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2 years ago

martin spent 6 hours on homework every day . what percentage of the day did martin spend doing homework ?

Mathematics

1 answer:

Ann [662]2 years ago

6 0

1/4 or .25 because 6 * 4 = 24 so 6 would be a quarter of 24

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Evaluate the six trigonometric functions of the angle 0

Alla [95]

# Sin θ = 9/15.

# Cos θ = 12/15.

# Cosec θ = 15/9.

# Sec θ = 5/4

Step-by-step explanation:

$by \: using \: pythagorian \: triplets$

${a}^{2} + {b}^{2} = {c}^{2}$

${9}^{2} + {12}^{2} = {c}^{2}$

$81 + 144 = {c}^{2}$

$225 = {c}^{2}$

$c = 15.$

$\sin θ = \frac{9}{15}$

$\cos θ = \frac{12}{15} = \frac{4}{5}$

$\csc θ = \frac{15}{9}$

$\secθ = \frac{5}{4}$

7 0

3 years ago

Petrov ran 7 laps around a track.Each lap around the track is a distance of 1/4 mile. What is the total distance Petrov ran in f

Alla [95]

Answer:

9240 feet

Step-by-step explanation:

Petrov ran 7 laps around a track.Each lap around the track is a distance of 1/4 mile.

Step 1

The total distance Petrov ran in miles is calculated as:

1 lap = 1/4 mile

7 laps = x mile

Cross Multiply

x = 7 × 1/4 mile

x = 1.75 miles

Step 2

What is the total distance Petrov ran in feet?

1 mile = 5280 feet

1.75 miles = x

Cross Multiply

x = 1.75 × 5280 feet

x = 9240 feet

Therefore, the total distance Petrov ran in feet is 9240 feet

3 0

3 years ago

Using fermat's little theorem, find the least positive residue of $2^{1000000}$ modulo 17.

torisob [31]

Fermat's little theorem states that
$a^p$ ≡a mod p

If we divide both sides by a, then
$a^{p-1}$ ≡1 mod p
=>
$a^{17-1}$ ≡1 mod 17
$a^{16}$ ≡1 mod 17

Rewrite
$a^{1000000}$ mod 17 as
$=(a^{16})^{62500}$ mod 17
and apply Fermat's little theorem
$=(1)^{62500}$ mod 17
=>
$=(1)$ mod 17

So we conclude that
$a^{1000000}$ ≡1 mod 17

6 0

3 years ago

Suppose a tank contains 400 gallons of salt water. If pure water flows into the tank at the rate of 7 gallons per minute and the

Strike441 [17]

Answer:

Step-by-step explanation:

This is a differential equation problem most easily solved with an exponential decay equation of the form

$y=Ce^{kt}$ . We know that the initial amount of salt in the tank is 28 pounds, so

C = 28. Now we just need to find k.

The concentration of salt changes as the pure water flows in and the salt water flows out. So the change in concentration, where y is the concentration of salt in the tank, is $\frac{dy}{dt}$ . Thus, the change in the concentration of salt is found in

$\frac{dy}{dt}=$ inflow of salt - outflow of salt

Pure water, what is flowing into the tank, has no salt in it at all; and since we don't know how much salt is leaving (our unknown, basically), the outflow at 3 gal/min is 3 times the amount of salt leaving out of the 400 gallons of salt water at time t:

$3(\frac{y}{400})$