Answer:
a) = 3.96
b) = 0.72
c) = 7.94
Step-by-step explanation:
Complete question.
(A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by h(x) = -0.046x2+ 0.364x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c.What is the length of the jump? Round to 1 decimal place.)
Solution.
Data
Θ = 20
v = 11m/s
h(x) = -0.046x² + 0.364x
x = horizontal distance
h = height
a.
h(x) = -0.046x² + 0.364x
at maximum height,
d / dx (h) = 2(-0.46x) + 0.364
d / dx (h) = -0.092x + 0.364
at maximum height d / dx (h) = 0
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96.
b).
Hmax = -0.046x² + 0.364x
Hmax = -0.046(3.96) + 0.364(3.96)
Hmax = -0.72 + 1.44
Hmax = 0.72
c) the length of the jump can be calculated using the formula for range of a projectile
R = v² sin2Θ / g
g = 9.8m/s²
R = 11² * sin 2(20) / 9.8
R = 121 * sin40 / 9.8
R = 77.777 / 9.8
R = 7.936 = 7.94
a. The maximum height occurs at a horizontal distance of 3.96 meters.
b. The maximum height of the long jumper is 0.72 meters.
c. The length of the long jumper's jump is approximately 7.94 meters.
a. The maximum height occurs when the derivative of the height function with respect to horizontal distance is equal to zero.
Given h(x) = -0.046x² + 0.364x
Taking the derivative of h(x) with respect to x:
dh/dx = -0.092x + 0.364
Setting dh/dx to zero and solving for x:
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96
Therefore, the maximum height occurs at a horizontal distance of 3.96 meters.
b. To find the maximum height, substitute x = 3.96 into the height function h(x):
h(3.96) = -0.046(3.96)² + 0.364(3.96)
h(3.96) = -0.72 + 1.44
h(3.96) = 0.72
The maximum height of the long jumper is 0.72 meters.
c. The length of the jump, also known as the range, can be calculated using the formula for the range of a projectile:
R = v^2 * sin(2θ) / g
Given:
v = 11 m/s
θ = 20°
g = 9.8 m/s²
Substitute these values into the formula:
R = 11^2 * sin(40°) / 9.8
R = 121 * sin(40°) / 9.8
R = 121 * 0.6428 / 9.8
R = 77.777 / 9.8
R ≈ 7.94
Therefore, the length of the long jumper's jump is approximately 7.94 meters.
Complete question :
(A long jumper leaves the ground at an angle of 20° above the horizontal, at a speed of 11 m/sec. The height of the jumper can be modeled by h(x) = -0.046x2+ 0.364x, where h is the jumper's height in meters and x is the horizontal distance from the point of launch. a. At what horizontal distance from the point of launch does the maximum height occur? Round to 2 decimal places. b. What is the maximum height of the long jumper? Round to 2 decimal places. c.What is the length of the jump? Round to 1 decimal place.)
Solution.
Data
Θ = 20
v = 11m/s
h(x) = -0.046x² + 0.364x
x = horizontal distance
h = height
a.
h(x) = -0.046x² + 0.364x
at maximum height,
d / dx (h) = 2(-0.46x) + 0.364
d / dx (h) = -0.092x + 0.364
at maximum height d / dx (h) = 0
0 = -0.092x + 0.364
0.092x = 0.364
x = 3.96.
b).
Hmax = -0.046x² + 0.364x
Hmax = -0.046(3.96) + 0.364(3.96)
Hmax = -0.72 + 1.44
Hmax = 0.72
c) the length of the jump can be calculated using the formula for range of a projectile
R = v² sin2Θ / g
g = 9.8m/s²
R = 11² * sin 2(20) / 9.8
R = 121 * sin40 / 9.8
R = 77.777 / 9.8
R = 7.936 = 7.94.
Can you explain it and help me out please
Answer:
D. two real solutions
Step-by-step explanation:
p²+5 = 6p
p² - 6p +5 =0
D = b² - 4ac = (-6)² - 4*(1)*5 = 36 - 20 = 16
D > 0, so this equation has 2 real solutions
Which of these is not a Pythagorean Triple?
Select one:
a. 5,12,13
b. 3,4,5
c. 1,2,3
d. 7,24,25
Answer:
C because the rest are pythagoreaum theroems 1 squared plus 2 squared does not equal 3 squared.
Step-by-step explanation:
wo lengths of a triangle are shown. wo lengths of a triangle are shown. Triangle J K L. Side J K is 5 inches and side J L is 10 inches. Which could be the length of Side K L? 4 in. 9 in. 16 in. 19 in.Triangle J K L. Side J K is 5 inches and side J L is 10 inches. Which could be the length of Side K L? 4 in. 9 in. 16 in. 19 in.
Answer:
B/2: 9 inches
Please answer this correct:):)
Patel is solving 8x? + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options,
Answer:
8x+16x+3=0
24x+3=0
24x=3
x=24÷3
x=8
2 Points
Multiply the polynomials.
(х- 7)(х2 + 3х – 3)
ОА. 3 – 4х2 – 24
21
О
В. x — 7х2 — 24х + 21
ооо
Ос. 3 – 72 - 3x+21
O
D. х3 – 4х2 – 3х+21
SUBM
Answer:
213
Step-by-step explanation:
Question 1
Factor the following expression using the GCF. Type your factored expression below.
4xy + 12w + 12Z
Answer:
4(xy + w + z)
Step-by-step explanation:
The expression to be factored is:
4xy + 12w + 12z
Factoring an equation involves taking out common terms from the expression that will then make it more simpler and simplified.
To solve this problem, we need to find the factors of the given terms:
4xy
12w
12z
The numbers given as coefficients of the variables are;
4 12 12
A factor is any integer that divides a number evenly;
Factors of 4 are 1, 2 and 4
12 are 1, 2,3,4,6 and 12
The common factors between 4 and 12 are those numbers that can divide both digits:
These are 1, 2, and 4, they are common to both
Now, the greatest common factor is the highest of this factors which is 4
Therefore, the greatest common factor of 12 and 4 is 4
Also, xy, w and z has no common factors
Factoring
4xy + 12w + 12z = 4(xy + w + z)
pls help thankssssssssssssssssssssssssssssss
Answer: The answer is 525.
Step-by-step explanation:
7*(5)^2*(3)= 525
Find the exact volume of the cylinder.
A) 14π m3
B) 28π m3
C) 56π m3
D) 112π m3
(the height is 7 and the radius is 2)
Answer:
Option B) [tex]28\pi\text{ m}^3[/tex]
Step-by-step explanation:
We are given the following in the question:
Radius of cylinder, r = 2 m
Height of cylinder, h = 7 m
We have to find the volume of the cylinder.
Volume of cylinder =
[tex]V = \pi r^2 h[/tex]
where r is the radius and h is the height of the cylinder.
Putting values, we get,
[tex]V = \pi (2)^2(7)\\V = 28\pi\text{ cubic meter}[/tex]
Thus, the volume of cylinder is
Option B) [tex]28\pi\text{ m}^3[/tex]
Hi, love!!
The correct answer is listed below:
A) 14π m3
B) 28π m3
C) 56π m3
D) 112π m3
A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i.e., which figure’s volume increases by a larger factor)? Justify your answer. Write “pi” for ''pi symbol'' and “r^2”.
Answer:
The change in the cone produces a greater increase in volume.
Step-by-step explanation:
Let's start with the cone.
[tex]V = \frac{1}{3} \pi r^{2} h[/tex]
[tex]V = \frac{1}{3} \pi 3r^{2} \frac{h}{2}[/tex] (In your case, you would type V = 1/3pi3r^2h/2)
The changes that occurred are [tex]3^{2}[/tex] and [tex]1/2[/tex]. When we add these together we get [tex]9/2[/tex].
Now the cylinder.
[tex]V = \pi r^{2} h[/tex]
[tex]V = \pi r^{2} 2h[/tex] (In your case, you would type V = pir^2 2h)
The change that occurred is [tex]2[/tex].
[tex]9/2[/tex] is greater than [tex]2[/tex] which means that the change in the cone produces a greater increase in volume.
Answer:
Step-by-step explanation:
For the cone V k1= (Pi/3) .R squared .H
V k2= (pi/3) . (3R)squared . (H/2)=(9/2) .(PI/3) . R squared.H
=(3pi/2) R.squared.H
3pi/2
nk= 2/ pi/3
N k= 9/2
For the cylinder
V c1=Pi .R squared.H
V c2= Pi.R squared.(2H)
N c=V c2/V c1=2
Cone has greatest change in volume
Hope this helps!!!!!!!!
My nephew was playing with a book and tore out the pages 7, 8, 100, 101, 222 and 223.
How many sheets did he tear out?
Answer:
Step-by-step explanation:
A sheet has 2 pages
6 pages are torn. So 6 ÷ 2 = 3 sheets
Answer:
3 pages
Step-by-step explanation:
7 and 8 are one page
100 and 101 are one page
222 and 223 are one page
He tore out 3 pages
compare the two groups of data. which statement is true?
Answer:
a) both have the same spread
Step-by-step explanation:
Mean of Brand A > Mean of Brand B
Median of A > Median of B
Spread of:
A: 22 - 18 = 4
B: 18 - 14 = 4
The spread of the data which is obtained by calculating the Interquartile range of each distribution since the distributions are skewed is 2 for brand A and brand B. Hence, the spread is the same.
The distribution of BRAND A chips :
18, 19, 19, 19, 19, 19, 19, 20,20,20,20,20,20,21,21,21,21,21,21,22
The Upper quartile, Q3 ;
Q3 = 0.75 × (n + 1)th term
Q3 = 0.75 × 21 = 15.75 th term = 21
The Lower quartile, Q1 ;
Q1 = 0.25 × (n + 1)th term
Q1 = 0.25 × 21 = 5.25 th term = 19
The IQR = Q3 - Q1 = (21 - 19) = 2
The distribution of BRAND B chips :
14,14,14,14,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,18
The Upper quartile, Q3 ;
Q3 = 0.75 × (n + 1)th term
Q3 = 0.75 × 21 = 15.75 th term = 16
The Lower quartile, Q1 ;
Q1 = 0.25 × (n + 1)th term
Q1 = 0.25 × 21 = 5.25 th term = 14
The IQR = Q3 - Q1 = (16 - 14) = 2
Therefore, the spread of distribution of BRAND A and B are the same.
Learn more :https://brainly.com/question/15191516
a 3rd grade teacher has 55 students everyday if those 55 students turned into 100 students how many students would it be.
Answer:
45 because you have to subtract 100-55 which would equal 45
Answer:
Yeah it would be 45
Step-by-step explanation:
Because:
100 - 55 = 45
Can someone help me out please
Answer:
The slope is one. I cant graph it for you though. Try plotting the points then drawing a straight line down those points.
Step-by-step explanation:
Mathematics VI
Which property is represented by the following equation?
5 x 13 x 2 = 5x 2 x 13
Answer:
commutative
Step-by-step explanation:
-The ability to change the order to terms in a addition or multiplication problem.
What is the effect on the graph of the function f(x) =^8x when f(x) is replaced with f(x − 2)?
Answer:
f(x - 2) = 8x - 16
Step-by-step explanation:
f(x) = 8x
f(x - 2) = 8(x - 2)
f(x - 2) = 8x - 16
5
10. George, Sandy, Carlos, and Michelle all ate a piece of a whole
pecan pie. George ate 0.15 of the pie, Michelle ate of the pie,
and Carlos ate of the pie. Sandy ate more than two of her
friends, but less than the other one. What is a possible
percentage of the ple Sandy ate?
Answer:
0.150 < (Proportion of Sandy's pie) < 0.167
15% < (Percentage of Sandy's pie) < 16.7%
Step-by-step explanation:
Total percentage of pie = 100% or 1
George, Sandy, Carlos, and Michelle all ate a piece of the pie.
George ate a fraction of 0.150
Michelle ate a fraction of (1/6) = 0.167
Carlos ate a fraction of (1/7) = 0.143
The amount of pie left = 1 - 0.15 - (1/6) - (1/7) = 0.5405
And Sandy is known to eat more than two of her friends, but less than one of them.
Of the amount of pie eaten by the first 3 friends, (1/6) is the highest proportion.
Hence, it is evident that Sandy ate more than 0.143 and 0.150 (Carlos and George) but less than Michelle (0.167).
So, mathematically, the possible proportion of cake that Sandy ate is
0.150 < (Proportion of Sandy's pie) < 0.167
Hope this Helps!!!
Evaluate 5 × (4.75 + 1.50) - 3 × 1.25
Answer:
The answer is 27.5
Answer:
25.50
Step-by-step explanation:
5(4.75+1.50)-3 x 1.25
23.75+5.50-3x 1.25
29.25-3x1.25
29.25-3.75
25.50
Can you please help me out plz asap
Answer:
1. A
2. B
3. C
you have to judge the fraction based on the other dilations and the answer choices
What does b mean, and how do I work out b and c? No need to answer a
What is the greatest common factor of 4x^3
and 8x^2?
Answer:
the gcf is 4
Step-by-step explanation:
Final answer:
To find the greatest common factor of 4x³ and 8x², we look at the numerical coefficients and the variables separately. The GCF of the coefficients 4 and 8 is 4, and since x² is the lowest power of x common in both terms, the GCF is 4x².
Explanation:
The greatest common factor (GCF) of two expressions, like 4x³ and 8x², involves finding the highest degree of common terms they share. First, let's compare the numerical coefficients; 4 and 8. The GCF of 4 and 8 is 4. Next, we'll look at the variable part. The lowest exponent of x that appears in both terms is 2. Therefore, the GCF is the product of the GCF of the coefficients and the lowest power of x, which is 4x².
A linear function has a slope of Negative StartFraction 7 Over 9 EndFraction and a y-intercept of 3. How does this function compare to the linear function that is represented by the equation y + 11 = Negative StartFraction 7 Over 9 EndFraction (x minus 18)?
Answer:
They are the same line written in different forms.
Step-by-step explanation:
Given a linear function with a slope of [tex]-\frac{7}{9}[/tex] and a y-intercept of 3.
The equation of the line in the slope-intercept form is given as:
[tex]y=-\frac{7}{9}x+3[/tex]
Given the other line,
[tex]y+11=-\frac{7}{9}(x-18)[/tex]
Simplified:
[tex]y+11=-\frac{7}{9}x+14\\y=-\frac{7}{9}x+14-11\\y=-\frac{7}{9}x+3[/tex]
The two lines are one and the same line.
Answer:
They are the same line written in different forms.
Construct a triangle with the given dimensions:
angle measure of 39°
angle measure of 76°
angle measure of 65°
You can create with the given measurements.
Answer:
you can make 3 different triangles by using the protector and setting the given angles.
Steps:-
1. Make a dot on the page.
2.Point the protector's intersecting point at the dot.
3.Now mark the given angle measurements as well as 0°.
Now connect the angle measurement with the dot and then dot with 0°
Which of the following best describes the algebraic expression x/3-15
O
A. Three divided by a number minus fifteen.
O
B. A number divided by three less than fifteen.
O
C. Three divided by a number less than fifteen.
O
D. A number divided by three minus fifteen.
Answer:
D. A number divided by three minus fifteen.
i neeeeeeeed heeeeeelp
Order the numbers from greatest to least.
2.34, 234, 94
Answer:
234, 94, 2.34
Step-by-step explanation:
Please help
Which shapes can be cross sections of the figure?
Check all that apply.
A,circle
B,rectangle
C,trapezoid
D,triangle
E,semicircle
Answer:
The answer is B,C, and D
Step-by-step explanation:
I GOT. THE. QUESTION. RIGHT. ON. EDUNUTITY
I would also love an explanation!
Answer:you go up one over three
Step-by-step explanation:
the nth term of a number sequence is 2n+5
Answer:
Step-by-step explanation:
hello you idiot
help meeeeeeeeeeeeeeee
Answer:
2 years
Step-by-step explanation: