We are given a function H(t) that represents the height of a cannon ball after t seconds as:
[tex]H(t)=-16t^2+48t+12[/tex]
and a second cannon ball is represented by the function g(t) as:
[tex]g(t)=10+15.2t[/tex]
PART A:
t 0 1 2 3
H(t) 12 44 44 12
g(t) 15.2 25.2 40.4 55.6
Hence, between t= 2 seconds and t=3 seconds the ball will meet
such that H(t)=g(t)
Since, we know that the Height H(t) decreases from 44 feet to 12 feet between t=2 to t=3 seconds.
and height g(t) increases from 40.4 feet to 55.6 feet between t=2 to t=3 seconds.
Hence, the two cannon balls will definitely meet between t=2 to t=3 seconds.
and the time at which they meet is calculated by solving:
[tex]H(t)=g(t)\\\\i.e.\\\\\\-16t^2+48t+12=10+15.2t\\\\\\i.e.\\\\\\16t^2-32.8t-2=0\\\\\\i.e.\\\\\\t=-0.059\ and\ t=2.109[/tex]
As t can't be negative.
Hence, we get:
t=2.109 seconds
PART B:
The solution from PART A means that the one of the ball first reach the highest point at 44 feet and then returns back to the initial position and hence follows a parabolic path while the second cannon ball reach a greater height with the increase in time and hence in this phenomena the two balls will definitely meet.
Chloe draws three parallelograms. In each figure, she measures a pair of angles, as shown. What is a reasonable conjecture for Chloe to make by recognizing a pattern and using inductive reasoning?
a) In a parallelogram, consecutive angles are supplementary.
b) In a parallelogram, all angles are congruent.
c) In a parallelogram, all angles are supplementary.
d) In a parallelogram, consecutive angles are congruent.
The conjecture Chloe can make based on the given information is that in a parallelogram, consecutive angles are congruent.
Explanation:Chloe's conjecture, based on the pattern she observed, would be that in a parallelogram, consecutive angles are congruent. To support this conjecture, we can explain that a parallelogram has opposite sides that are parallel, and therefore, the opposite angles are congruent. Since the consecutive angles are adjacent to these opposite angles, they must also be congruent.
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what is the difference between 506 and 233
The height H(in feet) of a ball T seconds after it is hit can be modeled by the function H(t)=-16t^2+32t+7
How long will it take you to bike a distance of 108 miles at a speed of 24 miles per hour ?
Given triangle JKL, sin 38 degree equals
Answer:
B. [tex]\text{cos}(52^{\circ})[/tex].
Step-by-step explanation:
We have been given a right triangle. We are asked to complete our given statement.
[tex]\text{sin}(38^{\circ})[/tex] equals ___.
We will use identity [tex]\text{sin}(x)=\text{cos}(90-x)[/tex] to solve our given problem.
[tex]\text{sin}(38^{\circ})=\text{cos}(90^{\circ}-38^{\circ})[/tex]
[tex]\text{sin}(38^{\circ})=\text{cos}(52^{\circ})[/tex]
Therefore, [tex]\text{sin}(38^{\circ})[/tex] equals [tex]\text{cos}(52^{\circ})[/tex].
A woman 5 ft tall walks at the rate of 3.5 ft/sec away from a streetlight that is 12 ft above the ground. at what rate is the tip of her shadow moving? at what rate is her shadow lengthening? ⇒
The rate at which her shadow is lengthening is 2.5ft/sec
Triangular altitude theorem:To get the rate of her shadow lengthening, we will use the similarity theorem of a triangle.
Find the triangle attached. From the triangle;
[tex]\frac{EA}{AC} =\frac{DB}{BC}[/tex]Substitute the sides as given in the diagram:
[tex]\frac{12}{x+a} =\frac{5}{x}\\12x = 5(x+a)\\ 12x=5x+5a\\7x = 5a[/tex]
Differentiate both sides with respect to t
[tex]7\frac{dx}{dt} = 5\frac{da}{dt} \\7\frac{dx}{dt}=5(3.5)\\7\frac{dx}{dt}=17.5\\\frac{dx}{dt} = 2.5ft/sec[/tex]
The rate at which her shadow is lengthening is 2.5ft/sec
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Add the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x. Find the sum of 4x3 + 2x2 - 4x + 3 and 7x3 -4x2 + 7x + 8.
Answer:
11x^3 - 2x^2 + 3x + 11
Step-by-step explanation:
we need to find the sum of 4x^3 + 2x^2 - 4x + 3 and 7x^3 -4x^2 + 7x + 8
To find the sum we add both the polynomials
4x^3 + 2x^2 - 4x + 3 + 7x^3 -4x^2 + 7x + 8
To add the polynomials we combine like terms
4x^3 + 7x^3 = 11x^3
2x^2 - 4x^2 = -2x^2
-4x+7x= 3x
3+8 = 11
So final expression is 11x^3 -2x^2 +3x+11
A student rolls a standard number cube. What is the probability the student rolled a 4, given that the number rolled was greater than or equal to 2?
How to know whether to use sin or cos in physics?
3xy=27 linear or not
The given function 3xy = 27 is not a linear function.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
What is a linear function?A linear function is defined as when the function has the highest degree of expression is 1, such as y = mx + c.
here,
Given function,
3xy = 27,
Simplifying the function,
3xy = 27
xy = 27/3
y = 9/x
Since, from the definition of the function, the given function is 9 reciprocal of x and is said to be a reciprocal function.
Thus, the given function 3xy = 27 is not a linear function.
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I need help with proofs
If a television is $117.00 and was marked down by 10% then what was the original price
Match the inequality to the graph of its solution.
a. n/4 ≤ -1
b. -10 ≥ -100
c. 5x ≥ 20
Answer:
its B
Step-by-step explanation:
John concludes that, since (x - 5) is a factor of the polynomial x2 - 25, if he performed the long division (x2 - 25) ÷ (x - 5), the remainder would be zero. This is an example of ___________ reasoning(x2 - 25)
Answer:
Deductive reasoning
Step-by-step explanation:
Given : John concludes that, since (x-5) is a factor of the polynomial [tex]x^2-25[/tex], if he performed the long division [tex](x^2-25)\div (x-5)[/tex], the remainder would be zero.
To find : This is an example of ___________ reasoning [tex]x^2-25[/tex]?
Solution :
The above situation make conclusion when we know the fact that (x-5)
is the factor as the factor of polynomial divide it completely.
Therefore, This is the example of deductive reasoning.
Deductive reasoning is the process by which a person makes conclusions based on previously known facts.
Please explain this math question to me!
6(4) ÷ 2 − 1 + 5
Solve:
r/5 - 6 = -1
A) r = 1
B) r = 5
C) r = 10
D) r = 25
r/5 - 6 = -1
add 6 to both sides
r/5 = 5
multiply both sides by 5
r = 5 *5 = 25
r = 25
Find the value of x for the rectangle
perimeter=26 meters
rectangle one the bottom is (x+3) m
on the right side of the rectangle (2x-6)m
Are Abel Fields’s actions protected by the First Amendment?
According to a 2012 decision by the US Supreme Court, Abel Fields's actions are protected by the First Amendment.
In the fictitious case study scenario of Abel Fields, he claimed to have received a Purple Heart for wounds suffered in combat, when in fact he had never served in the military. He asserted his claim as a freedom of speech issue.
In a real-life decision by the US Supreme Court, United States v. Alvarez, the the Court struck down the Stolen Valor Act of 2005 (signed into law by President G.W. Bush in 2006). The law had criminalized false statements about having a military medal. By a 6-3 majority, the Supreme Court determined that the Stolen Valor Act was unconstitutional under the First Amendment's protection of free speech.
According to a 2012 decision by the US Supreme Court, Abel Fields's actions are protected by the First Amendment.
The united states exports over 200 billion pounds of coal how many tons does the united states export
Answer:100,000,000 tons
word form: one hundred million tons
Step-by-step explanation:
Study the Proof Given.
List the reasons for Items 2,3, & 4.
Right the number and then the answer.
Question 1 options:
In which quadrant is θ located if cscθ is negative and tanθ is positive?
Answer:
[tex]\theta[/tex] is located in 3rd Quadrant.
Step-by-step explanation:
We are given that [tex]cos\,\theta[/tex] is negative and [tex]tan\,\theta[/tex] is positive
We have to find Quadrant in which [tex]\theta[/tex] is located.
We have 4 Quadrants.
In 1st Quadrant , All trigonometric ratios are positive.
In 2st Quadrant , sin and cosec are positive while others are negative.
In 3rd Quadrant , tan and cot are positive while others are negative.
In 4th Quadrant , cos and sec are positive while others are negative.
Therefore, According to given information [tex]\theta[/tex] located in 3rd Quadrant.
joy is planning to purchase a sweater that costs 30$ dollars at her local department store. The sweaters are on sale for for 20% off.
Which steps are needed to find the sale price of the sweater in words?
Answer:24
Step-by-step explanation:
9. Simplify the expression. 8 – 5(12x + 8) A) 36x + 24 B) –60x – 32 C) –60x + 16 D) –60x + 48
five times the sum of a number and 27 is greater than or equal to six times the sum of the number and 26 what is the solution to set of the problem
The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. if a room with a perimeter of 70 feet and 8-foot walls requires 5.6 quarts of paint, find the amount of paint needed to cover the walls of a room with a perimeter of 65 feet and 10-foot walls
What is the value of x?
A. 25 cm
B. 7 cm
C. 29 cm
D. 35 cm
Answer:
29 cm
Step-by-step explanation:
The central triangle is isosceles, so the length if its right side (x) is the same as the length of its left side (29 cm).
x = 29 cm
6% of 124 =
7.44
0.744
74.4
744
If you could explain would be great
What are the domain and range for the cube root function graphed below? Justify your answer in complete sentences.
Together, teammates pedro and ricky got 2671 base hits last season. pedro had 277 more hits than ricky. how many hits did each player have?
To find out how many hits each player had, we set up a system of equations and solve for the variables. Pedro had 2474 hits and Ricky had 1197 hits.
Explanation:To solve this problem, we need to set up a system of equations. Let's represent the number of hits Pedro had as x and the number of hits Ricky had as y. We are given that their combined hits is 2671, so we can write the equation:
x + y = 2671
Additionally, we are given that Pedro had 277 more hits than Ricky. This can be represented as:
x = y + 277
We can now substitute the second equation into the first and solve for y:
y + 277 + y = 2671
2y = 2394
y = 1197
Now we can substitute the value of y back into the first equation to solve for x:
x + 1197 = 2671
x = 2474
Therefore, Pedro had 2474 hits and Ricky had 1197 hits.
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p(5)=-3+4(5) solve please