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3 years ago

Find x. A. 21√2 B. 7 C. 21√3 over 2 D. 21√2 over 2

Mathematics

2 answers:

kkurt [141]3 years ago

5 0

Answer:

Step-by-step explanation:

for you to find x you first have to find the adjacent of the 45° angle you can do that by using the other triangle.using the sin ratio

sin60=opposite/hypotenuse

sin60=a/7√3

a=10.5

then after you have found the adjacent you can use the cos ratio

cos45=adjacent/hypotenuse

cos45=10.5/x

cos45x/cos45=10.5/cos45

x=14.849

which is the same as 21√2 over 2

I hope this helps

Evgesh-ka [11]3 years ago

4 0

Answer:

Step-by-step explanation:

Using sine ratio in left right angled triangle to find the altitude a of the large triangle which is common to both right triangles and the exact value

sin60° = $\frac{\sqrt{3} }{2}$ , then

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{a}{7\sqrt{3} }$ = $\frac{\sqrt{3} }{2}$ ( cross- multiply )

2a = 21 ( divide both sides by 2 )

a = $\frac{21}{2}$

Using the cosine ratio in the right side triangle and the exact value

cos45° = $\frac{1}{\sqrt{2} }$ , then

cos45° = $\frac{adjacent}{hypotenuse}$ = $\frac{a}{x}$ = $\frac{1}{\sqrt{2} }$ ( cross- multiply )

x = $\sqrt{2}$ a = $\sqrt{2}$ × $\frac{21}{2}$ = $\frac{21\sqrt{2} }{2}$ → D

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G = 4n is the correct equation to use. Eg 10 x 4 = 40, 18 x 4 = 72 and 21 x 4 = 84

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3 years ago

Jade buys a blouse and a skirt for 3/6 of their original price. Jade pays a total of $31 for the two items. If the original pric

Damm [24]

Answer:

3/4 times 18= 13.5

31.5-13.5=18

It cost 18 dollars for the skirt with a discount.

It cost 13.5 for the blouse as opposed to the original price of 18 dollars.

18(skirt)+13.5(blouse)=31.5

If you set up a proportion to find the original price of the skirt you will get the answer.

18/x=75/100

75x=18 times 100

75x=1800

75x/75=1800/75

x=24

The original price of the skirt is 24 dollars.

Step-by-step explanation:

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3 years ago

Apply the method of undetermined coefficients to find a particular solution to the following system.wing system.

jarptica [38.1K]

$y''-y'+y=\sin x$

The corresponding homogeneous ODE has characteristic equation $r^2-r+1=0$ with roots at $r=\dfrac{1\pm\sqrt3}2$ , thus admitting the characteristic solution

$y_c=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x$

For the particular solution, assume one of the form

$y_p=a\sin x+b\cos x$

${y_p}'=a\cos x-b\sin x$

${y_p}''=-a\sin x-b\cos x$

Substituting into the ODE gives

$(-a\sin x-b\cos x)-(a\cos x-b\sin x)+(a\sin x+b\cos x)=\sin x$

$-b\cos x+a\sin x=\sin x$

$\implies a=1,b=0$

Then the general solution to this ODE is

$\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}$

$y''-3y'+2y=e^x\sin x$

$\implies r^2-3r+2=(r-1)(r-2)=0\implies r=1,r=2$

$\implies y_c=C_1e^x+C_2e^{2x}$

Assume a solution of the form

$y_p=e^x(a\sin x+b\cos x)$

${y_p}'=e^x((a+b)\cos x+(a-b)\sin x)$

${y_p}''=2e^x(a\cos x-b\sin x)$

Substituting into the ODE gives

$2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x$

$-e^x((a+b)\cos x+(a-b)\sin x)=e^x\sin x$

$\implies\begin{cases}-a-b=0\\-a+b=1\end{cases}\implies a=-\dfrac12,b=\dfrac12$

so the solution is

$\boxed{y(x)=C_1e^x+C_2e^{2x}-\dfrac{e^x}2(\sin x-\cos x)}$

$y''+y=x\cos(2x)$

$r^2+1=0\implies r=\pm i$

$\implies y_c=C_1\cos x+C_2\sin x$

Assume a solution of the form

$y_p=(ax+b)\cos(2x)+(cx+d)\sin(2x)$

${y_p}''=-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x)$

Substituting into the ODE gives

$(-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x))+((ax+b)\cos(2x)+(cx+d)\sin(2x))=x\cos(2x)$

$-(3ax+3b-4c)\cos(2x)-(3cx+3d+4a)\sin(2x)=x\cos(2x)$

$\implies\begin{cases}-3a=1\\-3b+4c=0\\-3c=0\\-4a-3d=0\end{cases}\implies a=-\dfrac13,b=c=0,d=\dfrac49$

so the solution is

$\boxed{y(x)=C_1\cos x+C_2\sin x-\dfrac13x\cos(2x)+\dfrac49\sin(2x)}$

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3 years ago

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

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3 years ago

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Wally had two more marbled than ashan and together they have 88 marbles how many marbles does ashan have

labwork [276]

Represent as
w=wally
a=ashan
so wally has 2 more marbles than ashan
w=2+a

together they have 88
w+a=88

since w=2+a, subsitute (2+a) for w in the w+a=88 equation
2+a+a=88
add like terms
2+2a=88
subtract 2 from both sides
2a=86
divide by 2
a=43

ashan has 43 marbles

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3 years ago

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