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3 years ago

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2. What is the approximate value of b in the triangle below?

1 answer:

s344n2d4d5 [400]3 years ago

6 0

Answer:

d) 17.6

Step-by-step explanation:

Use the law of Sines

SinA/a=SinB/b=SinC/c

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C.) of a total of $10,000, part was invested at 10% simple interest and the remainder at

nlexa [21]

Answer:

$3,500 at 10% and $6,500 at 7%.

Step-by-step explanation:

M * 10% + (10000 - M) * 7% = 805

0.1M + 700 - 0.07M = 805

0.03M = 105

M = 3500

4 0

2 years ago

How do i solve that question?

yawa3891 [41]

a) The solution of this <em>ordinary</em> differential equation is $y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }$ .

b) The integrating factor for the <em>ordinary</em> differential equation is $-\frac{1}{x}$ .

The <em>particular</em> solution of the <em>ordinary</em> differential equation is $y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$ .

<h3>How to solve ordinary differential equations</h3>

a) In this case we need to separate each variable ( $y, t$ ) in each side of the identity:

$6\cdot \frac{dy}{dt} = y^{4}\cdot \sin^{4} t$ (1)

$6\int {\frac{dy}{y^{4}} } = \int {\sin^{4}t} \, dt + C$

Where $C$ is the integration constant.

By table of integrals we find the solution for each integral:

$-\frac{2}{y^{3}} = \frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32} + C$

If we know that $x = 0$ and $y = 1$ <em>, </em>then the integration constant is $C = -2$ .

The solution of this <em>ordinary</em> differential equation is $y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }$ . $\blacksquare$

b) In this case we need to solve a first order ordinary differential equation of the following form:

$\frac{dy}{dx} + p(x) \cdot y = q(x)$ (2)

Where:

$p(x)$ - Integrating factor
$q(x)$ - Particular function

Hence, the ordinary differential equation is equivalent to this form:

$\frac{dy}{dx} -\frac{1}{x}\cdot y = x^{2}+\frac{1}{x}$ (3)

The integrating factor for the <em>ordinary</em> differential equation is $-\frac{1}{x}$ . $\blacksquare$

The solution for (2) is presented below:

$y = e^{-\int {p(x)} \, dx }\cdot \int {e^{\int {p(x)} \, dx }}\cdot q(x) \, dx + C$ (4)

Where $C$ is the integration constant.

If we know that $p(x) = -\frac{1}{x}$ and $q(x) = x^{2} + \frac{1}{x}$ , then the solution of the ordinary differential equation is:

$y = x \int {x^{-1}\cdot \left(x^{2}+\frac{1}{x} \right)} \, dx + C$

$y = x\int {x} \, dx + x\int\, dx + C$

$y = \frac{x^{3}}{2}+x^{2}+C$

If we know that $x = 1$ and $y = -1$ , then the particular solution is:

$y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$

The <em>particular</em> solution of the <em>ordinary</em> differential equation is $y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$ . $\blacksquare$

To learn more on ordinary differential equations, we kindly invite to check this verified question: brainly.com/question/25731911

3 0

2 years ago

HELP PLSSSSsssssssssssssssss

KatRina [158]

3/10 hope this helps:)

6 0

3 years ago

Read 2 more answers

Two Parallel lines are intersected by a transversal /1 and /2 are alternate exterior angles. The measure of /1 is (5x - 16) the

Alecsey [184]

Answer:

C. m/1=m/2=54

Step-by-step explanation:

these two angles are equal hence:

5x-16=4x-2=-16+2 =-14

4x-5x=-x

-x=-14=x=14

then you substitute the value of 'x' with 14

therefore:(5×14-16)=54

(4×14-2)=54

m/1=m/2=54

6 0

3 years ago

If 3,8,9 and x are in proportion find the value of x

Rufina [12.5K]

Answer:

Step-by-step explanation:

since they are in continued proportion the ratio will be

3/8=9/x

do cross multiplication

8*9=3*x

72=3x

72/3=x

24=x

therefore x =24

8 0

2 years ago

Read 2 more answers