1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
weeeeeb [17]
3 years ago
10

How do you solve this problem?

Mathematics
1 answer:
Solnce55 [7]3 years ago
3 0
Use the pythagorean theorem.
You might be interested in
According to one cosmological theory, there were equal amounts of the two uranium isotopes 235U and 238U at the creation of the
FromTheMoon [43]

Answer:

6 billion years.

Step-by-step explanation:

According to the decay law, the amount of the radioactive substance that decays is proportional to each instant to the amount of substance present. Let P(t) be the amount of ^{235}U and Q(t) be the amount of ^{238}U after t years.

Then, we obtain two differential equations

                               \frac{dP}{dt} = -k_1P \quad \frac{dQ}{dt} = -k_2Q

where k_1 and k_2 are proportionality constants and the minus signs denotes decay.

Rearranging terms in the equations gives

                             \frac{dP}{P} = -k_1dt \quad \frac{dQ}{Q} = -k_2dt

Now, the variables are separated, P and Q appear only on the left, and t appears only on the right, so that we can integrate both sides.

                         \int \frac{dP}{P} = -k_1 \int dt \quad \int \frac{dQ}{Q} = -k_2\int dt

which yields

                      \ln |P| = -k_1t + c_1 \quad \ln |Q| = -k_2t + c_2,

where c_1 and c_2 are constants of integration.

By taking exponents, we obtain

                     e^{\ln |P|} = e^{-k_1t + c_1}  \quad e^{\ln |Q|} = e^{-k_12t + c_2}

Hence,

                            P  = C_1e^{-k_1t} \quad Q  = C_2e^{-k_2t},

where C_1 := \pm e^{c_1} and C_2 := \pm e^{c_2}.

Since the amounts of the uranium isotopes were the same initially, we obtain the initial condition

                                 P(0) = Q(0) = C

Substituting 0 for P in the general solution gives

                         C = P(0) = C_1 e^0 \implies C= C_1

Similarly, we obtain C = C_2 and

                                P  = Ce^{-k_1t} \quad Q  = Ce^{-k_2t}

The relation between the decay constant k and the half-life is given by

                                            \tau = \frac{\ln 2}{k}

We can use this fact to determine the numeric values of the decay constants k_1 and k_2. Thus,

                     4.51 \times 10^9 = \frac{\ln 2}{k_1} \implies k_1 = \frac{\ln 2}{4.51 \times 10^9}

and

                     7.10 \times 10^8 = \frac{\ln 2}{k_2} \implies k_2 = \frac{\ln 2}{7.10 \times 10^8}

Therefore,

                              P  = Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} \quad Q  = Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}

We have that

                                          \frac{P(t)}{Q(t)} = 137.7

Hence,

                                   \frac{Ce^{-\frac{\ln 2}{4.51 \times 10^9}t} }{Ce^{-k_2 = \frac{\ln 2}{7.10 \times 10^8}t}} = 137.7

Solving for t yields t \approx 6 \times 10^9, which means that the age of the  universe is about 6 billion years.

5 0
3 years ago
Tashia ate 1/3 of a pizza, and Jay ate 3/8 of the same pizza. What fraction of the pizza was eaten?
Sauron [17]
This is basically saying how much of the pizza did Tashia and Jay both ate, thus combining their portions together.

1/3 + 3/8 = fraction of pizza eaten

To add fractions, you must have a common denominator. Which is 24 in this case because 3*8 = 24.

So you multiply 1/3 with 8 and multiply 3/8 with 3.

1/3*8= 8/24
3/8*3= 9/24

Now you add the fractions.
8/24+9/24= 17/24. You add the numerator, the denominator stays the same.

17/24 of the pizza was eaten.
7 0
3 years ago
Clarke borrows $16000 to buy a car he pays simple interest at an annual rate of 6% over a period of 3.5 years how much does he p
uranmaximum [27]
<span>Clarke borrows $16000 to buy a car he pays simple interest at an annual rate of 6% over a period of 3.5 years how much does he pay all together?
Let’s calculate
=> 16 000 dollars is the amount he borrowed
=> 6% is the annual interest
=> 3.5 years us the total years that he will be paying it.
Solutions:
=> 16 000 dollars * .06 = 960 dollars is the annual interests
=> 960 * 3.5 = 3 360 dollars for 3.5 years
=> 16 000 + 3 360 = 19 360 dollars

</span>



4 0
3 years ago
Evaluate the expression when n=6<br> n² – 5n-2
eduard

Answer:

4

Step-by-step explanation:

(6^2) -5(6) -2 =4

that is the answer

8 0
3 years ago
Read 2 more answers
PLEASE HELP
Ronch [10]

Answer:

<em><u>1 and 5</u></em>

Step-by-step explanation:

The squares have a side length of 10 and 1 square side is the radius of the half-circles. Since there are two half-circles, find the circumference for one full circle:

C=2\pi r

Insert the radius:

r=10\\C=2\pi *10

Simplify pi:

C=2*3.14*10

Simplify multiplication:

C=6.28*10\\C=62.8

The circumference of the circles is 62.8. Now find the perimeter of the exposed squares with side length 10. There are 4 exposed sides, which equals one square. Find the perimeter:

P=10+10+10+10\\P=10+10+20\\P=10+30\\P=40

Add the perimeter of the circle and the square together:

P=62.8+40=102.8

Now see which of the options gives you the perimeter:

1. 40+20\pi =102.8  ****

2. unavailable

3. 120+20\pi =182.8

4. 300+100\pi =614.2

5. 10+10+10\pi +10+10+10\pi =102.8 ****

Finito.

7 0
3 years ago
Other questions:
  • The percent of a​ country's households with broadband Internet access can be modeled by the function f left parenthesis x right
    14·1 answer
  • The area of a square carpet tile is 900 square centimeters. What is the length of one edge of the tile in centimeters
    8·1 answer
  • You start driving north for 35 miles turn right and drive east for another 12 miles at the end of driving what is your straight
    6·2 answers
  • Write the equation of the line in point-slope form.<br><br> (-3,2) and (-1,-2)
    6·1 answer
  • Please help I need answers quick! please zoom in!
    11·2 answers
  • (3х – 6)(2x+2)<br><br> simplify by multiplying
    6·2 answers
  • Which graph represents the solution set of the compound inequality -453x-1 and 2x+45 18?
    12·1 answer
  • Help me quickly please
    15·2 answers
  • Someone plss helP TYSM IF U DO:)
    15·1 answer
  • there were 936,795 bankruptcy filings in 2018. If there were 310,061 chapter 13 filings, what percent were not chapter 13
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!