A soccer player who is 27 feet from a goal attempted to kick the ball in into the goal. the flight of the ball is modeled by a parabola. the ball reached a maximum height of 10 feet when it was 15 feet from the soccer player. the goal has a height of 8 feet. will the soccer ball land in the goal?
Answers
Answer:
The ball will land inside the goal.
Step-by-step explanation:
Given : The flight of the ball is modeled by a parabola.
To find : Will the soccer ball land in the goal?
Solution :
Let the equation of the parabola be,
[tex]y=a(x-h)^2+k[/tex]
Where, (h,k) are the vertex of the parabola,
According to question,
A soccer player who is 27 feet from a goal.
Let A be the point where player stand i.e, (27,0)
The height of the goal is 8 feet.
Let B be the point of height of goal i.e, (0,8)
The ball reached a maximum height of 10 feet when it was 15 feet from the soccer player.
The distance from goal to the distance 15 feet away from the player is
27-15=12 feet
Let C be the point with maximum height i.e, (12,10)
C is the vertex of the parabola and A is the point on the parabola.
Then, The equation of parabola is
[tex]y=a(x-12)^2+10[/tex]
Point A satisfy the equation,
[tex]0=a(27-12)^2+10[/tex]
[tex]0=a(15)^2+10[/tex]
[tex]a=-\frac{10}{225}[/tex]
Substitute back in equation,
[tex]y=-\frac{10}{225}(x-12)^2+10[/tex]
Now, we find the y-intercept of the equation i.e, x=0,
[tex]y=-\frac{10}{225}(0-12)^2+10[/tex]
[tex]y=-\frac{10}{225}(144)+10[/tex]
[tex]y=3.6[/tex]
If the y-intercept is greater than 8 then the ball will land outside the goal.
If the y-intercept is less than 8 then the ball will land inside the goal.
As 3.6<8
Therefore, The ball will land inside the goal.
Refer the attached figure below.
Final answer:
The soccer ball will not land in the goal due to its maximum height being above the height of the goal.
Explanation:
To determine if the soccer ball will land in the goal, we need to analyze its flight path. From the given information, we know that the ball reached a maximum height of 10 feet when it was 15 feet from the soccer player. This indicates that the ball's flight path is modeled by a downward-opening parabola.
Since the soccer player is 27 feet from the goal, we can consider the ball's horizontal distance from the player to the goal as the x-coordinate, and its height above the ground as the y-coordinate.
Based on the given information, the soccer ball will not land in the goal. The ball's maximum height is 10 feet, but the goal has a height of 8 feet. This means that at any point along its flight path, the ball's height will be above the height of the goal.
Related Questions
Which lines must be parallel if angle 10 is supplementary to angle 11?
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Khalid invested $9500 in a savings account with a yearly interest rate of 3% for 8 years. How much simple interest did he earn?
Answers
9500*[1+(0.03*8)]
giving us 9500*1.24 = $11,780
Answer:
$2280
Step-by-step explanation:
The __________ is the score that occurs most frequently in a distribution.
Answers
|2y+10|=-4 solve for y
Answers
2y+10=-4
2y=-14
y=-7
The absolute value of something can never be negative.
Need Answer ASAP!!!!!!!Solve the equation using the zero product property. -n(5n-4)=0
Answers
-5n^2+4n=0
n(-5n+4)=0
n=0
-5n+4=0
-5n=-4
n=4/5
Answer:
[tex]n=0\text{ or }n=\frac{4}{5}[/tex]
Step-by-step explanation:
We have been given an equation [tex]-n(5n-4)=0[/tex]. We are asked to solve our given equation using zero product property.
Zero product property states that the product of two expressions are zero, if and only if, one of them is zero.
Using zero product property, we will set each factor of our equation to zero as:
[tex]-n=0\text{ or }(5n-4)=0[/tex]
[tex]n=0\text{ or }5n-4=0[/tex]
[tex]n=0\text{ or }5n-4+4=0+4[/tex]
[tex]n=0\text{ or }5n=4[/tex]
[tex]n=0\text{ or }\frac{5n}{5}=\frac{4}{5}[/tex]
[tex]n=0\text{ or }n=\frac{4}{5}[/tex]
Therefore, the solutions for our given equation are [tex]n=0\text{ or }n=\frac{4}{5}[/tex].
How to find an equation in slope intercept form given two points?
Answers
(1,2)(3,4)
first we find the slope by using the slope formula
slope = (y2 - y1) / (x2 - x1)
now we label our points..
(1,2)...x1 = 1 and y1 = 2
(3,4)...x2 = 3 and y2 = 4
now we sub and find the slope
slope = (4 - 2) / (3 - 1) = 2/2 = 1....so we have a slope of 1
now we use y = mx + b
slope(m) = 1
use either of ur points...(1,2)...x = 1 and y = 2
now we sub into the formula and find b, the y int
2 = 1(1) + b
2 = 1 + b
2 - 1 = b
-1 = b ....this is ur y int
and in y = mx + b form, the slope will be in the m position and the y intercept will be in the b position
y = mx + b
slope(m) = 1
y int (b) = -1
so ur equation in slope intercept form is : y = 1x + (-1) which can be written as : y = x - 1
define a variable and write an inequality to model each situation. The school auditorium can seat at most 1200 people.
Answers
Evaluate 4x^3 + 2 for x
Answers
X=-1
Plug in x
4 (-1)^3+2
4 (-1)+2
-4+2
-2
Answer: -2 (D)
Check your work: -2=4x^3+2
-2 both sides
-4=4x^3
÷4 both sides
-1=x^3
(Square root by 3) both sides
X=-1
Answer is correct
= -4 + 2
= -2
A 10-pound weight in a 2-pound weight are dropped from the same height at the same time which weight will hit the ground first
Answers
they would drop at the same time
Answer:
explained below
Step-by-step explanation:
when two object one of 10 pound weight and another of 2 pound is dropped from same height
condition 1 : when body fall In vaccum
When body fall in vaccum then there will be no effect of weight.
Both the body will hit the ground at the same time.
Condition 2 : when body falls in normal condition
When body falls in normal condition then in this condition the heavy weight object will fall first as the light weight object will have more air resistance than the heavy one.
Find the point-slope form of the equation of the line passing through the points (–1, –3) and (4, 1).
Answers
Your y1 value is -3 and your x1 value is -1.
Before we can solve the equation, we need the slope first. To find the slope of a line, we need to use the equation y2-y1/x2-x1.
That would be 1-(-3)/4-(-1) which translates to 4/5. Your slope is 4/5.
Now we can plug this into the point slope form.
y-(-3)=4/5(x-(1))
That would be y+3=4/5x+4/5. You must then subtract 3 from 4/5.
This would mean that y=4/5x-2.2
Hope this helps.
Which expression is the factored form of 2/3x+4 ?
A 2/3(x+6)
B 2/3(x+12)
C 2/3(x+4)
D 1/3(2x+6)
Answers
2/3x+4
4/(2/3)=6
2/3(x+6)
5x + 2y = 8
x + y = 4
If you want to solve the system of equations by addition, which of the following could you do?
(A.) Multiply the second equation by 5 and add.
(B.) Multiply the second equation by 2 and add.
(C.) Multiply the second equation by -2 and add.
Answers
Answer: C. Multiply the second equation by -2 and add
Step-by-step explanation:
Answer:
Step-by-step explanation:
The solution is C
5x + 2y = 8
-2x -2y= -8
3x = 0
x = 0
2y = 8
y = 4
(0,4)
Whether or not a measurement gives the same results when it is repeated under the same conditions is an indication of the measurement’s _____
Answers
At Susie's school, 5/8 of all students play sports. Of the students who play sports, 2/5 play soccer. What fraction of the students in Susie's school play soccer?
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Dustin has only nickels and quarters in his piggy bank. He has 49 coins total for a combined value of $8.85. How many of each does he have
Answers
Answer:
Dustin has 17 nickels and 32 quarters.
Explanation:
Let's denote the number of nickels as [tex]\(n\)[/tex] and the number of quarters as [tex]\(q\).[/tex]
We can set up a system of equations based on the given information:
1. The total number of coins: [tex]\(n + q = 49\)[/tex]
2. The total value of the coins: [tex]\(0.05n + 0.25q = 8.85\)[/tex]
We can solve this system of equations to find the values of [tex]\(n\) and \(q\).[/tex]
From equation (1), we can express [tex]\(n\)[/tex] in terms of [tex]\(q\):[/tex]
[tex]\[n = 49 - q\][/tex]
Now, substitute this expression for [tex]\(n\)[/tex] into equation (2):
[tex]\[0.05(49 - q) + 0.25q = 8.85\][/tex]
[tex]\[2.45 - 0.05q + 0.25q = 8.85\][/tex]
Combine like terms:
[tex]\[0.20q + 2.45 = 8.85\][/tex]
Subtract 2.45 from both sides:
[tex]\[0.20q = 6.40\][/tex]
Now, divide both sides by 0.20:
[tex]\[q = \frac{6.40}{0.20} = 32\][/tex]
So, Dustin has 32 quarters.
To find the number of nickels, we can substitute the value of \(q\) into the equation [tex]\(n + q = 49\):[/tex]
[tex]\[n + 32 = 49\][/tex]
[tex]\[n = 49 - 32\][/tex]
[tex]\[n = 17\][/tex]
So, Dustin has 17 nickels.
If 6 cats can kill 6 rats in 6 minutes, how many cats will it take to kill 100 rats in 50 minutes? previous next
Answers
200
If a car travels 23 miles on 1.0 gal of gas, how many liters of gasoline are needed for a 135 mile trip?
Answers
Find all values of thetaθ, if thetaθ is in the interval [0degrees°, 360degrees°) and has the given function value cot thetaθ=1
Answers
The 2 angles are 45 and 180+45 = 225 degrees
Answer 45 , 225 degrees.
Loretta invested $1000 in a simple interest account yielding 5% paid annually. In 2 years, she will have $1100 in her account. From this example, we can conclude that 5% represents the:
Answers
Final answer:
The 5% represents the annual interest rate on Loretta's investment in a simple interest account.
Explanation:
The 5% represents the annual interest rate on Loretta's investment. In simple interest, the interest is calculated as a percentage of the initial investment. So, if Loretta invested $1000, and after 2 years her account has grown to $1100, the interest earned would be $100 (1100 - 1000).
To find the interest rate, we can use the formula:
Interest = Principal * Rate * Time
Using the given information, we can plug in the values and solve for the rate:
100 = 1000 * Rate * 2
Simplifying the equation, we get:
Rate = 100 / (1000 * 2) = 0.05 or 5%
Therefore, the 5% represents the annual interest rate in this scenario.
Approximately how many times greater is 9.75 * 10^6 than 1.25 * 10^2?
Answers
9.75 / 1.25 = 7.8
10^6 - 10^2 = 10^4
= 7.8 x 10^4 greater
A diver descends from an elevation of 6 feet below sea level to an elevation
of 98 feet below sea level in 4 equal intervals. What was the diver’s change in
elevation in each interval? Explain how you solved this problem.
Answers
Now, since he descended in four equal intervals, we can just divide 92 into four equal parts, or divide by 4, to get 23 feet.
So the diver's change in elevation in each interval was (negative?) 92 feet.
The perimeter of a rectangle is 42 inches, and its area is 110 square inches. find the length and width of the rectangle.
Answers
[tex]a = l * w[/tex] [tex]a = 108[/tex]
You want to make either the length or width variable (I chose the width variable to be by itself. It doesn't matter) by itself by:
Divide both sides by 2.
(p) ÷ 2 = (2w + 2l) ÷ 2
[tex]2's[/tex] [tex]cancel[/tex] [tex]out[/tex]
[tex] \frac{p}{2} = w + l[/tex]
Subtract both sides by either length or width depending on what variable you chose to make by itself (in this case I subtracted the length variable because I wanted the width variable by itself).
[tex]\frac{p}{2} - l = w + l - l[/tex]
[tex]l's[/tex] [tex]cancel[/tex] [tex]out[/tex]
p/2 - l = w
[tex]a = l * w[/tex]
You replace w with the equation above p/2 - l = w
[tex]a = l( \frac{p}{2} - l)[/tex]
Multiply out the L.
[tex]a = \frac{p}{2}l - l^{2}[/tex]
Plug in all your numbers a = 110 and p = 42
[tex]110 = \frac{42}{2}l - l^{2}[/tex]
[tex]110 = 21l - l^{2[/tex]
Move everything to the left side so [tex] l^{2} [/tex] would be positive (makes the equation easier when [tex] l^{2} [/tex] is positive).
[tex]l^{2} - 21l + 110 = 0[/tex]
Factor.
[tex](l -10)(l-11) = 0[/tex]
Make each parenthesis set equal to 0.
[tex]l-11=0[/tex] [tex]l-10=0[/tex]
Add.
[tex]l = 11[/tex] [tex]l = 10[/tex]
By doing this you solve for both the width and length so the answer is:
w = 11 L = 10
Compare 4:10 and 12:20 using fractions. Which ratio is smaller? How do you know?
Answers
Answer:
4:10 is smaller because when put into fraction form and making the denominators even, 12:20 comes out to be 6/10
Step-by-step explanation:
Which of the following is an odd function? f(x) = x3 + 5x2 + x mc023-1.jpg f(x) = x2 + x f(x) = –x
Answers
(a) f(x) = x³ + 5x² + x
(b) f(x) = x² + x
(c) f(x) = -x
Function (a)
f(-x) = (-x)³ + 5(-x)² + (-x)
= -x³ + 5x² - x
= -(x³ - 5x² + x)
The function is neither even nor odd.
Function (b)
f(-x) = (-x)² + (-x)
= -(-x² + x)
The function is neither even nor odd.
Function (c)
f(-x) = -(-x)
= x
= -f(x)
Because f(-x) = -f(x) the function is odd.
Answer: f(x) = -x is an odd function.
By evaluating each function in -x, we will see that the only odd one is:
f(x) = -x
What is an odd function?
We say that a function is odd if:
f(-x) = f(x)
Then we just need to check that for the given functions, let's see what we get:
1) f(-x) = (-x)^3 + 5*(-x)^2 + (-x) = -x^3 + 5x^2 - x ≠ -f(x)
2) f(-x) = (-x)^2 - x= x^2 - x ≠ -f(x)
3) f(-x) = -(-x) = x = -f(x)
So the only odd function is the third one, one useful thing that you may need to know is that usually when you see even exponents, that function will not be odd.
If you want to learn more about odd functions, you can read:
https://brainly.com/question/1561362
Group A has an elevation of -282 feet. group B has an elevation of 279 feet. which is closer to sea level
Answers
--- sea level ---
~ -282 feet
distance of group B = 279 ft
So group B is closer
A segment has an endpoint (14,-8) and (4,12) what are the coordinates of its midpoint
Answers
The coordinates of the midpoint of the segment that has endpoints as (14,-8) and (4,12) are (9,2).
What are the coordinates of the midpoint of the line segment AB?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
Suppose we've two endpoints of a line segment:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
x = (p+m) / 2
and
y = (q+n) / 2
Given that a segment has an endpoint (14,-8) and (4,12). Therefore, The coordinates of the midpoint of the segment can be written as,
X- coordinate = (14+ 4)/2
= 18/2
= 9
Y- coordinate = (-8+12)/2
= 4/2
= 2
Hence, the coordinate of the midpoint of the segment that has endpoints as (14,-8) and (4,12) is (9,2).
Learn more about Midpoint here:
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the base of a pyramid has n sides write an expression for the number of faces of the pyramid
Answers
This means that a pyramid always have the number of face which is one more than the number of sides of the base.
Therefore, given that a pyramid has n number of sides of the base, the expression for the number of faces of the pyramid is given by
number of faces = n + 1.
Curt just drank a cup of coffee to help him stay awake. The coffee had 130 milligrams of caffeine in it. If his body processes 7% of the caffeine every hour, how much will be left in 4 hours?
93
94
98
91
Answers
Answer:
After 4 hours, there will 91.31 miligrams of caffeine within his body.Step-by-step explanation:
Givens
Curt drank 130 miligrams of caffeine.His body processes 7% of caffeine everyhour.If Curt's body processes 7% every hour, we just need to that 7% after each hour. Also, we know that 7% equals 0.07.
First hour.
[tex]0.07(130)=9.1ml[/tex]
The first hour, his body processed 9.1 miligrams, so it remains
[tex]130-9.1=120.9ml[/tex]
There's still 120.9 miligrams in his body.
Second hour.
[tex]0.07(120.9)=8.46ml[/tex]
[tex]120.9-8.46=112.44ml[/tex]
Third hour.
[tex]0.07(112.44)=7.87ml[/tex]
[tex]112.44-7.81=104.63ml[/tex]
Fourth hout.
[tex]0.07(104.63)=7.32ml[/tex]
[tex]104.63-7.32=97.31ml[/tex]
Therefore, after 4 hours, there will 91.31 miligrams of caffeine within his body.
0.90 divided by 0.30 PLEASE SHOW WORK OR EXPLAIN YOUR REASONING!
Answers
Hope this helps!
first write it as a fraction =0.9/0.3
then you multiply the numerator and the denominator by 10= 9/3
divide the 9 and the 3 =3
hope this helps
for geometric sequence below, determine the explicit formula. be sure to enter your answer as a formula of the form a_n= a_1(r)^(n-1) with the correct a_1 and r values.
5/8, 25/8, 125/8, 625/8, . . ., a_n
Answers
Let's calculate r:
r = a₂ / a₁
r = (25/8) / (5/8)
r = 5.
Since a₁ = 5/8
[tex]\boxed{\mathsf{a_n = \frac{5}{8}\cdot 5 ^{n-1}}}[/tex]