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Ipatiy [6.2K]
3 years ago
8

96 is 32 percent of what number

Mathematics
1 answer:
deff fn [24]3 years ago
8 0

32% of 300 is 96. 100% of 300 is 32 percent of 300 equals 96 so it is 300

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What is the solution to the trigonometric inequality 2sin(x)+3>sin ^2(x) over the interval
navik [9.2K]

The intervals that satisfy the given trigonometric Inequality are; 0 ≤ x < 3π/2 and 3π/2 < x ≤ 2π

<h3>How to solve trigonometric inequality?</h3>

We are given the trigonometric Inequality;

2 sin(x) + 3 > sin²(x)

Rearranging gives us;

sin²(x) - 2 sin(x) - 3 < 0

Factorizing this gives us;

(sin(x) - 3)(sin(x) + 1) < 0

Thus;

sin(x) - 3 = 0 or sin(x) + 1 = 0

sin(x) = 3 or sin(x) = -1

sin(x) = 3 is not possible because sin(x) ≤ 1.

Thus, we will work with;

sin(x) = -1 for the interval 0 ≤ x ≤ 2π radians.

Then, x = sin⁻¹(-1)

x = 3π/2.

Now, if we split up the solution domain into two intervals, we have;

from 0 ≤ x < 3π/2, at x = 0. Then;

sin²(0) - 2 sin(0) - 3

= 0² - 0 - 3

= -3 < 0

Thus, the interval 0 ≤ x < 3π/2 is true.

From 3π/2 < x ≤ 2π, take x = 2π. Then;

sin²(2π) - 2 sin(2π) - 3

= 0² - 0 - 3

= -3 < 0

Thus, the interval 3π/2 < x ≤ 2π is also true.

Read more about trigonometric inequality at; brainly.com/question/27862380

#SPJ1

3 0
1 year ago
When a sprinkler is installed in the ground, the spray of water goes up and falls in the pattern of a parabola. The height, in i
Westkost [7]

Answer:

(1) 256 inches

(2) 5 feet

(3) 400 inches

(4) 10 feet

Step-by-step explanation:

(1) The function that gives the height in inches of the spray of water at a distance <em>x</em> from the sprinkler head is given as follows;

h(x) = 160·x - 16·x²

At x = 2 feet, we have;

h(2) = 160 × 2 - 16 × 2² = 256

Therefore, the height of the spray water at a horizontal distance of 2 feet from the sprinkler head h(2) = 256 inches

(2) The x-coordinate, x_{max}, of the maximum point of a parabola given in the form, y = a·x² + b·x + c is found using the following formula;

x_{max} = -b/(2·a)

The x-coordinate, x_{max}, of the maximum point of the given equation of the parabola, h(x) = 160·x - 16·x², (a = -16, b = 160) is therefore;

x_{max} = -160/(2 × (-16)) = 5

Therefore, the number of feet along the way, the function will reach maximum height, x_{max} = 5 feet

(3) The function, h(x) = 160·x - 16·x², will reach maximum height, h_{max}, at x = 5, therefore;

h_{max} =  h(5) = 160 × 5 - 16 × 5² = 400

The maximum height of the spray, h_{max} = 400 inches

(4) The water is at ground level where h(x) = 0, therefore;

At ground level, h(x) = 0 = 160·x - 16·x²

160·x - 16·x² = 0

∴ 16·x × (10 - x) = 0

By zero product rule, we 16·x = 0, or (10 - x)  = 0, from which we have;

x = 0, or x = 10

The water is at ground level at x = 0 and x = 10 feet, therefore, the water will hit the ground again (the second time after leaving the sprinkler head at x = 0) at x = 10 feet.

7 0
3 years ago
Estimate a 15% tip on a dinner bill of 71.85
Step2247 [10]
15% = 0.15
15% of 71.85 is equal 0.15*71.85 ≈ 10.78
4 0
3 years ago
Which of the following is NOT equivalent to 22/7?
jasenka [17]

Answer:

the option c is the answer for this question

5 0
2 years ago
Can someone help me with this
GREYUIT [131]

Answer:

2 5/5 is the anwser

Step-by-step explanation:

5 0
2 years ago
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