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marishachu [46]
3 years ago
7

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

Mathematics
1 answer:
rusak2 [61]3 years ago
3 0
A^2 = 16
a^2 = 4^2
a = 4

answer:<span> side length = 4 unit</span>
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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:

<u>Calculus</u>

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:

<u>Step 1: Define</u>

<em>Identify.</em>

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

<u>Step 2: Integrate</u>

  1. [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
  2. [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
  3. [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}}
  4. 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
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