X S2.0.2
A rocket is fired upward with an initial velocity v of 80 meters per second. The quadratic function S(t) = -52 + 80t can be used to find
the heights of the rocket, in meters, at any time t in seconds. Find the height of the rocket 8 seconds after it takes off. During the
course of its flight, after how many seconds will the rocket be at a height of 290 meters?
Answers
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Answer:
320 m after 8 seconds5.6 seconds, 10.4 seconds to height of 290 mStep-by-step explanation:
To find the height at 8 seconds, evaluate the formula for t=8.
S(t) = -5t^2 +80t
S(8) = -5(8^2) +80(8) = -320 +640 = 320
The height of the rocket is 320 meters 8 seconds after takeoff.
__
To find the time to 290 meters height, solve ...
S(t) = 290
290 = -5t^2 +80t
-58 = t^2 -16t . . . . . . . divide by -5
6 = t^2 -16t +64 . . . . . complete the square by adding 64
±√6 = t -8 . . . . . . . . . take the square root
t = 8 ±√6 ≈ {5.551, 10.449}
The rocket is at 290 meters height after 5.6 seconds and again after 10.4 seconds.
Related Questions
the voltage in a lightbulb is given by the equation V= IR. in this equation V is the voltage, I is the current , and R is the resistance. what is the current in a lightbulb with a voltage of 35.0 V and a resistance of 175
Answers
Answer:
a
Step-by-step explanation:
PLS HELP QUICK I WILL GIVE YOU BRAINLIEST:
Given that angle abc=70° and angle bcd=110°. Is it possible (consider all cases): That line AB intersects line CD?
Answers
Answer:
Given that angle abc = 70° and angle bcd = 110°. Is it possible (consider all cases): That line AB intersects line CD?
yes.Step-by-step explanation:
#CarryOnLearning
A motel in New Orleans charges $90 per day for double occupancy and $80 per day for single occupancy during off-season. If 80 rooms are occupied for a total of $6,930, how many rooms of each kind are occupied?
Answers
double occupancy room=x
single occupancy room=y
x + y = 80,
90x + 80y = 6930
x=53
y=27
Suppose f(x)=x^2 and g(x)=(1/2x)^2. Which statement best compares the graph of g(x) with the graph of f(x)?
Answers
Answer:
"A"
Step-by-step explanation:
A display case of toy rings are marked 5 for $1. If Zach wants to buy 50 toy rings, how much will Zach spend (not including tax)
Answers
Since it is five for $1 the amount of rings is 5x the amount of $
9514 1404 393
Answer:
$10
Step-by-step explanation:
Price is proportional to the number of rings, so Zack will spend D dollars, where ...
dollars/rings = D/50 = 1/5
D = 50/5 = 10
Zack will spend $10 to buy 50 toy rings.
For all positive integers n, let *n* equal the greatest prime number that is a divisor of n. What does *10*/*12* equal?
Answers
9514 1404 393
Answer:
5/3
Step-by-step explanation:
The prime factorizations are ...
10 = 2·5
12 = 2·2·3
Then *10* = 5 and *12* = 3, so *10*/*12* = 5/3.
Find the interquartile range of the data set represented by this box plot.
25
20
45
35
Answers
Answer:
25
Step-by-step explanation:
im pretty sure i think only ok i think no saying bad things in the comment
Round 620 to the nearest ten! Hurry please and please don't answer if you know you wrong !
Answers
Answer:
620 to the nearest ten is already rounded correctly.
Step-by-step explanation:
620 to the nearest ten is 620.
he parent function f(x) = x3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by graph B and graph C.
Graph B represents the function g(x) =
.
Graph C represents the function h(x) =
.
Answers
Answer is graph b I believe
Graph b
x - 3y +3=0
a) The length of the perpendicular drawn from the point (a, 3) on the line
3x + 4y + 5 = 0 is 4. Find the value of a.
Answers
Answer:
We know that for a line:
y = a*x + b
where a is the slope and b is the y-intercept.
Any line with a slope equal to -(1/a) will be perpendicular to the one above.
So here we start with the line:
3x + 4y + 5 = 0
let's rewrite this as:
4y = -3x - 5
y = -(3/4)*x - (5/4)
So a line perpendicular to this one, has a slope equal to:
- (-4/3) = (4/3)
So the perpendicular line will be something like:
y = (4/3)*x + c
We know that this line passes through the point (a, 3)
this means that, when x = a, y must be equal to 3.
Replacing these in the above line equation, we get:
3 = (4/3)*a + c
c = 3 - (4/3)*a
Then the equation for our line is:
y = (4/3)*x + 3 - (4/3)*a
We can rewrite this as:
y = (4/3)*(x -a) + 3
now we need to find the point where this line ( y = -(3/4)*x - (5/4)) and the original line intersect.
We can find this by solving:
(4/3)*(x -a) + 3 = y = -(3/4)*x - (5/4)
(4/3)*(x -a) + 3 = -(3/4)*x - (5/4)
(4/3)*x - (3/4)*x = -(4/3)*a - 3 - (5/4)
(16/12)*x - (9/12)*x = -(4/3)*a - 12/4 - 5/4
(7/12)*x = -(4/13)*a - 17/4
x = (-(4/13)*a - 17/4)*(12/7) = - (48/91)*a - 51/7
And the y-value is given by inputin this in any of the two lines, for example with the first one we get:
y = -(3/4)*(- (48/91)*a - 51/7) - (5/4)
= (36/91)*a + (153/28) - 5/4
Then the intersection point is:
( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4)
And we want that the distance between this point, and our original point (3, a) to be equal to 4.
Remember that the distance between two points (a, b) and (c, d) is:
distance = √( (a - c)^2 + (b - d)^2)
So here, the distance between (a, 3) and ( - (48/91)*a - 51/7, (36/91)*a + (153/28) - 5/4) is 4
4 = √( (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a + (153/28) - 5/4 )^2)
If we square both sides, we get:
4^2 = 16 = (a + (48/91)*a + 51/7)^2 + (3 - (36/91)*a - (153/28) + 5/4 )^2)
Now we need to solve this for a.
16 = (a*(1 + 48/91) + 51/7)^2 + ( -(36/91)*a + 3 - 5/4 + (153/28) )^2
16 = ( a*(139/91) + 51/7)^2 + ( -(36/91)*a - (43/28) )^2
16 = a^2*(139/91)^2 + 2*a*(139/91)*51/7 + (51/7)^2 + a^2*(36/91)^2 + 2*(36/91)*a*(43/28) + (43/28)^2
16 = a^2*( (139/91)^2 + (36/91)^2) + a*( 2*(139/91)*51/7 + 2*(36/91)*(43/28)) + (51/7)^2 + (43/28)^2
At this point we can see that this is really messy, so let's start solving these fractions.
16 = (2.49)*a^2 + a*(23.47) + 55.44
0 = (2.49)*a^2 + a*(23.47) + 55.44 - 16
0 = (2.49)*a^2 + a*(23.47) + 39.44
Now we can use the Bhaskara's formula for quadratic equations, the two solutions will be:
[tex]a = \frac{-23.47 \pm \sqrt{23.47^2 - 4*2.49*39.4} }{2*2.49} \\\\a = \frac{-23.47 \pm 12.57 }{4.98}[/tex]
Then the two possible values of a are:
a = (-23.47 + 12.57)/4.98 = -2.19
a = (-23.47 - 12.57)/4.98 = -7.23
Can someone please help me with this math problem.
Answers
Answer:
8 + 30 ÷ 2 + 4 = 27
8 + 30 ÷ (2 + 4 ) = 13
(8 + 30) ÷ 2 + 4 = 23
Step-by-step explanation:
The durations (minutes) of 26 electric power outages in Shah Alam over the past five years are shown below. 32 44 25 66 27 12 62 9 51 4 17 50 35 99 30 21 12 53 25 2 18 24 84 30 17 17 (a) Find the mean, median and mode.
Answers
Answer:
Mean = 33.31
Median = 26
Mode = 17
Step-by-step explanation:
Given the data:
32 44 25 66 27 12 62 9 51 4 17 50 35 99 30 21 12 53 25 2 18 24 84 30 17 17
Reordered data : 2, 4, 9, 12, 12, 17, 17, 17, 18, 21, 24, 25, 25, 27, 30, 30, 32, 35, 44, 50, 51, 53, 62, 66, 84, 99
The mean, xbar = Σx / n = 866 /26 = 33.31
The median = 1/2(n+1)th term
Median = 1/2(27)th term = 13.5th term
Median = (13 + 14)th / 2
Median = (25 + 27) / 2 = 26
The mode = 17 (highest frequency)
The functions f (x) = 1/2x-3 and g(x) = -2x+ 2 intersect
at x = -2. True or false?
Answers
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Answer:
False
Step-by-step explanation:
f(-2) = (1/2)(-2) -3 = -1 -3 = -4
g(-2) = -2(-2) +2 = 4 +2 = 6
The function values are not the same at x=-2, so the graphs do not intersect there.
__
The graphs intersect at x=2.
9. Mariah has 28 centimeters of reed
and 10 meters of reed for weaving
baskets. How many meters of reed
does she have? Write your answer as a
decimal and explain your answer.
Answers
25 x 2
help me
plz understand me by opening
Answers
Answer:
[tex]25 \times 2 = 50 \\ you \: are \: idiot \: [/tex]
really?! :|
Please help solve this problem.
Answers
Answer:
Ang hirap naman niyan bakit kaya lahat na module mahirap
Respond to each of the four questions.
Describe the steps to graphing a linear equation. Be sure to provide an example to illustrate your description.
Describe the steps to graphing a quadratic equation. Be sure to provide an example to illustrate your description.
Describe how to solve a linear equation. Be sure to provide an example to illustrate your description.
Describe how to solve a quadratic equation. Be sure to provide an example to illustrate your description.
Answers
Answer:hello
Step-by-step explanation:
1+1
which multiple choice answer is correct?
A, B, C or D?
Answers
Answer:
C
Step-by-step explanation:
ABD and CDB are both half of ABC
m∠ABD = m∠CBD
Because BD is the bisector of ∠ABC, so it divides it into 2 equal parts.
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Answers
Answer:
her salary will increase by $ 145 for every week
Step-by-step explanation:
x=1st paycheck (integer).
weekly raise = $ 145.
After completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get
$ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
Type the correct answer in each box. The volume of a cube is given by and the total surface area of a cube is given by , where s is the side length of the cube. If the side length of a cube is 5 inches , the volume of the cube is ____ cubic inches and its total surface area is ____ square inches.
Answers
Answer:
hope this will help you a lot
A group of 40 bowlers showed that their average score was 192. Assume the population standard deviation is 8. Find the 95% confidence interval of the mean score of all bowlers.
Answers
Answer:
[tex]CI=189.5,194.5[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=40[/tex]
Mean [tex]\=x =192[/tex]
Standard deviation[tex]\sigma=8[/tex]
Significance Level [tex]\alpha=0.05[/tex]
From table
Critical Value of [tex]Z=1.96[/tex]
Generally the equation for momentum is mathematically given by
[tex]CI =\=x \pm z_(a/2) \frac{\sigma}{\sqrt{n}}[/tex]
[tex]CI =192 \pm 1.96 \frac{8}{\sqrt{40}}[/tex]
[tex]CI=192 \pm 2.479[/tex]
[tex]CI=189.5,194.5[/tex]
In a particular year, the mean score on the ACT test was 22.5 and the standard deviation was 5.3. The mean score on the SAT mathematics test was 526 and the standard deviation was 101. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places.
Answers
Question is incomplete ; The questions solved were picked from similar questions but different parameters. However, the solution pattern are exactly the same.
Answer:
- 0.0943
- 0.386
30.185
Step-by-step explanation:
Given :
ACT:
Mean score, m = 22.5
Standard deviation, σ = 5.3
SAT :
Mean score, m = 526
Standard deviation, σ = 101
1.)
Zscore for ACT score of 22:
Since the distribution is normal ; we use the relation ;
Zscore = (score - mean) / standard deviation
Score = 22
Zscore = (22 - 22.5) / 5.3 = - 0.0943
B.)
Zscore for SAT of 487
Zscore = (score - mean) / standard deviation
Score = 487
Zscore = (487 - 526) / 101 = - 0.386
C.)
ACT score, for ACT Zscore of 1.45
Zscore = (score - mean) / standard deviation
ZScore = 1.45
1.45 = (score - 22.5) / 5.3
1.45 * 5.3 = (score - 22.5)
7.685 = score - 22.5
Score = 7.685 + 22.5
Score = 30.185
Mischa wrote the quadratic equation 0=_x2+4x-7 in standard form. If a = -1, what is the value of c in her equation?
C=-7
C= 1
c=4
c=7
Answers
Answer:
A. c = -7
Step-by-step explanation:
Standard form of a quadratic equation is given as ax² + bx + c = 0, where,
a, b, and c are known values not equal to 0,
x is the variable.
Given a quadratic equation of -x² + 4x - 7, therefore,
a = -1
b = 4
c = -7
The annual demand for a product is 16,400 units. The weekly demand is 315 units with a standard deviation of 90 units. The cost to place an order is $31.00, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.20 per unit.
a. Find the reorder point necessary to provide a 95 percent service probability.
b. Suppose the production manager is asked to reduce the safety stock of this item by 55 percent. If she does so, what will the new service probability be?
Answers
Answer:
a) The reorder point necessary to provide a 95 percent service probability is 1557 units.
b) The Z value of 0.74 corresponds to 77% service probability.
Step-by-step explanation:
Average weekly demand (d) = 315 units
The standard deviation of weekly demand (\sigmad) = 90 units
Lead time (L) = 4 weeks
At 95% service level value of Z = 1.65
Reorder point = d x L + safety stock
[tex]= d \times L + (Z \times \sigma d \times \sqrt L)\\\\= 315 x 4 + (1.65 x 90 x \sqrt 4)\\\\= 1260 +(1.65 x 90 x 2)\\\\= 1260 + 297\\\\= 1557 units[/tex]
b) Earlier the safety stock was 297 units(calculated in part a)
Now the safety stock is reduced to 55%.so,55% of 297 = 163.35 units
So the new safety stock = 297 - 163.35 = 133.65
[tex]Safety stock = Z \times \sigma d \times \sqrt L\\133.65 = Z x 90 x 2\\133.65 = 180Z\\ Z = 133.65/180\\Z = 0.74[/tex]
The Z value of 0.74 corresponds to 77% service probability.
Use the P (A + B) = P (A) x P (B) rule to find the probability of system failure. Let A and B be the events that the first alarm and second alarm, respectively, fail. Do you get the same answer you did in the earlier question?
Answers
Answer:
answer is in the pic Mark me brainliest plz
Step-by-step explanation:
Answer:
The probability of the first alarm failing is (1 - 0.8) = 0.2
The probability of the second alarm failing is (1−0.9)=0.1.
Using the multiplication rule (since A and B are independent), the probability of failure is 0.2 * 0.1 = 0.02
Step-by-step explanation:
evaluate the expression when b=3
y = -7
4b-y
Answers
Answer:
5
Step-by-step explanation:
Given :
b = 3 y = -7To Find :
Value of 4b - y .Solution:
Put on the respective values ,
⇒ 4b - y = 4 × 3 - 7
⇒ 4b - y = 12 - 7
⇒ 4b - y = 5
Hence the required answer is 5 .
Answer: 5
Step-by-step explanation:
We can plug in the numbers for variables. So, our new equation would becomes 4x3-7. We first evaluate 4x3=12. Then, 12-7=5. Hence, your answer is 5.
When you compute with decimals you should always check your answer is reasonable why
Answers
Answer:
Ang pangit mo
Kamuka mo Yong clown
For the diagram below, which equation is the correct use of the distance
formula?
Answers
9514 1404 393
Answer:
D
Step-by-step explanation:
Any equation that does not have y2 as the first term in the second set of parentheses will be incorrect.
The correct usage is shown in equation D.
A nut mixture has peanuts,almonds and cashews in the ratio 5:3:1. Question:How much nust mixture should Helen buy if she wants to ensure she has 750g of almonds in the mix? please help!!will submit it today....
Answers
Answer:
2250 g of nut mixture
Step-by-step explanation:
In order to use the ratio, we have to divide that 750 g by 3.
So 250 g multiplied by 5 is 1250. That's the amount of peanuts. Then just 1 for the cashews.
So, adding all of that up, the answer is 2250 g of nut mixture.
Answer:
1350g of nut mixture
Step-by-step explanation:
5:3:1 = 5x + 3x + x
5x = 750
x = 150
5x + 3x + x
= 5(150) + 3(150) + (150)
=750 + 450 + 150
=1350g
Hope it helps...
Give two examples of subtraction of fractions ( between 0-1) with different denominators.
SHOW ALL STEPS
Answers
Answer:
3/4-1/2=1/4 4/5-3/15
Step-by-step explanation:
3/4-1/2
=3/4-2/4
=1/4
4/5-3/15
=4/5-1/5
=3/5
