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lorasvet [3.4K]
2 years ago
6

What is the answer to 7/2

Mathematics
2 answers:
SashulF [63]2 years ago
8 0

Your correct answer would be 3.5

Mariana [72]2 years ago
3 0

3.5 is the correct answer.

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What are the coordinates of the hole in the graph of the function f(x)?
jonny [76]

Answer:

The coordinates are (2,8)

Step-by-step explanation:

A hole is where both the numerator and the denominator are zero

f(x)=x^2+4x−12 / x−2

Factor the numerator

f(x) = (x+6) (x-2)/ (x-2)

The hole will occur where x-2 =0

x-2=0

Add 2 to each side

x-2+2 =0+2

x=2

There is a hole at x=2

If we could cancel the x-2 values from the top and bottom, we are left with

f(x) = x+6

At x=2

f(2) = 6+2

f(2) would be 8

The coordinates are (2,8)

There is a hole

8 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
You can afford a $1350 per month mortgage payment. You’ve found a 30 year loan at 7% interest.
Mice21 [21]
A) 45 because 1350 divide by 30 equals 45. So 45 dollars u can afford

B) 1350 because 45 x 30 = 1350


C) 7% because it’s 7% to begin with
4 0
3 years ago
The angles of a triangle are in the ratio 5:3:7 find the angles
omeli [17]

Answer:

60, 36, 84

Step-by-step explanation:

The angles of a triangle always add up to 180 degrees.

If the ratios are 5:3:7, that means that there are 15 pieces that we can break up the 180 degrees by.

180/15 = 12

Each value is 'worth' 12 degrees.

Thus the angles would be the ratios multiplied by 12.

5 x 12 = 60

3 x 12 = 36

7 x 12 = 84

3 0
3 years ago
What is 223 rounded to the nearest ten
ASHA 777 [7]
1. The number '2' is located in the tens place

2. Since the number '3' is located in the ones place, it's telling the number '2' to stay the same

Stays the Same: 1,2,3,4
Goes Up: 5,6,7,8,etc

223 ⇒ 220
4 0
3 years ago
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