Answer:
A volcano ejected with an initial velocity of 304 feet per second.
The height in feet is given by the equation H=-16t^2+ 304t where t is the time in seconds.
We will use the equation that traces the path of the projectile to determine the following information:
1) The time it takes the projectile to reach its maximum height (using the vertex formula: t=-b/2a)
The equation; H = -16t^2 + 304t, a=-16; b=304
t = -304/2°(-16)
t = 9.5 sec to reach max height
2) The maximum height of the projectile (use the result from part 1 to find the maximum height of the projectile)
t = 9.5
H = -16(9.5^2) + 304(9.5)
h = = -1444 + 2888
h = 1444 ft is the max height
3) Find the time it takes the projectile to return to the ground. Assume that the projectile starts at height H=0.
-16t^2 + 304t = 0
factor out -16t
-16t(t - 19) = 0
t = 19 sec to reach the ground
Step-by-step explanation:
PLS PLS PLS PLS HELP :D <33
Answer:
Value of x = 3
m∠HEB=27°
Step-by-step explanation:
1) CEH and HEB are complementary angles, therefore both of their angles added together will be 90 degrees
2) Set the two equations added together equal to 90 and solve for x
19x+6+9x=90
28x=84
x=3
3) Plug in x into 9x to get HEB
9(3)=27
PLEASE HELP ME GET ALL THESE QUESTIONS QUICKLY DONE I WILL MARK BRAINLIST PLS PLZ PLZZZZZ
Answer: look at explanation
Step-by-step explanation:
1st question: 48 / 60 = 80 %
2nd : 1/4 of 60 = 15 people
3rd : If 60% is 48 miles, than 10% is 8 miles. Therefore, 100% (his goal) = 80 miles.
4th: 1/4 of 88 = £22
right answers only plz and thank you :)
The required value of "k" is 8. Option B is correct
Given the polynomial function
[tex]P(x) =2x^3-4x^2+kx-3[/tex]
What is remainder theorem?
The remainder theorem is a formula used to find the remainder when a polynomial is divided by a linear function.
If this polynomial has a factor of x - 1 and remainder of 3, hence x = 1 and P(x) = 3. This means that P(1) = 3
[tex]P(1) =2(1)^3-4(1)^2+k(1)-3\\3 = 2-4+k-3\\6 = -2 + k\\k = 8\\[/tex]
Hence the required value of "k" is 8
Learn more on polynomial function here: https://brainly.com/question/10881257
What is quadratic spline?
The definition of a quadratic spline is that;
A Quadratic Spline is the creation of a set of polynomial functions that are quadratic and follow the format f(x) = ax² + bx + c.
Quadratic SplineA Quadratic Spline is simply defined as the creation of a set of polynomial functions that are quadratic, or relatively simple to comprehend and must follow the quadratic function format which is;
f(x) = ax² + bx + c
where;
a, b and c are the values gotten in the process of doing the Splines to create the desired functions.
Read more about quadratic functions at; https://brainly.com/question/1214333
Which of the following are steps in practical problem solving?
Answer:
Assign an identifying variable to the quantity to be found. Write a sentence stating conditions placed on the quantity. Solve the sentence for the variable.
Step-by-step explanation:
can you mark me as brainlist
what is an equation of the line that passes through points (-7,-5) and (-7,-2)?
Answer:
x=-7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-2-(-5))/(-7-(-7))
m=(-2+5)/(-7+7)
m=3/(0)
undefined
x=-7.
What is the distance, rounded to the nearest tenth, between the points (2, 1) and (6, 6)? Enter the answer in the box.
units
Answer:
6.4 should be the correct answer
Step-by-step explanation:
if im wrong and you wanted it in a different format im sorry
A U.S. citizen invested a $1200 government stimulus check they received on March 1, 2020,
into stocks that grew with an annual percentage rate of 20.2%, compounded continuously.
How much are these stocks worth 9 months later on December 1, 2020? Round to two
decimal place accuracy. (Hint: 9 months = 0.75 years)
The stocks are worth $ 1396.29 nine months later.
Using the continuous compounding formula,
[tex]A = Pe^{rt}[/tex] where
A = final amount of stocks P = initial amount of stocks = $1200, r = compounding rate = 20.2 % = 0.202 t = 9 months = 0.75 yearsSubstituting the values of the variables into the equation, we have
[tex]A = Pe^{rt}[/tex]
[tex]A = 1200e^{0.202 X 0.75}\\A = 1200e^{0.1515}\\A = 1200(1.1636)\\A = 1396.29[/tex]
So, the stocks are worth $ 1396.29 nine months later.
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7.RP.A.1 (NC)
8. Grant paddled a canoe, 3/4 mile in 1/2 hour. How fast did Grant paddle in miles per
hour?
Answer:
1.5 miles / hour
Step-by-step explanation:
The question is most easily done by converting to decimals
3/4 = 0.75 miles
1/2 = 0.5 hours
Formula
r = d/t
Solution
r = 0.75 miles / 0.5 hours
r = 1.5 miles per hour
When Alex went to work the temperature
was -2°F. When he got home from work the
temperature raised 14°. What was the
actual temperature when he got home from
work?
Michael drove 638 miles in 11 hours.
At the same rate, how many miles would he drive in 8 hours?
she will drive 754 miles in 13 hrs.
As a bowl of soup cools, the temperature of the soup is given by the twice-differentiable function H for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where H(t) is measured in degrees Celsius (C), and time t is measured in minutes. Values of H(t) at selected values of time t are shown in the table above.
a) Use the data in the table to approximate H'(5). Show the computations that led to your answer. Using correct units, explain the meaning of H'(5) in the context of the problem.
b) Is there a time t for 0[tex]\leq[/tex]t[tex]\leq[/tex]12 at which the temperature of the soup is 60C? Justify your answer.
c) The temperature of the soup is also modeled by the twice-differentiable function C for 0[tex]\leq[/tex]t[tex]\leq[/tex]12, where C(t) is measured in degrees Celsius (C), and time tis measured in minutes. It is known C(3)= 80 and the derivative of C is given by C'(t)= -3.6e-0.05t. Write an equation for the line tangent to the graph at t=3 and use it to approximate C(5).
d) Based on the model given in part c, at what rate, in degrees Celsius per minute minute, is the rate of change of the temperature of the soup changing at t=3 minutes?
The rate of change of temperature with time at a point in time is given by
the derivative of the function for the temperature of the soup.
The correct responses are;
a) H'(5) is approximately -2.6 degrees Celsius per minute.b) Yesc) The equation for the line tangent is y = -3.6·t + 90.8The approximate value of C(5) is 72.8 °Cd) The rate of change of the temperature of the soup at t = 3 minutes is -3.6 degrees Celsius per minute.Reasons:
a) From the data in the table, we have;
The approximate value of H'(5) is given by the average value of the rate of
change of the temperature with time between points, t = 3, and t = 8
Therefore;
[tex]\displaystyle H'(5) = \mathbf{\frac{H(8) - H(3)}{8 - 3}}[/tex]
Which gives;
[tex]\displaystyle H'(5) = \frac{80 - 67}{8 - 3} = \mathbf{2.6}[/tex]
Therefore, H'(5) = -2.6°C per minute
b) Given that the function is twice differentiable over the interval, 0 ≤ t ≤ 12, the function for the change in temperature is continuous in the interval 0 ≤ t ≤ 12
At t = 0, H(0) = 90 °C
At t = 12, H(12) = 58 °C
58 °C < 60 < 90 °CTherefore, there exist a temperature, of 60 °C between 90° C and 58 °C
c) The given derivative of C is, [tex]C'(t) = \mathbf{-3.6 \cdot e^{-0.05 \cdot t}}[/tex]
At t = 3, we have;
[tex]The \ slope \ at \ t = 3 \ is \ C'(3) = -3.6 \cdot e^{-0.05 \times 3} \approx -3.1[/tex]
Therefore, we have;
y - 80 ≈ -3.1 × (x - 3)
The equation for the tangent is; y = -3.6 × (x - 3) + 80
y = -3.6·x + 10.8 + 80 = -3.6·x + 90.8
The equation for the tangent is; y = -3.6·x + 90.8The value of C(5) is approximately, C(5) ≈ -3.6 × 5 + 90.8 = 72.8
C(5) ≈ 72.8°d) Based on the the model above, the rate at which the temperature of the
soup is changing at t = 3 minutes is -3.6 degrees per minute.
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Help needed rn i have a few minutes left
Answer:A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Given the perimeter of a rectangle and either the length or width, find the unknown measurement using the appropiate formula. The perimeter is 98 in. and the width is 22 in.
Answer:
the length of rectangle is 27 in
Please some urgent help!!!!
Answer:
brain less or i hack ur acc to ban
Step-by-step explanation:
u cant report me because im hacker
The given number line shows the solutions to which inequality
Answer:
B (x-7<-6)
Step-by-step explanation:
x < 1
Bidmass working out questions
Answer:
The answer will be 0
Step-by-step explanation:
Let me know Hope it helps
What is
( x + 1 ) ^2
[tex](x+1)^2 = x^2 +2x + 1[/tex]
Pls help! The question is: You are riding a bike up Elm Trail towards Deer trail. You plan to make a left turn on to Deer trail. What is the angle measure of the turn?
Answer:
110
Step-by-step explanation:
there is a angle of 70 in the other side is there is a total of 180 and subtract 70 you get 110
Answer:
110
Step-by-step explanation:
The distance between Mr. Tomback’s hometown and NYC is 36 centimeters on a road map. The map scale indicates that 5cm on the map represents 125 kilometers in real life. If Mr. Tomback drives at an average speed of 80 kilometers per hour, then how many hours will it take him to get home from NYC?
Answer:
First, we need to figure out the number of kilometers.
if 5 cm is equivalent to 125 kilometers in real life this means
1 cm is equivalent to 25 kilometers making the conversion much easier.
36 centimeters multiplied by 25 is 900, which means in real life the distance between Mr.Tomback's hometown and NYC is 900 kilometers.
900 km ÷ 80 kmh
= 11.25000000
= 11 hours
0.25000000 × 60
= 15.00000000
= 15 minutes
it will take him 11 hours and 15 minutes to get home to NYC
Hello please help straight up answer I’ll give points thanks I’m just trying to pass
Answer:
I think it's 34°.
Step-by-step explanation:
The angle to the right of 3x+7 is the alternate interior angle to 2x+3, meaning that they are the same.
Now, that angle, 2x+3, and 3x+7, are on a line, which I'm assuming is a straight line with an angle of 180°. If it is, then (2x+3)+(3x+7)=180
Now you can solve for x.
2x+3+3x+7=180
5x+10=180
5x=170
x=34
Therefore, x=34°
Hope I helped!
Help help help math math
Answer:
It is an example of a nonlinear function.
Step-by-step explanation:
Use a graphing calculator or graph the points and try to make a line, as it will not work
If a trench is 102’-6” long by 5’-4” wide and 3’-3” deep, what is the volume of the soil that was removed per cubic feet?
Considering that the trench is modeled by a rectangular prism, the volume that was removed is 1776 cubic feet.
The volume of a rectangular prism of length l, width w and height h is given by:
[tex]V = lwh[/tex]
In this problem, we want the measures in feet, and considering that 1 feet is 12 inches:
The length is of 102' 6''(102 feet and 6 inches), hence [tex]l = 102.5[/tex].The width is of 5' 4'', hence [tex]w = 5.33[/tex].The depth(height) is of 3' 3'', hence [tex]h = 3.25[/tex].Then:
[tex]V = lwh = 102.5(5.33)(3.25) = 1776[/tex]
The volume that was removed is 1776 cubic feet.
To learn more about the volume of rectangular prisms, you can take a look at https://brainly.com/question/17223528
A sequence begins with-3. Each term is calculated by multiplying the previous term by -4, then subtracting 1.
Which option correctly represents the sequence described?
A -3, 11, -45, 179, ...
B {-3, -13, -53, -213, ...}
C. {-3, 11, -45, 179, ...}
D -3, -13, -53, -213,...
Answer:
C
Step-by-step explanation:
[tex]a_{1}=-3\\a_{2}=(-3)(-4)-1=12-1=11\\a_{3}=11(-4)-1=-44-1=-45\\a_{4}=-45(-4)-1=180-1=179\\................................................\\[/tex]
Answer: Choice A) -3, 11, -45, 179, ...
=====================================================
Explanation:
1st term = -3
new term = -4*(previous term) - 1
2nd term = -4*(1st term) - 1
2nd term = -4*(-3) - 1
2nd term = 12 - 1
2nd term = 11
The answer is between choice A and C since both involve "-3, 11" as the first two terms in that order. The only difference between A and C are the outer surrounding curly braces. These braces tell the reader that we have a set of numbers.
When it comes to a set, the order does not matter. Something like {1,2,3} is identical to {3,2,1}. Because of this, we rule out choice C.
On the other hand, order does matter in a sequence. The sequence 1,2,3 is different from 3,2,1.
What is m∠JNK? Enter your answer in the box.
*NOT a question, I had trouble with this on my test and couldn't find anyone that had asked, so here is the correct answer. Merry Christmas everyone! :-)
Answer:
Merry Christmas too!!
Step-by-step explanation:
Stay safe lovelots
#LEARN WITH BRAINLY
100 points ‼️ (I would give more but that’s the limit)
Ava and Mary are 10 miles apart on a path when they start moving toward each other. Ava runs at a constant speed of 4 miles per hour, while Mary walks at a constant speed of 1 miles per hour. How long does it take until they meet?
Answer:
Step-by-step explanation:
You are after time. You know the total distance. They start off at the same time and meet after t hours
Let the meeting time = t
Let the distance from Mary's standpoint be d
Mary
d = r * t
r = 1 mile / hour
t = ?
Ava
d = r*t
d for Ava = 10 - d
r = 4 mile / hour
Solution
10 - d = 4 * t
The time is the same for both people
Ava: divide both sides by 4
10/4 - d/4 = t
Mary
d = 1 * t
d = t
10/4 - d/4 = d Add d/4 to both sides.
10/4 = d + d/4
10/4 = 5d / 4 Multiply both sides by 4
10 = 5d Divide both sides by 5
10/5 = 5d/5
d = 2
Since from Mary we have d = t
They will meet in 2 hours.
Please help me answer
Answer: Second Choice
Step-by-step explanation:
Answer each question and round your answer to the nearest whole number
A model power plant has a scale of 2 cm: 4 m. If the model power plant is 6 cm tall,
then how tall is the real power plant?
3 m
O 12 m
2 m
O 10 m
(I WILL GIVE BRAINLIEST) PLEASE HELP!
Answer:
Option D
Step-by-step explanation:
Step 1: Determine the correct option
Option A, this option doesn't work because -3.46 is not greater than -2 1/3. Although the number 3 is greater than 2, these numbers are negative therefore the bigger the negative number, the smaller the number actually is.
Option B, this option doesn't work because 16/5 is not greater than 6. If we convert 16/5 into a decimal we get 3.2 and this number isn't bigger than 6.
Option C, this option doesn't work because once again it states that -3.46 is greater than -2 1/3 when in reality it's actually smaller.
Option D, this option does work because everything goes according the way it should. -3.46 is smaller than -2 1/3 and -2 1/3 is smaller than -3/4 and -3/4 is smaller than 16/5 and 16/5 is smaller than 6.
Answer: Option D