A plumber worked 26 hours a week for half a year. If his hourly wage was $40, how much did he earn during this time period?

Determine the length of the hypotenuse in a right triangle with legs 5 inches and 12 inches

Alborosie

In a right angled triangle we can use Pythagoras theorem to determine third side in case two sides are given.

The formula of Pythagoras theorem is given by:

$x^{2} +y^{2} =z^{2}$

Where x , y and z are sides of triangle , z is hypotenuse.

Now we use this formula to find hypotenuse.

Plugging other two sides which are 5 in. and 12 in.

$5^{2} +12^{2} =z^{2}$

$25 +144 =z^{2}$

$169 =z^{2}$

Taking square root on both sides

square root of 169 is 13

so we have z=13

Hypotenuse is 13 inches.

7 0

3 years ago

PLEASE HELP FAST!! I MIGHT GIVE BRAINLIEST TO FASTEST AND ACCURATE

goldenfox [79]

Answer:

1/6

Step-by-step explanation:

We want to find how long it takes for the bacteria to lose half its size. We can do this by taking one point of the bacteria and finding how long it takes to go to half its size. When t=0, 9300 * (1/64)^t = 9300 * 1 = 9300 as anything to the power of 0 is 1. Therefore, we can solve for t when the end result of the bacteria is 9300/2= 4650, making our equation

4650 = 9300 * (1/64)^t

divide both sides by 9300

1/2 = (1/64)^t

First, we can tell that 2^6 = 64*. Because of this, we can say that (1/2)^6 = 1^6/2^6 = 1/64, so (1/64)^(1/6) = 1/2. We know this because

(1/2)^6 = 64

take the 6th root of both sides

(1/2) = (64)^(1/6)

. This means that t=1/6, so the bacterial culture loses 1/2 of its size every 1/6 seconds

* if this is harder to figure out, e.g. 3 and 729, we can plug (log₃729) into a calculator

3 0

3 years ago

Sven has a lawn mowing business. He earns $30 for every 2 weeks of mowing

NeX [460]

Whats your question? What are you trying to find?

4 0

2 years ago

The rate of change of the downward velocity of a falling object is the acceleration of gravity (10 meters/sec 2) minus the accel

Alexus [3.1K]

Answer:

See below

Step-by-step explanation:

Write the initial value problem and the solution for the downward velocity for an object that is dropped (not thrown) from a great height.

if v(t) is the speed at time t after being dropped, v'(t) is the acceleration at time t, so the the initial value problem for the downward velocity is

v'(t) = 10 - 0.1v(t)

v(0) = 0 (since the object is dropped)

<em> The equation v'(t)+0.1v(t)=10 is an ordinary first order differential equation with an integrating factor </em>

$\bf e^{\int {0.1dt}}=e^{0.1t}$

so its general solution is

$\bf v(t)=Ce^{-0.1t}+100$

To find C, we use the initial value v(0)=0, so C=-100

and the solution of the initial value problem is

$\bf \boxed{v(t)=-100e^{-0.1t}+100}$

what is the terminal velocity?

The terminal velocity is

$\bf \lim_{t \to\infty}(-100e^{-0.1t}+100)=100\;mt/sec$

How long before the object reaches 90% of terminal velocity?

90% of terminal velocity = 90 m/sec

we look for a t such that

$\bf -100e^{-0.1t}+100=90\rightarrow -100e^{-0.1t}=-10\rightarrow e^{-0.1t}=0.1\\-0.1t=ln(0.1)\rightarrow t=\frac{ln(0.1)}{-0.1}=23.026\;sec$

How far has it fallen by that time?

The distance traveled after t seconds is given by

$\bf \int_{0}^{t}v(t)dt$

So, the distance traveled after 23.026 seconds is

$\bf \int_{0}^{23.026}(-100e^{-0.1t}+100)dt=-100\int_{0}^{23.026}e^{-0.1t}dt+100\int_{0}^{23.026}dt=\\-100(-e^{-0.1*23.026}/0.1+1/0.1)+100*23.026=1,402.6\;mt$

3 0

3 years ago

Find the distance between R(-2,2) and S(4,1)

Fiesta28 [93]

the square root of 37 is the answer

5 0

3 years ago