Answer:
(i) The value of m when t = 30 is 13.2
(ii) The value of t when the mass is half of its value at t=0 is 34.7
(iii) The rate of the mass when t=50 is -0.18
Step-by-step explanation:
(i) The m value when t = 30 is:
[tex] m = 24e^{-0.02t} = 24e^{-0.02*30} = 13.2 [/tex]
Then, the value of m when t = 30 is 13.2
(ii) The value of the mass when t=0 is:
[tex] m_{0} = 24e^{-0.02t} = 24e^{-0.02*0} = 24 [/tex]
Now, the value of t is:
[tex] ln(\frac{m_{0}/2}{24}) = -0.02t [/tex]
[tex] t = -\frac{ln(\frac{24}{2*24})}{0.02} = 34.7 [/tex]
Hence, the value of t when the mass is half of its value at t=0 is 34.7
(iii) Finally, the rate at which the mass is decreasing when t=50 is:
[tex] \frac{dm}{dt} = \frac{d}{dt}(24e^{-0.02t}) = 24(e^{-0.02t})*(-0.02) = -0.48* (e^{-0.02*50}) = -0.18 [/tex]
Therefore, the rate of the mass when t=50 is -0.18.
I hope it helps you!
How many ways are there to put 9 differently colored beads on a $3\times3$ grid if the purple bead and the green bead cannot be adjacent (either horizontally, vertically, or diagonally), and rotations and reflections of the grid are considered the same
Answer:
20,160
Step-by-step explanation:
The arrangement of the 9 differently colored bead can be presented as follows;
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
Where 1 is the purple bead and 2 is the green bead, the number of ways of arrangement where the green bead cannot be adjacent to the green either horizontally, vertically, or diagonally
Placing the purple bead at 1, the location of the green bead = 3, 6, 7, 8, or 9
The number of ways = 5 ways × 7! ways of arranging the other beads
With the purple bead at 2, the location of the green bead = 7, 8, or 9
The number of ways = 3 × 7!
With the purple at 3, we also have 5 × 7! ways
At 4, similar to 2, we have, 3 × 7! ways
At 5, we have, 0 × 7!
At 6, we have 3 × 7!
For 7, 8, and 9, we have, (5 + 3 + 5) × 7!
The total number of ways = (5 + 3 + 5 + 3 + 0 + 3 + 5 + 3 + 5) × 7! ways
However, placing the purple bead at 1, 2, 3, 4, 6, 7, 8, and 9, (8 positions) can be taken as reflection and rotation of each other and can be considered the same
Therefore, the total number of acceptable ways = (5 + 3 + 5 + 3 + 0 + 3 + 5 + 3 + 5) × 7!/8 = 20,160 ways
FOR EASY BRAINLIEST ANSWER QUESTION BELOW!
1. Solve each word problem .twice a number added three times the sum of the number and 2 is more than 17. Find the numbers that satisfy condition
Answer:
28
Step-by-step explanation:
Using appropriate properties find 2/3 x (– 3/5) + 1/5 x 4/3 + 2/3 x ( – 3/2)=
Answer:
- [tex]\frac{17}{15}[/tex] -1 [tex]\frac{2}{15}[/tex] , 1.13
Step-by-step explanation:
i need help in this question that is in the photo
1 + 3 + 4 = 4 + 3 + 1. What property is being described here?
Associative Property of Addition
Commutative Property of Addition
Associative Property of Multiplication
Answer: Commutative property of addition
Step-by-step explanation:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\text{1 + 3 + 4 = 4 + 3 + 1}[/tex]
[tex]\large\text{1 + 3 + 4}[/tex]
[tex]\large\text{4 + 4}[/tex]
[tex]\large\text{= \bf 8}[/tex]
[tex]\large\text{4 + 3 + 1}[/tex]
[tex]\large\text{7 + 1}[/tex]
[tex]\large\text{= \bf 8}[/tex]
[tex]\large\text{\bf 8 = 8}[/tex]
[tex]\large\textsf{We could remove Option C. because there’s no sign of multiplication.}[/tex]
[tex]\large\textsf{This leaves us to Option A and Option B because the equation(s) has}\\\large\textsf{sum/addition}[/tex]
[tex]\large\textsf{Associative Property of Addition formula is:}[/tex]
[tex]\bullet\large\text{ \bf (a + b) + c = a + (b + c)}[/tex]
[tex]\large\textsf{Commutative Property of Addition formula is:}[/tex]
[tex]\bullet\large\text{ \ \bf a + b = b + a}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf Commutative Property of Addition}}}\\\boxed{\huge\textsf{(Option B.)}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A particle is projected with a velocity of [tex]40ms^-^1[/tex] at an elevation of 60°. Calculate the vertical component of its velocity at a height of 50m. (Take g = [tex]9.8ms^-^2[/tex])
A. [tex]25\sqrt{3} ms^-^1\\\\B.20\sqrt{3} ms^-^1\\\\c. 2\sqrt{545} ms^-^1[/tex]
Answer:
[tex]2\sqrt{55}\text{ m/s or }\approx 14.8\text{m/s}[/tex]
Step-by-step explanation:
The vertical component of the initial launch can be found using basic trigonometry. In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. Let the vertical component at launch be [tex]y[/tex]. The magnitude of [tex]40\text{ m/s}[/tex] will be the hypotenuse, and the relevant angle is the angle to the horizontal at launch. Since we're given that the angle of elevation is [tex]60^{\circ}[/tex], we have:
[tex]\sin 60^{\circ}=\frac{y}{40},\\y=40\sin 60^{\circ},\\y=20\sqrt{3}[/tex](Recall that [tex]\sin 60^{\circ}=\frac{\sqrt{3}}{2}[/tex])
Now that we've found the vertical component of the velocity and launch, we can use kinematics equation [tex]v_f^2=v_i^2+2a\Delta y[/tex] to solve this problem, where [tex]v_f/v_i[/tex] is final and initial velocity, respectively, [tex]a[/tex] is acceleration, and [tex]\Delta y[/tex] is distance travelled. The only acceleration is acceleration due to gravity, which is approximately [tex]9.8\:\mathrm{m/s^2}[/tex]. However, since the projectile is moving up and gravity is pulling down, acceleration should be negative, represent the direction of the acceleration.
What we know:
[tex]v_i=20\sqrt{3}\text{ m/s}[/tex] [tex]a=-9.8\:\mathrm{m/s^2}[/tex] [tex]\Delta y =50\text{ m}[/tex]Solving for [tex]v_f[/tex]:
[tex]v_f^2=(20\sqrt{3})^2+2(-9.8)(50),\\v_f^2=1200-980,\\v_f^2=220,\\v_f=\sqrt{220}=\boxed{2\sqrt{55}\text{ m/s}}[/tex]
Round the $40435.29 to the nearest thousand dollar
Answer:
$40000
Step-by-step explanation:
The nearest thousand dollar is rounding the thousand value from its hundred value, which in this case is 4. Since 4 is less than half of 10, the thousand value must round down to $40000.
Answer:
$40000.00
Step-by-step explanation:
Report this answer if its incorrect ^_^
HELPP!
The functions f(x) and g(x) are described using the following equation and table:
f(x)=-4(1.09)x
Given:
The function is:
[tex]f(x)=-4(1.09)^x[/tex]
The table of values for the function g(x).
To find:
The equation that best compares the y-intercepts of f(x) and g(x).
Solution:
We have,
[tex]f(x)=-4(1.09)^x[/tex]
Putting [tex]x=0[/tex], we get
[tex]f(x)=-4(1.09)^0[/tex]
[tex]f(x)=-4(1)[/tex]
[tex]f(x)=-4[/tex]
So, the y-intercept of the function f(x) is -4.
From the given table of values, it is clear that the function f(x) passes through the point (0,-4). So, the y-intercept of the function g(x) is -4.
The y-intercept of f(x) is equal to the y-intercept of g(x).
Therefore, the correct option is A.
Answer:
A) The y-intercept of f(x) is equal to the y-intercept of g(x).
Use the distributive property to write the next step in simplifying the numerical expression. Use the asterisk symbol (*) to represent multiplication. Do not multiply factors fully and do not use spaces. 4(x + 9)
Answer:
This is the expression:
4*x+4*9
People pack seeds into foils and store them in a seed vault. Each foil contains 500 seeds. If the vault has 145,000 seeds altogether, how many foils are in the vault?
Step-by-step explanation:
dbdhdhbdbshsjakkakkajnwbsbdbdbdbbdbdbdvdvdvvvddvvdvd
Answer:
290 foils
Step-by-step explanation:
145,000÷500=290
Find the perimeter of ΔJKL. Round your answer to the nearest tenth if necessary
Answer:
3.25
Step-by-step explanation:
the triangle=15+9 8.5=3.25 in answer find x.8 ∆JKL OPTIMIZE 1 UP 3...At a football stadium, 25% of the fans in the attendance were teenagers. If there were 190 teenagers at the football stadium, what was the total numbers of the people at the stadium?
Answer:
760
Step-by-step explanation:
25%= 190
100 = 25 × 4
100% (total number of people) = 190 × 4 = 760
I need some help with this one. Please give it a go! Thank you for your time.
Answer:
Step-by-step explanation:
Hello there
I'm also a student so I'm not 100% sure on this one, but I think I know.
Usually when you have functions you just replace the letters for their value:
f = 11x
g = x² - 6x + 3
h = -x + 4
Th exercise is asking for (g * h) (x)
Since there are parenthesis, here's what we have:
[(x² - 6x + 3)(-x + 4)](x)
Use the left side of the equation:
[(x² - 6x + 3)(-x + 4)](x)
And solve it:
-x³ + 6x² -3x + 4x² - 24x + 12
That's equal to
-x³ + 10x² -27x + 12
Multiply all that by that x on the left:
-x^4 + 10x³ -27x² + 12x
No idea if that's right so please tell me
Easy
a) -2,-5.-8.-11,...
Step-by-step explanation:
???????? what is easy??
simplyfy using appropiate properties 1/4×2/5+-1/6×3/2+3/7×2/5
Answer:
-1/35
Step-by-step explanation:
* means multiply
because of pemdas you should do three multiplication parts first
(1/4×2/5)+(-1/6×3/2)+(3/7×2/5)
1/20 - 3/12 + 6/35
3/60 - 15/60 + 6/35
-12/60 + 6/35
-1/5 + 6/35
-7/35 + 6/35
-1/35
Answer:
3/140
Step-by-step explanation:
1/4 × 2/5 + (-1/6) × 3/2 + 3/7 × 2/5 =
= 2/20 - 3/12 + 6/35
**********************************************
We need the LCD of 20, 12, 35.
20 = 2^2 * 5
12 = 2^2 * 3
35 = 5 * 7
LCD = 2^2 * 3 * 5 * 7 = 420
**********************************************
= 42/420 - 105/420 + 72/420
= 9/420
= 3/140
look at image for question and answers
Answer:
ANSWER :
it's x + 3 + x
What is the equation of the following line?
(-4, 8)
(0,0)
Answer
Step-by-step explanation:
y = -2x + 0
Therefore; y = -2x
jayce travels 30 miles per hour in her car.how many miles does she travel in 4 hours
Answer:
120 miles
Step-by-step explanation:
30 miles per hour * 4 hours
120 miles
Answer:
She travels 120 miles in 4 hours.
Step-by-step explanation:
She travel in 4 hours = 30 miles × 4 = 120 milesShe travels 120 miles in 4 hours
Which of the following inequalities matches the graph?
Answer:
second one
Step-by-step explanation:
just read where the purple line finishes on the x axis, in this case it’s 5 so it’s greater than 5 or equal to it.
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
Have a good day everybody.......
thank you, you too! :D
Which of the following statements are always true?
A trapezoid is a rhombus.
A trapezoid is a parallelogram.
A trapezoid is a quadrilateral.
A trapezoid is a rectangle.
Answer:
„A trapezoid is a quadrilateral.” ⇒ trueStep-by-step explanation:
This is a trapezoid. It is a quadrilateral with one pair of parallel sides while other sides are non-parallel. Here, the opposite angles are alternate, that is, they have together 180°.
Isosceles trapezoid
An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. Here, the base angles are the same.
The line segment joining the midpoints of the parallel sides is perpendicular to the bases and the diagonals are the same in length.
Right-angled trapezoid
Trapezoid with two right angles and necongruent non-paralell sides.
Good luck:)
Find the measure of angle A.
54.99
35.1°
50.7°
39.3°
Hi there!
[tex]\large\boxed{35.1^o}}[/tex]
We can once again use right triangle trig:
We are given the hypotenuse and adjacent sides, so cosine must be used:
cosA = A / H
thus:
cosA = 9/11
Use inverse trig to solve:
cos⁻¹(9/11) ≈ 35.1°
# If two vectors whose direction ratios are 1,2,3 and -k,2,1 are perpendicular to each other then, a) k=7 b) k=4 c) k=3 O d) k=6 me especially since we had be 1 poir 82) I don't know why he turned friends for so long.
Answer:
(a)k=7
Step-by-step explanation:
We are given that
Two vectors whose direction ratios are 1,2,3 and -k,2,1.
Let
[tex]a_1=1,b_1=2,c_1=3[/tex]
[tex]a_2=-k,b_2=2,c_2=1[/tex]
We have to find the value of k.
We are given that two vectors are perpendicular to each other.
We know that two vectors are perpendicular to each other then
[tex]a_1a_2+b_1b_2+c_1c_2=0[/tex]
Substitute the values
[tex]1(-k)+2(2)+3(1)=0[/tex]
[tex]-k+4+3=0[/tex]
[tex]-k+7=0[/tex]
[tex]\implies k=7[/tex]
Hence, option a is correct.
PLEASE ANSWER IT CORECTLY
Answer:
Q24=A
25=B
26=A
Step-by-step explanation:
he area of a rectangle is 44m , and the length of the rectangle is less than twice the width. Find the dimensions of the rectangle.
Answer:
4m x 11m
Step-by-step explanation:
4 is your width. 11 is your length.
4 x 4=16 > 11
Johnny asks you to guess the specific coins he has in his pocket if he has $3.70 in change. You say you need a little
more information, to guess. So he tells you all he has is quarters and dimes and that he has 22 colns in all.
Answer:
10 quarters and 12 dimes :)
Step-by-step explanation:
F= P(1 + r)!
Rearrange the formula to highlight the present value.
P=
[tex]\tt\displaystyle\ P(1+r)!= r*(r-1) *(r-2)*(r-3) ..... *1[/tex]
For 12-15, find the missing measures
Answer:
12. d= 14, C=14π, A=49π
13. r= 13, d=26, A=169π
14. r=9, C=18π, A=81π
15. r=10, d=20, C=20π
Step-by-step explanation:
(9-3)+18÷8
show your work
Answer:
(9-3)+18÷8
=6+ 9/4
Step-by-step explanation:
.............
Answer:
8.25
Step-by-step explanation:
(9-3) + 18 ÷ 8
6 + 18 ÷ 8
6 + 2.25
8.25
I hope it helps ^_^