A baseball is thrown in a parabolic arc. It's position above the ground at a given point in time can be represented by the quadratic function LaTeX: p\left(t\right)=\frac{1}{2}gt^2+v_0t+p_0p ( t ) = 1 2 g t 2 + v 0 t + p 0, where LaTeX: t\ge0t ≥ 0, LaTeX: gg is -32 ft/sec/sec, LaTeX: v_0v 0 is initial velocity, and LaTeX: p_0p 0 is its initial position above the ground. If the ball was thrown straight up at 16 ft/sec when it was 5 ft above the ground, how high did it go?
Answers
Answer:
The baseball reached 9 feet high above the ground
Step-by-step explanation:
The given quadratic function representing the position of the baseball above ground is p(t) = 1/2·g·t² + v₀·t + p₀
Where;
t ≥ 0
g = -32 ft./sec²
v₀ = The initial velocity
p₀ = The initial position
Given that when the ball is thrown, we have;
The initial, straight up, velocity, v₀ = 16 ft./sec
The initial position, p₀ = 5 ft.
Substituting the above values in the quadratic function representing the position of the baseball above ground, we have;
p(t) = 1/2·(-32)·t² + 16·t + 5 = 16·t - 16·t² + 5
At the maximum point, the rate of change of the height with time = 0, therefore;
dp(t)/dt = 0 = d(16·t - 16·t² + 5)/dt = 16 - 32·t
16 - 32·t = 0
16 = 32·t
t = 16/32 = 0.5 seconds
Therefore, the time takes to reach the maximum height = 0.5 seconds
The height (maximum) reached in 0.5 seconds is given as follows;
h(t) = 16·t - 16·t² + 5, from which we have;
h(0.5) = 16 × 0.5 - 16 × (0.5)² + 5 = 9
Therefore, the height baseball reached = 9 ft. above ground
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Answer:
step by step
Step-by-step explanation:
y = 3x - 4
Root (x-intercept): y=0 3x-4=0 x=4/3 (or 1 1/3, 1.33333)
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The sum of the first (n) terms of the sequence is given by the formula (given below) . If this sequence is a geometric progression, find q. If this sequence is an Arithmetic progression, find d
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Answer:Example 1:
Find the sum of the first 8 terms of the geometric series if a1=1 and r=2.
S8=1(1−28)1−2=255
Example 2:
Find S10 of the geometric sequence 24,12,6,⋯.
First, find r.
r=r2r1=1224=12
Now, find the sum:
S10=24(1−(12)10)1−12=306964
Example 3:
Evaluate.
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In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1. Then as n increases, rn gets closer and closer to 0. To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.
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Step-by-step explanation:
Show work on this smart people
Answers
Answer:
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Step-by-step explanation:
LMNO is a square.
All sides of square are equal
MN = LM
3x + 1 = x + 7
3x - x = 7 - 1
2x = 6
x = 6/2
x = 3
LM = x + 7 = 3 + 7 = 10
LM = 10 units
EMERGENCY
i+i+i+i=-8
i=
Answers
Answer
i=2
Step-by-step explanation:
i+i+i+i=8
4i=8
i=8/4
i=2
First, combine like terms (i’s)
4i=-8
Divide both sides by 4 to isolate i
4i=-8
—- —-
4 4
i=-2
You can plug this back in to see if it works.
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Therefore, i= -2
if x²+y²=6xy then prove that 2log(x+y)=logx+logy+3log2
Answers
Answer:
Given that
x² + y² = 6xy
or, (x + y)² - 2xy = 6xy
or, (x + y)² = 8xy
or, (x + y)² = 2³xy
Taking (log) in both sides, we get
log (x + y)² = log (2³xy)
or, 2 log (x + y) = log (2³) + logx + logy
or, 2 log (x + y) = 3 log2 + logx + logy
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find the value of
x in
-8x + 8
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Answers
Answer:
-8x + 8 =0
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8x=8
x=8/8=1
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Answers
Answer:
95
Step-by-step explanation:
I hope this help
(-19)×(-5)
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Answer:
the answer is x >0 hope this helped
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Answers
Step-by-step explanation:
log(z) is defined when z > 0.
For log(9 - x²) to be defined, we have 9 - x² > 0.
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28 points and brainliest!!!!!!!!!!!
Answers
Answer:
Multiplication
Step-by-step explanation:
Can i have branliest?
You would multiply the speed the vehicles are moving and the feet its going
Step-by-step explanation:
Ted sells cleaning supplies. He earns a monthly salary of $850.00, plus commission. He earns 5% commission on the first $10,000 in sales, and 7% commission on any sales over $10,000. If he sold $14,000 worth of supplies this month, how much will his pay be this month?
Answers
Answer:
$1830Step-by-step explanation:
Step one:
Ted's monthly salary =$850.00
since he made sales over $10,000. that is he sold supplies worth $14,000
his commission will be 7% of $14,000
=7/100*$14,000
=0.07*$14,000
=$980
Required
His total earnings
Step two:
Hence his total earnings is, his monthly salary plus 7% commission of supplies worth $14,000
=$850.00+$980.00
=$1830
Solve the system of equations. (1 point)
2x − 5y = 3
x − 3y = 1
(4, 1)
(5, 2)
(7, 2)
(9, 3)
Answers
Answer:
The answer is (4,1). Substitute the x and y values into the system and you should have the answer.
Answer:
option one
Step-by-step explanation:
A bag contains 40 cups of dog food. You feed 2 2/3 cups to your dog each day. In how many days will you need to buy more dog food?
Answers
Answer:
15 days
Step-by-step explanation:
You'd divide 40 by 2 2/3, getting you 15.Therefore there will be enough food for the dog to eat for 15 days.
5 + 0.08 + 0.004 in word form plz
Answers
Answer:
Five plus eight hundredths plus four thousandths
Answer:
five plus zero point zero eight plus zero point zero zero four equals five point zero eighty four
Step-by-step explanation:
. True or False? Write your response next to the statements below. A) Sam computed a 90% confidence interval for µ from a specific random sample of size n. He claims that at the 90% confidence level, his confidence interval contains µ. Is his claim true or false? B) Sam computed a 95% confidence interval for µ from a specific random sample. His confidence interval was 10.1 < µ < 12.2. He claims that the probability that µ is in this interval is 0.95. Is his claim true or false? C) If we fail to reject (i.E., "accept") the null hypothesis, this means that we have proved it to be true beyond all doubt. Is this true or false?
Answers
Answer:
A) True , B) True , C) False
Step-by-step explanation:
A) True : Confidence Interval is the interval range around sample statistic, which is certain by extent of confidence level, to consist the actual population parameter.
B) True : Confidence Interval is the interval range around sample statistic, which is certain by extent of confidence level, to consist the actual population parameter.
C) False : Null Hypothesis can be accepted, despite of being actually false. This is called Type 2 Error.
In a lab experiment, 100 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 26 hours. How long would it be, to the nearest tenth of an hour, until there are 168 bacteria present?
Answers
9514 1404 393
Answer:
19.5 hours
Step-by-step explanation:
The number in the dish at time t (in hours) can be described by ...
n(t) = 100·2^(t/26)
We want to find t such that ...
n(t) = 168
100·2^(t/26) = 168
2^(t/26) = 1.68 . . . . . . divide by 100
(t/26)log(2) = log(1.68) . . . . . take logarithms
t = 26·log(1.68)/log(2) ≈ 19.459992 . . . . divide by the coefficient of t
t ≈ 19.5 . . . hours
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Answers
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Answers
Answer:
Blank #1. 4
Blank #2. 25
Blank #3. 5
Blank #4. 32
Step-by-step explanation:
Blank #1. If a farm lets you pick 3 pints of raspberries for $12.00, then the cost per pint would be $4.00.
Blank #2. If one pint costs $4.00, then you would get a quarter of a dollar per pint, or 0.25 (this is because four quarters are in a dollar, one quarter=25 cents).
Blank #3. If you continue at this rate, for $20.00, you would be able to get 5 pints of raspberries because if you pick 3 pints of raspberries for $12.00, and one pint costs $4.00 (multiply 3 and 4 to get the total cost of $12.00), and if you pick 5 pints, that cost $4.00 each, for $20.00 (multiply 4 and 5 to get $20.00). So, if you had $20.00, you would be able to pick 5 pints of raspberries for a total of $20.00.
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Hope that helps and please give me brainliest!!
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Answers
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Answers
Answer:
Step-by-step explanation:
if in the bank account is 1600 dollars
the rate is 5%
1600*5%=80 dollars
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Answers
Answer:
a = -2
Step-by-step explanation:
15 = 3(a+7)
15 = 3a + 21
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a = -2
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Answer:
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Step-by-step explanation:
y varies inversely with x. If x= 1 and y= 3 what is x if y = 0.3
Type your answer...
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Answer:
Step-by-step explanation:
hjyr kiknbvcctt t
Determine the constant of variation for the direct variation given. Type a numerical answer in the space provided.
Answers
Answer:
B. 4
Step-by-step explanation:
Determine the constant of variation for the direct variation given.
(0, 0), (3, 12), (9, 36)
A. 3
B. 4
C.12
Direct variation is given by:
y = kx
Where,
k = constant of variation
(3, 12)
x = 3; y = 12
y = kx
12 = k*3
12 = 3k
k = 12 / 3
k = 4
(9, 36)
x = 9; y = 36
y = kx
36 = k * 9
36 = 9k
k = 36 / 9
= 4
k = 4
Constant of the variation = 4
how do you write a linear equation when given a graph or table? and how do you analyze key features of a function when given its graph?
Answers
Next, you want to find the y intercept.
Look at the y value when x is 0. If the y is -2 when x=0, then b=-2.
When given its graph, find a y value when x is 0. If the y is 4 when x=0 then b=4
Is 8 < x the same as 8 > x ( please explain this )
Answers
Answer:
No
Step-by-step explanation:
It is No because if you switch up the first inequality you get x>8 and when you switch up the inequality you get x<8. I hope this explanation is satisfactory .
Which expression makes the equation true for all values of x?
60x- 12 = 6(__?_)
Answers
Carter has $105 to buy a cake and pizza for his cousin's birthday party. He knows he needs to set aside $25 for the cake, and the rest of the money he can spend on pizzas. Each pizza costs $9.25. How many pizzas can Carter afford to buy? Use the inequality 9.25x + 25 ≤ 105
Answers
Answer:
8
Step-by-step explanation:
Here, we want to use the inequality to know the number of pizza that can be bought
We simply proceed to solve the inequality recently and we have the following;
9.25x + 25 ≤ 105
9.25x ≤ 105-25
9.25x ≤ 80
x ≤ 80/9
x ≤ 8.65
Since we cannot have fractional pizzas, what he can afford is rather written as 8
Offering 100 Points for someone to complete the worksheet.
Answers
Answer:
what is the question?
please post the question
Pls help fast will give brainliest
Answers
Answer:
23
Step-by-step explanation:
6×3+5(3-2)
6×3+5×1
18+5
23