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3 years ago

If Ian has 4 times as many nickels as dimes and they have a combined value of 180 cents, how many of each coin does he have?

Mathematics

1 answer:

algol [13]3 years ago

8 0

4 (.05) x +( .10)x =180
.20x + .10x = 180
.30x = 180
X= 6
So. 4 times 6 = 24 nickels and 6 dimes = 180 cents

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Can u help me with this question

Troyanec [42]

Answer:

Step-by-step explanation:

The question is asking for the value of A when n = 2

So we just need to plug in 2 for n

A(2) = 10 + (2-1)(4) = 10 + (1)(4) = 10 +4 = 14

6 0

3 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

The diagram represents the shape and dimensions of Kayla's garden. A special fertilizer is used for the vegetable garden. Each b

Serjik [45]

Answer:

B. 18 bags

Step-by-step explanation:

First you need to determine the area of the vegetable garden. The vegetable garden is a rectangle with the following dimensions:

L = 24 ft

W = 9 ft

The Formula for the area of a rectangle is:

$A = L\times W$

So let's solve it:

$A = L\timesW\\A = 24 ft\times9ft\\A= 216ft^{2}$

With that, we can figure out how many bags of fertilizer would be needed by dividing the area of the vegetable garden by how much one bag of fertilizer covers:

$\dfrac{214ft^2}{12ft^2/bag}=18\;bags$

3 0

2 years ago

Read 2 more answers

List the single-digit divisors of 2100. I really need help

liberstina [14]

Answer:

1, 2, 3, 4, 5, 6, 7

Step-by-step explanation:

Prime factors of 2100 are:

2100 = 2*2*3*5*5*7

The single-digit divisors are:

1, 2, 3, 2*2= 4, 5, 2*3= 6, 7

-----------------------------------------------------------------

Another solution is you divide 2100 by all numbers 1 through 9 and list those divisible:

2100/1 = 2100, yes
2100/2 = 1050, yes
2100/3 = 700, yes
2100/4 = 525, yes
2100/5 = 420, yes
2100/6 = 350, yes
2100/7 = 300, yes
2100/8 = 262.5, no
2100/9 = 233.33, no

So all the numbers from 1 to 7

5 0

2 years ago

A loan for $4000 with interest at 6.75% compounded semi-annually is repaid after 5 years. What is the amount of interest paid?

Artyom0805 [142]

4,000 multiplied by 6.75%=27,000

27,000 multiplied by 5 = 135,000

4,000-135,000=131,000 amount of interest paid

5 0

3 years ago