Which expression is equivalent to the given expression?

Dawn Dough and Dale earned different amounts $9.35,$8.52,and$8.25 dale and Doug earned about $9.00 Dawn earned exactly $1.10less

Zielflug [23.3K]

We know that the amounts earned by Dawn, Doug and Dale are from the list of numbers: $9.35, $8.52 and $8.25

We also know that Dale and Doug earned close to $9.00

And that Dawn earned $1.10 less than Dale

Let the amount earned by Dale be x

⇒ Amount earned by Dawn is x - 1.1

If we notice the list of numbers, we see that $9.35 and $8.25 differ by $1.1

Hence, Dale earned $9.35 and Dawn earned $8.25

We are now left with $8.52, which should be the amount earned by Doug. This is correct, since we also know that Doug earned close to $9.

Hence, the amounts earned are:

Dale: $9.35

Doug: $8.52

Dawn: $8.25

8 0

3 years ago

Consider f and c below. f(x, y) = (3 + 4xy2)i + 4x2yj, c is the arc of the hyperbola y = 1/x from (1, 1) to 3, 1 3 (a) find a fu

irga5000 [103]

We want to find a scalar function $f(x,y)$ such that $\nabla f(x,y)=\mathbf f(x,y)=\dfrac{\partial f}{\partial x}\,\mathbf i+\dfrac{\partial f}{\partial y}\,\mathbf j$ .
So we need to have
$\dfrac{\partial f}{\partial x}=3+4xy^2$
Integrating both sides with respect to $x$ gives
$f(x,y)=3x+2x^2y^2+g(y)$
Differentiating with respect to $y$ gives
$\dfrac{\partial f}{\partial y}=4x^2y+\dfrac{\mathrm dg}{\mathrm dy}=4x^2y$ $\implies\dfrac{\mathrm dg}{\mathrm dy}=0$ $\implies g(y)=C$
So we find that
$f(x,y)=3x+2x^2y^2+C$
By the fundamental theorem of calculus, we then know the line integral depends only on the values of $f(x,y)$ at the endpoints of the path. Therefore

$\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f\left(3,\frac13\right)-f(1,1)=11-5=6$

4 0

4 years ago

What is the slope of o line that passes through (-4,-14) and (19,11)?

DerKrebs [107]

Answer:

D, see description below.

There is a possible typo in the problem since these points have slope 25/23.

Step-by-step explanation:

To find the slope of a line, calculate the distance between points with a ratio of vertical to horizontal distance. This is done using the formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Here the points are (-4,-14) and (19,11). Substitute and simplify.

$m=\frac{11--14}{19--4}=\frac{11+14}{19+4}=\frac{25}{23}$

I think there is a typo in your points (-4,-14) and (19,11) because the answer doesn't align to the answer choices. But based on them, I would answer D or 24/23 since it's the closest value.

6 0

3 years ago

Which function has the greater maximum value: f(x) = -2x2 + 8x-1, or g(x),

aleksklad [387]

Answer:

It’s f(x)

Step-by-step explanation:

4 0

3 years ago

The sum of five consecutive multiples of 4 is 20.Find the smallest integer.

Aloiza [94]

Answer:

The smallest integer is -4.

Step-by-step explanation:

Let the smallest integer be x.

Since the integers are all multiples of 4, they are

=> x, x+4, x+8, x+12 and x+16

=> x + x+4 + x+8 + x+12 + x+16 = 20

=> 5x + 40 = 20

Subtract 40 from both sides of the equation

5x +40 - 40 = 20 - 40

5x = -20

Divide both sides by the coefficient of x(which is 5)

$\frac{5x}{5} = \frac{-20}{5}$

x = -4

∴ the smallest integer is -4.

Hope this helps!!!

6 0

3 years ago