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3 years ago

6

To be able to do the problem 5(10+4) mentally, zach does 50+20 instead of 5(14). Zach is using which of the following properties

? associative, commutative, inverse, or distribute

1 answer:

liberstina [14]3 years ago

6 0

Answer:

Zach is using the distributive property.

Step-by-step explanation:

He distributes the 5 to the numbers inside the ().

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Graph the inequality y

nadezda [96]

Where is the inequality?

3 0

2 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

3 years ago

Adult tickets to a play cost $1.75 each and student tickets cost $1.25 each. Suppose there are twice as many student tickets sol

nikitadnepr [17]

Answer: the number of adult tickets sold is 400

the number of student tickets sold is 200

Step-by-step explanation:

Let x represent the number of adult tickets sold at the play.

Let y represent the number of student tickets sold at the play.

Adult tickets to a play cost $1.75 each and student tickets cost $1.25 each. If the income from the play was $1,700, it means that

1.75x + 1.25y = 1700 - - - - - - - - - -1

Suppose there are twice as many student tickets sold as adult tickets. This means that

y = 2x

Substituting y = 2x into equation 1, it becomes

1.75x + 1.25 × 2x = 1700= 1700

1.75y + 2.5y = 1700

4.25y = 1700

y = 1700/4.25 = 400

x = y/2 = 400/2 = 200

8 0

3 years ago

Diego solved an equation by multiplying both sides of the equation by 6. Then he checked that 6 is the correct solution by subst

Studentka2010 [4]

C. on e2020 . Good luck!

6 0

3 years ago

Write an expression to represent the product of 6 and the square of a number plus 15.

inn [45]

Answer:

6x² + 15

6

Step-by-step explanation:

Let the number be x.

"the square of a number"

x²

"the product of 6 and the square of a number"

6x²

"the product of 6 and the square of a number plus 15"

6x² + 15

The coefficient is the number that multiplies the variable, so it is 6.

8 0

2 years ago