a. The rocket splashes down after 31.23 seconds.
b. The rocket is 1374.7 meters above sea level.
NASA launches a rocket at t=0 seconds.
Its height, in meters above sea-level, as a function of time is given by
h(t)=-4.9t²+142t+346.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
When splash down occurs, h(t) = 0, therefore
-4.9t²+142t+346 = 0
find t using the quadratic formula; a=4.9, b=142, c=346
t = -142 ± √(142)² - 4(-4.9)(346) / 2(-4.9)
t = -142 ± 164.15 / -9.8
t = -142+164.15/-9.8 , -142-164.15/-9.8
t = 22.15/-9.8 , -306.15/-9.8
t = -2.26 , 31.23
time cannot be negative so t = 31.23
The rocket splashes down after 35.8229 seconds.
The max occurs on the axis of symmetry, use x=-b/(2a) to find it
t = -142/2(-4.9)
t = 142/9.8
t = 14.48 sec
replace t with 17.2449 in the equation
h(t) = -4.9(14.48)² + 142(14.48) + 346
= 1374.7 m
The rocket peaks at 1374.7 meters above sea-level.
Hence we get the answers.
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7x - 7; x = 4................
Answer:
21
Step-by-step explanation:
7x - 7
=> substituting x = 4
=> 7(4) - 7
=> 28 - 7
=> 21
ANSWER QUICK I WILL GIVE BRAINLIEST
Solve k over negative 1.8 is less than negative 4.9 for k.
k < −8.82
k > 8.82
k < −6.7
k > −6.7
The solution of the inequality is k > 8.82
How to solve inequality?The expression is in words so we have to convert it to an inequality to be able to solve for k.
An inequality is an expression that has the following symbols: <, >, ≤ and ≥.
Therefore, the inequality can be solved as follows:
k / - 1.8 < - 4.9
Therefore, let's solve for the variable k.
k / - 1.8 < - 4.9
multiply both sides of the inequality by - 1.8
Hence,
k / - 1.8 (-1.8) < - 4.9 (-1.8)
k / 1 > 8.82
Note the sign had to change after we multiply both side of the inequality with a negative number.
Therefore,
k > 8.82
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don’t know what to do
A power function has the formula f(x) = kxⁿ,
A power function is a function that has a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real value. (A coefficient is a value that increases an exponent by a variable.)
A power function has the formula f(x) = kxⁿ, where k and n are both real numbers. You can change the appearance of a power function's graph by changing the values of k and n. As a result, in this graph, n is greater than zero.The Power function produces an integer that has been raised to a particular power. Power is an alternative for the exponent operator in a mathematical equation (^). The Power function only takes two arguments: number and power. Number must be a numeric value that is either a hardcoded constant or a cell reference.Monomial functions:
Linear: y=3x+5
Quadratic: y = x²
Constant: y = 6
Cubic: y = x³+5
Quartic : y = x⁴
Quantic : y = x⁵
Therefore the function with a power function is given by y = k xⁿ
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The value of y varies directly with x. If y = 8, when x = 4, what is y when x = 48?
Answer:
96
Step-by-step explanation:
If Y is directly proportional (or in this case varies directly) then whatever you do to one value you do to the other.
So in this case, when Y = 8 and X = 4 that means that Y is double of X (cause 8 is double 4).
So when X = 48 all you need to do is double X which will give you 96.
Vă rog mult de tot
√ ( 2√2-3 ) ² + |2√2 + 5|-|-2,5 |
Answer: 4√2-0.5
Step-by-step explanation:
[tex]\sqrt{(2\sqrt{2}-3)^2 } +|2\sqrt{2}+5|-|-2.5|=\\\\|2\sqrt{2}-3|+(2\sqrt{2}+5)-(2.5 )=\\\\2\sqrt{2}-3+2\sqrt{2}+5-2.5 =\\\\4\sqrt{2} -0.5[/tex]
identify the y-intercept: 6 - 2y = -6
We know that the equation of a line is given by
y = mx + b, where m and b are numbers:
m is the slope of the line and b is the y intercept.
In this case we have the equation:
6 - 2y = - 6
We clear y so we can identify m and b
6 - 2y = -6
6 = -6 + 2y
6 + 6 = 2y
12 = 2y
12/2 = y
6 = y
In this case
y = 6
Then m=0 and b = 6
Then, the y-intercept is b =6What is the minimum additional information would you need in order to be able to state that the triangles are congruent by AAS?
The minimum additional information needed in order to be able to state that the triangles are congruent by AAS is . Option A
[tex]\angle A B C=\angle A D C[/tex]
This is further explained below.
What is the congruent angle?Generally, The triangles are said to be congruent if they satisfy the AAS (Angle-Angle-Side) condition, which states that if two angles and a non-included side in one triangle are congruent to two angles and the equivalent non-included side in another triangle, then the triangles are congruent.
In conclusion, The following pieces of knowledge are the bare minimum that is required in order to be able to make the assertion that the triangles are congruent according to AAS:
[tex]\angle A B C=\angle A D C[/tex]
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2 is subtracted from twice a number.
early beginner in geometry
Answer:
2x-2 (x is your number)
Step-by-step explanation:
Not sure if this is what you mean lol
:]
15. what are the coordinates of point u, point v, and point w
Answer:
is there a picture because this can't be solved without a picture
WILL GIVE BRAINLEIST
Which steps show how to use distributive property to evaluate 5 x 38
Answer:
The answer is most definitely A. It is the only answer that reaches the correct value of 190, which is what 5 * 38 equals. However, to put it into perspective...
Step-by-step explanation:
When we use the distributive property we are breaking down something sometimes, and in this case, very simple into a more extended form.
5 * 38 is the same as saying 5(40 - 2). We also know that if we subtract the sum of 5 * 2 from 5 * 40, it will end up the same as 5 * 38 because you are multiplying 5 two times less.
5 * 40 = 200
5 * 2 = 10
200 - 10 = 190
The answer is A
;)
i need help ASAP show your work
Answer:
a=5
Step-by-step explanation:
1/3(6a-15)=(a-2)+2
1/3(6a-15)=a
6a-15=3a
3a=15
a=5
:]
Step-by-step explanation:
1.multiply in first bracket
[tex]2a - 5 = a + 0[/tex]
2.Take unknowns to left and constants to the right
[tex]2a - a = 5[/tex]
3.solve for a
[tex]a = 5[/tex]
Given P(A) = 0.6, P(B) = 0.42 and P(B|A) = 0.63, find the value ofP(An B), rounding to the nearest thousandth, if necessary
Here, we are given;
P(A)=0.6
P(B)=0.42
P(B/A)=0.63
We have to find;
[tex]P(A\cap B)[/tex]Now,
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]This is the formula for finding conditional probability.
From here,we can see that we have values of P(B/A) and P(A) and we can easily find P(Aand B) from here.
Since P(A)>0 so we can use this formula.
Therefore,
[tex]\begin{gathered} P(A\cap B)=P(A)\times P(\frac{B}{A}) \\ P(A\cap B)=0.6\times0.63 \\ P(A\cap B)=0.378 \end{gathered}[/tex]the number of students in the school went from 1028 down to 755 what is the percent decrease?
Step-by-step explanation:
100% = 1028
1% = 100%/100 = 1028/100 = 10.28
the decrease was
1028 - 755 = 273
these 273 were how many % ?
as many % as how often 1% fits into 273 :
273 / 10.28 = 26.55642023... %
this was a 26.55642023...% decrease.
What is a hour and how manyyyy
Answer:
An hour is a unit of time.
Step-by-step explanation:
An hour is a period of 60 minutes.
1 hour = 60 minutes.
Answer:
an hour is the si unit of time
1 hour = 60 minutes
1 minutes = 60 seconds
pls mark as brainliest
Step-by-step explanation:
In a right triangle ABC, < B = 90°. If AC=13cm, BC= 5cm, find AB
Answer:
AB = 12cm
Step-by-step explanation:
ABC is the right triangle, that means we can use theorem: AC²=AB²+BC²
AB²=AC²-BC²=13²-5²=169-25= 144
AB=√144
AB=12cm
Write an equivalent expression for -3(7+5g)
Answer:
-3(12g)
Step-by-step explanation:
Because if we simplify the 7+5g to 12g because 7+5=12.
Therefore,
-3(7+5g)= -3(12g)
(last question) but does anyone know the answer (s)??!?!
Answer:
MN = 3
Step-by-step explanation:
MN = 3
Similar triangles :)
1,1.8,3
2,3.6,6
Triangle AMN is half the size of triangle ABC :)
hope this helps
:]
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
7b + 6
Step-by-step explanation:
Given expression,
→ 5b + 10 + 2b - 4
Let's solve the expression,
→ 5b + 10 + 2b - 4
→ (5b + 2b) + (10 - 4)
→ 7b + 6
Hence, answer is 7b + 6.
A hiker walked 15 miles from 8:00 a.m. to noon. He walked an additional 18 miles from 1:00 p.m. to 7:00 p.m.
What is his average rate for the entire walk, in miles per hour?
The average rate for the entire walk of hiker is 3.75 miles per hour by the concept of average speed.
What is average speed?The instantaneous speed is the upper limit of the average speed as the duration of the time interval approaches zero. An object's average speed during a certain period of time is equal to its distance traveled over that period divided by its duration. Speed and velocity are distinct concepts.
The whole distance traveled divided by the total time results in the average rate for the entire walk, expressed in miles per hour.
Given that:
Distance A = 12.8 miles
Distance B = 17.2 miles
Total distance = Distance A + Distance B
Total distance= 12.8 + 17.2
Total distance= 30 miles
Time A = 9:00 a.m. to noon = 3 hours
Time B = 1:00 p.m. to 6:00 p.m. = 5 hours
Total time = Time A + Time B
Total time= 3 + 5
Total time= 8 hours
Average rate = Total distance/Total time
Average rate= 30 miles/8 hours
Average rate= 3.75 miles per hour
Therefore, the average rate for the entire walk of hiker is 3.75 miles per hour.
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Please help me!!!!!!!!!
Answer:
m∠TQS = 137°
m∠RQS = 43°
Step-by-step explanation:
It is given that ∠RQT is a straight angle
That means that this angle is 180° and RQT is a straight line
Therefore m∠TQS + m∠RQS = m∠RQT = 180°
Given
m∠TQS = (6x + 20)° and m∠RQS = (2x + 40)°
adding the two angles together will imply
(6x + 20)° + (2x + 40)° = 180°
=> 6x + 20 + 2x + 4 = 180
=> 6x + 2x + 20 + 4 = 180
=> 8x + 24 = 180
=> 8x = 180 - 24= 156
=> x = 156/8 = 19.5
Substitute for x in the angle expressions
m∠TQS = 6x + 20 = 6(19.5) + 20 = 117 + 20 = 137°
m∠RQS 2x + 4 = 2(19.5) + 4 = 39 + 4 = 43°
(or we could subtract m∠TQS from 180 to get 180 - 137 = 43°)
Check if they add up to 180°
137° + 43° is indeed 180°
Julia owns a food truck that sells tacos and burritos. She only has enough supplies to make 67 tacos or burritos. She sells each taco for $3.75 and each burrito for $6. Julia must sell no less than $330 worth of tacos and burritos each day. If 42 burritos were sold, determine all possible values for the number of tacos that Julia must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Julia must sell 21 tacos to meet the requirement .
Given: Price of each taco = $ 3.75
Price of each burrito = $ 6
Total amount of money she needs to earn = $ 330
Also the number of burritos sold= 42.
So the total amount earned on selling these burritos= 42× 6 = $ 252
And as it is given that total money she needs to earn is $ 330 .
so required money= $ 330- $ 252
=$ 78
Thus the total number of tacos she needs to sell = 78/ price of 1 taco
= 78/ 3.75
= 20.8 ≈ 21
Thus Julia must sell 21 tacos to meet the requirement .
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In 1924, the temperature in St. Louis, Missouri, dropped from 53 degrees to −11 degrees in 8 hours. What was the average hourly change in temperature?
(pls this is for a test rn)
Answer: -8°
Step-by-step explanation: the temperature dropped by 64 degrees over the span of 8 hours. 64/8 = 8.
Solve the given system of equations.S =t =-6s+ 3t = - 45-s-5t= -2
1. Solve s in the second equation:
[tex]\begin{gathered} -s-5t=-2 \\ -s=-2+5t \\ s=-(-2+5t) \\ s=2-5t \end{gathered}[/tex]2. Substitute the s in the first equation by the value you get in the previous step:
[tex]-6(2-5t)+3t=-45[/tex]3. Solve t:
[tex]\begin{gathered} -12+30t+3t=-45 \\ -12+33t=-45 \\ 33t=-45+12 \\ 33t=-33 \\ t=\frac{-33}{33} \\ \\ t=-1 \end{gathered}[/tex]4. Use the value of t to solve s:
[tex]\begin{gathered} s=2-5t \\ s=2-5(-1) \\ s=2+5 \\ s=7 \end{gathered}[/tex]Then, the solution of the given system of equations is s=7t= -1Circle the two subtraction problems that have a difference of 10.2.
The problems with a difference of 10.2 are:
16.29 - 6.09 = 10.236.1 - 25.9 = 10.2We are given some subtraction problems for which we need to find the ones with a difference of 10.2.
The problems are:
12.05 - 2.03
16.29 - 6.09
36.1 - 25.9
22.09 - 21.07
10.82 - 9.8
We find the difference for each of them one-by-one after subtraction.
12.05 - 2.03 = 10.0216.29 - 6.09 = 10.236.1 - 25.9 = 10.222.09 - 21.07 = 1.0210.82 - 9.8 = 1.02The question is incomplete. Find the complete question below:
Circle the two subtraction problems that have a difference of 10.2.
12.05 - 2.03
16.29 - 6.09
36.1 - 25.9
22.09 - 21.07
10.82 - 9.8
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76,300,000 in scientific notation
Answer:
7.63 x 10⁷
Step-by-step explanation:
To convert to scientific notation you have to move the decimal place to where there is only one number in front of it. In this cause the number in front is 7. You have to maintain the same number of significant figures which in this case was 3 then multiply by 10 to the exponent of how many times you moved the decimal place.
Answer:
=76.3×10⁶
Step-by-step explanation:
=76,300,000÷1,000,000
=76.3×10⁶
Given three points of a quadratic function, find the equation of the function: (-1, -3), (0, -4), (2, 6)
A) f(x)=2x^2+2x−4f
B) f(x)=x^2+2x−4f
C) f(x)=x^2+x−4f
D) f(x)=2x^2+x−4f
The quadratic function has an equation of f(x) = 2x²+ x - 4
How to determine the equation of the functionFrom the question, the ordered pairs are given as
(-1, -3), (0, -4), (2, 6)
A quadratic function is represented as
f(x) = ax²+ bx + c
Using the point (0, -4), we have
a(0)²+ b(0) + c = -4
So, we have
c = -4
This gives
f(x) = ax²+ bx - 4
Using the point (-1, -3), we have
a(-1)²+ b(-1) - 4 = -3
So, we have
a - b = 1
Using the point (2, 6), we have
a(2)²+ b(2) - 4 = 6
So, we have
4a+ 2b = 10
So, we have
a - b = 1
This gives
a = b + 1
Substitute a= b + 1 in 4a+ 2b = 10
4(b + 1) + 2b = 10
This gives
4b + 4 + 2b = 10
Evaluate
6b = 6
Divide
b = 1
So, we have
a = 1 + 1
a = 2
So, we have
f(x) = 2x²+ x - 4
Hence, the equation is f(x) = 2x²+ x - 4
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A model of a famous statue is 3 1/2 inches tall. The actual statue is 5 1/4 feet tall. What is the ratio of the height of the model to the height of the actual statue in simplest form?
A model of a famous statue is [tex]3\frac{1}{2}[/tex]inches tall. The actual statue is [tex]5\frac{1}{4}[/tex] feet tall, the ratio of the height of the model to the height of the actual statue in simplest form is [tex]3\frac{1}{2}[/tex]:63
What is a ratio mean?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of the lemons to oranges is 6:8 (or 3:4). (or 4:7).
A ratio can have any number of quantities, such as counts of people or things or measurements of the length, weight, time, etc. Both the numbers must be positive in most situations.
You can specify a ratio by either writing out both of the integers that make it up, "a to b" or "a:b", or by giving just the value of their quotient a/b. Equal quotients correspond to the equal ratios.
A ratio can therefore be thought of as an ordered pair of integers, a fraction with first number in the numerator and the second in the denominator, or as the value represented by this fraction. Ratios of the counts that are expressed in terms of (non-zero) natural numbers are rational numbers and occasionally natural numbers as well. The ratio of the two numbers is a dimensionless number when they are measured using the same unit, which happens frequently. A rate is product of two quantities that are divided by their respective units of measurement.
Given,
A model of a famous statue is [tex]3\frac{1}{2}[/tex] inches tall.
The actual statue is [tex]5\frac{1}{4}[/tex] feet tall
1 feet = 12 inches
21/4 ft = 12*21/4 inches = 63 inches
Therefore the ratio is
[tex]3\frac{1}{2}[/tex]:63
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which situation is best modeled by an exponential distribution? tafadzwa runs between 10 and 16 laps every day. his times get slower as he gets tired, but his daily average is 48.2 s per lap. what is the probability that his mean lap time tomorrow will be less than 45 s? suppose that meteors large enough to cause mass extinction strike the earth at regular, although exceedingly large, intervals. what is the probability that a large meteor strike will cause a mass extinction event within the next 1000 years? on a dark desert highway, drivers fall asleep and run off the road randomly. what is the probability that a driver will run off the road in one particular 10-mile stretch of this highway? suppose that people call in sick randomly and independently of one another at a business called acme anvil supply. on average, one person calls in sick per week. what is the probability that no one will call in sick next week? suppose that 0.76% of tires are defective, and defective tires occur independently of one another. what is the probability that no more than three of the next 100 tires are defective?
The situation that is best represented by an exponential distribution is given by the following option:
Tafadzwa runs between 10 and 16 laps every day. his times get slower as he gets tired, but his daily average is 48.2 s per lap. what is the probability that his mean lap time tomorrow will be less than 45 s?.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following mass function:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
From this, we get that the exponential distribution is used when we want to study the time between events in a distribution, and only the first option in this problem gives it.
As for the other options, the distributions are as follows:
Meteor: Poisson distribution or binomial distribution, mean in a given time, we want to find the probability of a number.Drivers asleep in the highway: Poisson or binomial, also number of events in an interval.People calling in sick: Binomial distribution.Defective tires: Binomial distribution.More can be learned about the exponential distribution at https://brainly.com/question/16371214
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PLease help it’s due tomorrow morning
Explain the step that is used to solve the equation
-x = -16
Answer:x=16
Step-by-step explanation:
just divide both sides by negative 1
a=3p+1
Solve for p
please help me solve this
Answer:
Step-by-step explanation:
p= a/3 - 1/3