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3 years ago

What is the quotient of Three-fifths and StartFraction 1 Over 10 EndFraction?

Mathematics

2 answers:

Grace [21]3 years ago

6 0

Answer:

D:6

Step-by-step explanation:

3/5 = 6/10

6/10 divided by 1/10 equals 6

so 6 is your answer.

harina [27]3 years ago

6 0

Answer:

Step-by-step explanation:

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3 years ago

Solve the initial value problem

tigry1 [53]

$9(t+1)\dfrac{\mathrm dy}{\mathrm dt}-7y=14t\implies\dfrac{\mathrm dy}{\mathrm dt}-\dfrac7{9(t+1)}y=\dfrac{14t}{9(t+1)}$

Look for an integrating factor $\mu(t)$ :

$\ln\mu=\displaystyle-\frac79\int\frac{\mathrm dt}{t+1}=-\frac79\ln(t+1)\implies\mu=(t+1)^{-7/9}$

Multiply both sides by $\mu$ :

$(t+1)^{-7/9}\dfrac{\mathrm dy}{\mathrm dt}-\dfrac79(t+1)^{-16/9}y=\dfrac{14}9t(t+1)^{-16/9}$

Condense the left side as the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[(t+1)^{-7/9}y\right]=\dfrac{14}9t(t+1)^{-16/9}$

Integrate both sides:

$(t+1)^{-7/9}y=\displaystyle\frac{14}9\int t(t+1)^{-16/9}\,\mathrm dt$

For the integral on the right, substitute

$u=t+1\implies t=u-1\implies\mathrm dt=\mathrm du$

$\displaystyle\int t(t+1)^{-16/9}\,\mathrm dt=\int(u-1)u^{-16/9}\,\mathrm du$

$\displaystyle=\int\left(u^{-7/9}-u^{-16/9}\right)\,\mathrm du=\frac92u^{2/9}+\frac97u^{-7/9}+C$

$\implies(t+1)^{-7/9}y=\dfrac{14}9\left(\dfrac92(t+1)^{2/9}+\dfrac97(t+1)^{-7/9}+C\right)$

$\implies(t+1)^{-7/9}y=7(t+1)^{2/9}+2(t+1)^{-7/9}+C$

$\implies y=7(t+1)+2+C(t+1)^{7/9}=7t+9+C(t+1)^{7/9}$

Given that $y(0)=12$ , we get

$12=9+C\implies C=3$

$\implies\boxed{y(t)=7t+9+3(t+1)^{7/9}}$

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3 years ago

A TV screen has a diagonal length of 156cm, the angle in the top corner is 37◦. Calculate the height of the TV screen

Arte-miy333 [17]

The TV screen is an illustration of a right triangle

The height of the TV screen is 124.6 cm

<h3>How to calculate the height</h3>

The diagonal is given as:

d = 156 cm

The angle at the top is given as:

Angle = 37 degrees

The height is then calculated using the following cosine ratio

$\cos(37) = \frac h{156}$

Make h the subject

$h = 156 * \cos(37)$

Evaluate

h = 124.6

Hence, the height of the TV screen is 124.6 cm