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3 years ago

the point (4,0) lies on a circle with the center at the orgin. what is the area of the circle to the nearsest hundreth?

Mathematics

1 answer:

kvasek [131]3 years ago

3 0

Answer:

50.27 units²

Step-by-step explanation:²

The standard equation of a circle with center at the origin is x² + y² = r², where r is the radius. Substituting 4 for x and 0 for y yields 4² + 0² = r², so we see immediately that r = 4 units.

The formula for the area of a circle is A = πr².

Here, with r = 4, the area is A = π(4 units)² = 16π units², or

50.27 units² to the nearest hundredth.

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Let z be the product of any 5 consecutive three digit odd natural numbers. When you multiply

Charra [1.4K]

Answer:

Step-by-step explanation:

If x is the middle number of the 5 consecutive odd numbers, their product is ...

x(x -2)(x +2)(x -4)(x +4) = x(x² -4)(x² -16) = x⁵ -20x³ +64x

The first 3-digit prime is 101, so the product of that with this is ...

101(x⁵ -20x³ +64x) = 101x⁵ -2020x³ +6464x

Since we're only interested in the units digit, we can find the mod 10 value of this to be ...

(x⁵ +4x) mod 10

Possible units digits of x are 1, 3, 5, 7, 9, so possible units digits of this product are ...

x(x⁴ +4) = 1(1⁴ +4) = 5

3(3⁴ +4) = 3(1 +4) = 5 . . . . mod 10

5(5⁴ +4) = 5(5 +4) = 5 . . . . mod 10

7(7⁴ +4) = 7(1 +4) = 5 . . . . mod 10

9(9⁴ +4) = 9(1 +4) = 5 . . . . mod 10

In every case, the units digit of 101z will be 5.

4 0

2 years ago

What is 89 divide into 4356

ValentinkaMS [17]

Divide 89 by 4356
$\frac{89}{4356}$ = 0.02 is the answer

6 0

3 years ago

Read 2 more answers

PICK ME!!! Abel uses a probability simulator to roll a six-sided number cube 100 times and to flip a coin 100 times. The results

tatuchka [14]

I think it is 1/3 but I am not sure. Sorry if wrong.

4 0

3 years ago

What is the equation of the sinusoid shown in the graph?

ololo11 [35]

Answer:

<em>Answer: C</em>

Step-by-step explanation:

<u>The Cosine Function</u>

The graph of a cosine function is a sinusoid that starts at its maximum value of 1 at x=0 and takes x=2π radians to complete a full cycle. The function of the parent cosine function is:

$y=\cos x$

Both the amplitude A and the angular frequency w of a cosine can be modeled by the function

$y=A\cos(\omega x)$

The graph of the cosine function shown in the figure has an amplitude of A=3 and it completes a full cycle at x=π/2, thus:

$\frac{\pi}{2}\omega =2\pi$

Thus:

$\omega = 4$

Therefore, the equation of the sinusoid is:

$y=3\cos (4x)$

Answer: C

3 0

3 years ago

Read 2 more answers

Sarah has 284 coins in a piggy bank with a total value of $22.78. Sarah has 173 pennies, 5 more dimes than nickels, the rest are

pickupchik [31]

Let P = number of coins of pennies (1 penny = 1 cent)
Let N = number of coins of nickels (1 nickel = 5 cents)
Let D = number of coins of dimes (1 dime = 10 cents)
Let Q = number of coins of quarters (1 quarter = 25 cents)

a) P + N + D + Q = 284 coins, but P = 173 coins, then:
173 + N + D + Q =284 coins
(1) N + D + Q = 111 coins

b) D = N + 5 OR D - N =5 coins
(2) D - N = 5 coins

c) Let's find the VALUE in CENTS of (1) that is N + D + Q = 111 coins
5N + 10D + 25 Q = 2,278 - 173 (1 PENNY)
(3) 5N + 10D + 25Q = 2105 cents
Now we have 3 equation with 3 variables:

(1) N + D + Q = 111 coins
(2) D - N = 5 coins
(3) 5N + 10D + 25Q = 2105 cents
Solving it gives:
17 coins N ( x 5 = 85 cents)
22 coins D ( x 10 = 220 cents)
72 coins D ( x 25 = 1,800 cents)
and 173 P,
proof:
that makes a total of 85+2201800+172 =2,278 c or $22.78

7 0

3 years ago