Answer:
exponential decay
Step-by-step explanation:
a value is less than 1 but greater than 0, making it decay.
A particle moves along the x-axis so that time t>0 the position is given by x(t)=0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1. What is the velocity of the particle at the first instance the particle is at the origin?
The velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.
To find the velocity of the particle at the first instance it is at the origin, we need to find the value of t when x(t) = 0.
Since the particle is at the origin when x(t) = 0, we have:
[tex]0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1 = 0[/tex]
Using numerical methods or graphing the equation, we find that the roots are approximately t ≈ -0.618, t ≈ 1.532, t ≈ 3.143, and t ≈ 2.944.
Since t > 0, the first instance the particle is at the origin corresponds to t ≈ 2.944 (the smallest positive real root).
Now, to find the velocity of the particle at this instance, we need to find the derivative of the position function x(t) with respect to time t, which gives us the velocity function v(t):
v(t) = dx/dt
[tex]v(t) = d/dt (0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1)\\v(t) = 2t^3 - 4.5t^2 - 4t + 6[/tex]
Now, we can find the velocity at t ≈ 2.944:
[tex]v(t = 2.944) = 2(2.944)^3 - 4.5(2.944)^2 - 4(2.944) + 6[/tex]
v(t ≈ 2.944) ≈ 16.885
So, the velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.
learn more on velocity :
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And,( -7,3) is the image of an after a reflection in the X-axis. what are the coordinates of N
what is the distance between (5,8) and (2,4) by using distance formula
Answer:
Distance = 5
Step-by-step explanation:
D= sqrt (x1-x2)^2 + (y1-y2)^2
(5-2)^2 + (8-4)^2=3^2 + 4 ^2 = 9 +16 = 25
Sqrt of 25 = 5
Distance = 5
Hope this helps
Answer:
d=3.605551
Step-by-step explanation:
d=(8−5)2+(4−2)2−−−−−−−−−−−−−−−√
d=(3)2+(2)2−−−−−−−−−√
d=9+4−−−−√
d=13−−√
d=3.605551
1. Find two numbers such that the sum of the first and three times the secondis 5 and the sum of second and two
times the first is 8.
help asap
Answer:
[tex]x + 3y = 5...(1) \\ 2x + y = 8...(2) \\ 2 \times (1) \\ 2x + 6y = 5...(3) \\ (3) - (2) \\ 5y = 5 \\ y = \frac{5}{5} \\ \color{red} \boxed{y = 1} \\ sub \: in \: (1) \\ x + 3(1) = 5 \\ x = 5 - 3 \\ \color{blue} \boxed{x= 2}[/tex]
Please solve with explanation
9514 1404 393
Answer:
4 : 1
Step-by-step explanation:
Each segment joining midpoints is called a "midline." It is parallel to the segment not being joined, and is half its length. All the dimensions of the smaller triangle are half those of the larger triangle. (They are similar triangles.) The ratio of areas is the square of the ratio of side lengths:
2² : 1² = 4 : 1 . . . . . . ratio of triangle areas
Given h(x) = 4x – 1, solve for x when h(x) = -9.
Answer:
x = —2
Step-by-step explanation:
h(x) = 4x — 1
if h(x) = -9 then 4x — 1 = -9
So:
[tex]4x - 1 = - 9 \\ 4x = - 9 + 1 \\ 4x = - 8 \\ x = - 2[/tex]
Answer:
x = -2
Step-by-step explanation:
[tex]-9=4x-1\\-8=4x\\-2=x[/tex]
can we help me? guys
Answer:
a = 3x
b = -6x^2
c = 4
Step-by-step explanation:
to find b we have to multiply (x - 3) with 2x^2
= 2x^3 - 6x^2
b = - 6x^2
to find a
in the second step of division to get -9x
we have to multiply x - 3 with 3x
a = 3x
to find c we have to add next term after x in the first equation that is 4
in equation 8x + 4
so c = 4
-7m+10<-39
Solve the Inequality using the format M<1
Answer:
m>7
Step-by-step explanation:
-7m+10<-39
-7m<-39-10
-7m<-49
7m>49
m>7
Which statements are true about the angles in this diagram? Select all that apply.
Answer:
<3 and <6 are alternate interior angles
<4 and <6 are consecutive interior angles
<4 and <5 are alternate interior angles
<3 and <5 are consecutive interior angles
Step-by-step Explanation:
See attached images for examples of the angles.
Hope this helps!
state the slope of the line.
y=−5x+2
five is your slope line
Hi there!
The slope is -5.
Because
The equation of the line is written in slope-intercept form (y=mx+b)
m is the slope (-5)
Hope it helps!
If you have any question or query, feel free to ask!
~An excited gal
[tex]SparklingFlower[/tex]
City planners are planning to build a new community pool. They agree that the pool will be rectangular in shape, but the proposed dimensions changed. At the most recent meeting, it was determined that the width would remain at 12.3 meters but that the length would increase by 4.3 meters. So, the pool would now cover an area of 213.65 square meters. Which equation can be used to determine the original length of the pool, I?
A. 213.65 = 4.3(1+ 12.3)
B. 213.65(I+16.6)
C. 213.65 = 12.3(I+ 4.3)
Answer:
C. 213.65 = 12.3(I+ 4.3)
Step-by-step explanation:
Original length: l
New length: l + 4.3
area: LW
area: 213.65 m²
area = LW = (l + 4.3)(12.3)
(l + 4.3)(12.3) = 213.65
12.3(l + 4.3) = 213.65
Answer: C. 213.65 = 12.3(I+ 4.3)
Find the measurement of the two angles
Please !
Answer:
1 -9 09u and than add
Step-by-step explanation:
Alex, an eighth grader, and Eric, a seventh grader, need to determine who came closer to their grade’s state record for the triple jump. Alex jumped 39.75 feet and Eric jumped 37 feet and inches. Who was closer to the state record if the eighth-grade record is 42.25 feet and the seventh-grade record is 39 feet 3 inches?
Answer:
✓ 42.25-39.85=2.437+1 1/4= 38.2539.25-38.25=1Eric came closer.\\
Step-by-step explanation:
:]
Answer:
eric came closer
Step-by-step explanation:
What is the domain of F
Answer:
-5 ≤x≤6
[-5,6]
Step-by-step explanation:
The domain is the values that the input takes
x goes from -5 (inclusive) to 6 (inclusive)
-5 ≤x≤6
[-5,6]
Answer:
[-5, 6]
Step-by-step explanation:
The domain of a function is the list of x values. Since the endpoints are shaded, that means those x values are included as well. Therefore, the domain of f is [-5, 6].
What is the value of l 3 l?
Answer:
3
Step-by-step explanation:
Hey y’all pls help me I’m struggling soo bad
Answer:138
Step-by-step explanation:
2x+49=5x+19
x=10
mqp = 7x+68
mqp = 138
4(y - 3) using distributive property
Answer:
4y - 12
Step-by-step explanation:
4(y - 3)
(4 x y) - (4 x 3)
Choose the equation that represents the graph shown
Answer:
y = |x| + 5
Step-by-step explanation:
Calculate the points with x = -4 to 4 and match the plots. (Attached)
Help me on this math question please
Answer:
Solution:-
Let the angle vertical to 64°be y.
y=64°(being vertically opposite angle)
Now,
X+y+62°=180°
X+64+62=180°
X=180°-126°
Therefore,x=54°
find the area of the triangles with the following base and heights:
a) base 10m and height 6m. b) base 25 cm and height 14 cm.
Answer:
triangle 1. 10•6=60m²
triangle 2. 25•14= 350cm²
* in case u need help, to find the area of a triangle use this formula;
b • h = a
base • height = area
hope this helps
#1
B=10mH=6mArea:-
[tex]\\ \sf\longmapsto \dfrac{1}{2}BH[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{2}(6)(10)[/tex]
[tex]\\ \sf\longmapsto 3(10)=30m^2[/tex]
#2
B=25cmH=15cmArea:-
[tex]\\ \sf\longmapsto \dfrac{1}{2}(25)(14)[/tex]
[tex]\\ \sf\longmapsto 25(7)[/tex]
[tex]\\ \sf\longmapsto 175cm^2[/tex]
What is the solution of 1/x+1/3<1/5 ?
Step-by-step explanation:
hope it helps thanks this is the answer
A company makes a profit of 1.38 million. This is 2.54 million more than last year. What was the profit last year?
Answer:
negative 1.16 million
Step-by-step explanation:
P = 1.38 - 2.54 = -1.16 = a negative profit of $1.16 million = a loss of $1.16 million
PLEASE HELP WILL GIVE FULL PONITS! 3. Using the known angle, what side is known? What side is unknown? Use opposite, adjacent, or hypotenuse in your answer. (2 points)
Known side: ____________________
Unknown side: ___________________________
4. What trigonometric ratio would you use to find the distance from the base of the tower to your keys? Identify your choice, and then calculate the distance. (4 points: 1 point for the ratio, 2 points for shown work, 1 point for the answer)
Trigonometric ratio (name): ___________________________
Calculation (Show your work):
5. While you're at the top of the tower, you see an ant walking along the edge of the building. If the ant were to walk straight down the side of the tower until it reached the ground, how far would the ant travel? Which trigonometric ratio would you use to find this distance? Use the ratio to find the measurement. (4 points: 1 point for the method, 2 points for shown work, 1 point for the answer)
6. Confirm that your answer to question 5 is correct using the Pythagorean Theorem instead of trig ratios. (3 points)
Answer:
The trigonometric ratio that I would use to find the distance from the base of the tower to the keys is the tangent; tan (86°) = height / distance.
Step-by-step explanation:
You can draw a right triangle with angle 86°, opposite leg equal to the height (50 meter) and adjacent leg equal to the distance from the base of the tower to the keys: tan (86°) = 50 m / x
=> x = 50 m / tan(86°)
x = 50 m / 14.30 = 0.98 m
PLEASE HELP ASAP
WILL GIVE BRAINLIEST
The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.
Which means that DB = CB
Which means that 10x + 16 = 5x + 20
10x - 5x = 20 - 16
5x = 4
x = 4/5
And so the length of CB is
5 * 4/5 + 20 = 4+20 = 24
Good LUCK :)
A sporting goods company can ship
6 footballs in each carton. How many
cartons are needed to ship 75 footballs?
Answer:
12.5
Step-by-step explanation:
75 ÷ 6
math subject huhubels
Answer:
yes
Step-by-step explanation:
because i used my brain#
Sarah stands at the corner of a rectangular field. If the field measures 180 m by 210 m, how far would Sarah need to walk to
reach the opposite corner in a straight line
Answer:
30√85 or 276.5863 meters
Step-by-step explanation:
Use pythag theorom. a^2+b^2=c^2
180^2+210^2=c^2
c=276.5863
Sample Response: The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes. Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.
What did you include in your response? Check all that apply.
The full bottle doubled after 5 minutes.
The 2 full bottles doubled after 5 minutes.
Exponential growth is a multiplicative rate of change.
Answer:
At 10:05 a.m., there are 2 microscopic bacteria cells in the bottle. How many cells will be in the bottle at 10:15 a.m.?
Step-by-step explanation:
1/x + 1/3x = 4 help help pls thank you
Find the value of x, then the perimeter of the regular polygon.
I have attached the image that shows the ploygon.
Answer:
x = 3
perimeter: 18 units
Step-by-step explanation:
1. First, we should know that a regular polygon is a polygon that has all angles the same angle measure and all sides the same side length.
For example, an equilateral triangle is a regular polygon because all angles are 60 degrees and all sides are the same length.This means that for the polygon in the image, 5(x+2) = 7x + 42. (Solving)
Step 1: Simplify both sides of the equation.
[tex](5)(x)+(5)(2)=7x+4[/tex] [tex]5x + 10 = 7x + 4[/tex]Step 2: Subtract 7x from both sides.
[tex]5x + 10 - 7x = 7x + 4 - 7x[/tex] [tex]-2x + 10 = 4[/tex]Step 3: Subtract 10 from both sides.
[tex]-2x + 10 - 10 = 4 - 10[/tex] [tex]-2x = -6[/tex]Step 4: Divide both sides by -2.
[tex]\frac{-2x}{-2} = \frac{-6}{-2}[/tex] [tex]x = 3[/tex]Step 5: Check if solution is correct.
[tex]5(3+2)=7(3)+4[/tex] [tex]5(5)=21+4[/tex] [tex]25 = 25[/tex]3. Now, since this polygon has 6 sides, it's a hexagon. To find the perimeter of a hexagon, we just multiply the length of one side 6 times.
[tex]3(6)[/tex] [tex]18[/tex]Therefore, x = 3 and the perimeter is 18 units.
