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3 years ago

Give the center and radius of the circle. (x - 5)2 + y2 = 16

Mathematics

1 answer:

olasank [31]3 years ago

7 0

Answer:

Centre: (5,0)

Radius: 4

Step-by-step explanation:

r² = 16

r = 4

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Find dy/dx for y=log (tan2x)

nekit [7.7K]

Answer:

$\frac{dy}{dx} = \frac{2}{sin2x cos2x}$

Step-by-step explanation:

y = log (tan 2x)

Applying chain rule:

$\frac{dy}{dx} = \frac{d}{dx} (1st function) . \frac{d}{dx} (2nd function). \frac{d}{dx}(3rd function)$

$\frac{dy}{dx} = \frac{d}{dx} log(tan 2x) . \frac{d}{dx} tan2x. \frac{d}{dx} 2x$

$\frac{dy}{dx} = \frac{1}{tan2x} \times sec^{2}2x \times 2$

$\frac{dy}{dx} = \frac{2sec^{2}2x }{tan2x}$

Now since $sec^{2}x = \frac{1}{cos^{2}x } \ and\ tanx = \frac{sinx}{cosx}$

∴ $\frac{dy}{dx} = \frac{2cos2x }{sin2x cos^22x}$

∴ $\frac{dy}{dx} = \frac{2}{sin2x cos2x}$

7 0

4 years ago

A substance with a half life is decaying exponentially. If there are initially 12 grams of the substance and after 70 minutes th

77julia77 [94]

Answer: 233 min

Step-by-step explanation:

This problem can be solved by the following equation:

$A=A_{o} e^{-kt}$ (1)

Where:

$A=7 g$ is the quantity left after time $t$

$A_{o}=12 g$ is the initial quantity

$t=70 min$ is the time elapsed

$k$ is the constant of decay for the material

So, firstly we need to find the value of $k$ from (1) in order to move to the next part of the problem:

$\frac{A}{A_{o}}=e^{-kt}$ (2)

Applying natural logarithm on both sides of the equation:

$ln(\frac{A}{A_{o}})=ln(e^{-kt})$ (3)

$ln(\frac{A}{A_{o}})=-kt$ (4)

$k=-\frac{ln(\frac{A}{A_{o}})}{t}$ (5)

$k=-\frac{ln(\frac{7 g}{12 g})}{70 min}$ (6)

$k=0.00769995 min^{-1}$ (7) Now that we have the value of $k$ we can solve the other part of this problem: Find the time $t$ for $A=2 g$ .

In this case we need to isolate $t$ from (1):

$t=-\frac{ln(\frac{A}{A_{o}})}{k}$ (8)

$t=-\frac{ln(\frac{2 g}{12 g})}{0.00769995 min^{-1}}$ (9)

Finally:

$t=232.697 min \approx 233 min$

5 0

3 years ago

What is the additive inverse of -61<br>

Airida [17]

Answer:

The additive inverse of -61 is 61. For additive inverse just reverse the sign.

3 0

3 years ago

PLEASE ANSWER QUICKLY I WILL GIVE BRAINLYEST

Agata [3.3K]

Answer:

a) 17

b) 45

Step-by-step explanation:

a) $9+3 x 2^{2} - 1 x 4$

use pemdas first,

$2^{2}\\$ = 4

3x4 = 12

1x4 = 4

now the equation is $9+12 - 4$

9+12 = 21

that makes the equation 21-4

21-4 = 17

a) 17

now for b

the equation would then be $9+3 x (2^{2} - 1) x 4$

so youd use pemdas as always

start in the parenthases

$2^{2}$ = 4

4-1 = 3

the equation is now $9+3 x 3 x 4$

now, multiply 3x3x4

3x3 = 9

9x4 = 36

now the equation is 9+36

9+36 is 45

b) 45

hope this helped!

4 0

2 years ago

Sam is delivering two refrigerators that each weigh 105 kilograms there is an elevator with a weight limit of 1,00 pounds

rosijanka [135]

Question:

Sam is delivering two refrigerators that each weigh 105 kilograms. There is an

elevator with a weight limit of 1,000 pounds. Can he take both refrigerators on the

elevator in one trip? (1 kilogram 2.2 pounds)

Answer: yes he can

Step-by-step explanation:

Yes he can.

He can if the total weight of the 2 refrigerator didn't exceed the weight limit of the elevator.

Therefore:

Since 1 refrigerator weigh 105kg

2 refrigerator = 2 x 105kg = 210kg

The weight limit of the elevator 1000pounds convert to kg.

Since

2.2 pounds = 1kg

1000 pounds = 1000/2.2 kg

=454.55kg

Weight limit of the elevator = 454.55kg.

Since Weight of the 2 refrigerator is less than

weight limit of the elevator, he can take both refrigerators on the elevator in one trip

5 0

3 years ago