A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=52t-16t^2 . What is the maximum height that the ball will reach? Do not round your answer.
Height: ________Feet
The maximum height would be 42.25 feet that the ball will reach.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
A vertical upward throwing of a ball Its height h after t seconds (in feet) is given by the function h(t) = 52t - 16t²
Here h(t) = 52t - 16t²
Differentiate with respect to t to get maximum height
h'(t) = 52 - 2 × 16t
h'(t) = 52 - 32t
In this position, the acceleration would be zero,
So 0 = 52 - 32t
32t = 52
t = 52/ 32
t = 1.625
Substitute the value of t = 1.625 in the given function,
⇒ h = 52(1.625) - 16(1.625)²
⇒ h = 84.5 - 42.25
⇒ h = 42.25
Therefore, the maximum height would be 42.25 feet that the ball will reach.
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What are the spherical coordinates of the point whose rectangular coordinates are (4,1,4)?
The spherical coordinates for the given rectangular coordinates (4,1,4) can be calculated using formulas for the transformation. They approximately yield (sqrt(33), 0.505, 1.540).
Explanation:In mathematics, we can convert rectangular coordinates to spherical coordinates using given formulas. Here, we have the rectangular coordinates (4,1,4). The transformation from rectangular to spherical involves three-step calculations:
First, calculate the radial coordinate, r, which is the distance from the origin to the point. It is given by r = sqrt(x^2 + y^2 + z^2).Second, find the polar angle, theta, measured relative to the vertical z-axis. It is given by cos(theta) = z/r.Lastly, find the azimuthal angle, phi, measured relative to the x-axis. It is given by cos(phi) = x/(r*sin(theta)).
Applying the formulas, we get: r = sqrt(4^2 + 1^2 + 4^2) = sqrt(33), theta = cos^-1(4/sqrt(33)) which is approximately 0.505, and phi = cos^-1(4/sqrt(33)*sin(0.505)) which is approximately 1.540.
So, the spherical coordinates of the point whose rectangular coordinates are (4,1,4) are approximately (sqrt(33), 0.505, 1.540).
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In a glide reflection, what comes first and what comes second?
first the glide, and second another glide
first the glide, and second a reflection
first the reflection, and second another reflection
first the reflection, and second a glide
In a glide reflection, the reflection comes first and the glide comes second.
Explanation:In a glide reflection, first the reflection is applied, and second a glide is performed. The reflection is a transformation that flips the shape across a line of reflection, while the glide is a transformation that slides the shape along a vector. The combination of the reflection and glide creates a glide reflection.
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What is the next number of 2 7 8 3 12 9
Answer with Step-by-step explanation:
We are given a pattern
2 7 8 3 12 9
and we are asked to find the next term of this pattern
2+1=3
7+5=12
and 8+1=9
We can view this pattern in the set of three numbers and then, the next three are formed by adding one, five & one, respectively.
See these COLUMNS of groups of three:
2 3 4
7 12 17
8 9 10
Hence, next number in the pattern is:
4
Differentiate
1/√x^2-1
Perform the indicated operation. (5 - 2i 2) 2
A line passes through the point (6−6) and has a slope of 3/2 . Write an equation in point-slope form for this line.
The length of the hypotenuse is:
0.
1.
2.
4.
divide the base by the sin of the opposite angle
base = 2
opposite angle = 30 degrees
2/sin(30) = 4
x = 4
Rewrite the equation in standard form and identify a, b, and c. 2x^2 + 6x - 9 = 3x^2 - 11x - 7
there were 137 tickets purchased for a major league baseball game the lower box tickets cost $12.50 and the upper box tickets cost $10 the total amount of money spent was $1,502.50 how much of each kind of ticket
lower box = x
upper box = y
x+y=137
x=137-y
12.50x + 10y=1502.50
12.50(137-y) + 10y=1502.50
1712.5-12.50y+10y=1502.50
1712.5-2.50y=1502.50
-2.5y=-210
y=-210/-2.50 = 84
y = 84
x=137-84=53
53 lower box tickets
84 upper box tickets
2^-1 ∙ 2^-4 is what?
A student was asked to use the formula for the perimeter of a rectangle, P = 2l + 2w, to solve for l. The student came up with an answer, P -2w=2l. What error did The student make? Explain. Then solve for l
A collection of quarters and nickels is worth $3.75. There are 27 coins in all. Find how many of each there are.
Q +N =27
Q=27-N
0.25Q + 0.05N =3.75
0.25(27-N) + 0.05 =3.75
6.75-0.25N+0.05N=3.75
6.75-0.2N=3.75
-0.2N=-3
N=-3/-0.2 = 15
15 nickels
27-15 = 12
12 quarters
15x0.05 = 0.75
12 x 0.25 = 3.00
3.00 + 0.75 = 3.75
12 quarters & 15 nickels
Assume the Poisson distribution applies. Use the given mean to find the indicated probability.
Find P(4) when μ = 8.
Using the Poisson distribution formula, substitute the given mean and the number of occurrences into the formula to find the probability. Hence P(4; 8)= e^-8 * 8^4 / 4!. The answer will be in decimal form, signifying the probability.
Explanation:The probability in a Poisson distribution that an event happens exactly k times when the mean occurrence rate (μ or Lambda) is given is determined using the following formula:
P(k; μ) = (e^-μ * μ^k) / k!
Where e is Euler's number (approximately equal to 2.71828), k is the number of occurrences (in this case, it is 4) and μ is the mean number of occurrences (in this case, it is 8).
Applying the values into the formula, we have:
P(4;8) = (e^-8 * 8^4) / 4!
You can calculate the above expression using a calculator to find the probability. Remember, the answer will be in decimal form, representing the probability of the event occurring 4 times when the average rate of occurrence is 8.
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Find the surface area of a regular pentagonal prism with side length 8, altitude 20, and apothem approximately 5.5
The surface area of a regular pentagonal prism can be found by calculating the area of the pentagonal bases and the area of the rectangular sides and then summing those areas together.
Explanation:Calculating the Surface Area of a Regular Pentagonal Prism
To find the surface area of a regular pentagonal prism with given dimensions, we need to calculate the area of two components: the area of the pentagonal bases and the area of the rectangular sides (also called the lateral faces). We are given that the side length (s) of the pentagon is 8 units, the prism's altitude (h), or height, is 20 units, and the apothem (a) is approximately 5.5 units.
Firstly, the area of a pentagon (Apentagon) is calculated using the formula Apentagon = ½ * perimeter * apothem, where the perimeter (P) of a regular pentagon is the side length multiplied by 5. Thus, the area of one pentagonal base is ½ * 5 * 8 * 5.5. Next, to find the entire area of the two pentagonal bases, we multiply this result by 2.
The area of each of the rectangular sides can be found by multiplying the side length by the prism's altitude. Since there are 5 identical rectangular sides in a regular pentagonal prism, their total area is 5 * 8 * 20.
Adding these two results together gives us the total surface area of the prism. So, the formula for the surface area is Total Surface Area = (2 * ½ * 5 * 8 * 5.5) + (5 * 8 * 20).
Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?
Answer:
in other words b
Step-by-step explanation:
Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. suppose a sample of 100 major league players was taken. find the approximate probability that the mean salary of the 100 players exceeded $4.0 million.
Final answer:
The probability is approximately 0.267.
Explanation:
To find the approximate probability that the mean salary of the 100 players exceeded $4.0 million, we can use the Central Limit Theorem and the Z-score formula. The Z-score formula is:
Z = (x - μ) / (σ / sqrt(n))
where x is the value we want to find the probability for (in this case $4.0 million), μ is the mean of the population ($3.26 million), σ is the standard deviation of the population ($1.2 million), and n is the sample size (100).
We calculate the Z-score as follows:
Z = (4.0 - 3.26) / (1.2 / sqrt(100)) = 0.617
We then use a Z-table or a calculator to find the probability corresponding to a Z-score of 0.617. The probability is approximately 0.267.
y=-x y=2x+3 graph the equation to solve the system
Translate to an algebraic expression. 5 INCREASED BY y
Ricky is filling an 8 inch by 4 inch by 4 1/2 inch rectangular box with packing peanuts. The peanuts are cubes that come in two different sizes ,1 cubic inch and 1/8 inch .How many peanuts of each size are needed to fill the box?
Preston goes on a camel safari in Africa. They travel 5 km north, then 3km east and then 1 km north again. What distance did he cover? What was his displacement?
The total distance Preston covered on his camel safari is 9 km, and his displacement is 6.71 km toward the northeast.
Determining Distance and Displacement
To answer the student's question about Preston's journey during his camel safari, we need to consider the definitions of distance and displacement.
Distance is the total length of the path traveled regardless of direction. In Preston's case, he traveled 5 km north, then 3 km east, and then 1 km north again. Therefore, the total distance covered is the sum of these individual distances
Displacement, on the other hand, measures the change in position from the starting point to the final point and is direction-dependent. It is a vector quantity with both magnitude and direction. To find the displacement, we can represent Preston's movement on a coordinate system with north being the positive y-direction and east being the positive x-direction.
From the starting point, moving 5 km north and then 1 km north results in a total of 6 km in the positive y-direction.
The magnitude of the displacement can be calculated using the Pythagorean theorem:
√((6 km)² + (3 km)²) = √(36 km² + 9 km²) = √(45 km²) = 6.71 km (rounded to two decimal places)The direction of the displacement would be to the northeast. Therefore, Preston's displacement is 6.71 km toward the northeast.
What is a ratio equivalent to 8/10 with lower terms
what is the product x 2-16/2 x+8 . x3-2x2+x/x2+3x-4
Answer:
A on Edge 2021
[tex] \frac{x(x - 4)(x - 1)}{2(x + 4)} [/tex]
A cylinder has a base area of 169π cm2 . Its height is 4 cm more than the radius. Identify the volume of the cylinder. Round to the nearest tenth, if necessary.
Answer:
V = 9025.8 cm3
Step-by-step explanation:
this box can be packed with 48 unit cubes the edge length each unit cube is 1 meter what is the voume of the box
Answer:
48 cubic meters.
Step-by-step explanation:
48x1
unit meter is cubic meters
The formula can be used to find the velocity v in feet per second of an object that has fallen h feet. Find the velocity of an object that has fallen 25 feet. Round your answer to the nearest tenth.
A triangle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board?
Pamela is 13 years older than Jiri. The sum of their ages is 53 what is Jiri's age?
The solution is: Jiri is 20 years old.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
Pamela is 13 years older than Jiri so:
p=j+13
Then you are told that the sum of their ages is 53 so:
p+j=53
We already know from the first statement that p=j+13, this makes p+j=53 become:
(j+13)+j=53 so we combine the two j's on the left side
2j+13=53 subtract 13 from both sides
2j=40 divide both sides by 2
j=20
So Jiri is 20 years old.
Hence, The solution is: Jiri is 20 years old.
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Write 935.97 in expanded form
Write 337,060 in expanded form using exponents