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3 years ago

Draw a number line that shows the distance between 3 and -2 is 5

Mathematics

2 answers:

Firlakuza [10]3 years ago

8 0

I hope this is able to help you!!

NISA [10]3 years ago

4 0

This is how I would do it, hope this helps!

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On Friday,65% of the students at Plainview Middle School bought a hot lunch and the rest of the students packed their lunch. Wha

oksano4ka [1.4K]

35% packed their lunch. 65/100 bought hot lunch. 100-65=35.

7 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

2 years ago

How do u write 1.2 as a fraction

Ivahew [28]

Split the number into its whole number component and decimal component.

for the decimal component, 0.2 is the same as 2/10

Find the GCF of both 2 and 10 and that would be 2

divide both the numerator and denominator by the GCF

simplify and you get 1/5

Lastly combine the whole number component with the fraction and your answer would be 1 1/5.

6 0

3 years ago

Ms. Lane borrowed $1,000 from her bank for one year at an interest rate of 10 percent. During that year, the price level went up

Lunna [17]

Answer:

Consider the complete question is,

'Ms. Lane borrowed $1,000 from her bank for one year at an interest rate of 10 percent. During that year, the price level went up by 15 percent. Which of the following statements is correct?

a. Ms. Lane will repay the bank fewer dollars than she initially borrowed.

b. Ms. Lane's repayment will give the bank less purchasing power than it originally loaned her.

c. Ms. Lane's repayment will give the bank greater purchasing power than it originally loaned her.

d. Ms. Lane's repayment will give the bank the same purchasing power that it originally loaned her.'

Solution :

We have,

The borrowed amount, P = $ 1,000,

Interest rate, r = 10% = 0.1,

Time, t = 1 year,

Thus, the returned amount,

$A=P(1+r)^t=1000(1+0.1)^1=1000(1.1) = \$ 1100$

∵ A > P

⇒ Ms. Lane will repay the bank greater dollars than she initially borrowed.

Now, the price level went up by 15 percent,

∵ 1000 + 15% of 1000 = 1000 + 150 = 1500

And, 1500 > 1100

⇒ Ms. Lane's repayment will give the bank less purchasing power than it originally loaned her.

8 0

2 years ago

How to do this! Completely lost!!

Korvikt [17]

The solution is 3, -9
x = 3, y = -9

4 0

3 years ago