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3 years ago

11

Using only whole numbers Nikki wrote as many multiplication equations as she could with 12 as the product what where her equatio

ns

1 answer:

erastovalidia [21]3 years ago

4 0

1 times 12,2 times 6,and 3times 4

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3 years ago

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Use separation of variables to solve dy dx − tan x = y2 tan x with y(0) = √3. Find the value of c in radians, not degrees

a_sh-v [17]

Answer:

$y(x)=tan(-log(cos(x))+\frac{\pi }{3} )$

Step-by-step explanation:

Rewrite the equation as:

$\frac{dy(x)}{dx}-tan(x)=y(x)^{2} *tan(x)$

Isolating $\frac{dy}{dx}$

$\frac{dy}{dx} =tan(x)+tan(x)*y^{2}$

Factor:

$\frac{dy}{dx} =tan(x)*(1+y^{2} )$

Dividing both sides by $(1+y^{2} )$ and multiplying them by $dx$

$\frac{dy}{1+y^{2} } =tan(x)dx$

Integrate both sides:

$\int\ \frac{dy}{1+y^{2} } = \int\ tan(x) dx$

Evaluate the integrals:

$arctan(y)=-log(cos(x))+C_1$

Solving for y:

$y(x)=tan(-log(cos(x))+C_1)$

Evaluating the initial condition:

$y(0)=\sqrt{3} =tan(-log(cos(0))+C_1)=tan(-log(1)+C_1)=tan(0+C_1)$

$\sqrt{3} =tan(C_1)\\arctan(\sqrt{3} )=C_1\\60=C_1$

Converting 60 degrees to radians:

$60degrees*\frac{\pi }{180degrees} =\frac{\pi }{3}$

Replacing $C_1$ in the diferential equation solution:

$y(x)=tan(-log(cos(x))+\frac{\pi }{3} )$

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3 years ago

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Answer:

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3 years ago

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If triangle ABC is congruent to triangle XYZ, then which of the following is congruent to segment XY? (5 points)

givi [52]

Answer:

Segment AB!

hope this helps

Step-by-step explanation:

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3 years ago

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What is the simple interest of a note that has a face value of $12,000, a rate of 8%, and a term of 1 year?

Tju [1.3M]

Solution:

Given:

$\begin{gathered} P=\text{ \$}12,000 \\ R=8\text{ \%} \\ T=1year \end{gathered}$

Using the simple interest formula,

$\begin{gathered} I=\frac{PTR}{100} \\ I=\frac{12000\times1\times8}{100} \\ I=\text{ \$}960 \end{gathered}$

Therefore, the simple interest is $960.

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1 year ago