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2 years ago

6. In right triangle ABC, mZC=3y-10,

Mathematics

1 answer:

lorasvet [3.4K]2 years ago

6 0

Answer:

scalene

Step-by-step explanation:

step 1

Find the value of y

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

In this problem

m∠A+m∠B+m∠C=180°

substitute the given values

$90\°+(y+40)\°+(3y-10)\°=180\°$

Solve for y

$4y+120=180$

$4y=180-120$

$4y=60$

$y=15$

step 2

<em>Find the measure of angle B</em>

m∠B=(y+40)°

substitute the value of y

m∠B=(15+40)=55°

step 3

<em>Find the measure of angle C</em>

m∠C=(3y-10)°

substitute the value of y

m∠C=(3(15)-10)=35°

The three interior angles are different

The three sides of the ABC triangle will also be different

therefore

The right triangle ABC is scalene

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Troyanec [42]

Answer:

Step-by-step explanation:

Lateral surface area of the triangular prism = Perimeter of the triangular base × Height

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

(34)² = (16)² + BC²

BC = $\sqrt{1156-256}$

= $\sqrt{900}$

= 30 in.

Perimeter of the triangular base = AB + BC + AC

= 16 + 30 + 34

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2 years ago

Let f(x) = 2x + 2. Solve f−1(x) when x = 4.

malfutka [58]

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2 years ago

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

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

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2 years ago

A leprechaun places a magic penny under a girl's pillow. The next night there are 2 magic pennies under her pillow. Each night

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Answer:

tn = 2097152 pennies
tn = 20971.52 dollars.

Step-by-step explanation:

A surprisingly large amount of money.

The question is "Does the amount of money just double or do the previous amounts add to the present amount?"

I think it just doubles. Not only that, but she can't spend any of it until night 22 is reached.

tn = a*2^(n - 1)
a = 1 She starts with 1 penny.
n = 22
tn = 1*2^(22 - 1)
tn = 1*2^21
tn = 2097152 pennies
tn = 20971.52 dollars.

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