The position of an object at time t is given by s(t) = -8 - 9t. Find the instantaneous velocity at t = 1 by finding the derivative. plz show work
Answer:
The instantaneous velocity at t = 1 will be:
[tex]\frac{d}{dt}\left(-8-9t\right)=-9[/tex]Step-by-step explanation:
Given the position of an object at a time [tex]t[/tex]
[tex]s\left(t\right)=-8-9t[/tex]
As we know that determining the derivative of the position function with respect to time t would give us the instantaneous velocity, so
[tex]\frac{ds}{dt}=\frac{d}{dt}\left(-8-9t\right)[/tex]
Applying the sum/difference rule:
[tex]\left(f\pm g\right)'=f\:'\pm g'[/tex]
[tex]\frac{ds}{dt}=-\frac{d}{dt}\left(8\right)-\frac{d}{dt}\left(9t\right)[/tex]
as
[tex]\frac{d}{dt}\left(8\right)=0[/tex] ∵ [tex]\frac{d}{dx}\left(a\right)=0[/tex]
and
[tex]\frac{d}{dt}\left(9t\right)=9[/tex] ∵ [tex]\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'[/tex] and [tex]\frac{d}{dt}\left(t\right)=1[/tex]
so the expression becomes
[tex]\frac{ds}{dt}=-\frac{d}{dt}\left(8\right)-\frac{d}{dt}\left(9t\right)[/tex]
[tex]=-0-9[/tex]
[tex]=-9[/tex]
As the derivative is constant.
Therefore, the instantaneous velocity at t = 1 will be:
[tex]\frac{d}{dt}\left(-8-9t\right)=-9[/tex]
Mercury freezes at -39 degrees Celsius and boils at 357 degrees C. which of the following intervals represents the temperature range in degrees Fahrenheit over which Mercury is a liquid?
Answer:
Man I wish I knew
Step-by-step explanation:
Answer:
The first answer is not helpful at all
What is the y-intercept of y=4/3x+4
Answer:
4
Step-by-step explanation:
I looked it up. Hope this helps
Answer:
its 4 or -4
Step-by-step explanation:
I used The Using the slope-intercept
Express 5 4/9 as a decimal.
Answer
look at the pic below
Step-by-step explanation:
PLEASE HELP ASAP.
A triangle with a vertex at point Y(-3, 7) is dilated by a scale factor represented by the coordinate pair (2/3x, 2/3y ). What is the location of Y'?
Please look at the picture below for the answer choices.
Answer:
[tex]Y' = (-2, 4\frac{2}{3})[/tex]
Step-by-step explanation:
Given
[tex]Y = (-3,7)[/tex]
[tex]Scale\ Factor = (\frac{2}{3}x,\frac{2}{3}y)[/tex]
Required
Determine Y'
Y' can be solved by multiplying the scale factor by Y
i.e.
[tex]Y' = Scale\ Factor * Y[/tex]
For, the x coordinates.
[tex]Y' = \frac{2}{3}x[/tex]
Where
[tex]x = -3[/tex]
[tex]Y' = \frac{2}{3} * -3[/tex]
[tex]Y' = \frac{-6}{3}[/tex]
[tex]Y = -2[/tex]
For the y coordinates:
[tex]Y' = \frac{2}{3}y[/tex]
Where
[tex]y = 7[/tex]
[tex]Y' = \frac{2}{3} * 7[/tex]
[tex]Y' = \frac{14}{3}[/tex]
[tex]Y' = 4\frac{2}{3}[/tex]
Hence:
[tex]Y' = (-2, 4\frac{2}{3})[/tex]
An item is priced at $13.11. If the sales tax is 5%, what does the item cost including sales tax?
OA. $0.66
OB. $19.67
OC. $26.88
OD. $13.77
Lost-time accidents occur in a company at a mean rate of 0.3 per day. What is the probability that the number of lost-time accidents occurring over a period of 9 days will be no more than 3? Round your answer to four decimal places.
Answer:
0.7295
Step-by-step explanation:
Given that :
Mean rate of lost time accident = 0.3 per day
probability that the number of lost-time accidents occurring over a period of 9 days will be no more than 3?
n = 9
Using binomial distribution formula :
P(x ≤3)
Probability of success (p) = 0.3
1 - p = 1- 0.3 = 0.7
nCx * p^x * (1 - p)^(n-x)
Using the binomial probability distribution calculator to save computation time :
P(x ≤3) = P(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)
P(x ≤3) = 0.0403 + 0.1556 + 0.2668 + 0.2668
P(x ≤3) = 0.7295
Probabilities are used to determine the chances of events.
The probability that accidents occur no more than 3 days in 9 days is 0.7296
The given parameters are:
[tex]p = 0.3[/tex] --- the probability that an accident occurs
The probability that an accident does not occur (q) is then calculated using the following complement rule
[tex]q= 1 - p[/tex]
[tex]q= 1 - 0.3[/tex]
[tex]q= 0.7[/tex]
The probability that accidents occur no more than 3 days in 9 days is
[tex]P(x \le 3) = P(0) + P(1) + P(2) + P(3)[/tex]
Each probability is calculated using:
[tex]P = ^nC_rp^rq^{n-r}[/tex]
So, we have:
[tex]P(x \le 3) = ^9C_0(0.3)^0(0.7)^9 +^9C_1(0.3)^1(0.7)^8 + ^9C_2(0.3)^2(0.7)^7 + ^9C_3(0.3)^3(0.7)^6[/tex]
This gives
[tex]P(x \le 3) = 0.0403 + 0.1556 + 0.2668 + 0.2669[/tex]
[tex]P(x \le 3) = 0.7296[/tex]
Hence, the probability that accidents occur no more than 3 days in 9 days is 0.7296
Read more about probabilities at:
https://brainly.com/question/7965468
A triangle has a perimeter of (12a^2 + 5a + 9b + 16) and side lengths (4a^2 + 9a - 8) and (2a + 2b + 10). What is the length of the third side?
I WILL GIVE BRAINLIEST !
Answer:
8x^2-6a+9b+14
Step-by-step explanation:
P=(12a^2 + 5a + 9b + 16)
(4a^2 + 9a - 8)+ (2a + 2b + 10) +(x)= (12a^2 + 5a + 9b + 16)
(4a^2+11a+2)+(x)=(12a^2 + 5a + 9b + 16)
subtract (4a^2+11a+2) from both sides
x= 8x^2-6a+9b+14
Answer:
ello luv
Step-by-step explanation:
Using the model, approximate the number of ice cream cones sold when it is 85°F. Round your answer to the nearest whole number.
Answer:
76.1
Step-by-step explanation:
y = ice cream
z = Tempreature
y = 1.8(85) - 76.9
1.8(85) = 153
153 - 76.9 = 76.1
Answer:
76
Step-by-step explanation:
y = 1.8(85) - 76.9
y = 153 - 76.9
y = 76.1
and when you round to the nearest whole number,
y = 76
solve by substitution
x - 2y = 10
1/2x - 2y = 4
Answer:
ypu can do this by using this please vote
Make a conjecture about the next item in the sequence 6, 18, 19, 57, 58
Answer:
Continuing from 58: 174, 175
Step-by-step explanation:
The pattern is multiply by 3, and add 1. 6 x 3 = 18, and 18 + 1 = 19. same pattern works for 19 times 3, and 57 times 1. 57 times 3 is 174, then add the 1 to get 175
Directions: Write your own recipe for trail mix with a catchy name that will make people want to eat it. You can also create a slogan, logo, or package design for the mix. Your recipe must meet the following contest guidelines:
1. It must have at least five different ingredients.
2. The amount of each ingredient should be represented by a different mixed number.
3. The recipe must make exactly 10 cups of trail mix.
After you write your recipe, complete the following for your contest entry:
• Prove that your recipe makes exactly 10 cups.
• Explain the most efficient method for measuring each ingredient using only
the following two measuring cups: 31 cup and 41 cup. You can use one or both of the measuring cups. Note: Depending on the fractions that you chose
for your ingredient amounts, it may not be possible to create each exact amount using only 13 and 14 measuring cups. If you need to, you can round your ingredient amounts using benchmarks and then explain how you would estimate that amount. For example, if you need 74 cup of an ingredient, 74
cup is slightly more than 12 cup. You could fill up your 14 measuring cup twice to make 12 cup of that ingredient, and then add just a tiny bit more to estimate 74 cup.
• Use equations or other models to show how you would measure each ingredient amount with only the two measuring cup sizes.
Answer:
add all of the # and that is your thing
Step-by-step explanation:
how to solve this geometry problem?
Answer:
x=7 A=41
Step-by-step explanation:
You do 180-69=111. You know that 11x-7 goes inside and then you do 11x-7+4x+13=111. You get x=7. Multiple 4x7=28+13=41
Find the slope of the line passing through the given points (5, 14) and (1, -2).
A) -3
B 3
D -4
E -9
Answer:
Answer:3
Explanation:Answer:
slope = 4
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, 14) and (x₂, y₂ ) = (1, - 2)
m = [tex]\frac{-2-14}{1-5}[/tex] = [tex]\frac{-16}{-4}[/tex] = 4
I NEED SOME HELP PLEASE!!!:)
Pamela received some gift cards for music and movie downloads for her birthday. Using one of them, she downloaded 4 songs and 1 movie, which cost a total of $16. Using another, she purchased 6 songs and 1 movie, which cost a total of $18. How much does each download cost?
Downloads cost $______for a song and $________for a movie.
Answer:
Downloaded music 1 EACH: $1
Movie 1 EACH: $12
Step-by-step explanation:
4 songs and 1 movie = $16
6 songs and 1 movie = $18
if we minus the two formulas we get:
2 songs = $2
Try it out on the formula, it will work.
$4 + x = $16
x = $12
$6 + $12 = $18
Which expression is equivalent to 5(w+4) when w=9?
O 5(9)
O 9(5)
O 5(9)+4
O 5(9) +20
Answer:
5(9)+20
Step-by-step explanation:
5(9+4) can be expanded to get 5(9)+5(4). And 5(4)=20.
Answer:
Option D
Step-by-step explanation:
This will seem weird but all you are is doing distrubitive property.
Replace w with nine and you have this.
Step 1 (Replace/Substitute)
5(9 + 4)
5(9) + 20
We distribute the five to the numbers in the parentheses. Or we multiply 5 to the other numbers within the parentheses.
Thus, D is your answer.
Marshall solved an equation using the process below.
Use the multiplication property of equality twice, by first multiplying both sides of the equation by x and then dividing both sides by 3.25.
Which equation is the one Marshall solved?
Answer:
b
Step-by-step explanation:
I don’t know it can someone help me
Answer:
23
Step-by-step explanation:
supplementary angles: 180-85 = 95
95 = 5x-20 ( i forgot the name of the rule, something relating to same side interior angles i think)
115 = 5x
23= x
hope that helped
the ratio of large triangles to small triangles is 2-6 .If there are 100 triangles in the design ,how many small triangles are there.
Answer:
75 small triangles
Step-by-step explanation:
1. Reduce the ratio: 2-6 = 1-3
2. Write each of them as a fraction of a whole:
Small total = 3/(1+3) = 3/4 of the total amount
3. Multiply the ratio to get the answer: 3/4 * 100 = 75
Plz help
Edna wants to know the height of a pine treeShe measures the shadow of the pine tree and finds that it is 12 meters long. Edna also knows that a nearby redwood tree that is 8 meters tall is casting a shadow 6 meters long. How tall is the pine tree?
Answer:
14 meters long
Step-by-step explanation:
if a 8 meter tree is casting a 6 meter shadow you add 2 meters from the orginal tree you want to measure.
12 meters +2 meters = 14 meters
HELP I REALLY NEED AN ANSWER WILL GIVE BRAINLIEST IF I CANNNNN
Answer:
62
Step-by-step explanation:
What is an equation of the line that passes through the points (5, 2) and (-5, 6)?
Answer:
In the pic
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)
21. Find the perimeter of the triangle: 60 degrees, 60 degrees,
[tex]4 \sqrt{15 } [/tex]
Answer:
120+ 4(square root)15
120+15.49=135.49
135.49 is the perimeter
The perimeter of the triangle having two angles 60 degrees, 60 degrees, and one side [tex]4\sqrt{15}[/tex] is, [tex]12\sqrt{15}[/tex] or 46.47
What is the perimeter?Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.
Perimeter = Sum of length of the all the sides
Given that,
the triangle having two angles 60 degrees, 60 degrees,
and one side
It is known that, total sum of all the angles of triangle is 180°
A = 60°
B = 60°
C = ?
A + B + C = 180°
60° + 60° + C = 180°
C =60°
Hence, it is a equilateral triangle
And for equilateral triangle length of all sides are equal
a = [tex]4\sqrt{15}[/tex]
b = [tex]4\sqrt{15}[/tex]
c = [tex]4\sqrt{15}[/tex]
Perimeter = [tex]4\sqrt{15}[/tex] + [tex]4\sqrt{15}[/tex] + [tex]4\sqrt{15}[/tex]
Perimeter = 12√15
So, the perimeter is 12√15
To know more about Perimeter check:
https://brainly.com/question/6465134
#SPJ1
1. Consider the system of equations below. What could be the first step in solving by elimination?
3x + 5y = 16
3x + 2y = 10
O Add the two equations together.
O Add 5 to both sides of the first equation.
Ο Multiply the first equation by -1.
Ο Multiply the second equation by 2.
Answer:
Multiple the first equation by -1
Step-by-step explanation:
After doing this you add the two equations together and follow the systems of equations as normal
[tex]-3x+-5y=-16\\3x+2y=10\\-3y=-6\\\frac{-3y}{-3} =\frac{-6}{-3} \\y=2[/tex]
Therefore y = 2
I will give brainlest
Answer:
-360
Step-by-step explanation:
Match each shape to its name
Answer:
I can’t really answer this because you didn’t show a picture. Here’s a thought though. Look up a shape chart on google and work from there. Hope this helps you out
(WILL GET 25 POINTS) what is 1 + 1 =?
Answer:
2
Step-by-step explanation:
haha
my sister is bugging me and i dont care so please help
(sorry about the name this is how it got sent to me)
**EXPLAIN LIKE DO STEPS SO IT DOESNT LOOK LIKE ITS CHEATING??
Number 3's answer: $2.89 per box
Explanation: take the total cost divided by the number of cereal boxes. $43.35÷15=$2.89 per box
Number 4's answer: 2.45
Explanation: number of points divided by minutes=points per minute. 98÷40=2.45 point a minute.
Number 5's answer:$0.89
Explanation:total cost of bananas divided by pounds=cost per pound. $1.89÷2.25 (2 1/4) =$0.89
Hope this helps
The table shows the lowest elevations in some countries.
A 2-column table with 5 rows. Column 1 is labeled Country with entries Dominican Republic, France, Hungary, India, Japan. Column 2 is labeled Elevation (meters) with entries negative 46, negative 2, 78, 0, negative 4.
If you plotted these elevations on a vertical number line, which would be the only country with a lowest elevation above 0?
Answer:
Hungary
Step-by-step explanation:
Just did the question
Answer:
Hungary
Step-by-step explanation:
just did it.
Julie buys 19 identical calculators.
The total cost is £143.64
Work out the total cost of 31 of these calculators.
Answer:
£234.36
Step-by-step explanation:
