a. It will take 1.53 seconds for the rocket to reach its maximum height.
b. The rocket will reach a maximum height of 38.04 ft (rounded to the nearest tenth).
c. The range of the function h(t) is bounded below by h0 (0 ft) and above by h_max (38.04 ft). In mathematical notation, the range is:
Range = {h | h ∈ R, h0 ≤ h ≤ h_max}
d. The maximum point on the graph of the function exists because of the negative coefficient of the t^2 term (-16).
**a. Time to reach maximum height:**
The rocket's motion can be modeled by the formula:
h(t) = -16t^2 + vt + h0
where:
* h(t) is the height of the rocket at time t
* t is the time in seconds
* v is the initial upward velocity (49 ft/s)
* h0 is the initial height (0 ft)
We need to find the time t when the height h(t) is maximum. Since the acceleration due to gravity (-16 ft/s^2) is negative, the maximum height happens at the vertex of the parabola represented by the equation.
The time to reach the vertex can be found using the formula:
t_vertex = -v / (2a) = -49 / (2 * -16) = 1.53 seconds (rounded to the nearest hundredth)
Therefore, it will take 1.53 seconds for the rocket to reach its maximum height.
**b. Maximum height:**
Now, plug the t_vertex value back into the equation to find the maximum height:
h(1.53) = -16(1.53)^2 + 49(1.53) + 0 = 38.04 ft
Therefore, the rocket will reach a maximum height of 38.04 ft (rounded to the nearest tenth).
**c. Range of the function:**
The range of the function depends on the initial parameters (velocity and height) and the gravitational acceleration. Since the acceleration due to gravity is always negative, it acts as a downward force pulling the rocket back down. This means the highest point the rocket can reach is its initial height plus the maximum height achieved due to the initial velocity.
Therefore, the range of the function h(t) is bounded below by h0 (0 ft) and above by h_max (38.04 ft). In mathematical notation, the range is:
Range = {h | h ∈ R, h0 ≤ h ≤ h_max}
**d. Reason for the maximum point:**
The maximum point on the graph of the function exists because of the negative coefficient of the t^2 term (-16). This term represents the downward force due to gravity, which continuously slows down the rocket's upward motion. Eventually, the upward velocity becomes zero, and the rocket starts descending due to gravity. This point of zero velocity corresponds to the vertex of the parabola, which represents the maximum height achieved.
Type the correct answer in the box. Use a decimal number instead of words.
Find the sum of a finite geometric series.
A ball is dropped from a height of 10 meters. Each time it bounces, it reaches 50 percent of its previous height. The total vertical distance down the ball has traveled when it hits the ground the fifth time is meters.
-3(n-6)-9 i need to simplify the expression.
What is the equation of the circle with center (11, 6) that passes through the point (17, 12)?
well, the distance from the center of a circle to any point "on" the circle is simply just its radius, thus
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{center}{(\stackrel{x_1}{11}~,~\stackrel{y_1}{6})}\qquad (\stackrel{x_2}{17}~,~\stackrel{y_2}{12})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(17-11)^2+(12-6)^2}\implies r = \sqrt{36+36}\implies r=\sqrt{72} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{11}{ h},\stackrel{6}{ k})\qquad \qquad radius=\stackrel{\sqrt{72}}{ r} \\\\\\ (x-11)^2+(y-6)^2=(\sqrt{72})^2\implies (x-11)^2+(y-6)^2=72[/tex]
Final answer:
The equation of the circle with center (11, 6) that passes through the point (17, 12) is (x - 11)² + (y - 6)² = 72.
Explanation:
To find the equation of the circle with center (11, 6) that passes through the point (17, 12), we first determine the radius of the circle. The radius can be found by calculating the distance between the two points using the distance formula: √[(x2-x1)² + (y2-y1)²]. Plugging in the coordinates, we get √[(17-11)² + (12-6)²] = √[6² + 6²] = √[36 + 36] = √72. The squared radius (r²) is therefore 72.
The general form for the equation of a circle is: (x - h)² + (y - k)² = r², where (h, k) is the center of the circle. Substituting the center (11, 6) and the squared radius 72 into this equation, we get: (x - 11)² + (y - 6)² = 72, which is the desired equation of the circle.
Find the values of x and y
Answer:
x = 12; y = 60
Step-by-step explanation:
The opposite sides of a parallelogram are always equal, so x+3 = 15, making x = 12
The opposite angles of a parallelogram are always equal, making y = 60
50 points and brainleist
A value of 500 increases by 12%. -Which equation could be used to find the new value? A) y=500+(0.12)
B) y=500(1.12)
C) y=500+(0.12)
D) y=500-(0.12) - What is the new value? Answer:Equation_______could be used to find the new value. The new value is______.
Solution:
Given that,
A value of 500 increases by 12%
To find: equation could be used to find the new value
Therefore,
Initial value = 500
Increase rate = 12 %
Let "y" be the new value
Thus the equation is:
new value = Initial value + 12 % of Initial value
[tex]y = 500 + 12 \% \text{ of } 500\\\\y = 500 + 12 \% \times 500\\\\y = 500(1 + 12 \%)\\\\y = 500(1 + \frac{12}{100})\\\\y = 500( 1 + 0.12)\\\\y = 500(1.12)[/tex]
Thus the equation is found. Option B is correct
Solve it
[tex]y = 500 \times 1.12\\\\y = 560[/tex]
Thus the new value is 560
Answer:
Hat he said
Step-by-step explanation:
State the slope and the y-intercept of this equation: y = -4x - 9
Answer:
slope = - 4, y- intercept = - 9
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 4x - 9 ← is in slope- intercept form
with slope m = - 4 and y- intercept c = - 9
A = 3 b = 4 c=4
1) 3a + 5=
2)4b - 7=
3)6a - 1 =
4) bc -a=
Answer:
1.) 3(3) + 5 = 9 + 5 = 14
2.) 4(4) - 7 = 16 - 7 = 9
3.) 6(3) - 1 = 18 - 1 = 17
4.) (4)(4) - (3) = 16 - 3 = 13
Complete the table. Original Price Percent of Discount Sale Price $42 15% $
Answer:
35.70
Step-by-step explanation:
42. x 15%=6.30
42-6.30 is 35.70
or you can multiply 42 x 85=35.70
Answer:
$35.70
Step-by-step explanation:
$35.70
The diameter is { ? }
cm.
r = 5.4 cm
The circumference in terms of pi { ? } is
cm.
Using 3.14 for pi , the approximate circumference of the
circle is { ? } cm. Find the answers for the “?”’s .
The diameter of the circle is 10.8 cm
The circumference of the circle is 33.9 cm
Explanation:
Given that the radius of the circle is 5.4 cm
Diameter:
The diameter of the circle can be determined using the formula,
[tex]d=2r[/tex]
where r = 5.4
Thus, we have,
[tex]d=2(5.4)=10.8[/tex]
Thus, the diameter of the circle is 10.8 cm
Circumference:
The circumference of the circle can be determined using the formula,
[tex]C=2\pi r[/tex]
Substituting [tex]\pi=3.14[/tex] and [tex]r=5.4[/tex], we have,
[tex]C=2(3.14)(5.4)[/tex]
[tex]C=33.9[/tex]
Thus, the circumference of the circle is 33.9 cm
Plz help in ASAP I need it I will give you BRAINLEIST whatevrr it is called
Answer:
1.)x≤9
2.)x≥0.5
Step-by-step explanation:
1.)x+6≤15
x+6-6≤15-6
x≤9
2.)x+1.5≥2
x+1.5-1.5≥2-1.5
x≥0.5
What is the volume ,in cubic meter ,of a cylinder with a height of 3 neters and a base radius of 4 meters ,to the nearest theths place
Answer:
volume = 150.9m³
Step-by-step explanation:
in order to find the volume ,in cubic meter ,of a cylinder with a height of 3 meters and a base radius of 4 meters ,to the nearest theths place wee apply the formular for finding the volume of a cylinder which is πr²h
v = πr²h
given that
height = 3meters
radius = 4meters
volume=?
going by the formulae v= πr²h
v = π × (4)² × 3
v = π × 16 ×3
v= 48πm³
note the value of π = 22/7
v = 48 × 22/7
v = 1056/7
v= 150.87m³
therefore the volume of the cylinder to the nearest tenth place is 150.9m³
what is 2+4 in the world today
Answer:
i guess it is 6? maybe
Step-by-step explanation:
Answer: I WOULD SAY 24 BUT FOR SOME REASON IT IS 6
Step-by-step explanation:
pens cost x pence and pencils cost y pence. Write a formula for the total cost (T) of 7 pens and 11 pencils
Answer:
erhaerah
Step-by-step explanation:
hearherharehr
Simplify 4-6+2x-9x-8
Answer:
x = -10/7
Step-by-step explanation:
Step 1: Combine like terms
4 - 6 + 2x - 9x - 8
-7x - 10
Step 2: Solve for x
-7x - 10 = 0
-7x - 10 + 10 = 0 + 10
-7x / -7 = 10 / -7
x = 10/-7
Answer: x = -10/7
Is {(-5,1),(4,9),(6,10)} a function
Willie had some candy to give to his five
children. He first took nine pieces for
himself and then evenly divided the rest
among his children. Each child received
three pieces. With how many pieces did
he start?
Answer he had 24 pieces
Step-by-step explanation: 5 children had 3 each 5 x 3 = 15
and 9 for him self 15+9=24
A line that includes the points (10,g) and (9,4) has a slope of 2. What is the value of g?
g=
Answer:
g = 6
Step-by-step explanation:
Calculate the slope m using the slope formula and equate to 2
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (10, g) and (x₂, y₂ ) = (9, 4)
m = [tex]\frac{4-g}{9-10}[/tex] = [tex]\frac{4-g}{-1}[/tex] = 2 ( multiply both sides by - 1 )
4 - g = - 2 ( subtract 4 from both sides )
- g = - 6 ( multiply both sides by - 1 )
g = 6
how many 9s are in 54??
Answer:
Whats 's' mean?
Step-by-step explanation:
Answer: 6
Step-by-step explanation:
9s=54
divdie 9 by 54 to get the s alone. 54/9 is 6. t
The cost of 3 gallons of milk is $6.75. What is the cost of 7 gallons of milk?
Answer:
1. The cost of 7 gallons of milk is $15.75
2. 5 cups served and 40 ounces drank
Step-by-step explanation:
Answer:
$15.75
Step-by-step explanation:
Let the cost of 7 gallons of milk be x
Since
3 gallons of milk = $6.75
7 gallons of milk = x
Cross multiply
7 x 6.75 = 3 x X
47.25 = 3x
Divide both sides by 3
47.25/3 = 3x/3
15.75 = x
x = $15.75
7 gallons of milk cost $15.75
What is the answer to $2.48 for 10 slices of cheese
Answer:
2.48 / 10 = 0.248
About $0.25 for each slice of cheese.
Answer:
.248 or .25
Step-by-step explanation:
Write the quadratic equation in standard form that represents the table below:
20 POINTS IF YOU HELP!
Final answer:
The quadratic equation in standard form is t² + 14.3t - 20 = 0. It can be solved using the quadratic formula.
Explanation:
The quadratic equation in standard form that represents the given table is:
t² + 14.3t - 20 = 0
Where t represents the variable and the constants are a = 1.00, b = 14.3, and c = -20.0. The solutions to this equation can be found using the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
In the figure, △
ABC are in adjacent planes. AB = AC = 5cm, BC = 6cm and o then AE is equal to
Answer: its = to 6 cuz AB/AC = BC/AE and BC is 6 so give brainless psl
Step-by-step explanation:
ez ezz
The value of x in the right-angle triangle is 2√3.
What is a right-angle triangle?A triangle is also known as a right-angled triangle if one of its three angles is 90 degrees. A right-angled triangle's three interior angles all add-up to 180 degrees, thus if one angle is always 90 degrees, the other two must also always add up to 90 degrees.
In the given figure,
BC = 6cm
DC = 6/2 = 3cm
By formula of angle on a straight line,
∠EDB = 180° - (90°+60°)
= 180° - 150°
= 30°.
From right-angled triangle ADC,
AD² = 5² -3² (As per Pythagoras theorem)
= 25 - 9
= 16.
So, AD = √16
= 4cm.
From ∠AEC. let AS = x.
w/Sin60° = 4/Sin90°
We know,
Sin90° = 1
Sin60° = √3/2
⇒ x = (4 × Sin60°)/Sin90°
⇒ x = 4 × √3/2
⇒ x = 2√3
To know more about right-angled triangles, visit:
https://brainly.com/question/3770177
#SPJ1
The complete question is:
In the figure, △
ABC are in adjacent planes. AB = AC = 5cm, BC = 6cm and o then AE is equal to
Which of the following tables represents a function?
Answer:
Table D represents the function.
Step-by-step explanation:
Because for every value of x, there is an unique value of y.
Answer:
D
Step-by-step explanation:
the answer is d because the x doesn't repeat itself and for a -7 repeats it self, for b -8 repeats and for c -6 has 2 times. That's why those 3 can not be answer.
12. Judith randomly selected 20% of the
seventh-grade students in her school
and asked them their favorite genre of
music of these students surveyed 41
chose pop music as the favorite music
genre. Based on the data, what is the
most reasonable prediction of the
number of seventh-grade students in
her school who would choose pop
music as their favorite season?
i believe the answer is 205
hope this helps
The most reasonable prediction of the number of seventh-grade students in Judith's school who would choose pop music as their favorite genre is 205.
To find the prediction, we first need to determine the total number of seventh-grade students in Judith's school. Since 41 students represent 20% of the total, we can set up a proportion to find the total number of students. Let [tex]\( T \)[/tex] represent the total number of students.
[tex]\[ 20\% \times T = 41 \][/tex]
[tex]\[ 0.20 \times T = 41 \][/tex]
To find [tex]\( T \)[/tex], we divide both sides of the equation by 0.20:
[tex]\[ T = \frac{41}{0.20} \][/tex]
[tex]\[ T = 205 \][/tex]
Now that we have the total number of students, we can predict the number of students who would choose pop music as their favorite genre. Since 41 students represent 20% who chose pop music, the remaining 80% of the students would also be expected to choose pop music if the sample is representative of the entire population. Therefore, we multiply the total number of students by 100% to find the prediction:
[tex]\[ \text{Prediction} = T \times 100\% \][/tex]
[tex]\[ \text{Prediction} = 205 \times 1 \][/tex]
[tex]\[ \text{Prediction} = 205 \][/tex]
Thus, the most reasonable prediction is that 205 seventh-grade students in Judith's school would choose pop music as their favorite genre.
Write the coordinate of the point in the diagram.
Answer:
(2, 2, 1)
Step-by-step explanation:
You can see that the point is moved 2 units (x axis), 2 units (y axis) and 1 unit (z axis). Because you write coordiantes as (x,y,z), you write (2,2,1)
Angle a and angle b are complementary angles. The measure of ∠a is 42°.
Which equation represents this situation with x representing the measure of ∠b ?
A) 90+42=x
B) 42+x=90
C) 42−x=90
D) 90+x=42
Answer: B) 42 + x = 90
Step-by-step explanation:
A complementary angle always equals 90 degrees. So, with that information, all you have to do is list the measurement of b as x and create an equation. Knowing that the measurement of angle a is 42 degrees, we can now find an equation. So, we would take the measurement of angle a, 42 degrees, and add the measurement of angle b, listed as x, which should equal 90 degrees.
A parallelogram gas an area of 4 feet squared and a base length of 8 in. What is the height of the parellelogram
Answer:
0.5
Step-by-step explanation:
The formula for area of a parallelogram is b × h, so we can use this to find the missing value.
b × h = a
8 × h = 4
÷ 8 ÷ 8
h = 0.5
To check:
8 × 0.5 = 4, which is correct.
Your real answer is
16
10
160
got it right on edg.
An equiangular triangle can be scalene
Answer:
No, as a scalene triangle's sides are are different, while an equilateral's sides are all the same.
Hope that helps, :)
Round 562 to the nearest ten
Answer:
560
Step-by-step explanation:
Answer: 560
Since it did not hit 565 it is 560.
The points (–1,–1) and (a,–5) fall on a line with a slope of 4. What is the value of a?
a=
Answer:
The value of a is -2
Step-by-step explanation:
We are asked to give the value of a
We are provided with some information
We are given slope to be 4
And two points ( -1 ,-1) and
( a, -5)
Given the formula for slope
m = y_2 - y_1 / x_2 - x_1
Points ( -1 , -1)
(a, -5)
x_1 = -1
y_1 = -1
x_2 = a
y_2 = -5
Inserting the values given into
m = y_2 - y_1 / x_2 - x_1
= -5 - (-1) / a - (-1)
= -5 + 1 / a + 1
= -4 / a + 1
We are given the slope to be 4
i. e. m = 4
4 = -4 / a + 1
Cross multiply
4( a + 1) = -4
Open the bracket with 4
4a + 4 = -4
Collect like terms
4a = -4 - 4
4a = - 8
Divide both sides by 4 to get the value of a
4a / 4 = -8/4
a = -2
Therefore, x_2 = -2
the value of a = -2