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xxTIMURxx [149]

2 years ago

12

A number when divided by 38, leaves quotient 116 and

1 answer:

inessss [21]2 years ago

5 0

104827291 and then add 10404

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2 (2f+2)= help me fast

8_murik_8 [283]

Distribute

2 × 2f + 2 × 2

Simplify 2 × 2f to 4f

4f + 2 × 2

Simplify 2 × 2 to 4

<u>4f + 4</u>

4 0

3 years ago

Read 2 more answers

The digits 2, 3, 4, 7, and 8 are each used once in a random order to form a five-digit number. What is the probability that the

ololo11 [35]

Answer:

23748 or 27348 (as 48 is divisible by 4)

5 0

2 years ago

Andru [333]

Answer:

E. 19

Step-by-step explanation:

z = (5)(11)(2·2·7)(2·19)

z = 2³·5·7·11·19

The greatest prime factor is 19.

4 0

2 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

2 years ago

Translate this sentence into an equation.

mr Goodwill [35]

Answer:

r - 12 = 74

Step-by-step explanation:

The difference between his height with 12 would signify subtraction with 12, and that difference is 74. Meaning, his height, minus 12, would equal 74.

6 0

2 years ago