A ball is thrown vertically from the top of a building. The height of the ball after t seconds can be given by the function
Answers
Answer:The instantaneous velocity of the ball after 4 seconds is -0.4 m/s
Step-by-step explanation:
Step-by-step explanation:
If f(x) is the function which represents the distance that a particle moves after x seconds, with velocity v and acceleration a, then
v(x) = f'(x) ⇒ first derivative
a(x) = f"(x) ⇒ second derivative
∵ A ball is thrown vertically from the top of a building
∵ The height of the ball after t seconds can be given by the
function s(t)= -0.1(t -2)² + 10
- To find the function of the velocity differentiate s(t)
∵ s(t) = -0.1(t - 2)² + 10
- Solve the bracket
∵ (t - 2)² = t² - 4t + 4
∴ s(t) = -0.1(t² - 4t + 4) + 10
- Multiply the bracket by -0.1
∴ s(t) = -0.1t² + 0.4t - 0.4 + 10
- Add the like terms
∴ s(t) = -0.1 t² + 0.4t + 9.6
Now let us differentiate s(t)
∵ s'(t) = -0.1(2)t + 0.4(1)
∴ s'(t) = -0.2t + 0.4
- s'(t) is the function of velocity after time t seconds
∵ s'(t) = v(t)
∴ v(t) = -0.2t + 0.4
We need to find the instantaneous velocity of the ball after 4 seconds
Substitute t by 4
∴ v(4) = -0.2(4) + 0.4
∴ v(4) = -0.8 + 0.4
∴ v(4) = -0.4
∴ The v is -0.4 m/s ⇒ -ve means the velocity is downward
The instantaneous velocity of the ball after 4 seconds is -0.4 m/s
Related Questions
i need help w/ this!! thank you
Answers
[tex]\boxed{\pink{\sf \leadsto Yes \ there \ is \ a \ solution \ of \ the \ given \ inequality .}}[/tex]
Step-by-step explanation:A inequality is given to us and we need to convert it into standard form and see whether if it has a solution . So let's solve the inequality.
The inequality given to us is :-
[tex]\bf\implies |2y + 3 | - 1 \leq 0 \\\\\bf\implies |2y+3|\leq 1 \\\\\bf\implies (|2y+3|)^2 \leq 1^2 \\\\\bf\implies (2y+3)^2 \leq 1 \\\\\bf\implies (2y)^2+3^2+2(2y)(3) \leq 1 \\\\\bf\implies 4y^2+9+12y - 1 \leq 0 \\\\\bf\implies 4y^2+12y+8 \leq 0 \\\\\bf\implies 4( y^2 + 3y + 2 ) \leq 0 \\\\\bf\implies y^2+3y +2 \leq 0 \:\:\bigg\lgroup \purple{\bf Standard \ form \ of \ inequality }\bigg\rgroup \\\\\bf\implies y^2y+2y+y+2 \leq 0 \\\\\bf\implies y(y+2)+1(y+2)\leq 0 \\\\\bf\implies ( y+2)(y+1)\leq 0 \\\\\bf\implies \boxed{\red{\bf y \leq (-2) , (-1) }}[/tex]
Let's plot a graph to see its interval . Graph attached in attachment .
Now we can see that the Interval notation of would be ,
[tex]\boxed{\boxed{\orange \tt \purple{\leadsto}y \in [-2,-1] }}[/tex]
Hence the standard form of inequality is y²+3y +2 ≤ 0 and the Solution set of the inequality is [ -2 , -1 ] .The rectangle shown has a perimeter of 84 cm and the given area. Its length is 6 more than 5 times its width. Write and solve a system of equations to find the dimensions of the rectangle.
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What is an equivalent ratio for 7:9
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plz answer my question
Answers
When you diffuse (multiply) the 4 to the rest of the number r become 4r and 3 becomes 12 giving you the equivalent of 4r+12
a group of hikers is progressing steadily along up uphill trail. the graph shows their elevation
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What is a point-slope equation of the line with slope -12 that goes through the point (5, 3)?
A. y- 3 = -12(x - 5)
B. y + 3 = 12(x + 5)
C. y + 3 =-12(x + 5)
D.y-3 = 12(x - 5)
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Answer:
A. y- 3 = -12(x - 5)
Step-by-step explanation:
find the difference.
(4−5y)−2(3.5y−8)
Answers
Answer:
-12y + 20
Step-by-step explanation:
First, you simplify each term:
apply the distributive property:
4 - 5y - 2 (3.5y) - 2 x -8
Multiply 3.5 by -2:
4 - 5y - 2 (3.5y) - 2 x -8
Multiply -2 by -8:
4 - 5y - 7y +16
Next, we simplify by adding terms:
Add 4 + 16:
-5y - 7y + 20
Subtract 7y from 5y:
-12y + 20
Hence the simplified form is -12y + 20
Answer:
-4·(3y-5)
Step-by-step explanation:
Josiah and his children went into a grocery store and he bought $15 worth of peaches and mangos. Each peach costs $0.50 and each mango costs $1.50. He bought 2 more mangos than peaches. Graphically solve a system of equations in order to determine the number of peaches, x,x, and the number of mangos, y,y, that Josiah bought.
Answers
p = peaches, m = mangos
1.75p + 1.50m = 22
m = p + 6
1.75p + 1.50(p + 6) = 22
1.75p + 1.50p + 9 = 22
1.75p + 1.50p = 22 - 9
3.25p = 13
p = 13 / 3.25
p = 4 <====== she bought 4 peaches
m = p + 6
m = 4 + 6
m = 10 <===== she bought 10 mangos
check...
1.75p + 1.50m = 22
1.75(4) + 1.50(10) = 22
7 + 15 = 22
22 = 22 (correct)
If $600 was placed in a savings account with an interest rate of 0.5%,
find the total amount in the account after 8 years and 3 months (8.25
years)?
Answers
I got it wrong so oof
A mix of 32 quarters and dimes totals $6.35. Find the system of equations that would help you answer the question and then find how many quarters (x) and dimes (y) you would have?
Answers
Answer:
21 quarters and 11 dimes = 32 coins
Step-by-step explanation:
x + y = 32
0.25x + 0.10y = 6.35 [take the first equation and make it equal to x]
x = 32 - y [now take this equation and plug it in the above]
0.25 (32-y) + 0.10y = 6.35
8 - 0.25y + 0.10y = 6.35
8 - 0.15y = 6.35 [subtract 8 from both sides]
-0.15y = -1.65 [divide by -0.15 to isolate y]
y = 11 so there are 11 dimes
plug it into the first equation: x + 11 = 32; x = 21 so there are 21 quarters
rob has 7.8 ounces of tuna salad. If she makes three sandwiches with an equal amount of tuna on each, how much tuna does she put on each one?
Answers
Answer:
2.6 tuna
Step-by-step explanation:
Amount of tuna salad rob has = 7.8ounces
Amount of sanndwiches made = 3sandwiches
If she had equal amount of tuna on each sandwiches
Amount of tuna in each = Total amount of tuna/Amount of sandwiches
Amount of tuna in each = 7.8/3
Amount of tuna in each = 2.6 tuna
Hence she put 2.6 tuna in each sandwiches
A scuba diver ascends 5 3/4 feet to the top of a boat platform. The diver then descends 20 1/8 feet by jumping off the boat. Write and evaluate on subtraction expression to show what lever under sea level the scuba currently is
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5 6/8- 20 1/8
Two boats leave the same place at the same time. The first boat heads due north at 10 kilometers per hour. The second boat heads due west at 16 kilometers per hour. After 2.5 hours, how fast is the distance between the boats increasing
Answers
Answer:
18.87 km/hr
Step-by-step explanation:
First boat is heading North with a speed of 10 km/hr.
Second boat is heading West with a speed of 16 km/hr.
Time for which they move = 2.5 hours
To find:
The speed at which the distance is increasing between the two boats.
Solution:
Let the situation be represented by the attached diagram.
Their initial position is represented by point O from where they move towards point A and point B respectively.
[tex]Distance = Speed \times Time[/tex]
[tex]Distance\ OA = 10 \times 2.5 = 25\ km[/tex]
[tex]Distance\ OB = 16 \times 2.5 = 40\ km[/tex]
We can use Pythagorean Theorem to find the distance AB.
AB is the hypotenuse of the right angled [tex]\triangle AOB[/tex].
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^2 = 25^2 + 40^2\\\Rightarrow AB^2 = 2225^2\\\Rightarrow AB^2 \approx 47.17\ km[/tex]
The speed at which distance is increasing between the two boats is given as:
[tex]\dfrac{47.17}{2.5} \approx 18.87\ km/hr[/tex]
PLEASE HELP!!! I DESPERATELY NEED THE ANSWER!!!
Answers
Answer: y = x + 4
Step-by-step explanation:
y = mx + b
y is going up by 1 and x is going up by 4.
so y = x + 4.
to check if it's the correct answer plug in one of the numbers to x and y.
for example:
y = x + 4
2 = -2 + 4
Your wellcome
What's the probability of drawing a green marble out of a bag with 2 green marbles and 4 blue marbles?
Answers
Answer:
2/6= 1/3
Step-by-step explanation:
Answer:
p=0.4
Answer and Explanation:
Probability of drawing a green marble is p=0.4.
Help! Marking Brainliest (Check Screenshot) Please show work, thank you.
Answers
Step-by-step explanation:
Area of Square picture = 20.25 in²
Side lengths of Square picture
= √(20.25 in²) = 4.5 in.
Therefore the dimensions of the picture
is 4.5in by 4.5in.
The scholastic assessment test is standardized to be normally distributed with a mean μ=500 and a standard deviation σ=100. What percentage of SAT scores falls
a. between 500 and 600
b. between 400 and 600
c. between 500 and 700
d. between 300 and 700
e. above 600
f. below 300
Answers
Answer:
68.27%.
Step-by-step explanation:
Here we have [tex]\mu=500,\sigma=100[/tex]
Let X shows the SAT score. z-score for X=400 is
[tex]z=\frac{X-\mu}{\sigma}=\frac{400-500}{100}= -1[/tex]
z-score for X=600 is
[tex]z=\frac{X-\mu}{\sigma}=\frac{600-500}{100}=1[/tex]
So the proportion of SAT scores falls between 400 and 600 is
[tex]P(400<X<600)=P(-1<z<1)=0.6827[/tex]
hence, required percentage is 68.27%.
one can use the same method to find the% for all other cases as
well.
Valeria's Cupcakes recently sold 3 pumpkin cupcakes and 9 other cupcakes. Considering this data, how many of the next 8 cupcakes sold would you expect to be pumpkin cupcakes?
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Answer: 24 Pumpkin cupcakes.
Step-by-step explanation:
We know that:
They recently sold 6 Pumpkin cupcakes and 8 other cupcakes.
Then we can model this with the ratio 6:8
This means that for each 6 Pumpkin cupcakes sold, they also sell 8 of another type of cupcakes.
With this information, if they sell 56
Hello!
I am here with a few geometry questions today.
What would x equal?
You are given the options:
63
64
65
66
When you answer this question please be sure to explain your answer and show work.
Good luck! Have a great day!
Answers
Answer:
C. 65Step-by-step explanation:
As KL║JM and JL is transversal, we already have:
∠KLJ≅∠MJLTo satisfy AAS we need to have ∠JKL≅LMJ, therefore:
m∠JKL = m∠LMJ2x+ 18 = 3x - 473x - 2x = 18 + 47x = 65Correct option is C
Jamie's quilt is made of 9 green squares and 12 yellow squares. What is the ratio of the number of yellow squares compared to the total number of squares on the quilt? Please write your answer in one of the three ways we learned about.
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Answer:
yellow = 12:9 = green
yellow = 4:3 = green
Here is a rectangle.
9 cm
7 cm
Work out the perimeter of the rectangle.
Answers
Answer:
P=32cm
Step-by-step explanation:
Answer: 32
Step-by-step explanation: 9+9 =18
7+7= 14
14+18=32
The concept of hope is nothing more than giving up. A word that holds no true meaning.
Answers
Answer:
lol fr
Step-by-step explanation:
Answer:
Big pp
Step-by-step explanation:
Can anyone help with this?
Answers
Answer:
figure it out yourself
Step-by-step explanation:
remember, all three of the triangle's interior angles should add up to 180 degrees.
Answer:
can someone pls explain to me a good dream you had in like a paragraph nothing weird because my grandmother is making me write about that and she wants me to read it to her at the end of the day
Step-by-step explanation:
be quick! i will mark the correct one brainliest :)
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If Fran were to paint her living room alone, it would take 6 hours. Her sister Denise
could do the job in 8 hours. How long would it take them working together? If needed,
submit your answer as a fraction reduced to lowest terms.
Please show steps !! my last test for the semester!! 20 points PLEASE!!!
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Answer:
r1 =6
r2 =8
t = ?
[(1/r1) * t] + [(1/r2)*t] = 1
t/6 + t/8 = 1
multiply by common denominator... 24
24 (t/6 + t/8 = 1)
4t + 3t =24
7t = 24
t = 24/7 = 3.4hrs
What is the answer to this ? PLEASE HELP I HAVE 3 minutes
Answers
Answer:
(2, 4)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 2x
x = -y + 6
Step 2: Solve for y
Substitution
Substitute in x: y = 2(-y + 6)Distribute 2: y = -2y + 12Isolate y terms: 3y = 12Isolate y: y = 4Step 3: Solve for x
Define equation: x = -y + 6Substitute in y: x = -4 + 6Add: x = 2HELP ASAP GIVING BRAINLIST
Answers
Step-by-step explanation:
An open circle means that it isn't equal to the number so the sign would either be < or >
The number that the circle is on is -1 so x is either < or > to -1
x is anything to the left to -1 so the inequality would be x< -1
I hope this helps!!!
In the number 2,222, how many times larger is the value of the value of the digit in the tens place than the value of the digit in the ones place?
Answers
Answer:
the one in the tens place is 10 times more then the number in the ones place
Step-by-step explanation:
((11-7)+(14/7)^2)=
A. 4
B. 2
C. 5
D. 8
Answers
lmk if it’s right
A new health drink has 120% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 50 mg. How many milligrams of the vitamin is in the drink?
Answers
Answer:
60 mg
Step-by-step explanation:
Given that:
Recommended daily allowance for the Vitamin = 50mg
Drink contains 120% of the recommended daily allowance ;
Number of milligram of the Vitamin contained in the drink is :
120% of recommended daily allowance
(120 /100) * 50
1.2 * 50
= 60 mg