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3 years ago

Ratio of three angles of a triangle is 1 : 2 : 3. Find the angles.

Mathematics

2 answers:

Anvisha [2.4K]3 years ago

8 0

Answer:

30⁰ , 60⁰ , 90⁰

Step-by-step explanation:

Let the angles x , 2x , 3x

By angle sum property:

x + 2x + 3x = 180⁰

6x = 180⁰

x = 30⁰

Angles are : 30⁰ , 60⁰ , 90⁰

Nikolay [14]3 years ago

4 0

Let one angle be x, the second 2x and the third 3x.

x + 2x + 3x = 180 degrees (angle sum property of a triangle)

6x = 180 degrees

x = 180/6

x = 30 degrees

So one angle is 30°, the second is 60°, and the third is 90°.

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

3 years ago

If 2a - b = 4 , find a.

julia-pushkina [17]

<h2>Answer: a = ¹/₂ (4 + b)</h2>

<h3>Step-by-step explanation:</h3>

To solve for 'a' we have to make it the subject of the equation. Since there are two unknowns ('a' & 'b'), we won't get a numerical value of 'a', but an expression in terms of the second unknown 'b'.

Since 2a - b = 4 <em> [add 'b' to both sides]</em>

then 2a = 4 + b <em>[divide both sides by 2 = multiplying by ¹/₂]</em>

a = ¹/₂ (4 + b)

3 0

3 years ago

When a = 6 and b = 22, C = 33. If c varies directly with b and inversely with a, which equation models the situation?

S_A_V [24]

Step-by-step explanation:

C=b/a

c=kb/a

where as k is the constant

c=kb/a

we substitute

33=22k/6

crossed multiply

33*6= 22k

198=22k

we divide both sides by 22

198/22=22k/22

K=9

4 0

2 years ago

Ninety-one percent of products come off the line within product specifications. Your quality control department selects 15 produ

Allisa [31]

Answer:

Probability of stopping the machine when $X < 9$ is 0.0002

Probability of stopping the machine when $X < 10$ is 0.0013

Probability of stopping the machine when $X < 11$ is 0.0082

Probability of stopping the machine when $X < 12$ is 0.0399

Step-by-step explanation:

There is a random binomial variable $X$ that represents the number of units come off the line within product specifications in a review of $n$ Bernoulli-type trials with probability of success $0.91$ . Therefore, the model is ${15 \choose x} (0.91) ^ {x} (0.09) ^ {(15-x)}$ . So: