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3 years ago

A house sells for 2.95×10^5 dollars. Write this number in standard form.

Mathematics

1 answer:

dimulka [17.4K]3 years ago

8 0

Answer:

295000

Step-by-step explanation:

It would 295,000

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Quadrilateral ABCD has vertices at A(0,0), B(0,2), C(6,2), and D(6,0). Find the vertices of the quadrilateral after a dilation w

valentinak56 [21]

Answer:

A=0

B=0,3

C=9,3

D=9,0

Step-by-step explanation:

Multiplies all the vertices bay scale factor 3/2

5 0

3 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

(-3,-4) with slope 3

Anvisha [2.4K]

Answer:

Do you want me to graph it

Step-by-step explanation:

5 0

3 years ago

(2x-10)(x+3)+(x3+1)(x-4) what does it equal to

Solnce55 [7]

Answer:

Step-by-step explanation:

Use FOIL method.

(2x - 10)(x + 3) = 2x*x + 2x*3 + (-10)*x + (-10)*3

= 2x² + 6x - 10x - 30 {Combine like terms}

= 2x² - 4x - 30

(x³ + 1)(x - 4) = x³*x + x³ *(-4) + 1*x + 1*(-4)

= x⁴ - 4x³ + x - 4

(2x - 10)(x +3) +(x³ +1)(x - 4) = 2x² - 4x - 30 + x⁴ - 4x³ + x - 4

Combine like term

= x⁴ - 4x³ + 2x² - 4x + x -30 - 4

= x⁴ - 4x³ + 2x² - 3x - 34

7 0

3 years ago

Read 2 more answers

Use properties to evaluate 2/3 • (- 3/4 / 1/8) 1/3 A.-4 B. 4 C.-4/3 D.4/3

Bond [772]

Answer:

Step-by-step explanation:

First you do the division in parentheses and you get (-3/4*8/1) = -24/4 = -6

The new exercise becomes 2/3 *(-6)*1/3

Next, since there are only multiplication we have to do then in order from left to right so we have

-12/3*1/3 = -12/9

We can simplify by 3 and we get -4/3

Anwer choice C

7 0

3 years ago