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Y_Kistochka [10]

3 years ago

15

Katheryn gets paid $80,250 per year. How much is each one of her monthly paychecks? *

1 answer:

nikklg [1K]3 years ago

5 0

Answer:

$6,687.50

Step-by-step explanation:

80,250 = paycheck

12 = number of months in a year

80,250 ÷ 12 = 6,687.5

Answer: $6,687.50 is the amount of each of her monthly paychecks.

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(Score for Question 1: _____ of 5 points)

slava [35]

Answer:

$x = 13.8$

Step-by-step explanation:

Given

See attachment for triangle

Required

Find x

To find y, we make use of the relationship between sides lengths 11 & x and angle 37

The relationship is:

$cos(37) = \frac{11}{x}$

i.e.

$cos(\theta) = \frac{Adjacent}{Hypotenuse}$

Make x the subject

$x = \frac{11}{cos(37)}$

$x = \frac{11}{0.7986}$

$x = 13.7741$

$x = 13.8$ -- approximated

7 0

3 years ago

Use Lagrange multipliers to find the maximum and minimum values of (i) f(x,y)-81x^2+y^2 subject to the constraint 4x^2+y^2=9. (i

sp2606 [1]

i. The Lagrangian is

$L(x,y,\lambda)=81x^2+y^2+\lambda(4x^2+y^2-9)$

with critical points whenever

$L_x=162x+8\lambda x=0\implies2x(81+4\lambda)=0\implies x=0\text{ or }\lambda=-\dfrac{81}4$

$L_y=2y+2\lambda y=0\implies2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_\lambda=4x^2+y^2-9=0$

If $x=0$ , then $L_\lambda=0\implies y=\pm3$ .
If $y=0$ , then $L_\lambda=0\implies x=\pm\dfrac32$ .
Either value of $\lambda$ found above requires that either $x=0$ or $y=0$ , so we get the same critical points as in the previous two cases.

We have $f(0,-3)=9$ , $f(0,3)=9$ , $f\left(-\dfrac32,0\right)=\dfrac{729}4=182.25$ , and $f\left(\dfrac32,0\right)=\dfrac{729}4$ , so $f$ has a minimum value of 9 and a maximum value of 182.25.

ii. The Lagrangian is

$L(x,y,z,\lambda)=y^2-10z+\lambda(x^2+y^2+z^2-36)$

with critical points whenever

$L_x=2\lambda x=0\implies x=0$ (because we assume $\lambda\neq0$ )

$L_y=2y+2\lambda y=0\implies 2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1$

$L_z=-10+2\lambda z=0\implies z=\dfrac5\lambda$

$L_\lambda=x^2+y^2+z^2-36=0$

If $x=y=0$ , then $L_\lambda=0\implies z=\pm6$ .
If $\lambda=-1$ , then $z=-5$ , and with $x=0$ we have $L_\lambda=0\implies y=\pm\sqrt{11}$ .

We have $f(0,0,-6)=60$ , $f(0,0,6)=-60$ , $f(0,-\sqrt{11},-5)=61$ , and $f(0,\sqrt{11},-5)=61$ . So $f$ has a maximum value of 61 and a minimum value of -60.

5 0

3 years ago

The table shows the cost of Girl Scout cookies in order to continue the proportional relationship how much would 5 boxes of cook

LUCKY_DIMON [66]

Answer:18.75

Step-by-step explanation: each cookie costs 3.75 so 3.75 times 7= 18.75

3 0

3 years ago

Find the exact circumference of a circle with the given radius 3 1/4

matrenka [14]

20.4 is the exact circumference of the circle

8 0

3 years ago

(8 x 106 ) / (4 x 103 ) = ? <br>(the 10 stands for the 0 in scientific notation)

Kazeer [188]

Answer:

3.2 x 10^12

Step-by-step explanation:

80000000/40000

3 0

3 years ago