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3 years ago

Find the length of the hypotenuse.

Mathematics

1 answer:

Yuliya22 [10]3 years ago

3 0

Answer:

Hypotenuse =10

$\sin(45) = \frac{5 \sqrt{2} }{hypoetenuse} \\ \frac{ \sqrt{2} }{2} = \frac{5 \sqrt{2} }{x} \\ x = 10 \\ hypotenuse = 10$

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Given the following exponential function, identify whether the change representsgrowth or decay, and determine the percentage ra

jeka57 [31]

The equation of a exponential function is of the form

$y=a(b)^x$

where

b is the base of the exponential function

If the value of b>1 -----> is a growth function

If the value of b<1 ----> is a decay function

In this problem

b=1.04

1.04 > 1

therefore

<h2>Is a growth function</h2>

Part b

Determine the percentage rate of increase

we have that

b=1+r

r=b-1

r=1.04-1

r=0.04

convert to percentage

r=0.04*100

7 0

2 years ago

Set up but do not solve for the appropriate particular solution yp for the differential equation y′′+4y=5xcos(2x) using the Meth

taurus [48]

Answer:

So, solution of the differential equation is

$y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

Step-by-step explanation:

We have the given differential equation: y′′+4y=5xcos(2x)

We use the Method of Undetermined Coefficients.

We first solve the homogeneous differential equation y′′+4y=0.

$y''+4y=0\\\\r^2+4=0\\\\r=\pm2i\\\\$

It is a homogeneous solution:

$y_h(t)=c_1e^{-2i t}+c_2e^{2i t}$

Now, we finding a particular solution.

$y_p(t)=A5x\cos 2x\\\\y'_p(t)=A5\cos 2x-A10x\sin 2x\\\\y''_p(t)=-A20\sin 2x-A20x\cos 2x\\\\\\\implies y''+4y=5x\cos 2x\\\\-A20\sin 2x-A20x\cos 2x+4\cdot A5x\cos 2x=5x\cos 2x\\\\-A20\sin 2x=5x\cos 2x\\\\A=-\frac{x}{4} \cot 2x\\$

we get

$y_p(t)=A5\cos 2x\\\\y_p(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x\\\\\\y(t)=y_p(t)+y_h(t)\\\\y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

So, solution of the differential equation is

$y(t)=-\frac{5x^2}{4}\cot 2x\cdot \cos 2x+c_1e^{-2it}+c_2e^{2it}\\$

7 0

3 years ago

A coordinate plane with 4 lines. The first line is labeled a(x) and passes through (2, negative 4) and (0, 2) and continues past

goblinko [34]

Answer:

the answer is g(x)

Step-by-step explanation:

8 0

4 years ago

Which rational expression has a value of 0 when x = 2 ? A) 7x -5/x2 + 10 B) -3x +6/8x-9 C) -5x + 8 / x-2

shepuryov [24]

answer for this question is (b) - 3 x + 6 x /8x- 9

7 0

3 years ago

Read 2 more answers

Write an equation that represents a vertical translation 7 units down of the graph g(x)=|x|

natulia [17]

Answer:

f(x) = |x| - 7

Step-by-step explanation:

The given equation is g(x) = |x|......... (1)

The vertical translation by 7 units down will not change the value of x, the only change will be in the value of g(x).

The vertical translation by 7 units down will change the value of g(x) by [g(x) + 7] in the left-hand side of the equation (1).

Therefore, the equation will become g(x) + 7 = |x|

⇒ g(x) = |x| - 7.

Otherwise we can represent the function as some other name say f(x).

So, f(x) = |x| - 7. (Answer)

6 0

4 years ago