(a) The differential equation for Q(t) is: Q'(t) = -0.08664Q(t)
(b) It takes approximately 24.03 days for the substance to decay to 1/3 of its original mass.
(a) The differential equation for Q(t) is given by:
Q'(t) = -kQ(t)
where k is the decay constant. We know that the half-life of the substance is 8 days, which means that:
0.5 = e^(-8k)
Taking the natural logarithm of both sides and solving for k, we get:
k = ln(0.5)/(-8) ≈ 0.08664
Therefore, the differential equation for Q(t) is:
Q'(t) = -0.08664Q(t)
(b) The general solution to the differential equation Q'(t) = -0.08664Q(t) is:
Q(t) = Ce^(-0.08664t)
where C is the initial quantity of the substance. We want to find the time required for the substance to decay to 1/3 of its original mass, which means that:
Q(t) = (1/3)C
Substituting this into the equation above, we get:
(1/3)C = Ce^(-0.08664t)
Dividing both sides by C and taking the natural logarithm of both sides, we get:
ln(1/3) = -0.08664t
Solving for t, we get:
t = ln(1/3)/(-0.08664) ≈ 24.03 days
Therefore, it takes approximately 24.03 days for the substance to decay to 1/3 of its original mass.
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!ANSWER QUICK! the volume of a cone is 84π ft³. If the hole is 7ft deep, what is the radius of the hole?
Answer:
6 ft
Step-by-step explanation:
volume of cone πr^2 (h/3)
84π = πr^2 (7/3)
84π/(7/3) = r^2π
84/(7/3) = r^2
sqrt (84 /(7/3)) = r
6 = r
8.6 is what percent of 32?Round to the nearest hundredth.
Answer:
2.75
Step-by-step explanation:
8.6 is what precent of 32? =2.752
round to nearest hundredth= 2.75
I hope this helps :)
Answer:
2.75
Step-by-step explanation:
BIG BRAIN
Una calidad de queso vale los 2/5 de $30.000; una segunda calidad vale 1/3 de $24.000 y una tercera calidad vale el doble de un tercio de $15.000. ¿Cuánto valen juntas las tres calidades de queso?
Answer:
2/5+1/3=6/15+5/15=11/15
30.000+24.000+15.000 =69.000
8x-7=-5x+19 denklemini sağlayan, x'in değeri kaçtır?
Answer: X=2
Step-by-step explanation:
8x-7=-5x+19
=> 8x+5x=19+7 [Transforms]
=> 13x=26
=> x=26/13
So, x=2
To get the right shade of paint, the paint store mixes 1 part yellow with
every 7 parts blue. If 42 parts blue are used, how many parts yellow will be
added to the paint? *
Answer:
6 parts yellow
Step-by-step explanation:
What is the slope of the line passes through the points (-2,-3) and (5,4)?
The slope is 1.
Step-by-step explanation:
a rock is thrown in the air from the edge of a seaside cliff. it's height in feet is represented by f(x) = - 16(ײ-8x-9), where is the numbers of seconds since the rock was thrown. the height of the rock is 0 feet when it hits water
Answer:
6 seconds
Step-by-step explanation:
Just took the test :)
Need help on number 26 and 27!!
Answer:
26. H. (-4, -2)
27. A. x - 4
Step-by-step explanation:
26.
Use translations.
Start at point A(2, 6). To go from this point to the center of the circle, you must go from A(2, 6) to C(-1, 2). That means you need to go from 2 to -1 in x, a change of -3 in x, and from 6 to 2 in y, a change of -4 in y.
Since points A and B are the endpoints of a diameter, then AC and BC are radii of the circle. All radii are congruent, so if you apply the same transformation as from A to C to point C, you will get the coordinates of point B.
C(-1, 2) now is transformed by -3 in x and -4 in y.
B(-1 - 3, 2 - 4) ----> B(-4 , -2)
Answer: H. (-4, -2)
27.
Recall the factoring of a difference of cubes.
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
You have
x^3 - 64
x^3 is obviously the cube of x.
64 is the cube of 4, so you have
x^3 - 4^3
Following the factorization above, you get
(x - 4)(x^2 + 4x + 16)
Answer: A. x - 4
Select the correct answer.
If the factors of function f are (x − 6) and (x − 1), what are the zeros of function f?
A.
-6 and -1
B.
-1 and 6
C.
1 and 6
D.
-6 and 1
Answer:
6 and 1
Step-by-step explanation:
Let x - 6 = 0 and x - 1 = 0
x = 6 and x = 1
Point s and point t are located at -6, 13 and 8, 13 on the coordinate plane what is the distance between the two points
Answer:
[tex]14[/tex] units
Step-by-step explanation:
Since both points have the same y-coordinate, we can calculate the distance between them by taking the absolute difference of their x-coordinates. Therefore, the distance between them is [tex]|-6-8|=|-14|=14[/tex] units. Hope this helps!
write an equation for a line perpendicular to y=-4x-4 and passing through the point (4,-4)
Answer:
Step-by-step explanation:
perp. 1/4
y + 4 = -1/4(x - 4)
y + 4 = -1/4x + 1
y = -1/4x - 3
Determine whether the relation represents a function. If it is a function, state the domain and range. {(-3, 7), (2, 5), (5, -3), (8, -2)}
Answer:
(a) The relation is a function
(b)
[tex]Domain = \{-3,2,5,8\}[/tex]
[tex]Range = \{7,5,-3,-2\}[/tex]
Step-by-step explanation:
Given
[tex]\{(-3, 7), (2, 5), (5, -3), (8, -2)\}[/tex]
(a): Is it a function?
A relation has the form: [tex]\{(x_1,y_1),(x_2,y_2)....(x_n,y_n)\}[/tex]
For the relation to be a function, all the x values must be unique and not repeated.
In [tex]\{(-3, 7), (2, 5), (5, -3), (8, -2)\}[/tex], the x values are: -3, 2, 5 and 8.
None of the values are repeated.
Hence, the relation is a function
(b): The domain and the range:
The x values represent the domain while the range are represented by the y values.
So, we have:
[tex]Domain = \{-3,2,5,8\}[/tex]
[tex]Range = \{7,5,-3,-2\}[/tex]
Which theorem proves these triangles are similiar for brainliest
[tex]{\huge{\pink{\mathcal{AA\:postulate࿐❤}}}} [/tex]
Consider the inequality.
x + 3x < 24
Which value of x makes the inequality true?
A.5
B.6
C.7
D.8
Answer:
A.
Step-by-step explanation:
Solve inequality:
[tex]x + 3x<24\\4x<24\\x<6[/tex]
only one less than 6 is A. 5
Answer:
A
Step-by-step explanation:
(5) + 3(5) < 24
20 < 24
Vienna bought 8 yards of fabric and paid $38.40. How many more yards can she purchase with $30?
Answer:
vienna can purchase 6 more yards
HELLPPP ASAP PLEASEEE!!!
Answer:
angle G = 64.9 is because the sum of interior angle is 180
4. If you buy 7 hamburgers and 3 slices of pizza from the Sizzler, you get Sl in change back from a
$20 bill. If you buy 8 hamburgers and 2 slices of pizza, you get $0.50 back from a $20 bill. Find
the price of a hamburger and the price of a slice of pizza.
Answer:
the price of a hamburger and the price of a slice of pizza is $0.5 and $7.75 respectively
Step-by-step explanation:
Let us assume the price of a hamburger be x
And, the price of a slice of pizza be y
So the equations are
7x + 3y = 20-1
7x + 3y = 19........(1)
And,
8x + 2y = $19.50........(2)
Now multiply by 2 in equation 1 and 3 in equation 2
So,
14x + 6y = 38
16x + 6y = 39
-2x = -1
x = 0.5
so y =
4 + 2y = $19.50
2y = $19.50 - 4
y = 7.75
Hence, the price of a hamburger and the price of a slice of pizza is $0.5 and $7.75 respectively
There are four hundred twenty-three people attending luncheon. If a table can hold 6 people, how many tables do they need?
Answer:
the answer is 71
Step-by-step explanation:
423/6
42÷6=7
42-42=0
6÷3=×
30÷6=5
70.5--> 71
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. If and , what is ? Write your answer in simplest form. When and , .
1. When x is 1, what value of y makes the equation true?
Answer:
Step-by-step explanation:
-0.5
Step-by-step explanation:
If x is 1, plug it into the equation.
So, y=-3(1) + 2.5
-3(1) = -3
now add.
-3+2.5 = -0.5
so that should give you y = -0.5
Which number is equal to 100?
Answer:
10 square2
36 + 64 = 100. In other words, 6² + 8² = 10²
Answer:
C. 10^2
Step-by-step explanation:
When you have an exponent and the base is 10, the exponent is how many zeros there are total that come after the 1. There are 2 zeros after the 1 in 100, so 10^2 is the answer.
Write the polynomial below in the factored form.
y=x³+10x²+25x
y=[?](x+[ ])²
Answer:
apsppspspppp9ğpğğ999
Describe y= -3x+4 in words.
Answer:
y=-3x+4
put x =0
y=-3(0)+4
y=4
putx=1
y=-3(1)+4
y=-3+4
y=1
Josh bought 3 bags of potting soil and 10 bags of mulch from Home Depot.
a) Write an equation torepresent the total cost.
Answer:
3x+10y=C
x=cost of potting soil
y=cost of mulch
C=total cost
An equation which represent the total cost will be,
⇒ 3P + 10M = C
Where, P is cost of potting soil bags.
M is cost of Mulch bags.
C is total cost.
What is an expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
Josh bought 3 bags of potting soil and 10 bags of mulch from Home Depot.
Now,
Let cost of potting soil bags = P
Cost of Mulch bags = M
Total cost = C
Then, An equation to represent total cost is;
3P + 10M = C
Thus, An equation which represent the total cost will be,
⇒ 3P + 10M = C
Where, P is cost of potting soil bags.
M is cost of Mulch bags.
C is total cost.
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what is 4(3x 6y) equivalent to?
Answer:
2x/y ??
Step-by-step explanation:
Answer: If the sign missing is supposed to be a plus sign, then the answer is 12x+24y
Step-by-step explanation:
Write a system of equations, with one equation describing the cost to bowl at Bowl-o-Rama and the other describing the cost to bowl at Bowling Pinz. For each equation, let x represent the number of games played and let y represent the total cost.
Complete question :
Write a system of equations, with one equation describing the cost to bowl at Bowl-o-Rama and the other describing the cost to bowl at Bowling Pinz. For each equation, let x represent the number of games played and let y represent the total cost.
Bowl-O-Rama rents shoes for $2 and each game cost $2.50
Bowling Pinz rents shoes for $4 and each game cost $2
Answer:
Bowl-O-Rama:
y = $2 + $2.50x
Bowling pinz:
y = $4 + $2x
Step-by-step explanation:
The total cost is the sum of shoe rental plus the product of the unit game rate and the number of games played.
Total cost, y
x = number of games played
Bowl-O-Rama:
y = Shoe rent + (unit rate per game * number of games)
y = $2 + ($2.50 * x)
y = $2 + $2.50x
Bowling Pinz :
y = Shoe rent + (unit rate per game * number of games)
y = $4 + ($2 * x)
y = $4 + $2x
Escribir un numero entero que represente cada una de las expresiones a. Un globo aerostatico 200 m sobre el nivel del mar. b. 500 años antes de cristo. c. Una deuda de L. 600.00 d. 7 minutos de retraso e. 2 grados bajo cero f. El delfin salto 4 metros sobre el nivel del mar.
Answer:
a) [tex]h = +200[/tex], b) [tex]t = -500[/tex], c) [tex]c = -600[/tex], d) [tex]t = +7[/tex], e) [tex]T = +2[/tex], f) [tex]h = +4[/tex].
Step-by-step explanation:
a) Sea [tex]h[/tex] la distancia vertical con respecto al nivel del mar. Asúmase como positiva la distancia vertical por encima del nivel del mar. Entonces, la forma matemática equvalente es [tex]h = +200[/tex].
b) Sea [tex]t[/tex] el año con respecto al momento cuando nace el Cristo. Asúmase como positivo el año posterior al año del nacimiento del Cristo. Entonces, la forma matemática equivalente es [tex]t = -500[/tex].
c) Sea [tex]c[/tex] el balance de cuenta. Asúmase como positiva la acreencia de dinero. La acreencia es lo opuesto de la deuda. Entonces, la forma matemática equivalente es [tex]c = -600[/tex].
d) Sea [tex]t[/tex] el tiempo con respecto al instante de referencia y esperado de un evento. Asúmase como positivo el retraso. El retraso es lo opuesto del adelanto. Entonces, la forma matemática equivalente es [tex]t = +7[/tex].
e) Sea [tex]T[/tex] la temperatura con respecto al punto de referencia o de "temperatura cero". Asúmase como positiva toda temperatura mayor que ese punto de referencia. Entonces, la forma matemática equivalente es [tex]T = +2[/tex].
f) Sea [tex]h[/tex] la distancia vertical con respecto al nivel del mar. Asúmase como positiva la distancia vertical por encima del nivel del mar. Entonces, la forma matemática equvalente es [tex]h = +4[/tex].
. Evaluate x2+ 2y÷ 2w+ 3zfor w= -2, x= -5, y= 8, and z= -3
A flagpole is 35 feet tall. A girl standing nearby who is 4 feet tall casts a shadow that
is 3 feet long. How long is the shadow of the flagpole (at the same time) to the
nearest foot?
Answer:
26 ft. = the length of the flagpole's shadow to the nearest foot
Step-by-step explanation:
Let f = the length of the flagpole's shadow
girl's height/flagpole's height = girl's shadow length/flagpole's shadow length
4/35 = 3/f
4f = 105
f = 26.25 ft. ≅ 26 ft = the length of the flagpole's shadow to the nearest foot.
geometry multiple choice question HELPP