A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum height of 10 mm halfway across a horizontal distance of 80 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
The spider's movement is an illustration of a parabola.
The equation of the parabola is: [tex]\mathbf{y = -\frac{1}{320}(x - 80)^2 + 20}[/tex]The focus of the parabola is [tex]\mathbf{Focus = (80 ,-60)}[/tex]The directrix is: [tex]\mathbf{y = 100}[/tex].The axis of symmetry is: [tex]\mathbf{x = 80}[/tex](a) The equation
The spider passes through the origin.
So, we have:
[tex]\mathbf{(x,y) = (0,0)}[/tex]
The spider jumps to a maximum height of 20mm, midway 160mm.
So, the vertex is:
[tex]\mathbf{(h,k) = (80,20)}[/tex]
The equation of a parabola is:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
So, we have:
[tex]\mathbf{0 = a(0 - 80)^2 + 20}[/tex]
[tex]\mathbf{0 = 6400a + 20}[/tex]
Subtract 20 from both sides
[tex]\mathbf{6400a =- 20}[/tex]
Solve for a
[tex]\mathbf{a =- \frac{1}{320}}[/tex]
Substitute [tex]\mathbf{a =- \frac{1}{320}}[/tex] and [tex]\mathbf{(h,k) = (80,20)}[/tex] in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
[tex]\mathbf{y = -\frac{1}{320}(x - 80)^2 + 20}[/tex]
(b) The focus, directrix and the axis of symmetry
The focus of a parabola is:
[tex]\mathbf{Focus = (h,k+p)}[/tex]
Where:
[tex]\mathbf{p = \frac{1}{4a}}[/tex]
So, we have:
[tex]\mathbf{p = \frac{1}{4\times -1/320}}[/tex]
[tex]\mathbf{p = -\frac{320}{4}}[/tex]
[tex]\mathbf{p = -80}[/tex]
So, we have:
[tex]\mathbf{Focus = (80 , 20-80)}[/tex]
[tex]\mathbf{Focus = (80 ,-60)}[/tex]
The axis of symmetry is:
[tex]\mathbf{x = h}[/tex]
So, we have:
[tex]\mathbf{x = 80}[/tex]
The directrix is:
[tex]\mathbf{y = k - p}\\[/tex]
So, we have:
[tex]\mathbf{y = 20+80}[/tex]
[tex]\mathbf{y = 100}[/tex]
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Choose all of the ordered pairs that are solutions to the equation y = x2 + 1.
A. (-2, 5)
B. (-1,0)
7. (1, 2)
D. (2, 4)
E. (3, 10)
Answer:
A, C, E
Step-by-step explanation:
Substitute the x- coordinate of the points into the equation and if the result is equal to the y- coordinate of the point then it is a solution.
A (- 2, 5 )
y = 2² + 1 = 4 + 1 = 5 → (- 2, 5 ) is a solution
B (- 1, 0 )
y = (- 1)² + 1 = 1 + 1 = 2 ≠ 0 ← not a solution
C (1, 2 )
y = 1² + 1 = 1 + 1 = 2 → (1, 2 ) is a solution
D (2, 4 )
y = 2² + 1 = 4 + 1 = 5 ≠ 4 ← not a solution
E (3, 10 )
y = 3² + 1 = 9 + 1 = 10 → (3, 10 ) is a solution
plsssssssssssssssshelppppppppppppppppppppppppppppppppppppp
Answer:
Help with what?
prove cos a = 5/13 pls solve it and no link pls..........
Answer : The demonstration is below :)
Step-by-step explanation :
We use Pythagoras' theorem :
In the triangle ABC we have :AB² = AC² - BC² = 15² - 9² = 144 = 12²
In the triangle ABD we have :DB² = AD² - AB² = 13² - 12² = 5²
cos(a) = BD/AD = 5/13
giải bài tập toán giúp tôi
Answer:
5x2 + 5x -1
Step-by-step explanation:
jus multiply 3x to 2x because there to the same power. it becomes a postive and you leave the rest.
Answer:
the first answer is right
6. Write the following cubes in expanded form:
(iii) (3a + 4b)³
8. Evaluate the following cubes using suitable Identities:
(ii) (999)³
Answer:
Step-by-step explanation:
we can use this algebraic identity:
[tex](a+b)^{3} =a^{3} +b^{3} +3ab(a+b)[/tex]
So,[tex](3a+4b)^{3} =(3a)^{3} +(4b)^{3}+3(3a)(4b)(3a+4b)[/tex]
=[tex](3a+4b)^{3} =27a^{3} +64b^{3} +36ab(3a+4b)[/tex]
=[tex](3a+4b)^{3} =27a^{3} +64b^{3} +108a^{2} b+144ab^{2}[/tex]
[tex](999)^{3}[/tex]=[tex](1000-1)^{3}[/tex]
Now, we can use the following identity:
[tex](a-b)^{3} =a^{3} -b^{3} -3ab(a-b)[/tex]
=[tex](1000-1)^{3} =1000^{3} -1^{3} -3(1000)(1)(1000-1)\\[/tex]
[tex](1000-1)^{3} =1,000,000,000-1-2,997,000[/tex]
[tex](1000-1)^{3} =997,002,999[/tex]
Look at the point in the picture. What is the y coordinate?
(3,-2)
Answer:
-2
Step-by-step explanation:
It's (x,y)
Here, (3,-2)
-2 is y
:)
if i had 475 cannolis ans a box can only carry 15 how many boxes will i need.
Answer:
you would need 32 boxes
Step-by-step explanation:
475/15 = 31.666
32 boxes
475/15=31.7 but you can't get 0.7 boxes so you would need 32 to carry all of the cannolis.
What is the two perfect squares of 237?
Answer:
What is the two perfect squares of 237?
Step-by-step explanation:
The Two perfect squares of 237
I guess It didn't have any square
although its square is 15.39480432
Help me please! I need this solved.
Answer:
c(10) = 10c i believe
Step-by-step explanation:
or the answer in the picture
The next model of a sports car will cost 4.1%, more than the current model. The current model costs $58,000 How much will the price increase in dollars? What
will be the price of the next model?
Answer:
$60378
Step-by-step explanation:
$58,000 represents 100% of the original cost
100 + 4.1= 104.1% = 104.1/100 = 1.041
Multiplying by 1.041 gives the cost after the increase
price = 53000 x 1.041 = $60378
The graph shown below expresses a radical function that can be written in the for f(x)=a(x+6)
Answer:
Step-by-step explanation:
MY SISTER HAVE DIS EQUETION I TELL YOU
find x if the base angles of an isosceles triangle are 47 degrees and 3x+14
Answer:
Step-by-step explanation:
The value of x is 11.
Given,
The base angles of an isosceles triangle are 47 degrees and 3x+14 degrees.
We need to find x.
What is an isosceles triangle?An isosceles triangle is a triangle that has two equal sides and two equal angles.
The equal angles are the base angles.
Find x.
We have,
Base angles: 47 degrees and (3x + 14) degrees
Since base angles are equal in an isosceles triangle.
We have,
47 = 3x + 14
47 - 14 = 3x
33 = 3x
x = 33/3 = 11
x = 11
Thus the value of x is 11.
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The product of twice a number and four is the same as the difference of seven times the number and 2/7 Find the number.
Answer:
the number is -2/7
Step-by-step explanation:
let the number be x
2x ×4= 7x-2/7
8x = 7x-2/7
collect like terms
8x-7x = -2/7
X= -2/7
What is the slope of a line parallel to y = 4x + 3.
Answer:Using the slope-intercept form, the slope is −4 - 4 .
Step-by-step explanation:To find an equation that is parallel to y=−4x−3 y = - 4 x - 3 , the slopes must be equal.
Answer:
the slope is −4 - 4
sorry if it’s wrong
Compare the graph of Car A to the table of Car B to determine which car is traveling at the greates
speed and by how much. Show work.
What is the slope of Car A’s graph? What does it mean
What is the slope of Car AB’s table? What does it mean?
Select the correct letter choice.
a. Car A is going 2 times faster than Car B
b. Car A is going 3 times faster than Car B
c. Car B is going 2 times faster than Car A
d. Car B is going 3 times faster than Car A
Answer:
A
Step-by-step explanation:
We can see that graph A has reached 8 and graph B has reached 4 so its 2 times faster then graph B! hope that helps.
Answer:
hey i am in k12 too can you help me
Step-by-step explanation:
Use the following graph to find the slope, y-intercept, and x-intercept. 2 (-6,0) (2,-2)
f(x) = -x^2-3x
find f (10)
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
f*(x)-(-x^2-3*x)=0
STEP
1
:
STEP
2
:
Pulling out like terms
2.1 Pull out like factors :
fx + x2 + 3x = x • (f + x + 3)
Equation at the end of step
2
:
x • (f + x + 3) = 0
STEP
3
:
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
3.2 Solve : x = 0
Solution is x = 0
Equation of a Straight Line
3.3 Solve f+x+3 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line f+x+3 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of f is -3/1 so this line "cuts" the f axis at f=-3.00000
f-intercept = -3/1 = -3.00000
Calculate the X-Intercept :
When f = 0 the value of x is -3/1 Our line therefore "cuts" the x axis at x=-3.00000
x-intercept = -3/1 = -3.00000
Calculate the Slope :
Slope is defined as the change in f divided by the change in x. We note that for x=0, the value of f is -3.000 and for x=2.000, the value of f is -5.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -5.000 - (-3.000) = -2.000 in f. (The change in f is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -2.000/2.000 = -1.000
Geometric figure: Straight Line
Slope = -2.000/2.000 = -1.000
x-intercept = -3/1 = -3.00000
f-intercept = -3/1 = -3.00000
x = 0
Can anyone help me solve this? Thank you. The question is provided on the attachment
Answer:
V I R T U E
Step-by-step explanation:
I) 3d = 3 × 3 = 9
E) 4d + a = 4(3) + 1 = 12 + 1 = 13
R) d² + 5 = (3)² + 5 = 9 + 5 = 14
V) bc + 3d = 1/2 × (-2) + 3(3) = -1 + 9 = 8
T) a - 3c = 1 - (3 × -2) = 1 - -6 = 7
U) √3c²d = √3 × (-2)² × 3 = √3 × 4 × 3 = √36 = 6
Correct order:
V I R T U E
- Equation Editor A set of curtains normally
sells for $58.99. Roberta used a coupon
good for 20% off the regular price. To the
nearest cent, how much did Roberta pay for
the curtains before sales tax?
Answer:
89.99
Step-by-step explanation:
u add i48934yr84 r84
Roberta paid the amount of $47.19 for the curtains before the sales tax.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that equation editor A set of curtains normally sells for $58.99. Roberta used a coupon good for 20% off the regular price.
To determine the amount for the curtains before the sales tax
According to the given conditions, the solution would be as:
⇒ 58.99 × (1 - 20%)
⇒ 58.99 × (1 - 0.20)
Calculate the sum or difference and we get
⇒ 58.99 × 0.80
Apply the multiplication operation to get
⇒ 47.192
Round the number nearest to the hundredth,
⇒ 47.19
Therefore, Roberta paid the amount of $47.19 for the curtains before the sales tax.
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What is the domain of the relation {(0,4), (4,9), (5,2), (10,4)}
a. 0, 2, 9, 10
b. 0, 2, 4, 10
c. 0, 4, 9, 10
d. 0, 4, 5, 10
Answer:
The domain is the set of all the values of x .
The range is the set of all the values of y.
Domain:
{0,4,5,10}
Range:
{4,9,2}
Step-by-step explanation:
your answer is is from an algebra solver called mathwey but an a instead of an e it solves everything i promise i use it all the time
8(-x - 7) > 16 I need the answer for it, I honestly don’t get it
Answer:
x > 8.125 or 8 & 1/8
Step-by-step explanation:
8( -x - 7) > 16
-8x - 49 > 16
+ 49 + 49
-8x > 65
x > 8.125 or 8 & 1/8
Bentley is deciding between two truck rental companies. Company A charges an initial fee of $50 for the rental plus $2 per mile driven. Company B charges an initial fee of $10 for the rental plus $3 per mile driven. Let AA represent the amount Company A would charge if Bentley drives xx miles, and let BB represent the amount Company B would charge if Bentley drives xx miles. Graph each function and determine the interval of miles driven, x,x, for which Company A is cheaper than Company B.
Company A is cheaper than Company B when x ___ _ ___
Answer:
after 41 miles A is cheaper than B
Step-by-step explanation:
not sure if this is what the question is asking for
guys pls help me!!!!!!
Answer:
Step-by-step explanation:
i think its 64 degrees
Angles on a straight line equals 180⁰
180⁰-64⁰
116⁰
x=116⁰
2 3/5 + 5 1/4 in a fraction
Step-by-step explanation:
[tex]2\frac{3}{5} +5\frac{1}{4}[/tex]
= [tex]\frac{13}{5} +\frac{21}{4}[/tex]
= [tex]\frac{52 + 105}{20}[/tex]
= [tex]\frac{157}{20}[/tex] Or [tex]7\frac{17}{20}[/tex]
Please give me a brainliest answer
Find the measures of the interior angles.
The three inside angles of a triangle when added together need to equal 180 degrees.
To find x subtract the other two angles from 180:
X = 180 - 65 - 40
X = 75
On the grid below draw a right triangle
with vertices at P(2, 4), Q(7, 9), and
R(10,6). what is the lengths of the three sides to the nearest tenth.
Answer: See attached image for graph
PQ: √50
QR: √18
PR: √68
Step-by-step explanation: We will use the 2D distance formula in order to get each side length. The distance formula is:
distance = √(x₂-x₁)² + (y₂-y₁)²Thus, we just apply this formula for each side length.
A spinner has 8 sections: 2 purple, 2 yellow, 3 blue,
and 1 red.
What is the probability of spinning and landing on
a color that is not yellow?
6
3
P(not yellow) = 6
P(not yellow) = 6/8
P(not yellow) = 2/8
Answer:
p=6/8
Step-by-step explanation:
there are 8 sections total and 6 sections that are not yellow
you have a 6 in 8 chance of landing on a color that isn't yellow/
6/8
hope this helps!
What is the number if 4 is subtracted from sum of 1 fourth of 5 times of 8 and 10
Answer:
Answer:18.5
Step-by-step explanation:
10+8=18
18*5=90
90/4
22.5-4=18.5
Have a happy day! <3Miss Hawaii
Answer:
16
Step-by-step explanation:
sum of 8 and 10=18
5 times of sum of 8 and
10= 18×5=80
1/4 of 5 times of sum of 8 and
10= 1/4×80=20
and then subtracted 4 from
20 =20-4=16
The table shows sets of ordered pads that form a relation
Does each set of ordered pairs represent a function?
Select Function or Not a Function for each set of ordered pairs
{(2,4),(3,1),(0,5),(-1,3)}
{(2,4),(4,1),(0,4), (3,0)}
{(-23),(4,1),(4,4),(3, 2)}
{(7-3),(3; -7), (2,4),(4, 2)}
Answer:
(5,2) (-2,5) this is how you solve an equation using simple graphd