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2 years ago

This is 6th grade math

Mathematics

2 answers:

MA_775_DIABLO [31]2 years ago

7 0

Answer: 70

Step-by-step explanation: so first you cout all of the whole squares and then you add up all the portions of squares. hope this helps/ let me know if wrong

ASHA 777 [7]2 years ago

4 0

Answer: 72

Step-by-step explanation:

I counted one of the sides then took all of the answers and divided it by 12

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A book has 150 pages, every page is numbered. how many digits are used?

IrinaK [193]

300 digits/numbers are used.

150pages * 2(two sides to one page) = 300numbers

Hope this helps!!!

7 0

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

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

7 0

3 years ago

What is the solution of x-7= ir+14,

weqwewe [10]

Answer:

x=12

Step-by-step explanation:

put the x at one side and the numbers ar the other

5/2x-3/4x=14+7

10/4x-3/4x=21

7/4x=21

7x=84

x=12

3 0

3 years ago

I need help please im only in the 7th grade &’ i don’t know what to do !

dedylja [7]

Answer: In the chart, put 6 in place of the question mark.

The equation should be something like w = 2/3 p

W is the number of quarts of water. P is the number of quarts of Pineapple juice.

This week they will need 3 times the previous week so 18 quarts of pineapple juice and 12 quarts of sparkling water.

Step-by-step explanation:

If the basic recipe is 2 water to 3 juice, and they used 4 quarts if water, you can see that is double the amount of water so you need double the amount of juice. 2 times 3 is 6.

Unit rate means for ONE quart of juice, how much sparkling water is used. that should be 1 Pineapple Juice for 2/3 Sparkling water

for EACH quart of sparkling water, how much juice do you need.

that would be 1 unit of Sparkling Water for 1 1/2 units of Pineapple Juice

4 0

3 years ago

Two girls and two boys went to the festival. The total cost of their tickets was $20. Each child paid the same amount for a tick

sattari [20]

Answer: $5

Step-by-step explanation: 4 children divided by 20 equals 5

6 0

3 years ago