
6 is independent because the first flip of the coin does nothing to affect the second
7 is independent because the first draw from the bag does nothing to impact the second, if they didn't place a marble back then it would become dependent.
8 is dependent because by keeping the first marble you change the odds for the second draw. The second draw depends on the first.
9 is dependent because there is a set amount of names placed into this raffle. Say to start you have 12. That means you have a 1/12 chance of being chosen. Once your name is drawn it goes up to a 1/11 chance. The first action directly impacts the second making it dependent.
How many (and of what nature) roots does the function have?
Step-by-step explanation:
(x+1) (x+4)
x * x make x^2
1 & 4 when multiplied make 4 and when added make 5
What is the length of the missing side of the triangle below?(round to the nearest tenth)
Answer:
[tex] \sqrt{ {2}^{2} + {6}^{2} } = \sqrt{40 } = 2 \sqrt{10} [/tex]
Please help (no links or I will report you)
Answer:
0.60 or 0.6
Step-by-step explanation:
Divide three by five :)
3÷5= 0.6
Find the surface of each pyramid. round to the nearest tenth if necessary.
Given P(A) = 0.56, P(B) = 0.45 and P(B|A) = 0.7, find the value of
P(A and B), rounding to the nearest thousandth, if necessary.
Answer:
P(A and B) = P(AnB)
Step-by-step explanation:
[tex]P( \frac{A}{B} ) = \frac{P(AnB)}{P(B)} \\from \: bayes \: theorem \\ P(AnB) = P(B) \times P( \frac{A}{B}) \\ = 0.45 \times 0.7 \\ = 0.315[/tex]
Answer: 0.392
Step-by-step explanation:
So P(A)xP(B|A)= P(AnB)
Plug in
0.56x0.7=0.392
Explain your answer please ;w; : Change -2Y - 2X = -6 to the slope intercept form of the equation of a line.
Answer:
y = -x + 2
Step-by-step explanation:
The desired equation must have the form y = mx + b.
Start with -2Y - 2X = -6 and solve for y: y + x = 2
Now solve this result for y:
y = -x + 2
All right so i need someone to walkthrough the way to do this cause i'm lost. please do it step by step! Thanks!
Step-by-step explanation:
Hey there! Your answer :-
The skeletal formula of a quadratic equation is :-
[tex]\sf{ax^2 + bx + c}[/tex]
According to this question, we have :-
[tex]\sf{3x^2 + 8x + 4}[/tex]
So, the answers :-
a = 3b = 8c = 4Hope it helps :) Best of luck for your future!
Find each of the following angles and arcs formed in circle R. (PLEASE HELP!! WILL MARK BRAINLIEST!)
Answer:
m<RTV = 90°
m<TRU = 129°
m<TVU = 51°
m<TSU = 64.5°
mST = 101°
mSTU = 230°
Step-by-step explanation:
i just did it:)
The measure of each angles are; m<RTV = 90°, m<TRU = 129°, m<TVU = 51°, m<TSU = 64.5°, mST = 101° and mSTU = 230°.
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
Since Angle RTV is formed by the segments RT - that is the radius of the circle, and TV, which is tangent to the circle at point T. The radius always forms a right angle with the tangent lines.
Hence, the measure of angle RTV is; 90°.
The measure of a central angle and the measure of the intercepted arc would be equal. Hence, the measure of angle TRU is 129°.
Since RTVU is a quadrilateral. We know that 3 of the interior angles' measures are 90°, 90°, and 129°. The measures of the interior angles of any quadrilateral add up to 360°, the measure of angle TVU is 51°.
Thus the measure of angle TSU is 64.5°.
Also the sum of all consecutive arcs in a circle is 360°,
We know that mTU = 129° and mUS = 130° then the measure of arc ST is 101°.
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Evaluate each expression for n = 5. 6n + n2
Answer:
40
Step-by-step explanation:
1. Plug in the given value for n
6(5) + (5)2
2. Solve using PEMDAS
(I'm not sure if the 2 after the n is supposed to be squared, but if it was n^2 then the correct answer would be 55, I think)
30 + 10 = 40
Therefore, the answer is 40
Hope this helps :)
Mary wanted to solve the system of equations shown. She first used row reduction to get the system into 2 equations with 2 variables, x and y. She then used her calculator and got the graph shown. What is the solution to her system?
Answer: (2, -1, 3)
Step-by-step explanation:
The graph shows you that x=2 and y=-1 so, plug those values back into one of the equations to solve for z. You should get z=3 giving you a solution of (2, -1, 3).
Rewrite the quadratic equation in standard form y=5(x-2)^2+7
Answer:
To write a polynomial in standard form, simplify and then arrange the terms in descending order.
y=ax²+bx+c Simplify each term.
y=5x²−20x+20+7
Add 20 and 7.
y=5x²−20x+27
by-step explanation:
Find the radius when d=18
Answer:
9
Step-by-step explanation:
radius is half of the diameter
Use the graph at the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of 5.
Answer:
What image? (9/ -0) Is 9 - 8 =1
Step-by-step explanation:
Answer:
you dont have the image of the graph.
Step-by-step explanation:
Can someone help me solve this, I don't understand it.
Step-by-step explanation:
this, I don't understand it.can someone help me?? i’ll mark brainlist
Abby wants to ride her bicycle more than 70 miles this week. On Monday, Abby rode her bicycle for 25 miles. Abby plants to ride the same number of miles in the next six days. Write an inequality that can be used to determine the number of miles, m, that Abby will ride her bicycle each day to achieve her goal.
Answer:
25d > 70
Step-by-step explanation:
Abby wants to ride her bicycle more than 70 miles this week.
More than = >
On Monday, Abby rode her bicycle for 25 miles. Abby plants to ride the same number of miles in the next six days.
Let the number of days of week she would ride her bike = d
On Monday = 25 miles
And the rest of the week = The same = 25 miles
The inequality is written as:
25d > 70
I really need help on this, PLEASE HELP 20 POINTS!!
the question is in the picture please help efgahedn
Answer:
A) 3/56 + 27/56 = 30/56 ÷ 2/2 = 15/28
Step-by-step explanation:
So, there's 3/56 cities that have a lake and 27/56 cities that have a river.
Since the question is asking how much have a lake or river, we add them up.
3/56 + 27/56 = 30/56
(Divide by 2 since that's the common factor)
30/56 ÷ 2/2 = 15/28