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ANTONII [103]
3 years ago
5

D(t) = 50 – 23 sin (11 (t +0.23)).

Mathematics
1 answer:
dlinn [17]3 years ago
4 0

Answer:

0.0566 units of time

Step-by-step explanation:

The average value for the depth of the waves is 50 and occurs when sin (11 (t +0.23)) = 0. It is known that sin(π) = 0, therefore:

sin (11 (t +0.23)) = sin(\pi)\\11t+2.53=\pi\\t=0.0556\ units

Since the units of time used were not specified, the first time the depth of the waves is at its average value is 0.0566 units of time after she starts measuring.

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In the diagram, the radius of the outer circle is
JulijaS [17]

the value of x is 8 cm.

<u>Step-by-step explanation:</u>

Correct Question : In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded region is 220π cm2. What is the value of x? Enter your answer in the box.

We have ,

the area of a circle =  πr²

the outer circle area = \pi(2x)^2 =4\pi x^2

the inside circle area = \pi (6)^2= 36\pi

According to Question,

the outer circle area - the inside circle area = he shaded region

⇒ \pi (4x^2)-36\pi =220\pi

⇒ x^2-9 =55

⇒ x^2=64

⇒x =\sqrt{64}=8

Therefore , the value of x is 8 cm.

5 0
3 years ago
Determine which numbers could not be used to represent the probability of an event. Select all that apply. A. StartFraction 64 O
vova2212 [387]

Answer:

A. \frac{64}{25} ​, because probability values cannot be greater than 1.

C. -1.5, because probability values cannot be less than 0.

Step-by-step explanation:

Probability is the extent to which an event is likely to happen. It ranges from 0(impossible) to 1(certain). Probability values can be written in decimal form or in fractional form.

The following numbers could not be used to represent the probability of an event.

A. \frac{64}{25} ​, because probability values cannot be greater than 1.

C. -1.5, because probability values cannot be less than 0.

6 0
3 years ago
What is the least common multiple (LCM) that could be
tensa zangetsu [6.8K]

Answer:

the greatest common factor will be 3

8 0
3 years ago
Solve this equation for x: 2x^2 + 12x - 7 = 0
zhannawk [14.2K]

Answer:

x=0.5355 or x=-6.5355

First step is to: Isolate the constant term by adding 7 to both sides

Step-by-step explanation:

We want to solve this equation: 2x^2 + 12x - 7 = 0

On observation, the trinomial is not factorizable so we use the Completing the square method.

Step 1: Isolate the constant term by adding 7 to both sides

2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7

Step 2: Divide the equation all through by the coefficient of x^2 which is 2.

x^2 + 6x=\frac{7}{2}

Step 3: Divide the coefficient of x by 2, square it and add it to both sides.

Coefficient of x=6

Divided by 2=3

Square of 3=3^2

Therefore, we have:

x^2 + 6x+3^2=\frac{7}{2}+3^2

Step 4: Write the Left Hand side in the form (x+k)^2

(x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\

Step 5: Take the square root of both sides and solve for x

x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355

6 0
3 years ago
PLS HELP!<br> solve by completing the square<br> x²+4x=8
masya89 [10]

Step-by-step explanation:

x²+4x=8

rearrange

x² + 4x - 8 = 0

half of 4 is 2

so

x² + 4x + 2² - 2² - 8 = 0

do x² + 4x + 2²

multiplies to give 4 adds to give 4

2+ 2

(x + 2)²

(x + 2)² - 2² - 8

(x + 2)² - 4 - 8

(x + 2)² - 12

(x + 2 + √12) (x + 2 - √12)

√12 = √4 * √3 = 2 √3

(x + 2 + 2√3) (x + 2 - 2√3)

4 0
2 years ago
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