Step-by-step explanation:
4.5 s, 324 ft
Explanation:
The object is projected upward with an initial velocity of
v_0 = 144 ft/sv
0
=144ft/s
The equation that describes its height at time t is
s(t) = -16t^2 + 144 ts(t)=−16t
2
+144t (1)
where t, the time, is measured in seconds.
In order to find the time it takes for the object to reach the maximum height, we must find an expression for its velocity at time t, which can be found by calculating the derivative of the position, s(t):
v(t) = s'(t) = -32t +144v(t)=s
′
(t)=−32t+144 (2)
At the maximum heigth, the vertical velocity is zero:
v(t) = 0
Substituting into the equation above, we find the corresponding time at which the object reaches the maximum height:
\begin{gathered}0=-32t+144\\t=\frac{144}{32}=4.5 s\end{gathered}
0=−32t+144
t=
32
144
=4.5s
And by substituting this value into eq.(1), we also find the maximum height:
s(t) = -16(4.5)^2+144(4.5)=324 fts(t)=−16(4.5)
2
+144(4.5)=324ft
used this way i even don't know sorry:))A bicycle costs $240 and it loses 3/5 of its value each year.
A. Write expressions for the value of the bicycle,in dollars, after 1,2, and 3 years
B. When will the bike be worth less than $1?
Answer:
A. $96.00, $38.40, $15.36
B. after 6 years
Step-by-step explanation:
An exponential function has the general form ...
y = (initial value) × (growth factor)^t
__
A.The growth factor is 1 more than the growth rate. Here, the "growth" is actually a decay at the rate of 60% per year, so the growth rate is -0.60. The initial value is $240. The value equation can be written ...
y = 240(1 -0.60)^t
We want the value after t=1, t=2, and t=3 years.
y = $240(0.4)^1 = $96 . . . value after 1 year
y = $240(0.4)^2 = $38.40 . . . value after 2 years
y = $240(0.4)^3 = $15.36 . . . value after 3 years
__
B.We want to find t when y < 1.
240(0.4)^t < 1
0.4^t < 1/240 . . . . . . . . . . . . divide by 240
t × log(0.4) < log(1/240) . . . take logs
t > log(1/240)/log(0.4) . . . . . . . inequality reverses because log(0.4) < 0
t > 5.98
The bike will be worth less than $1 after about 6 years.
_____
Additional comment
For part A, we have shown the values after 1, 2, and 3 years. The expressions are shown on the same line preceding the value.
ΔA'B'C' was constructed using ΔABC and line segment EH.
2 triangles are shown. Line E H is the line of reflection. Line segment B B prime has a midpoint at point D. Line segment A A prime has a midpoint at point F. Line segment C C prime has a midpoint at point G.
For to be the line of reflection between and , which statements must be true? Select three options.
BD = DB'
DF = FG
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
ΔABC is not congruent to ΔA'B'C'.
Answer: 1,3,4
Step-by-step explanation:
Answer: 1., 3., and 4.
Step-by-step explanation: On Edge!!
683+1738x175220=
Chose you answer:
304533043. 194739421. 345802178. 643221. 24753
I need help please give correct answer
A- 5 = 31
0.5b - 5 = 31
2c - 5 = 31
Answer:
what is the question?
Step-by-step explanation:
How do I solve this problem step by step?
Answer:
392.5 in²
Step-by-step explanation:
The area of a composite figure is found by decomposing it into areas that you have formulas for. This figure is easily decomposed to a trapezoid and a rectangle.
TrapezoidThe base lengths of the trapezoid are 20 in and 9 in. Its height is the difference between the height of its top base (21 in) and the height of its bottom base (16 in). That difference is 5 in.
A = 1/2(b1 +b2)h
A = 1/2(20 in + 9 in)(5 in) = 72 1/2 in²
__
RectangleThe area of a rectangle is the product of its base and height.
A = bh
A = (20 in)(16 in) = 320 in²
__
Total areaThe area of the whole figure is the sum of the areas of its parts.
area = trapezoid area + rectangle area
area = 72 1/2 in² +320 in² = 392 1/2 in²
Help me please! I’ll give Brainliest to the right answer!
Answer:
(x,y) ---> (x+9, y+8)
Step-by-step explanation:
you simply take one point (ex point R to R^1) and count the distance from left to right/right to left which is 9 so that is your X and count up which will be your Y in this case is 8.
2. A football is punted into the air. Its height h, in metres, after t seconds is given by the equation
h(t) = -4.91? + 24.5t + 1
a) How high is the ball after 1 second?
b) Find the maximum height of the ball to one decimal place.
c) When does the ball reach its maximum height?
d) When does the ball hit the ground?
Answer:
I'll assume the ? is supposed to be t^2
See the answers below.
Step-by-step explanation:
h(t) = -4.91t^2 + 24.5t + 1
a) How high is the ball after 1 second?
h(1) = -4.91*(1)^2 + 24.5*(1) + 1
h(1) = 20.59 meters
b) Find the maximum height of the ball to one decimal place.
We can find the maximum height by graphing or by taking the first derivative and setting it equal to zero (the slope is zero at the top of the curve):
First Derivative
h(t) = -4.91*(t)^2 + 24.5*(t) + 1
'h(t) = -9.82*(t) + 24.5
0 = -9.82*(t) + 24.5
9.82t = 24.5
t = 2.49 seconds is the time the ball reaches maximum height. Use that is the equation to find the height:
h(2.49) = -4.91*(2.49)^2 + 24.5*(2.49) + 1
h(2.49) = 31.6 meters
Graph
See attached graph. The maximum height occurs at t = 2.49 seconds and the height is 31.6 meters.
c) When does the ball reach its maximum height?
From the first derivative calculation above, t = 2.49 seconds to reach maximum height. The graph also shows 2.49 seconds. Better hurry.
d) When does the ball hit the ground?
The can be determined by either direct calculation of from the graph (attached).
Calculation:
h(t) = -4.91t^2 + 24.5t + 1
0 (ground) = -4.91t^2 + 24.5t + 1
4.91t^2 - 24.5t - 1 = 0 Solve with the quadratic equation. I get t = 5.04 seconds
Graph:
The graph shows 4.95 seconds. Both agree when rounded to one decimal point: 5.0 seconds.
Determine whether each relation is a function. Explain. {(2,0), (2, 2), (2, 4), (2, 6)}
helppppppppppppppppppppppp
Answer:
0.13m
Step-by-step explanation:
1m = 100cm
0.13m = 13cm
Answer:
0.13 meters
Step-by-step explanation
In metric measures the conversion from meters to centimeters is
1 meter = 100 centimeter
because centi means one hundredth and meter means the unit meter.
Therefore, 1 cm = 0.01 meter. Now you just multiply 13 on both sides and you get 13 cm = 0.13 meters
a rectangle has a perimeter of 36 feet. The length of the mat is twice the width. Write and solve an equation to determine the length, in feet, of the mat.
Then find the area, in square feet, of the mat.
❍ Concept :-
⠀
We have been provided with some information regarding a rectangular shaped mat. And on the basis of that information, we will create some assumptions and create and equation and equate it to get our required answer.
⠀
✱ Given Information :-
⠀
A rectangular mat with,
Perimeter = 36 ft. Length = twice the width⠀
✱ To Find :-
⠀
The dimensions of the matArea of the mat⠀
✱ Formula Used :-
⠀
[tex] \diamond \: \underline{ \boxed{\begin{array}{cc} \sf1. \: Perimeter_{Rectangle} = 2(l+b) \\ \\ \sf 2. ~Area_{Rectangle} = l\times b \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{array}}} \: \star \\ [/tex]
⠀
✱ Solution :-
⠀
Let the breadth of the mat be x, therefore,
Length = 2x⠀
Now, according to the question,
⠀
[tex] \sf \hookrightarrow 36 \: = 2(2x + x) \\ \\ \\ \sf \hookrightarrow 6x = 36 \: ft. \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow x = \cancel\frac{36}{6} = 6 \: ft. \: \: \\ [/tex]
Thus,
Length = 2x = 2 x 6 = 12 ft. Breadth = x = 6 ft.⠀
Now, we have to find out the area of the mat, thus,
⠀
[tex] \sf \hookrightarrow Area=6 \times 12 \\ \\ \\\sf \hookrightarrow Area=72 \: sq. ~ft. \\ \\ [/tex]
Thus, the area of the mat is 72 sq. ft.
⠀
[tex]\underline {\rule{221pt}{2.5pt}} \\ \\ [/tex]
Answer:
72 sq. feet
Step-by-step explanation
Since the perimeter is 36 feet and the length is 2w, you have to do the guess and check method.
I already did the guess and check method. So, here's how it became:
length =12
width=6
because 6x2=12 or 12 divide 2=6.
12 + 6 + 12 + 6.
12+6= 18. 12+6=18. 18+18=36 feet.
To find the area of a rectangle, you have to do L times W.
Which means 12x6.
12x6=72 sq. feet.
I hope this helps!!!
Consider this composite figure made of a cone and a cylinder. a cone has a height of 8 centimeters and radius of 3 centimeters. a cylinder has a height of 7 centimeters and radius of 3 centimeters. what is the volume of the cone? cone v = 1 3 bh v = 1 3 πr2h v = 1 3 π32(8) v = 1 3 π(9)(8) v = 1 3 π(72) the cone has a volume of π cm3
The volume of the cone with a radius of 3 cm and height of 8 cm is 24 π cm³. Then the correct option is D.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
Consider this composite figure made of a cone and a cylinder.
A cone has a height of 8 centimeters and a radius of 3 centimeters.
A cylinder has a height of 7 centimeters and a radius of 3 centimeters.
Then the volume of the cone will be
We know that the volume of the cone
[tex]\rm Volume = \dfrac{1}{3} \pi r^2 h[/tex]
Then we have
[tex]\rm Volume = \dfrac{1}{3} \ \pi \ 3^2 *8\\\\\rm Volume = \dfrac{1}{3} \ \pi *9*7\\\\\rm Volume = \dfrac{1}{3} \ \pi \ 72\\\\Volume = 24 \ \pi[/tex]
More about the geometry link is given below.
https://brainly.com/question/7558603
Answer:
24
Step-by-step explanation:
Got it right on the question
For each set of three lengths, determine if they can be the side lengths of a triangle.
Answer:
Yes, No, Yes, NoStep-by-step explanation:
Use the triangle inequality theorem, which states that the sum of any two side lengths must be greater than the third side length.
Apply this to each combination.
Use one inequality, compare the sum of smallest two sides with the largest side.
1) 4, 9, 8
4 + 8 = 12 > 9, so Yes2) 7, 25, 7
7 + 7 = 14 < 25, so No3) 8.8, 24, 15.8
8.8 + 15.8 = 24.6 > 24, so Yes4) 5, 9, 3
3 + 5 = 8 < 9, so NoWhat is the circumference
Each tick mark shows 1 third. What's
1
3
more than 1?
2
1
2
3
1
3
0
Answer:
Step-by-step explanation:
1/3 more than 1 is 1 1/3 or 4/3.
What is the constant term in the expression 8xy − 9x2 y − 5x 6
Answer:
6
Step-by-step explanation:
A constant is a term without a variable.
Every other number has a variable (x,y) to it except for 6.
Feel free to save this for whenever you get stuck on things like this! I know this section is hard.
In the expression 8xy − 9x^2+ y − 5x +6 the constant term is 6 which is a fixed quantity or cannot be changed.
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have an expression:
[tex]\rm 8xy-9x^2+y-5x+6[/tex]
Let's denote it with f(x,y)
[tex]\rm f(x,y) =8xy-9x^2+y-5x+6[/tex]
As we know the constant term means which cannot be changed that values are fixed or fixed quantity.
From the above expression, the constant value in the expression is 6
Thus, in the expression 8xy − 9x^2+ y − 5x +6 the constant term is 6 which is a fixed quantity or cannot be changed.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ4
The population of Hampton was 7,490 people when Malik moved there. Currently it is 10% smaller. What is the current population?
people
Answer:
6741
Step-by-step explanation:
if its 10% smaller you would have to do the original precent, which is 100%, and subtract 10%, (90%) then divide 90 by 100 to get 0.9 and multiply it by the total population, in this case 7,490, and you get your answer. i hope this helps :)
9 halves of a cupcake for my family plus extra for my 6 friends how many should I
buy.
Answer :- 7½ or 8 ( explained below)
Explanation:-
Given :-
9 halves for family6 halves for friendsSo in total :- 15 halves for both of them
It means :- 7½ cupcakes in total u required
if u can buy an half cupcake then u need to buy :- 7½
If u can't but an half cupcake then u need to buy :- 8
Answer:
Step-by-step explanation:
8 for learning games
The area of a square is 9ft find the area of a square with 4 times as large
Answer:
36ft
Step-by-step explanation:
9ft times 4ft= 36ft
Unit 10: circles homework 2: central angles & arc measures
The central angle (127 degrees) is the angle at point K
The measures of JL and JML are 127 and 233 degrees, respectively
How to determine the measures of angles JL and JML?From the complete question, we have:
JL = 127 degrees.
The sum of angles at a point is 360 degrees
So, we have:
JML + 127 = 360
Subtract 127 from both sides
JML = 233
Hence, the measures of JL and JML are 127 and 233 degrees, respectively
Read more about circles and arcs at:
https://brainly.com/question/25305793
18 less than the quotient of a number and -5 is greater than 3
Step-by-step explanation:
x = "a number"
x/-5 - 18 > 3
help! complete the table with the missing measurements. the perimeter is 40ft is that helps
therer sorry for the cropped pic btw lol
19. Which of the following statements about the number line is true?
A. Numbers get smaller as you move to the left on the number line.
B. Number lines can't help you compare numerals.
O C. Numbers get larger as you move to the left on the number line.
D. Number lines end with the number 10.
Answer:
A. Numbers get smaller as you move to the left on the number line.
Step-by-step explanation:
A number line is typically drawn so that smaller, more negative numbers are on the left, and larger, more positive numbers are on the right.
__
Numbers get smaller as you move to the left on the number line.
_____
Additional comment
Number lines can be drawn with any scale and range, depending on what they are intended to represent. For representation of small integers, it is not uncommon for a number line to range from -10 to +10. However, that is not the only possible range that might be used.
Any number line can be used to show number order (least to greatest ≡ left to right). A number line with a linear scale can also be used to show relative differences between numbers: a greater distance on the number line corresponds to a greater difference between numbers.
I have five apples and ten oranges. If a fruit basket must contain at least one piece of fruit, how many kinds of fruit baskets can I make
Answer:
answer is 15
please that is what I'm thinking
The owner of a music store ordered new compact disks. Of the new compact disks ordered,1/4 are Jazz, 2/7 are Classical, and the rest of the compact disks are Soft Rock. What fraction of the compact disks ordered are Soft Rock?
The fraction of the compact disks ordered by the owner of the music store that are Soft Rock is 13/28.
What are fractions?A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator. The numerator is the number above while the denominator is the number below.
What fraction is Soft Rock?1 - (1/4 + 2/7)
1 -[ (7 + 8) /28]
1 - 15/28 = 13/28
c) d) When 3 is subtracted from the number, the remainder is 5.
Answer:
so the equation would look like this, x - 3 = 5
the number or x = 8
Step-by-step explanation:
8 - 3 = 5
Hope this helps! :)
that are equivalent to 4(3x + 3)
Answer: 4(3 x + 3) would be equivalent to 12 x + 12 .
Step-by-step explanation: because both expressions remains the same for the value of x . *your welcome <3* .
Solve the system using substitution
y+8x=10
2y-4x=40
(_,_)
Step-by-step explanation:
i used the two methods....I hope this will help you!
A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 6?
A. 13/2
B. 7/26
C. 2/13
D. 6/52
Answer:
C
Step-by-step explanation:
There are 4 aces and 4 sixes. 4 + 4 is 8 (since it says or) so the chance is 8 / 52. 8 / 52 simplified, divide both sides by 4 and you get 2 / 13.
Answer:
C
Step-by-step explanation:
there are 4 aces and 4 sixes in a deck of 52 cards.
"And" means a probability * another probability
"Or" means a probability + another probability.
In this case, it is (probability of picking an ace) + (probability of picking an six).
[tex]\frac{4}{54} + \frac{4}{54} = \frac{8}{54} = \frac{2}{13}[/tex]
Please pick as brainliest!
ILL GIVE THE BRAINLIEST TO THE PERSON WHO DOES THIS FOR ME THANK YOU
(Statistics hw)
11% of the total are left handed
so if we take random 100 students then 11% will be applicable to it also
so :-
[tex] \frac{11}{100} \times 100 \\ 11students[/tex]
HELP PLEASE I NEED IT NOW.
Answer:
Below :)
Step-by-step explanation:
1) 5^2 = 25
2) 12^2 = 144
3) 9^2 = 81
4) 15^2 = 225
5) 8^2 = 64
6) 7^2 = 49
7) 20^2 = 400
8) 13^2 = 169
9) 30^2 = 900
10) 25^2 = 625