The time taken to reach the maximum height = 3 s
Further explanationQuadratic function is a function that has the term x²
The quadratic function forms a parabolic curve
The general formula is
f (x) = ax² + bx + cwhere a, b, and c are real numbers and a ≠ 0.
The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value
So the maximum is if a <0 and the minimum if a> 0.
After t seconds, a ball height h (in feet) is given by the function h (t) = 96t-16t²
The maximum value of the function is obtained if the first derivative of the function h (t) = 0
96-32t = 0
96 = 32t
t = 3 s
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Final answer:
The ball reaches its maximum height after 3 seconds. This is determined by finding when the derivative of the height function h(t) = 96t - 16t² equals zero and solving for t.
Explanation:
To determine the time at which the ball reaches its maximum height, we need to analyze the function h(t) = 96t - 16t². Here, h(t) represents the height of the ball after t seconds. The ball achieves its maximum height when the derivative of the height function with respect to time is zero (i.e., when its upward velocity is zero).
To find this, we can take the derivative of h(t) and set it equal to zero to find the critical points:
h'(t) = d/dt (96t - 16t²) = 96 - 32t.
Setting the derivative equal to zero:
96 - 32t = 0
32t = 96
t = 96/32 = 3 seconds.
Therefore, the ball reaches its maximum height after 3 seconds.
Cylindrical soup radius 4 centimeters height 12 centimeters what is the volume of the soup to the nearest tenth?
The volume of a rectangular prism is b3 + 8b2 + 19b + 12 cubic units, and its height is b + 3 units. The area of the base of the rectangular prism is square units.
Answer:
b^2 + 5b +4
Step-by-step explanation:
A businessman has 10 employees. His salary is equal to 6 times the average of employees salaries. If the 11 of them receive a total of $64,000 in one year, what was the business mans salary that year ??
x = business man's salary
y = employee's salary
x + 10y = 64000
x = 6y
6y + 10y = 64000
16y = 64000
y = 64000/16 = 4000
x = 6*4000
x = 24000
business man's salary was $24,000
In △ABC, m∠A=72°, c=61, and m∠B=16°. Find a to the nearest tenth.
Using the law of sines, the length of side a to the nearest tenth is 58.1 units.
What is law of sines?Law of sines states that When we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C.
In ΔABC,
∠A=72°
∠B=16°
∠A + ∠B + ∠C = 180° (angle sum property)
72° + 16° + ∠C = 180°
∠C = 180° - (72° + 16°) = 92°
Using sine law, (refer to the figure attached)
[tex]\frac{sin\ A}{a} = \frac{sin\ B}{b} =\frac{sin\ C}{c} \\\\\frac{sin72}{a} = \frac{sin16}{b} = \frac{sin92}{61} \\\\\frac{sin72}{a} =\frac{sin92}{61} \\\\a = sin72 * \frac{61}{sin92} \\\\= 0.9511 * \frac{61}{0.9994} \\\\=58.05193116\\\\= 58.1[/tex]
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95 is described as what
What is the probability of rolling a number less than or equal to 8 with the sum of two dice, given that at least one of the dice must show a 6?
Simplify x^2-4x-32/x^2+7x+12
If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.
what is the square root of -1?
A group of ladies meet for an afternoon tea party. They bring all their cats. In all, there are 26 heads and 84 feet. How many ladies and how many cats are in the room
On a resent business trip it took 7 hours 30 minutes to drive 375 miles how many miles per hour was the average
Answer:
50 miles / hours.
Step-by-step explanation:
Speed may be defined as the distance covered by the object per unit time.
Speed = [tex]\frac{distance}{time}[/tex]
the distance of the business trip = 375 miles.
the time taken by the business trip = 7 hours 30 minutes = 7.5 hrs.
Speed = [tex]\frac{375}{7.5}[/tex]
Speed = 50 miles / hours.
Here, the average of miler per hour is 50 miles / hours.
Product A is an 8 oz bottle of cough medication that sells for $1.36. Product B is a 16oz bottle of cough medication that cost $3.20. Which product has the lower unit price
Find the value of 4 + (27 - 12·2) ÷ 2.
Answer's are 3.5,5.5 and 19
Which one is it
The value of 4 + (27 - 12·2) ÷ 2 would be 5.5.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
A Simplification usually involves making the expression simple and easy to use later.
WE follow the rule PEMDAS parenthesis, exponent, multipy, divide, add, substart.
4 + (27 - 12·2) ÷ 2
4 + (27 - 24 ) ÷ 2
4 + (3) ÷ 2
4+3/2, do 3/2=1.5
then add it
4+1.5 = 5.5.
Therefore, the correct answer is 5.5
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You deposit $70 in a savings account that pays an annual interest rate of 30%. How much simple interest would you earn in 2.5 years?
how do you make a equivalent ratio?
The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are less than 81?The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are less than 81?
We are given the following variables:
Normal distribution
u = sample mean = 74
s = standard deviation of the samples = 7
x = sample value = 81
Since we are asked to find percent of the scores less than 81, this means we have to find the proportion using the z-score. The formula for z score is:
z = (x – u) / s
Substituting the given values:
z = (81 – 74) / 7
z = 1
Using the standard normal distribution tables for z, we find that:
P = 0.8413 at z = 1
Therefore this means that 84.13% of scores are less than 81.
The Answer is the two small boxes just got it right For Plato
FAR LEFT FAR RIGHT
"apply quickselect to find the median of the list of numbers 9, 12, 5, 17, 20, 30, 8."
Final answer:
To find the median using quickselect, choose a pivot value, partition the list, and repeat the process with the appropriate partition until the pivot index matches the desired median index.
Explanation:
The median of a list of numbers is the middle value when the numbers are arranged in ascending order. To apply quickselect to find the median, start by choosing a pivot value from the list. Partition the list and move all values smaller than the pivot to the left and all values larger than the pivot to the right. If the pivot index is equal to the desired median index, then the pivot value is the median. Otherwise, if the pivot index is smaller, repeat the process with the right partition; if the pivot index is larger, repeat with the left partition.
In the given example, let's apply quickselect to find the median:
Choose a pivot value, let's say 17.
Partition the list: 5, 8, 9, 12, 17, 20, 30
The pivot index is 4, which is less than the desired median index.
Repeat the process with the right partition: 17, 20, 30
Choose a new pivot value, let's say 20.
Partition the list: 17, 20, 30
The pivot index is 1, which is equal to the desired median index.
Therefore, the median of the list of numbers 9, 12, 5, 17, 20, 30, 8 is 17.
Cos (pi/11)+cos (3pi/11)+cos (5pi/11)+cos (7pi/11)+cos(9pi/11)
Answer:
1/2
Step-by-step explanation:
((81x^3 y^(-1/3))^1/4)/(x^2 y)^1/4 simplify
What type of graph would have the title, "Monthly Company Profit for the Year?"
bar graph
line plot
line graph
pictograph
Answer:
line graph
Step-by-step explanation:
a mechanic charges 50 am hour plus parts if a bill is 450 including 150 in parts how many hours did it take
total = 450
parts = 150
450-150 = 300
50 per hour
300/50 = 6
it took 6 hours
Find the area of the shaded region when r = 4 feet and the area of the triangle is: 123√ square feet
Use 1.73 for 3√ and 3.14 for π. Round your answer to two decimal places.
Compare the 3 in 536 to the 3 in 1,36 7.
Draw number 536 using base ten block?
is a kiloliter greater than one liter
Tessa had $110 in her checking account. She paid her cable/internet bill for $75. She deposited $50 from her part-time job before writing a check for $85 to pay her credit card bill. What is Tessa's account balance?
110-75+50-85 =
110+50=160
75+85 = 160
160-160=0
her balance is 0
If the total price paid for an item is $20.25 and the cost of the item before sales tax is $18.90, what is the rate of sales tax?
20.25 -18.90 = 1.35
1.35 / 18.90 = 0.071428571
= 7.14%
check:
18.90 x 1.34946 Round to 1.35
18.90 + 1.35 = 20.25
Sales tax = 7.14%
Which is equivalent to “12 chairs for every 3 tables”?
Answer:
A 12 chairs per 3 table
Step-by-step explanation:
4/1 is equivalent to 12 chairs for every 3 tables.
What is fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given a statement, 12 chairs for every 3 tables.
The statement represents 12 chairs per 3 tables, which means 12/3 = 4/1
Therefore, there are 4 chairs for every table.
Hence, 4/1 is equivalent to 12 chairs for every 3 tables.
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What is the next number in the series? 83 79 75 71 67 ?
Answer:
Given the series : 83 , 79 , 75 , 71 , 67, ?
Difference of two consecutive terms;
79 -83 = -4
75 -79 = -4
71-75 = -4
67-71= -4
Since, you can see that the number is decreases by 4 every time.
Let unknown term be x
then;
x - 67 = -4
x = 67-4
x = 63.
Therefore, the next term in the series is 63.
The next number in the series is 63.
In the given series, each number is decreasing by 4.
We can observe that the first number, 83, is decreased by 4 to get the next number, 79.
Similarly, each subsequent number is obtained by subtracting 4 from the previous number.
Following this pattern, the next number would be obtained by subtracting 4 from the last number in the series, which is 67.
67 - 4 = 63
Therefore, the next number in the series is 63.
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a commercial jet airplane climbs at takeoff with slope m=4/9. How far in the horizontal direction will the airplane fly to reach am altitude of 20,000 ft above the takeoff point?
The horizontal direction in will the airplane flies to reach an altitude of 20,000 ft above the takeoff point will be 45,000 feet.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A commercial jet airplane climbs at takeoff with slope m = 4/9.
Then the equation of the line will be given as,
y = (4/9)x
The y-intercept is zero.
The horizontal direction will the airplane fly to reach an altitude of 20,000 ft above the takeoff point will be
20,000 = (4/9)x
180,000 = 4x
x = 180,000 / 4
x = 45,000 feet
The horizontal direction in will the airplane flies to reach an altitude of 20,000 ft above the takeoff point will be 45,000 feet.
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The third term of an arithmetic sequence is 21, and the eighth term is 56. The first term is _____.
The first term of the given arithmetic sequence is 7. This can be determined by finding the common difference and moving backwards from the third term using this value.
Explanation:The subject of this question is Arithmetic Sequence which is a topic in mathematics. An arithmetic sequence is defined by a common difference (d) between consecutive terms.
To solve this problem, we have to find the common difference first. The difference between the 8th term (56) and the 3rd term (21) is 35. But since there are 5 steps from the 3rd term to the 8th term, each step (or the common difference) must be 35 ÷ 5 = 7.
Now that we have the common difference (7), we can reverse it from the 3rd term (21) back to the 1st term which gives us: 21 - 2(7) = 7. So, the first term is 7.
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