Find the missing side length,when the area is 16 square units

Prove the divisbility of the following numbers.

Anastaziya [24]

Answer:

3^16

Step-by-step explanation:

12^8 * 9^12

Rewrite 12 as 3*4 and 9 as 3*3

(3*4)^8 * (3*3)^12

We know that (ab)^c = a^c * b^c

3^8 4^8 3^12 3^12

We can write 4 as 2^2

3^8 2^2^8 3^12 3^12

We know a^b^c = a^(b*c)

3^8 2^(2*8) 3^12 3^12

3^8 2^(16) 3^12 3^12

We also know that a^b *a^c *a^d = a^(b+c+d)

2^(16) 3^8 3^12 3^12

2^(16) 3^(8+12+12)

2^16 3^(32)

But we need 6 ^16 so we will need a 3^16 3^32 = 3^16 * ^16 (16+16=32)

2^16 *3^16 *3^16

Remember a^b*c^b = (ac)^b

(2*3)^16 3^16

6^16 3^16

7 0

2 years ago

Evaluate the definite integral from pi/3 to pi/2 of (x+cosx) dx

Vadim26 [7]

Answer:

$\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{5 \pi ^2}{72} + 1 - \frac{\sqrt{3}}{2}$

General Formulas and Concepts:

Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx$

Step 2: Integrate

[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {x} \, dx + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx$
[Left Integral] Integration Rule [Reverse Power Rule]: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx$
[Right Integral] Trigonometric Integration: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \sin x \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}}$
Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{5 \pi ^2}{72} + \bigg( 1 - \frac{\sqrt{3}}{2} \bigg)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

3 0

1 year ago

Read 2 more answers

F(x) = x2 + 7, what is the equation for f–1(x)?

melomori [17]

F-1(x) = (x-7) / 2, you can get this by taking 2x + 7, and doing the opposite operations on x. you also need to go in the reverse direction of Order of Operations. So first, we take 7 away from x, since subtraction is opposite from addition, and it is the last thing we would do in order of operations. next we only have the 2 multiplier left, so we put the x-7 in parenthesis, and divide by 2.

6 0

3 years ago

Jeremy made 2 quarts of lemonade which expression can be use to find the number of fluid ounces of lemonade jerry made

djverab [1.8K]

32oz make 2 quart.Because 4 Quart is one gallon.

4 0

3 years ago

Find the solutions of the form x=a,y=0and x=0 ,y=b for the following equations: 2x+5y=10 and 2x+3y=6. is there any common soluti

Arlecino [84]

Answer:

x=0 and y=2

Step-by-step explanation:

We have been given system of equations:

2x+5y=10 (1)

And 2x+3y=6 (2)

Subtract equation (2) from(1) we get:

2y=4

y=2

Now, substitute y=2 in equation(2) we get:

2x+3(2)=6

2x+6=6

2x=0

x=0

Hence, x=0 and y=2

8 0

3 years ago