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4 years ago

11

liz is installing a tile backsplash. if each tile is an equilateral triangle with sides that measures 6 cm in length how many ti

les does she need to cover an area of 1800 cm²

1 answer:

Alina [70]4 years ago

8 0

Answer:

she will need 300

I hope this helped

Step-by-step explanation:

6 times 300= 1800

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The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find

9966 [12]

Answer:

<em>The particular integral of given differential equation</em>

<em> </em> $y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))$ <em></em>

<em> General solution of given differential equation</em>

<em> </em> $y = y_{c} + y_{p}$ <em></em>

<em> </em> $Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))$ <em></em>

<em></em>

Step-by-step explanation:

<u><em>Step(i)</em></u>:-

Given Differential equation y'' − 5 y' + 4 y = x

Given equation in operator form

D²y - 5 Dy + 4 y = x

⇒ ( D² - 5 D + 4 ) y =x

⇒ f(D) y = Q

where f(D) = D² - 5 D + 4 and Q(x) = x

<em>The auxiliary equation f(m) =0</em>

<em> m²-5 m + 4 =0</em>

m² - 4 m - m + 4 =0

m ( m -4 ) -1 ( m-4) =0

(m - 1) =0 and ( m-4) =0

<em> m = 1 and m =4</em>

<em>The complementary function </em>

<em></em> $Y_{c} = C_{1} e^{x} + C_{2} e^{4x}$ <em></em>

<u><em>Step(ii)</em></u>:-

<u><em>particular integral</em></u>

<em>Particular integral</em>

<em> </em> $y_{p} = \frac{1}{f(D)} Q(x) = \frac{1}{D^{2} - 5 D + 4} X$ <em></em>

<em>taking common '4' </em>

<em> </em> $= \frac{1}{4(1 + (\frac{D^{2} - 5 D}{4} ))} X$ <em></em>

<em> </em>

<em> </em> $=\frac{1}{4} (1 + (\frac{D^{2} -5D}{4})^{-1} )} X$ <em></em>

<em>applying binomial expression</em>

<em> ( 1 + x )⁻¹ = 1 - x + x² - x³ +..... </em>

<em> </em> $=\frac{1}{4} (1 - (\frac{D^{2} -5D}{4}) +((\frac{D^{2} -5D}{4})^{2} -...} )X$ <em></em>

<em>Now simplifying and we will use notation D = </em> $\frac{dy}{dx}$ <em></em>

<em> </em> $=\frac{1}{4} (x - (\frac{D^{2} -5D}{4})x +((\frac{D^{2} -5D}{4})^{2}(x) -...}$ <em></em>

<em>Higher degree terms are neglected</em>

<em> </em> $=\frac{1}{4} (x - (\frac{ -5 D}{4}) x)$ <em></em>

<em>The particular integral of given differential equation</em>

<em> </em> $y_{p} = \frac{1}{4} ( x - (\frac{-5}{4} ) (1))$ <em></em>

<u><em>Final answer</em></u><em>:-</em>

<em> General solution of given differential equation</em>

<em> </em> $y = y_{c} + y_{p}$ <em></em>

<em> </em> $Y (x) = C_{1} e^{x} + C_{2} e^{4x} + \frac{1}{4} ( x + (\frac{5}{4} ))$ <em></em>

<em></em>

<em></em>

<em> </em>

<em> </em>

4 0

3 years ago

The Value of x is???

Zolol [24]

Answer:

30

Step-by-step explanation:

5 0

3 years ago

Hii, Ok so basically I really need help with these questions they are really difficult and don't worry rewards are plenty a come

posledela

So begin by doing 360-284=76
90+76=166
180-166=14

X=14

5 0

3 years ago

What is the vertex of the parabola?

Leya [2.2K]

Answer:

A.

Step-by-step explanation:

go to demos calculator and type it in. itll give u the answer kinda. I mean u have to type the thingy and graph it butyoull still find the answer

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3 years ago

Plz help! (I will give brainliest)

lianna [129]

Answer:

25 mph, 5 mph

Step-by-step explanation:

Speed of the boat = x
Speed of the current = y

<u>Travel downstream, speed is:</u>

x + y = 120/4 = 30

<u>Travel upstream, speed is:</u>

x - y = 120/6 = 20

<u>Add up the equations:</u>

x + y + x - y = 30 + 20
2x = 50
x = 25

<u>Find y:</u>

y = 25 - 20 = 5

Speed of the boat is 25 mph

Speed of the current is 5 mph

7 0

3 years ago