Answer:
a. 304 feet
b. 425 feet
c. 3.75 seconds
d. It will take the rocket approximately 8.9 seconds to hit the ground
Step-by-step explanation:
1. The given data of the question including the question relationships are listed as follows;
The height of the cliff from which the rocket was launched = 200-ft.
The initial velocity of the rocket, u = 120 feet per second
The equation that models the height of the rocket with respect to time 't' is h(t) = -16·t² + 120·t + 200
a. The height of the rocket after 1 second is given by plugging in t = 1 in the equation that models the height as follows;
h(1) = -16 × (1)² + 120 × (1) + 200 = 304
The height of the rocket after 1 second, h(1) = 304 feet
b. The maximum height can be found by finding the value of the maximum point of the curve of the equation for the height as follows;
At the maximum point, h'(t) = d(-16·t² + 120·t + 200)/dt = 0
∴ d(-16·t² + 120·t + 200)/dt = -32·t + 120 = 0
t = 120/32 = 3.75
At the maximum point, t = 3.75 seconds
The maximum height can also be found by finding the vertex of the parabola formed by the height equation as follows;
At the vertex (the maximum point), t = -b/(2·a) = -120/(2 × (-16)) = 3.75
At the vertex (the maximum point), t = 3.75
The height at the maximum point = h(3.75) = -16 × (3.75)² + 120 × (3.75) + 200 = 425
The height at the maximum point, h(3.75) = 425 feet
c. The time it will take the rocket to reach the maximum point is given by the value of 't' at the maximum point, the vertex, which is t = -b/(2·a) = -120/(2 × (-16)) = 3.75
Therefore;
The time it takes the rocket to reach the maximum point, [tex]t_{max}[/tex] = 3.75 seconds
d. The time it takes the rocket to hit the ground (height h(t)) is given by finding the values of 't' that satisfy the height equation where h(t) = 0 as follows;
At the ground level, h(t) = 0 = -16·t² + 120·t + 200
Therefore, we get;
-16·t² + 120·t + 200 =
t = (-120 ± √(120² - 4×(-16) × 200))/(2 × (-16))
t ≈ 8.9 or t ≈ -1.4
Therefore, the time it takes the rocket to hit the ground is given by the natural number, t ≈ 8.9 seconds.
What is the value of v?
The volume of the cube is 4,913 cubic millimeters. In order to find out the value of V, we must find the cube root of 4913, which is 17 = V.
V = 17
i need help as soon as possible the answers are
7
102
14
51
Answer:
The length of diagonal TU is 102 units
Step-by-step explanation:
Mathematically, the diagonals of a parallelogram bisect each other
This means that the lengths on either of the either of the sides are equal
Mathematically, we have it that;
7x + 2 = 6x + 9
7x - 6x = 9-2
x = 7
The diagonal TU has the measure of ;
(7x + 2) + (6x + 9)
7x + 6x + 2 + 9
= 13x + 11
substituting the value of x, we have
13(7) + 11
= 102
x2 + 7y if x = -5 and y = -8
Answer:
x2 + 7y = -64 (if x = -5 and y = -8)
Step-by-step explanation:
x2 + 7y
(-5 × 2) + (7 × -8)
-10 + -54 which is the same as -10 - 54
-64
The value of expression x² + 7y at x = - 5 and y = - 8 is, - 31.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ x² + 7y
And, x = - 5 and y = - 8
Now, Substitute the value of x and y in the expression, we get;
⇒ x² + 7y
⇒ (-5)² + 7×- 8
⇒ 25 - 56
⇒ - 31
Thus, The value of expression is, - 31.
Learn more about the mathematical expression visit:
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two angles in a triangle have measures of 13° and 65° what is the measure of the third angle
Answer:
102
Step-by-step explanation:
All angles added together=180
180-13-65
180-78
102
Are the two figures below similar?
Answer:
No
Step-by-step explanation:
While both legs of the triangle are similar with a ratio of 3:4, the hypotenuses of the triangles have a ratio of 8:11
can someone please help me
PLEASE HELP THIS IS VERY IMPORTANT I WILL GIVE YOU BRAIN THING IF ITS CORRECT (you can use a calculator if you want)
Answer:
1. B.
2. A, E.
3. D.
Step-by-step explanation:
1. 8.225 ÷ 5 = 1.645
2. 892 ÷ 8 = 111.5
8920 ÷ 80 = 111.5
894 ÷ 10 = 89.4
89.2 ÷ 0.08 = 1115
8.92 ÷ 0.8 = 11.15
0.892 ÷ 0.008 = 111.5
3. 4367 ÷ 0.004 = 1,091,750
pls help solve this math problem
Step-by-step explanation:
the answer is 3 following triangle law
Can one of y’all help me pls
Answer:
D) x - 7 + 3
Step-by-step explanation:
gave sister = subtract
aunt gave = addition
Equation:
x - 7 + 3
I need help please thank you
Answer:
1) 4x^2-x+1
2) -4x^2+3x
3) 6r^3 - 15r
Step-by-step explanation:
Given a bag of 4 red marbles, 5 blue marbles & 6 green marbles, find the probability of drawing a blue marble, replacing it, and then drawing a green marble.
Answer:
15
Step-by-step explanation:
helpoooooo please hhhb
Answer:
Step-by-step explanation:
that vector is in the 4th quadrent. This means that it will be between 270 and 360 degrees.
setting up directions over the graph (like a compass), the vector would be between East and South
using the diagram below it would most likly be south of east and 350 degrees
Find the solution to the system of equations. Please Help
Answer:
x=−2
y=−4
Step-by-step explanation:
−2x+2y=−4
3x+3y=−18
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
−2x+2y=−4,3x+3y=−18
To make −2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by −2.
3(−2)x+3×2y=3(−4),−2×3x−2×3y=−2(−18)
Simplify.
−6x+6y=−12,−6x−6y=36
Subtract −6x−6y=36 from −6x+6y=−12 by subtracting like terms on each side of the equal sign.
−6x+6x+6y+6y=−12−36
Add −6x to 6x. Terms −6x and 6x cancel out, leaving an equation with only one variable that can be solved.
6y+6y=−12−36
Add 6y to 6y.
12y=−12−36
Add −12 to −36.
12y=−48
Divide both sides by 12.
y=−4
Substitute −4 for y in 3x+3y=−18. Because the resulting equation contains only one variable, you can solve for x directly.
3x+3(−4)=−18
Multiply 3 times −4.
3x−12=−18
Add 12 to both sides of the equation.
3x=−6
Divide both sides by 3.
x=−2
The system is now solved.
x=−2,y=−4
Aeryn spent 5 days building a
brick wall that had 100 bricks in
it. She got better each day and
managed to lay 4 more bricks
than the previous. How many
bricks did she lay her first day?
Una empresa de elaboración de helados es capaz de producir 800 litros de helado de tres leches, con 8 máquinas en 42 minutos. Si fallaran dos de las máquinas, pero debieran mantener la producción de helado ¿Cuánto tiempo tardarían?
Answer:
I dont understand spanish!
Step-by-step explanation:
HELP HELP ASAP!!!!!!!!!!!!!!!!!!!!
if the central angle is 3pie/4 and the radius is 13 what's the arc length
Answer:
The arc length is 9.75 pi units
Step-by-step explanation:
Mathematically, we use the formula below to get the length of an arc
Length of an arc is;
theta/360 * 2 * pi * r
where theta is the central angle
for 3pi/4 ; let us convert to degrees
The degree measure is 180 degrees for pi
so 3pi/4 will be (3 * 180)/4 = 135 degrees
So we have the arc length as follows;
135/360 * 2 * pi * 13 = 9.75 pi unit
Sophia is going to invest $7,900 and leave it in an account for 6 years.
Assuming the interest is compounded monthly, what interest rate, to the
nearest hundredth of a percent, would be required in order for Sophia to end
up with $9,400?
Answer:
r= 2.90%
Step-by-step explanation:
delta math
CAN SOMEONE PLEASE HELP
Answer:
The first one.
Step-by-step explanation:
The symbol that you are comparing the numbers with is equal two or greater than and you have to be 48 inches or taller.
HELP ASAP GEOMETRY CIRCLES 10TH GRADE
Answer:
a): 68
b): 32
Step-by-step explanation:
In a triangle, there is a total of 180 degrees
We are given 2 out of the 3 angles, 54 and 58 degrees
180-54-58= 68 degrees
In the other angle, both lines form a 90-degree angle
We are given 58 degrees, so the rest must be 32.
Help please. No links
Answer:
C
Step-by-step explanation:
The question is asking which one is equal to the absolut value of 12. The absolute value of -12 equals 12, so it is the same as the absolute value of 12.
What is the probability of rolling a 3 on a 6-sided 8)
number cube and then NOT rolling a 3 on a 6-
sided number cube?
Answer:
the chances of rolling a 3 are 1/6
the changes of not doing it is 5/6
HELP REALLY QUICK PLEASE
Answer:
The answer is 140
The yellow part which is shaded is 14x10 which equals 140
Given f(x)=2x^2+1 and g(x)=3x−5 , find the following. g(f(x))
9514 1404 393
Answer:
g(f(x)) = 6x^2 -2
Step-by-step explanation:
Evaluate the expression using the given argument value.
g(f(x)) = g(2x^2 +1) = 3(2x^2 +1) -5
= 6x^2 +3 -5 = 6x^2 -2
__
g(f(x)) = 6x^2 -2
Triangle ABC is congruent to triangle A′′B′′C′′ . Which sequence of transformations could have been used to transform triangle ABC to produce triangle A′′B′′C′′ ? Triangle ABC was translated 10 units right and then reflected across the x-axis. Triangle ABC was reflected across the y-axis and then translated 7 units down. Triangle ABC was reflected across the x-axis and then translated 9 units right. Triangle ABC was translated 7 units down and then 9 units right. A coordinate graph with triangle A B C and triangle A double prime B double prime and C double prime. Triangle A B C has points at A begin ordered pair negative 6 comma 2 end ordered pair, B begin ordered pair negative 3 comma 6 end ordered pair, C begin ordered pair negative 3 comma 2 end ordered pair. Triangle A double prime B double prime C double prime has points at A double prime begin ordered pair 6 comma negative 5 end ordered pair, B double prime begin ordered pair 3 comma negative 1 end ordered pair, C double prime begin ordered pair 3 comma negative 5 end ordered pair.
Answer:
The answer is B
Step-by-step explanation:
Triangle ABC was reflected across the y-axis and then translated 7 units down.
Mr. Pennington had a board 2 1/4 feet long. He
used 21 inches. How much of the board did he
have left?
find the value of x and find the value of the angle with a star in it
Answer:
x = 25
angle measure = 55
Step-by-step explanation:
The two angles are supplementary
2x+5+5x = 180
7x+5 = 180 subtract 5 from both sides
7x = 175 divide both sides by 7
x = 25 to find the angle with the star replace x with 25
25*2 + 5 = 55
i need help with this asap
decide whether each if the pairs if angles given and illustrated are
alternate exterior
alternate interrior
correspondkn
vwrtical
1,2,3,4,5,6
Answer: i think its alternate interior
PLEASE HELP!! I will make you brainiest and give you 5 stars if you help me!
Answer:
D
Step-by-step explanation:
You multiply each coordinate by 1/4 to get the new coordinates of the triangle
I hope this helps you
pleaseeeee pleaseeee helppppppppp
Given:
The two vectors are:
[tex]\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}[/tex]
[tex]\overrightarrow{b}=\hat{i}-3\hat{j}+5\hat{k}[/tex]
To find:
The value of [tex]|\overrightarrow{a}\times \overrightarrow{b}|[/tex].
Solution:
We have,
[tex]\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}[/tex]
[tex]\overrightarrow{b}=\hat{i}-3\hat{j}+5\hat{k}[/tex]
The cross product of these two vectors is:
[tex]\overrightarrow{a}\times \overrightarrow{b}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\2&-1&1\\1&-3&5\end{vmatrix}[/tex]
[tex]\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[(-1)(5)-(1)(-3)]-\hat{j}[(2)(5)-(1)(1)]+\hat{k}[(2)(-3)-(-1)(1)][/tex]
[tex]\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[-5+3]-\hat{j}[10-1]+\hat{k}[-6+1][/tex]
[tex]\overrightarrow{a}\times \overrightarrow{b}=-2\hat{i}-9\hat{j}-5\hat{k}[/tex]
Now the magnitude of the cross product is:
[tex]|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{(-2)^2+(-9)^2+(-5)^2}[/tex]
[tex]|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{4+81+25}[/tex]
[tex]|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{110}[/tex]
Therefore, the value of [tex]|\overrightarrow{a}\times \overrightarrow{b}|[/tex] is [tex]\sqrt{110}[/tex].