Using an exponential function, it is found that:
a) [tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
b) 37.5 grams of the gas remains after 3.8 days.
c) The amount remaining will be of 10 grams after approximately 11 days.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.Item a:
We start with 75 grams, and then work with a half-life of 3.8 days, hence the amount after t daus is given by:
[tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
Item b:
This is N when t = 3.8, hence:
[tex]N(t) = 75(0.5)^{\frac{3.8}{3.8}} = 37.5[/tex]
37.5 grams of the gas remains after 3.8 days.
Item c:
This is t for which N(t) = 10, hence:
[tex]N(t) = 75(0.5)^{\frac{t}{3.8}}[/tex]
[tex]10 = 75(0.5)^{\frac{t}{3.8}}[/tex]
[tex](0.5)^{\frac{t}{3.8}} = \frac{10}{75}[/tex]
[tex]\log{(0.5)^{\frac{t}{3.8}}} = \log{\frac{10}{75}}[/tex]
[tex]\frac{t}{3.8}\log{0.5} = \log{\frac{10}{75}}[/tex]
[tex]t = 3.8\frac{\log{\frac{10}{75}}}{\log{0.5}}[/tex]
[tex]t \approx 11[/tex]
The amount remaining will be of 10 grams after approximately 11 days.
More can be learned about exponential functions at https://brainly.com/question/25537936
Write an equation to represent the following statement. The product of 7 and j is 91. Solve for j. j
Answer:
13
Step-by-step explanation:
7j=91
91/7=j
13
hope that helps:)
7. An arched window has dimensions as
shown at the right. Consider the top of the
window to be a semicircle. How much plastic
covering is needed to cover the window,
following the outline of the window?
The amount of plastic covering needed to cover the window is 25.71.
How much plastic covering is needed?The window consists of a semi circle and a rectangle. The circumference and the perimeter of the semi circle and a rectangle has to be determined.
Circumference of the semi circle = 1/2πd + d
Where:
π = 3.14
d = diameter = 3
1/2 x 3.14 x 3 + 3 = 7.71
Perimeter of the rectangle = 2(length + width)
2x (6 + 3) = 18
18 + 7.71 = 25.71
Please find attached an image of the window. To learn more about the perimeter of a rectangle, please check: https://brainly.com/question/3205029
Evaluate the following expression: (2,3)-3(1,1). Enter your answer as a vector
Answer:
Step-by-step explanation:
An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The given expression can be solved as shown below.
(2,3) - 3(1,1)
Multiply 3 in the second vector,
= (2,3) - (3,3)
Subtracting vectors
= (2-3, 3-3)
= (-1, 0)
Hence, the value of the given expression(2,3) - 3(1,1) in vector form is (-1, 0).
Learn more about Expression:
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Find the GCF for the set of numbers.
18, 36, and 60
Step-by-step explanation:
Factors of 36 are {1,2,3,4,6,9,12,18,36}
.
Factors of 60 are {1,2,3,4,5,6,10,12,15,20,30,60}
Common factors are }1,2,3,4,6,12} .
greatest Common Factor is 12 .
how do I simplify this expression
3x+4+2x+7
Step-by-step explanation:
3x + 4 + 2x +7
= 3x + 2x + 4 + 7
= 5x + 11
Each patron can borrow up to 6 books. If all the patrons are currently holding on to 6 books each, how many books are left in the library?
Answer:
Your answer would be:
3,384 books are left in the library
If each patron has 6 books, and there are 564 patrons:
564 x 6 = 3,384 books left
In conclusion, there are 3,384 books left in the library.
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
Lucy bought 4 pairs of pants for $21.79 each. She paid the cashier using as few $20 bills as necessary. How much change did she receive?
The amount of change Lucy receives if she paid with few $20 bills is $12.84
How to find amount of change to receiveCost of each pair of pants = $21.79Number of pairs of pants = 4Total cost of pants = $21.79 × 4
= $87.16
Amount paid to the cashier = few $20 billsIf the total cost of the pants exceeds $80, then she paid with 5 $20 bills
5 $20 bills = $100
Her change = $100 - $87.16
= $12.84
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Starting at an initial height of 364 feet, an object is projected
upward at 60 feet per second. In how many seconds will it
reach the ground? I’m
Step-by-step explanation:
4.5 s, 324 ft
Explanation:
The object is projected upward with an initial velocity of
v_0 = 144 ft/sv
0
=144ft/s
The equation that describes its height at time t is
s(t) = -16t^2 + 144 ts(t)=−16t
2
+144t (1)
where t, the time, is measured in seconds.
In order to find the time it takes for the object to reach the maximum height, we must find an expression for its velocity at time t, which can be found by calculating the derivative of the position, s(t):
v(t) = s'(t) = -32t +144v(t)=s
′
(t)=−32t+144 (2)
At the maximum heigth, the vertical velocity is zero:
v(t) = 0
Substituting into the equation above, we find the corresponding time at which the object reaches the maximum height:
\begin{gathered}0=-32t+144\\t=\frac{144}{32}=4.5 s\end{gathered}
0=−32t+144
t=
32
144
=4.5s
And by substituting this value into eq.(1), we also find the maximum height:
s(t) = -16(4.5)^2+144(4.5)=324 fts(t)=−16(4.5)
2
+144(4.5)=324ft
used this way i even don't know sorry:))What is the distance between (-2, 4) and (5, 4) on a coordinate grid?
Answer:
7 units
Step-by-step explanation:
(Background info, skip if not interested or needed for you)
The equation for distance on a cartesian plane coordinate system is based off the pythagorean theorem.
[tex]a^2 + b^2 = c^2[/tex]
a and b being sides of a right triangle, c being the hypotenuse.
When we are solving for distance we are solving for c essentially.
[tex]c[/tex] = [tex]\sqrt{a^2 + b^2}[/tex]
Because a and b are side lengths of the right triangle, we need to find a way to find that in terms of coordinates. So here we might say that a is equal to the horizontal distance between the 2 points or Δx, and we would say that b is the vertical distance between the 2 points Δy.
(solutions)
So essentially distance is:
[tex]d = \sqrt{(x_2 - x_1)^2+ (y_2-y_1)^2 }[/tex]
Now we just use the values given to us, and sub in the x and y values respectively.
(-2,4) [tex]x_1 = -2, y_1 = 4[/tex]
(5,4)[tex]x_2 = 5, y_2 = 4[/tex]
plug these values in:
[tex]d = \sqrt{((5) - (-2))^2+ (4-4)^2 } = \sqrt{(7)^2+ (0)^2 } = \sqrt{7^2 } = 7[/tex]
Therefore the distance is 7 units.
Evaluate the expression below for x = 2, y=-3, and z=-1.
x2 z2 - y2(x+z)
A. -23
B. -5
C. 13
D. 27
Answer:
It should be B
Step-by-step explanation:
2 2 -1 2 - -3 2 (2+-1)
1. Always do what's in parentheses
so we know that 1 is a negative and 2 is bigger than that number so you would just subtract normally.
2 2 -1 2 - -3 2 -1
Then get all exponents done.
4 -1 - 9-1
3-9-1
-6-1
Which should give u -5
How can we describe the relationships that exist between circles and lines?
circles are 360⁰ and lines are 180⁰
What is the solution to the system of equations?
y=2/3x+3
y = -2
Answer:
and
Step-by-step explanation:
we have
-----> equation A
------> equation B
we know that
The solution of the system of equations is equal to the intersection point of both graphs
Using a graphing tool
see the attached figure
There are two intersection points
Therefore
The system of equations has two solutions
The solutions of the system of equations are the points and
Find the missing value in the table
(Ignore all the writing I did already I think it’s wrong but I’m not sure)
Answer:
1.
+4
number: 11
2.
x × 3
number: 48
3.
+5
number 46
4.
÷2
number: 19
5.
-1.5
number: 19.5
6.
-0.2
number: 31.2
On average, Evie’s chicken lays 3 eggs every 15 days. At this rate, how many days will it take Evie’s chicken to lay 45 eggs?
Answer:
43 ffhfhfhfhfhfhchchchchchc
Answer:
It will take 225 days for Evie's chicken to lay 45 eggs
Step-by-step explanation:
Draw a number line to represent the street sign below
what is the answer i need help
Answer:
[tex]588mm^3[/tex]
Step-by-step explanation:
Each side of the blue pyramid is 3 times the size of the red pyramid.
Instead of just dividing by 3 for the volume we must divide by 9 instead because we're working in cubes.
someone help me please
What is the value of sin(80°)cos(20°) – cos(80°)sin(20°)?
The value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.
What is difference formula in trignometry?The difference formula in trignometry for the sine funciton is given as,
[tex]\sin(A-B)=\sin(A)\cos(B) -\cos(A)\sin(B)[/tex]
The trignometric equation given in the problem is,
[tex]\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)[/tex]
Compare this equation with the above eqution, we get,
[tex]A=80^o\\B=20^o[/tex]
Thus, this equation can be written as,
[tex]\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(80-20)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\sin(60)\\\sin(80^o)\cos(20^o) -\cos(80^o)\sin(20^o)=\dfrac{\sqrt{3}}{2}[/tex]
Hence, the value of sin(80°)cos(20°) – cos(80°)sin(20°) using the trignometry property is √3/2.
Learn more about the difference formula in trignometry here;
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PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
See below.
Step-by-step explanation:
The answer would be 2 3/4.
The third tick represents 3/4, and this is between 2 and 3.
-hope it helps
Answer:
My guess is 2 3/4
Step-by-step explanation:
Sorry if i'm wrong, if im right can i have brainliest? So explanation is that the plotted point on the number line is c so that will make the numerator is id.k the difference between them the top of the number would be three because c is ploted on c and id.k how to get 4.
(5.04×10^12)÷(6.3×10^9) in scientific notation
Answer:
i think the answer will be = 8 × 10^2
What is the volume of a sphere with a radius of 6.9 ft, rounded to the nearest tenth of a cubic foot?
Answer:
1376.1 ft^3
Step-by-step explanation:
The volume of a sphere formula: V=4/3πr^3
r = 6.9 ft
V = 4/3 * π * (6.9^3) = 1,376.055
to the nearest tenth it's 1376.1 ft^3
Casey wanted to find the intercepts of the graph of the equation 10x+4y=20. He decided to put the equation in slope-intercept form first. Here is his work:
10x+4y=20
4y=20−10x
y=20−10x4
y=5−10x
He concluded that the slope is m=12 and the y-intercept is (0, 5).
What error did Casey make? Within your explanation, give the correct solved for y equation, the correct slope, and the correct y-intercept.
Answer:
made a mistake in step 3
Step-by-step explanation:
there, he should have gotten y=5-2x which is then translated to y=-2x+5
this means the y-intercept is correct, but the slope is actually -2
Which of the following is equivalent to : 3x + 6 + 2x + 2 + x
A. 5x + 8
B. 6x + 8
C. 14x
Find the next three terms of the sequence 2000 ,200, 20 … and write the term to term rule.
Answer:
2 is the next number in the sequence
Step-by-step explanation:
in this pattern, you go down by one decimal spot ( zero)
this is a geometric sequence since there is a common ratio between each term.
which trig ratio
determine which trig ratio to use to solve for x
Answer:
sin = opp / hyp
cos = Adj / hyp
tan = opp / adj
7. cos 41 = x / 86
8. sin x = 5/13
9. cos x = 9/37
10. tan 61 = x/28
11. sin 41 = x/65
12. tan x = 79/84
Step-by-step explanation:
Write the log equation as an exponential equation. You do not need to solve for x.
In (3x + 2) = 3x
[tex]\ln(3x+2) = 3x\\\\\implies \log_e (3x+2) = 3x\\\\\implies e^{3x} = 3x+2[/tex]
Given triangle ABC is congruent to DEC find m
First, we know that angle B is congruent to angle E.
2x + 40 = 5x + 10
2x + 30 = 5x
30 = 3x
x = 10
Angle B and Angle E = 60 degrees
Angle C = 14 degrees
Remember that the interior angles of a triangle always add up to 180 degrees. Now that we know 2 of the 3 angles of these triangles, and because they are congruent, all that's left to do is find Angle A/D by setting up a simple equation.
60 + 14 + D = 180
74 + D = 180
D = 106
Angle D = 106 degrees
Hope this helps!
Answer:
Step-by-step explanation:
<E = <A property of congruency.
<A = 5x + 10 Comes from the fact that <A and <E are equal.
Three angles of the triangle are given. They add to 180 degrees.
2x + 40 + x + 4 + 5x + 10 = 180 Combine like terms
8x + 54 = 180 Subtract 54 from both sides.
8x + 54 - 54 = 180 - 54 Combine
8x = 126 Divide by 8
8x/8 = 126/8
x = 15.75
<B = <D Congruency and parallel lines
<D = 2x + 40 Substitute for x
<D = 2*15.75 + 40 Combine
<D = 31.5 + 40
<D = 71.5
I need it as a linear function thank you
[tex]5~~,~~\stackrel{5(6)}{30}~~,~~\stackrel{30(6)}{180}~~,~~\stackrel{180(6)}{1080}~~,~~\stackrel{1080(6)}{6480}~\hfill \boxed{f(x)=x_{n-1}(6)}[/tex]
now, that's recursive, we can also write it in explicit as [tex]5(6)^x[/tex]
Find the 53rd multiple of 62, if the 54th multiple is 3348.
Answer:
[tex]\displaystyle 3286[/tex]
Explanation:
Just multiply 62 and 53 to get 3286.
I am joyous to assist you at any time.
the vertices of ABC are points A(1,1), B(4,1), and C(4,5). find the cosines of the angles of the triangle.
Answer:
cos(A) = 3/5cos(B) = 0cos(C) = 4/5Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between the cosine of an angle and the sides of the triangle.
Cos = Adjacent/Hypotenuse
__
Angle AIn the given triangle, the hypotenuse is AC. The side adjacent to angle A is AB, so its cosine is ...
cos(A) = AB/AC
cos(A) = 3/5
__
Angle BThe right angle in the triangle is angle B. The cosine of a right angle is 0.
cos(B) = 0
__
Angle CThe side adjacent to angle C is CB, so its cosine is ...
cos(C) = CB/AC
cos(C) = 4/5
Answer:
cos <ABC=0
cos <BAC=3/5
cos<ACB=4/5
GIVE 5 STARS IF YOU DO RSM!!!