. What part of an hour is your school lunch time?

Explain why each of the following integrals is improper. (a) 4 x x − 3 dx 3 Since the integral has an infinite interval of integ

erma4kov [3.2K]

Answer:

a

Since the integral has an infinite discontinuity, it is a Type 2 improper integral

b

Since the integral has an infinite interval of integration, it is a Type 1 improper integral

c

Since the integral has an infinite interval of integration, it is a Type 1 improper integral

d

Since the integral has an infinite discontinuity, it is a Type 2 improper integral

Step-by-step explanation:

Considering a

$\int\limits^4_3 {\frac{x}{x- 3} } \, dx$

Looking at this we that at x = 3 this integral will be infinitely discontinuous

Considering b

$\int\limits^{\infty}_0 {\frac{1}{1 + x^3} } \, dx$

Looking at this integral we see that the interval is between $0 \ and \ \infty$ which means that the integral has an infinite interval of integration , hence it is a Type 1 improper integral

Considering c

$\int\limits^{\infty}_{- \infty} {x^2 e^{-x^2}} \, dx$

Looking at this integral we see that the interval is between $-\infty \ and \ \infty$ which means that the integral has an infinite interval of integration , hence it is a Type 1 improper integral

Considering d

$\int\limits^{\frac{\pi}{4} }_0 {cot (x)} \, dx$

Looking at the integral we see that at x = 0 cot (0) will be infinity hence the integral has an infinite discontinuity , so it is a Type 2 improper integral

7 0

2 years ago

23=30-g;6,7,8 what is the solution

Naya [18.7K]

7
30-7=23
7=g
Solve the equaton backwards to get the answer

3 0

2 years ago

x+2y+2z=3. 2x-2y-z=3. x-2z=-5

d1i1m1o1n [39]

Answer:

x = 1, y = -2, z = 3.

Step-by-step explanation:

x + 2y + 2z = 3 A

2x -2y - z = 3 B

x - 2z = -5 C

If we add equations A and B we eliminate y:

3x + z = 6 E

Multiply E by 2 :

6x + 2z = 12 F

Adding C and F we get:

7x = 7

x = 1.

Plug this into equaton C:

1 - 2z = -5

-2z = -5 - 1 = -6

z = 3.

Now plugging x = 1 and z = 3 in equation A:

1 + 2y + 2(3) = 3

2y = 3 - 1 - 6 = -4

y = -2.

8 0

2 years ago

Frank is making a pennant in the shape of a triangle for his senior class photo. He wants the base length of this triangle to be

Sav [38]

Answer:

Height should be ≤ 9 inches.

Step-by-step explanation:

Given:

Frank is making a pennant in the shape of a triangle for his senior class photo.

Base of triangle = 6 in

Area of triangle ≤ 27 $in^2$

Let height of the triangle be h

Now we now that,

Area of triangle = $\frac{1}{2}\times base \times height$

$\frac{1}{2}\times 6 \times h \leq 27\\\\3h\leq 27\\\\h\leq \frac{27}{3}\\\\h\leq 9 \ in.$

Hence the height of the triangle must be at most or ≤ 9 inches.

5 0

2 years ago

I have a water tank that holds 5 gallons of water I drink 4 pints of water a day how many full tanks of water I will be drinking

julsineya [31]

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4 0

2 years ago