How many ways can the letters of the word ORGANISM be arranged so the third letter is G?

Answers

Answer 1

Answer: 7 to 8 i think............................

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Ex 3.7
12. find the area between the curve y=x³-2 and the y-axis between y= -1 and y=25

Answers

$y=x^3-2\nx^3=y+2\nx=\sqrt[3]{y+2}\n\n\int \limits_(-1)^(25)\sqrt[3]{y+2}\, dy=\n\int \limits_(-1)^(25)(y+2)^{\tfrac{1}{3}}\, dy=\n\left[\frac{(y+2)^{\tfrac{4}{3}}}{(4)/(3)} \right]_(-1)^(25)=\n$
$\left[(3)/(4)(y+2)^{\tfrac{4}{3}} \right]_(-1)^(25)=\n\left[(3)/(4)(y+2)\sqrt[3]{y+2} \right]_(-1)^(25)=\n(3)/(4)(25+2)\sqrt[3]{25+2}-\left((3)/(4)(-1+2)\sqrt[3]{-1+2}\right)=\n(3)/(4)\cdot27\sqrt[3]{27}-\left((3)/(4)\sqrt[3]{1}\right)=\n(3)/(4)\cdot27\cdot3-(3)/(4)=\n(3)/(4)(81-1)=\n(3)/(4)\cdot 80=\n3\cdot20=\n60$

Yeah, you'd have to use the inverse function to produce this result.

Let's get the inverse function first:

$y={ x }^( 3 )-2\n \n { x }^( 3 )=y+2\n \n x=\sqrt [ 3 ]{ y+2 }$

$\n \n \therefore \quad { f }^( -1 )\left( x \right) =\sqrt [ 3 ]{ x+2 }$

Now, we can solve the problem using:

$\int _( -1 )^( 25 ){ \sqrt [ 3 ]{ x+2 } } dx$

But to solve the problem more easily we make u=x+2, therefore du/dx=1, therefore du=dx.

When x=25, u=27.

When x=-1, u=1.

Now:

$\int _( 1 )^( 27 ){ { u }^{ \frac { 1 }{ 3 } } } du\n \n ={ \left[ \frac { 3 }{ 4 } { u }^{ \frac { 4 }{ 3 } } \right] }_( 1 )^( 27 )$

$\n \n =\frac { 3 }{ 4 } \cdot { 27 }^{ \frac { 4 }{ 3 } }-\frac { 3 }{ 4 } \cdot { 1 }^{ \frac { 4 }{ 3 } }\n \n =\frac { 3 }{ 4 } { \left( { 3 }^( 3 ) \right) }^{ \frac { 4 }{ 3 } }-\frac { 3 }{ 4 }$

$\n \n =\frac { 3 }{ 4 } \cdot { 3 }^( 4 )-\frac { 3 }{ 4 } \n \n =\frac { 3 }{ 4 } \left( { 3 }^( 4 )-1 \right)$

$\n \n =\frac { 3 }{ 4 } \cdot 80\n \n =60$

Answer: 60 units squared.

20x3 + 12x2 + 5x + 3

Answers

i hope this helps you

Answer: ( 5x+3) (4x2 (squared) + 1)

Step-by-step explanation:

On Monday, Maria leaves her house for work and heads 20° east of north for 11 miles. On Tuesday, Maria visits her friend before work. Maria's friend's house is 6 miles away from hers at 10° south of west. How far does Maria's friend live from her work? Round the answer to the nearest tenth. A. 9.2 miles B. 10.6 miles C. 12.5 miles D. 14.9 miles

Answers

The answer to this question is 14.9 miles.

Simplify: 8x - 6(5x + 6)

Answers

Answer:

-22x-36

Step-by-step explanation:

-6 x 5x = -30x

-6 x 6 =-36

8x - 30x - 36

8x - 30x = - 22x

So, it's -22x - 36.

Answer:

-22 x- 36

Step-by-step explanation:

8x - 6(5x + 6)

-6× 5x= -30x

-6 × 6= -36

8x -30x - 36

-22x - 36

What is the greatest common factor of the pair of numbers?312 and 444

Question 10 options:

3

6

9

12

Answers

The GCF of 312 and 444 is 12.

The sum of the roots of the equation (1/2)x^2-(5/4)x-3=0

a.5/2
b.2
c.1/2

Answers

(1/2)x² - (5/4)x - 3 = 0

0.5x² - 1.25x - 3 = 0

Comparing to the quadratic function, ax² + bx + c = 0,
a = 0.5, b = -1.2, c = -3.

Sum of roots = -b/a = -(-1.25)/0.5 = 1.25/0.5 = 2.5

2.5 = 5/2 Option (a)

A)5/2 is the answer.

Other Questions

Orlando invested $16,000 in an eight-year CD bearing 6.5% interest, but needed to withdraw $3,500 after five years. If the CD’s penalty for early withdrawal was one year’s worth of interest on the amount withdrawn, when the CD reached maturity, how much less money did Orlando earn total than if he had not made his early withdrawal?a. $227.50 b. $682.50 c. $910.00 d. $455.00

120/180 in simplest form

What value of c makes x^2 +5x+c a perfect square.

Factor x2 + 11x + 24A. (x + 6)(x + 4) B. (x + 2)(x + 12) C. (x + 3)(x + 8) D. (x + 1)(x + 11) Factor 2m2 + 27m + 70 A. (2m + 7)(m + 10) B. (m + 10)(2m + 7) C. (2m + 3)(m + 20) D. (2m + 7)(m – 10) Factor g2 – 64 A. (g – 1)(g + 64) B. (g + 8)(g – 8) C. (g – 8)(g – 8) D. (g + 8)(g + 8) Factor 49t2 – 9 A. (7t + 3)(7t + 3) B. (7t + 3)(–7t – 3) C. (7t + 3)(7t – 3) D. 7t – 3 The area of a rectangular field is given by the trinomial t2 – 4t – 45. The length of the rectangle is t + 5. What is the expression for the width of the field? A. t – 9 B. t – 5