Question:
A particle moves along the x-axis so that its position at time t>0 is given by [tex]x(t)=\frac{t^2 -9}{3t^2 +8}[/tex]
Show that the velocity of the particle at time t is given by [tex]v(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]
Answer:
[tex]v(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]
Step-by-step explanation:
Given
[tex]x(t)=\frac{t^2 -9}{3t^2 +8}[/tex]
Required
Show that:
[tex]v(t) = \frac{70t}{(3t^2 +8)^2}[/tex]
To calculate v(t), we use:
[tex]v(t) = x'(t)[/tex]
So, we have:
[tex]x(t)=\frac{t^2 -9}{3t^2 +8}[/tex]
Apply quotient rule
[tex]x'(t) = \frac{vu' - uv'}{v^2}[/tex]
Where
[tex]u =t^2 - 9[/tex]
[tex]v=3t^2 + 8[/tex]
So:
[tex]u =t^2 - 9[/tex]
[tex]u' = 2t[/tex]
[tex]v=3t^2 + 8[/tex]
[tex]v' = 6t[/tex]
So, we have:
[tex]x'(t) = \frac{vu' - uv'}{v^2}[/tex]
[tex]x'(t) = \frac{(3t^2 + 8) * 2t - (t^2 - 9) * 6t}{(3t^2 + 8)^2}[/tex]
Expand the numerator
[tex]x'(t) = \frac{6t^3 + 16t - 6t^3 + 54t}{(3t^2 + 8)^2}[/tex]
Collect like terms
[tex]x'(t) = \frac{6t^3 - 6t^3+ 16t + 54t}{(3t^2 + 8)^2}[/tex]
[tex]x'(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]
Recall that:
[tex]v(t) = x'(t)[/tex]
[tex]v(t) = \frac{70t}{(3t^2 + 8)^2}[/tex]
Proved
A builder had been asked to lay an octagonal patio using square paving slabs. To do this, he cuts some of the bricks in half down the diagonal. Each paving slab is 1m wide. What will the perimeter of the patio be
16(1/2x)⁴ whats the simplified expression
Answer:
1/x⁴
Step-by-step explanation:
=16(1/2x)⁴
=16(1/16x⁴)
=16×1/16x⁴(16 cancels)
=1/x⁴
This sphere has a diameter of 5 m.
A sphere with diameter 5 meters.
What is the volume of the sphere?
Answer:
65.45m^3
Step-by-step explanation:
volume = 4/3 * pi * radius ^3
v= 4/3 * pi* 2.5^3
v= 4/3* 22/7* 15.625
v= 64.45 m ^ 3
A. Right B. Isosceles C. Obtuse O D. Equilateral E. Scalene F. Acute
Answer:
B & C
Step-by-step explanation:
Isosceles- having two sides of the same length
Obtuse- having one obtuse angle and two acute angles
find ∅ round to the nearest degree
A. 24°
B. 66°
C. 64°
D. 26°
Answer:
C
Step-by-step explanation:
Using the cosine ratio in the right triangle
cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{7}{16}[/tex] , then
θ = [tex]cos^{-1}[/tex] ([tex]\frac{7}{16}[/tex] ) ≈ 64° ( to the nearest degree )
Mr. Lopez graded
homework from 4:30
to 6:30 on Friday. He
graded from 1:00 to 3:00 on Saturday, and from 12:20 to 2:00 on Sunday. How many total hours did Mr. Lopez spend grading this weekend?
Answer:
8:00
Step-by-step explanation:
A. Download the printable diagram of the real number system. B. Find 10 numbers in the real world, with at least one number from each of the categories in the diagram. Post your number set to the discussion board. (In your post, don't label your numbers with their categories.) C. View another student’s number set and choose 5 numbers to place into your diagram. Choose numbers that another student has not used in his or her diagram. Explain your placement of each number. Post a scan or a picture of your diagram in your response. D. Go to another student’s post and choose another 5 numbers. Place them into your diagram and explain your placement. Also post a scan or a picture of your diagram in your response. You can use the same diagram you used for the first 5 numbers. Just label each student's numbers.
Answer:
Natural Number: 1, 2, 3
Whole number: 7, 19, 24
Integer: 12
Rational Number: 8, 1.5
Irrational Number: π
Step-by-step explanation:
8th grade k-12 xx
Can someone please help me?
Answer: I think a
Step-by-step explanation:
Find the circumference of each circle. Leave your answer in terms of π
Answer:
13,188
Step-by-step explanation:
you have to times 4.2 by the C which is 4.14 adn that give you your anwser
I need some help with this, help please Imao
Answer:
D. 4Step-by-step explanation:
The degree of the function is:
1 + 3 = 4Correct choice is D
What is the factored form of the polynomial?
x2 − 12x + 27?
(x + 4)(x + 3)
(x − 4)(x + 3)
(x + 9)(x + 3)
(x − 9)(x − 3
Answer:
(x-9)(x-3)
Step-by-step explanation:
I hope it will help you
WILL MARK BRAINLIEST IF CORRECT
Answer: The answer would be C, I hope this isnt wrong so sorry if it is.
Step-by-step explanation:
determine the EXACT value of : ( 1235 x 0.24 ) - 1.32
Answer:
295.08
Step-by-step explanation:
Answer:
295.08
Step-by-step explanation:
296.4 - 1.32 = 295.08
Mr. Jones has 160 animals on his farm. Of these animals, 20% are cows, 30% are goats, 10% are horses, and the rest are chickens how many chickens are on Mr. Jones's farm
Answer:
64 chickens (40%)
Step-by-step explanation:
16 horses(10%), 32 cows(20%), 48 goats(30%),
Answer:
b
Step-by-step explanation:
Find the value of z.
Answer:
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.\
Step-by-step explanation:
Ummm ill make brainliest
Answer:
The value of t is 8
Step-by-step explanation:
¼ t - 6 = - 4
¼ t = 6 - 4
¼ t = 2
t = 2 × 4
t = 8
Thus, The value of t is 8
-TheUnknownScientist
15 points Math problem
Because of the unexpected cold snap the price of the oranges increased by 50% in one month. If the price was $0.75 after the increase what was the original price?
Answer:
increased=150%=0.75
original price =100%
100%*0.75/150
=$0.5
Help please I’d really appreciate it!
10 points
Carter is creating quilt pieces in the shape of a kite as shown below. One of the kite diagonals measures 6 inches, and the area of each piece must be between 20 and 25 square inches.
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]d_1 =6in[/tex] --- the first diagonal
[tex]Area = (20in^2,25in^2)[/tex]
The question is incomplete, as the image of the kite and what is required are not given
However, a possible question could be to calculate the length of the other diagonal
Calculating the length of the other diagonal, we have:
[tex]Area = 0.5 * d_1 * d_2[/tex]
Make d2 the subject
[tex]d_2 = \frac{Area }{0.5 * d_1}[/tex]
Multiply by 2/2
[tex]d_2 = \frac{2 * Area }{2* 0.5 * d_1}[/tex]
[tex]d_2 = \frac{2 * Area }{1 * d_1}[/tex]
[tex]d_2 = \frac{2 * Area }{d_1}[/tex]
When Area = 20, we have:
[tex]d_2 = \frac{2 * 20}{6}[/tex]
[tex]d_2 = \frac{40}{6}[/tex]
[tex]d_2 = 6.67[/tex]
When Area = 25, we have:
[tex]d_2 = \frac{2 * 25}{6}[/tex]
[tex]d_2 = \frac{50}{6}[/tex]
[tex]d_2 = 8.33[/tex]
So:
[tex]d_2 = (6.67,8.33)[/tex]
This means that the length of the other diagonal is between 6.67in and 8.33in
what is the slope of the line that passes through (9,3) and (2,11)?
Answer:
-8/7 is your answer
Solve for in the diagram below.
HELP ASAP
!!!!!!!!!!!!111111
Answer:
x = 43
Step-by-step explanation:
First, make the equation which is
x + 49 + 88 = 180
Next, add 49 + 88 which is 137
Now you have x + 137 = 180
Subtract 137 from both sides and you get your final answer:
x =43
Erin earns $2 200 per month her deduction amount to 28% of her paycheck. How much does she take home each month
Answer:
1584
Step-by-step explanation:
The take-home salary would be $1584 each month if Erin earns $2200 per month her deduction amount to 28% of her paycheck.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Erin earns $2200 per month.
The deduction amount to 28% of her paycheck.
Let's assume the 28% is deducted from the monthly salary.
The total dedcution = 28% of 2200
The total dedcution = (28/100)x2200
The total dedcution = 0.28x2200
The total dedcution = $616
Total net amount = Take home = 2200 - 616
Take home = 2200 - 616
Take home = $1584
Thus, the take-home salary would be $1584 each month if Erin earns $2200 per month her deduction amount to 28% of her paycheck.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ2
The relation defined by the set of ordered
pairs
{(0,3), (2,1),(3,0).(-1,2), (0,5),(-2,5)}
is not a function. Deleting which of the
ordered pairs will make the resulting set a
function?
a. (0,3)
c. (3.0)
b. (2.1)
d. (-1,2)
Answer:
a: (0,3)
Step-by-step explanation:
the input 0 currently has two outputs, deleting one, (0,5), would cause the set of ordered pairs to become a function
Find the value’s of x given that f(x) = x^2 - 2x - 3 and f(x) = 5
Answer:
4 and - 2
Step-by-step explanation:
f ( x ) = x^2 - 2x - 3
f ( x ) = 5
x^2 - 2x - 3 = 5
x^2 - 2x - 3 - 5 = 0
x^2 - 2x - 8 = 0
x^2 + 2x - 4x - 8 = 0
x ( x + 2 ) - 4 ( x + 2 ) = 0
( x - 4 ) ( x + 2 ) = 0
x - 4 = 0
x = 4
x + 2 = 0
x = - 2
x has 2 values,
x = 4, - 2
What is the sum of (-7x3 - 9x) + (5x + 4)?
An elevator descends into a mine shaft at the rate of 5 m/min. If the descend starts from 15m above the ground, by how long will it take to reach 350 m deep from the ground?
Answer:
Step-by-step explanation:
First we need to do 350 - 15 since 350 is our total and we already started at 15m.
Next divide the remainder (335) by 5 because that’s how fast we are moving, the final answer is 67 minutes.
Describe the following graph. Use terms
like increasing, decreasing, constant,
linear, non-linear, etc...
Which type of line of symmetry does the figure have?
diagonal
vertical
horizontal
none
Answer:
vertical
Step-by-step explanation:
This 'A' has vertical symmetry.
In how many games did Katy play catcher?
Answer:
we need more info hun.
Step-by-step explanation: