Initial amount, [tex]A_o=150\ g[/tex] .
Final amount, [tex]A =10\ g[/tex] .
Time taken, t = 6:00 - 2:00 = 4 hour.
We know,
[tex]A=A_o(\dfrac{1}{2})^{\dfrac{t}{h}}\\\\10 = 150 \times \dfrac{1}{2}^{\dfrac{4}{h}}\\\\2^{\dfrac{4}{h}}=15\\\\\dfrac{4}{h}= log_215\\\\h = \dfrac{4}{log_215}\\\\h = 1.024 \ hours[/tex]
Therefore, the half-life of the isotope is 1.024 hours.
Hence, this is the required solution.
3x-1/5=x+1/3 solve for x
Answer:
x = 2
Step-by-step explanation:
First, you cross multiply then that will give you
9x - 3 = 5x + 5
collect like terms
9x - 5x = +5 + 3
= 4x = 8
Divide both sides by the coefficient of x that's 4
= 2
Two helicopters leave a heliport at the same time. The first flies 160km/h in a direction of 290 degrees. The second flies 100km/h in a direction of 250 degrees. After 3 hours, how far apart are the helicopters? Round your answer to the nearest kilometer.
Answer: 315 km
Step-by-step explanation:
If the angle θ is measured from the x-axis, and we have a magnitude A, we can find the rectangular coordinates as:
Ax = A*cos(θ)
Ay = A*sin(θ)
Then:
The first helicopter has a speed of 160km/h, and it's angle is 290°.
Then the components will be:
Vx = 160km/h*cos(290°) = 54.7 km/h
Vy = 160km/h*sin(290°) = -150.4 km/h
Then the point location as a function of time, can be written as:
(where i assumed that the initial position of both helicopters was (0, 0))
P1(t) = (54.7 km/h*t, -150.4 km/h*t)
where t is time in hours.
We can do the same for the other helicopter:
The speed is 100km/h, and the angle is 250°
Then:
Vx = 100km/h*cos(250°) = -34.2 km/h
Vy = 100km/h*sin(250°) = -94 km/h
Then the point location as a function of time, will be:
P2(t) = (-34.2km/h*t, -94 km/h*t)
After 3 hours, the position of each helicopter will be:
P1(3h) = (54.7 km/h*3h, -150.4 km/h*3h) = (163.1 km, -451.2 km)
P2(3h) = (-34.2km/h*3h, -94 km/h*3h) = (-102.6km, -282km)
Now we can calculate the distance between these two points.
Remember that the distance between the points (a, b) and (c, d) is:
D = √( ( a - c)^2 + (b - d)^2)
In this case the distance will be:
D = √( (163.1 km - (-102.6km))^2 + (-451.2 km - (-282km))^2)
D = √( (163.1 km + 102.6km)^2 + (-451.2 km + 282km)^2)
D = 315km
Write each expression in standard form.
6(−5 − 4)− 2( − 7 − 3)
Answer:
heyyy wassuppp
Step-by-step explanation:
How many sides does a decagon have?
sides
Answer:
It has 10 sides.
Step-by-step explanation:
Answer:
12 sides.
Step-by-step explanation:
A good way to remember this is "decagon" is called that because it has 12 sides, and the month December is the 12th month of the year.
what is the range of this function (I NEED AN ANSWER RLLY FAST PLSSSS)
Answer:
d
Step-by-step explanation:
the first oval's domain and the second's range. so you just choose the choice that includes all the values in the ranger.
a line has a slope of -2/3 and passes through the point (-3, 8). what is the equation of the line
Answer:
y=-2/3x+6
Step-by-step explanation:
hope this helps
Which of these is equivalent to 1 over x to the power of 5 ? 1 fifth x negative x to the power of 5 x to the power of 5 x to the power of negative 5 end exponent
Answer:
x^-5 = x to the power of negative 5
Step-by-step explanation:
Which of these is equivalent to 1 over x to the power of 5 ?
Mathematically this is expressed as
(1/x)⁵
We have a rule when it comes to expressing power
(1/a)^b = a^-b
Hence, applying this rule to our question
(1/x)⁵ = (1/x)^5
= x^-5
This is written in words as:
x to the power of negative 5
Given f(x) = -x + 1, solve for x when f(x) = 0.
Answer:
1
Step-by-step explanation:
0=-x+1
-x=-1
x=1
Can someone help me with this fast please?
Thank You
Answer:
3/10 is greater
Step-by-step explanation:
2/7 is equal to 0.29... and 3/10 is equal to 0.3
So, 0.3 is bigger than 0.29
There are more boxes shaded in the picture to the right than the picture to the left. 21 > 20
f(x)=3x−5 and g(x)=x2 Find (f°g)(3)
Answer:
22
Step-by-step explanation:
3!(3)^2-5
3÷9-5
37-5=22
What is the length of the unknown side of the right triangle?
A right triangle with hypotenuse x and legs 21 and 20
21
29
400
441
According to Pythagoras theorem,
h² = b² + h²
=> x² = 21² + 20²
=> x² = 441 + 400
=> x = √841
=> x = 29
Thus, the length of the unknown side is 29 units.
Solve for X. -15 = 22x + 7
Answer: x=-1
Step-by-step explanation: Here is one way of answering this question. First you need to subtract 7 from both sides and that will leave you with -22=22x. Then you just divide 22 on both sides. So that will give you an answer of -1=x or x=-1
Hello can someone help me please..?
Answer:
From 3:23-3:24
Step-by-step explanation:
Increase 2800kg
by 21
Answer:
3388 kg
Step-by-step explanation:
If you mean to increase by 21%, then
You may
100% + 21% = 121%
2800 x 121/100
2800 x 1.21
= 3388 kg
2(6-2x)-2x=2(5+x)-4 value of x?
Answer:
x= 3/4
Step-by-step explanation:
I looked it up. Hope this helps
Answer:
x = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given
2(6 - 2x) - 2x = 2(5 + x) - 4 ← distribute parenthesis on both sides
12 - 4x - 2x = 10 + 2x - 4 ← simplify both sides
12 - 6x = 6 + 2x ( subtract 2x from both sides )
12 - 8x = 6 ( subtract 12 from both sides )
- 8x = - 6 ( divide both sides by - 8 )
x = [tex]\frac{-6}{-8}[/tex] = [tex]\frac{3}{4}[/tex]
Solve for X.
A. 168
B. 180
C. 21
D. 42
Answer:
Answer = C
Angle x = 21
Property = Angle sum of Triangle
A recipe calls for 3 1/2 cups of milk and makes 10 servings. How many cups of milk are needed for 8 servings? (Hint: Set up a proportion, don’t forget to label!)
Answer:
2.8 or 2 4/5
Step-by-step explanation:
Here's our proportion of cups of milk to servings
3 1/2:10 For my sake I'm using decimals
3.5:10
Now let's try to get our servings to 1 (a unit rate)
0.35:1 I divided by 10 on each side
We need 8 servings not 1 so let's multiply 8 on each side
2.8:8
In case you want it in fraction form we can do 2 8/10 and simplify it to 4/5 by dividing by 2. Our answer is 2.8 or 2 4/5 cups of milk for 8 servings.
Write an expression that can be used to determine the total cost of buying g pounds of granola for $3.25 per pound and f pounds of flour for $0.74 per pound. (Do not enter dollar signs or spaces in your expression.)
Answer:
3.25g + 0.74f = t
What is the probability of spinning an odd number on the spinner below?
Determine which of following table is NOT a function.
Answer: C
Step-by-step explanation:
C beacause one X cannot have two different Y values
Please help I have no idea what the answer is
Answer:
x = 59
Step-by-step explanation:
All the angles in a triangle add up to 180
Add all the known angles
83 + 38 = 121
To find the third angle, subtract the total of all the angles by the total of the known angles
180 - 121 = 59
One gallon of milk has 128 fluid ounces. How much milk is in 6.5 gallons?
Answer:
832 fluid oz
Step-by-step explanation:
Multiply 128 by 6.5
Answer:
832
Step-by-step explanation:
Multiply 128 by 6.5 gallons
Stacy paid $54 for 6 pizzas, which is a rate of $ ? per pizza.
Answer: it’s 9
Step-by-step explanation:
54 divined by 6 = 9
C-17 = 19
Hi please help
Answer:
C=36
Step-by-step explanation:
C-17=19
C=19+17
C=36
PLEASE HELP ME OUT! WIL GIVE BRAINLIEST TO ANYONE WHO ANSWERS BOTH OR ATLEAST ONE AND SHOW WORK!! THANK YOUU
Answer 1 is the attached pic
Answer:
16
Step-by-step explanation:
(-2i)(8i)
(2(cos(3π/2)+i×sin(3π/2)))×(8(cos(π/2)+i×sin(π/2)))
2×8(cos(3π/2+π/2)+i×sin(3π/2+π/2))
16(cos(2π)+i×sin(2π))
16(cos(0+2π)+i×sin(0+2π))
16(cos(0)+i×sin(0))
16(alternate form)
PLEASE ANSWER I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!
Answer:
1) third point
2) no is the answer
express 9 3/2 in simplest radical form
Answer:
Exact Form:
√93
Decimal Form:
27
Step-by-step explanation:
i'll mark you has brainliest
Answer:
y= 5 x+ 1
Step-by-step explanation:
Answer:
i think its 21x + 11 = y
Step-by-step explanation:
sorry if this is wrong, if it is someone correct me.
A diver descended 46.36 feet in 12.2 minutes.What was the divers average change in elevation per minute? The average change in elevation per minute was ?Ft per minute
Answer:
The average change in elevation per minute is 3.8 ft per minute
Step-by-step explanation:
Here. we want to calculate the average change in elevation per minute
To calculate this, we simply need to divide the total descent over the total number of minutes
Mathematically, that would be;
46.36 feet / 12.2 minutes = 3.8 feet per minute
helllppppleaseeeee.
Answer:c
Step-by-step explanation: