Answer the following!

Try, check, and revise or write an equation to solve

iragen [17]

Answer: 7 and 42.

Step-by-step explanation:

Let the two whole numbers be x and y.

From the question given, we can form an equation as:

x × y = 294 ........ i

x/y = 6 .......... ii

From equation ii

x/y = 6

x = 6y

Put the value of x back into equation i

x × y = 294

6y × y = 294

6y² = 294

y² = 294/6

y² = 49

y = ✓49

y = 7

Since x × y = 294 and y = 7,

x = 294/7

x = 42

The numbers are 7 and 42.

3 0

3 years ago

Jessica wants to buy 6 ounces of gluten-free edible cookie dough that costs $1.50 per ounce. Select all equations that correctly

mars1129 [50]

Answer:

9 dollars

Step-by-step explanation:

Hello you did not provide the options for me to select from. But I have gone ahead to calculate how much jessica would pay for her cookie dough.

I used this formula to arrive at this answer.

Cost of dough = quantity x price per ounce

Quantity = 6 ounces

Price per ounce = 1.5 dollars

Cost of dough = 6 x 1.50

= $9

Jessica is going to pay 9 dollars for her cookie dough

8 0

3 years ago

How do you do (a) and (b)?

bulgar [2K]

Answer:

See solution below

Step-by-step explanation:

(a) If n=0 or 1, the equation

(1) $y' = a(t)y + f(t)y^n$

would be a simple linear differential equation. So, we can assume that n is different to 0 or 1.

Let's use the following substitution:

(2) $z=y^{n-1}$

Taking the derivative implicitly and using the chain rule:

(3) $z'=(1-n)y^{-n}y'$

Multiplying equation (1) on both sides by

$(1-n)y^{-n}$

we obtain the equation

$(1-n)y^{-n}y' = (1-n)y^{-n}a(t)y+(1-n)y^{-n}f(t)y^n$

reordering:

$(1-n)y^{-n}y' = (1-n)y^{-n}ya(t)+(1-n)y^{-n}y^nf(t)$

$(1-n)y^{-n}y' = (1-n)y^{1-n}a(t)+(1-n)y^{0}f(t)$

$(1-n)y^{-n}y' = (1-n)y^{1-n}a(t)+(1-n)f(t)$

Now, using (2) and (3) we get:

$z'= (1-n)za(t)+(1-n)f(t)$

which is an ordinary linear differential equation with unknown function z(t).

(b)

The equation we want to solve is

(4) $xy'+ y = x^4 y^3$

Here, our independent variable is x (instead of t)

Assuming x different to 0, we divide both sides by x to obtain:

$y'+\frac{1}{x}y = x^3 y^3$

$y' = -\frac{1}{x}y+x^3 y^3$

Which is an equation of the form (1) with

$a(x)=-\frac{1}{x}$

$f(x)=x^3$

$n=3$

So, if we substitute

$z=y^{-2}$

we transform equation (4) in the lineal equation

(5) $z'=\frac{2}{x}z-2x^3$

and this is an ordinary lineal differential equation of first order whose

integrating factor is

$e^{\int (-\frac{2}{x})dx}$

but

$e^{\int (-\frac{2}{x})dx}=e^{-2\int \frac{dx}{x}}=e^{-2ln(x)}=e^{ln(x^{-2})}=x^{-2}=\frac{1}{x^2}$

Similarly,

$e^{\int (\frac{2}{x})dx}=x^2$

and the general solution of (5) is then

$z(x)=x^2\int (\frac{-2x^3}{x^2})dx+Cx^2=-2x^2\int xdx+Cx^2=\\\ -2x^2\frac{x^2}{2}+Cx^2=-x^4+Cx^2$

where C is any real constant

Reversing the substitution

$z=y^{-2}$

we obtain the general solution of (4)

$y=\sqrt{\frac{1}{z}}=\sqrt{\frac{1}{-x^4+Cx^2}}$

Attached there is a sketch of several particular solutions corresponding to C=1,4,6

It is worth noticing that the solutions are not defined on x=0 and for C<0

4 0

3 years ago

PLEASE HELP OMGGGGGGGG<br> also stan nct for clear skin :))))<br> ++no wreird link plssss

dolphi86 [110]

Answer:

its D

Step-by-step explanation:

C= n d

4 0

3 years ago

9(5x + 1) ÷ 3y

Ivan

Some definitions:

Sum - the result of adding values together

Term - a single number or variable (includes variables multiplied by numbers)

Factor - a number or variable that divides another number or expression evenly

Quotient - the result of dividing values by one another

Coefficient - a numerical or constant value often in front of a variable

In your equation:

Sum - (5x + 1)

5x and 1 are being added together, although we do not know the sum exactly, we know that the sum is equal to the value of 5 times x plus 1.

Term - (5x, 1, 3y)

All terms given above are applicable.

Factor - (9)

9 has been taken out of the expression that it is now being multiplied, which shows that it was factored out of that expression

Quotient - (9(5x + 1) / 3y)

The value of 9(5x + 1) is being divided by 3y. Though we do not know the quotient exactly, we know that the quotient is equal to the values given.

Coefficient - (5, 3)

Both 5 and 3 are numbers in front of variables.

Hope this helps!! :)

3 0

4 years ago