The object will take 2.5 seconds to reach its maximum height. The maximum height attained by the object will be 42.375 meters.
To find how long it takes for the object to reach its maximum height, we can use the projectile motion formula
h(t) = -4.9t² + v0t + h0.
The maximum height is achieved when the vertical velocity component is zero. This happens midway through the flight.
The time to reach maximum height can be found using the formula
t = v0 / g,
where v0 is the initial velocity and
g is the acceleration due to gravity (9.8 m/s²).
In this case, v0 = 24.5 m/s and g = 9.8 m/s², so the time (t) to reach maximum height is
t = 24.5 m/s / 9.8 m/s² = 2.5 s.
The maximum height (H) can be calculated as the initial height plus the displacement due to the initial velocity upwards before it starts coming down.
Since we know the time to reach the maximum height, we can plug it into the original equation h(t) to find the maximum height:
H = -4.9(2.5)² + 24.5(2.5) + 11
We then find that
H = 42.375 m.
Y=2x^2-x-10 write in intercept form
the sum of 2 3/5 + (-1/5) write in simplest form
I don't get why price(max)=$80
Can someone help me
Sampling is ordinarily used when the number of items comprising the population is relatively small.
Jennifer's grandmother buys carrots at the farm stand. She and her 3 grandchildren equally share the carrots. The total weight of the carrots she bought is 28 kilograms. How many kilograms of carrots will Jennifer get ?
What is the number 0.093 expressed in Scientific notation?
A. 9.3 * 10^2
B. 0.93 * 10^1
C. 9.3 * 10^-3
D. 9.3 * 10^-2
Option D is correct. 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex].
To express the number 0.093 in scientific notation, we need to determine the coefficient and exponent.
0.093 can be written as 9.3 multiplied by a power of 10.
Since 0.093 is less than 1, the exponent should be negative.
To shift the decimal point to the right to form the original number, we move it three places to the right:
[tex]0.093 \rightarrow 9.3 \times 10^{-2}[/tex]
Therefore, 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex], option D is correct.
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Stuck on this question. Any help would be appreciated.
For a laboratory assignment, if the equipment is working, the density function of the observed outcome x is f(x) = 2(1 − x), 0
The Variance is [tex]\int\limits^1_0 {(x- \mu)^2(2(1-x))} \, dx[/tex].
What is Variance?Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.
Given:
E(x) = [tex]\int\limits^1_0 {x(2(1-x))} \, dx[/tex]
= [tex]\int\limits^1_0 {(2x - 2x^2)} \, dx[/tex]
For the variance, if μ is the mean, then
Var(x) = E( x- μ)²
= [tex]\int\limits^1_0 {(x- \mu)^2(2(1-x))} \, dx[/tex]
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what square root lies between 17 and 18
What is the solution set of the equation
X^2+3x-4=6
Two solutions were found : x = 5; x = -2. Reformatting the input : Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". Rearrange: Rearrange the equation bAnswer:
Step-by-step explanation:Two solutions were found : x = 5; x = -2. Reformatting the input : Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". Rearrange: Rearrange the equation b
Suppose △DEF≅△MNO.
Which congruency statement is true?
A) DF≅NO
B) DE≅MN
C) EF≅MN
D) EF≅MO
When triangles are congruent, their corresponding sides and angles are the same. Hence in congruent triangles △DEF and △MNO, side DF is congruent to side MN, thus option B) DE≅MN is the correct answer.
Explanation:In the case of congruent triangles, the corresponding sides and angles are essentially the same. Therefore, we must match up the corresponding sides. A correct statement would be that side DF, from the first triangle, is congruent to side MN, from the second triangle. Hence the correct option is B) DE≅MN.
Additionally, DE would be congruent to MN, and EF would be congruent to NO, completing the congruence between triangles △DEF and △MNO.
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if today is wednsday what day will it be in 100 days and why
2x^5+12x^4+16x^3-12x^2-18x=0
The ordered pair (2, 1) is a solution of a direct variation equation. Write the equation and identify the constant of variation.
If each weighs 2/3 pound, how many potatoes are there in a 50-pound case?
The number of potatoes that are there in a 50-pound case are 75 potatoes.
In Mathematics and Euclidean Geometry, an expression simply refers to a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Since each potato weighs 2/3 pound, the number of potatoes that are there in a 50-pound case can be modeled by the following expression;
Number of potatoes = 50 ÷ 2/3
Number of potatoes = 50 × 3/2
Number of potatoes = 150/2
Number of potatoes = 75 potatoes.
Find the maximum and minimum values of the function.
y=7cosx
The price of one share of a stock fell $12.50 each day for 8 days. Which expression represents this situation?
On the blueprint of a house, 48 millimeters represents 7 meters. the length of the living room is 60 millimeters on the blueprint, what is the actual length of the living room?
A problem states
there are 5 more girls than boys and girls there are 27 students in the class in all How many boys are in the class
What are the unknowns in this problem
A Number of students in the class
B The number of boys in the class
C The number of girls in class
D The number of boys and the number of girls in class
the problem only stats there are 27 students and that there are 5 more girls than boys
it does not say how many boys or how many girls there are so D should be the answer
Point P is reflected across two lines. Point A is its reflection image. Which two lines is point P reflected across?
x = 3 and y = 2
x = -2 and y = 2
x = 3 and y = -3
x = -2 and y = -3
Answer: The two lines are x = -2 and y = 2.
Step-by-step explanation: Given that the point P on the co-ordinate plane is reflected across two lines and A is its image after the reflection.
We are to find the two lines across which the point P is reflected.
The co-ordinates of point P are (0, 0) and the co-ordinates of its image A after reflection from two lines are (-4, 4).
From the given figure, we can note that
the first line of reflection is y = 2. Point C(0, 4) is the image after reflection from first line.
The second line of reflection is x = -2. Point A(-4,4) is the final image after second reflection.
Thus, the two lines are x = -2 and y = 2.
Verify the identity Cotx/tanx+cotx = 1-sin^2x
tep 1: –10 + 8x < 6x – 4 Step 2: –10 < –2x – 4 Step 3: –6 < –2x Step 4: ________
A new iPhone user receives an average of 4.2 phone calls per hour. The calls occur randomly in time so if X = the number of calls received in an hour, then we can assume that X has a Poisson distribution with parameter λ = 4.2. Let Y = the number of phone calls received in a day. Assume all necessary independence in the following.
a. Y also has a Poisson distribution. What is the λ for Y?
b. What is the standard deviation of X?
c. What is the standard deviation of Y?
d. What is the probability that no calls are received in an hour?
e. What is the probability that more than 120 calls are received in a day?
f. What is the probability that Y is between 90 and 110 inclusive? (i.e. 90 ≤ Y≤110)
g. What is the variance of square root of 2Y?
h. Assume this distribution holds for all hours and days and that one call is independent from another. What is the probability that 120 or fewer calls are received for every day of this week? (Assume appropriate independence
Add any comments below.
Given four int values x1, x2, y1, y2 write the code to compute the distance between the two point
Can someone please solve this?
Write the equation for the following relation. Include all of your work in your final answer. Submit your solution. P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}
The fourth grade collected 40,583 cans and plastic bottles. Write the number in word form?
Answer is 'Forty thousand, five hundred eighty-three'.
When we write numbers in word form, we express each digit's value in words. In the number 40,583, we have:
"Forty" represents the digit 4 in the ten thousands place.
"Five hundred" represents the digit 5 in the hundreds place.
"Eighty" represents the digit 8 in the tens place.
"Three" represents the digit 3 in the ones place.
Simplify 3 + c (8n + 4) + 9n
A. 49n + 20
B. 3+33n
C. 25n + 11
D. 19n + 7
The table shows the steps for solving the given inequality for x.
−3(4−6x)
Select the reason for each step from the drop-down menus.
Answer:step justification
- 3 (4 - 6x) < x + 5
- 12 + 18x < x + 5 distributive property (to solve the left side)
-12 + 17x < 5 subtraction property of equality (to transpose x
from right to left side)
subtraction of like terms (18x - x = 17x)
17x < 17 addition property of equality (to tranpose - 12
from left to right side)
addition of like terms (12 + 5 =17)
x < 1 division property of equality
Step-by-step explanation:
Mia's cat weighs 13 pounds, 7 ounces
About how many kilograms is this