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IgorC [24]
3 years ago
14

A rotating lawn sprinkler sprays water in a circular area of grass. the Diameter of the grass shown is 10 feet. What is the area

of the grass covered by the sprinkler water?
Mathematics
2 answers:
julia-pushkina [17]3 years ago
6 0

Answer:

The area of the grass covered by the sprinkler water is approximately 78.54 feet^2

dedylja [7]3 years ago
3 0

Answer:

78.54 feet

Step-by-step explanation:

10 is the diameter so 5 is the radius,

A = πr2 = π·52 ≈ 78.53982

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Base: z(x)=cosx Period:180 Maximum:5 Minimum: -4 What are the transformation? Domain and Range? Graph?
garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is z'(x) = \frac{1}{2}  + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right).

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be z (x) = \cos x the base formula, where x is measured in sexagesimal degrees. This expression must be transformed by using the following data:

T = 180^{\circ} (Period)

z_{min} = -4 (Minimum)

z_{max} = 5 (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of 2\pi radians. In addition, the following considerations must be taken into account for transformations:

1) x must be replaced by \frac{2\pi\cdot x}{180^{\circ}}. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

\Delta z = \frac{z_{max}-z_{min}}{2}

\Delta z = \frac{5+4}{2}

\Delta z = \frac{9}{2}

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

z_{m} = \frac{z_{min}+z_{max}}{2}

z_{m} = \frac{1}{2}

The new function is:

z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)

Given that z_{m} = \frac{1}{2}, \Delta z = \frac{9}{2} and T = 180^{\circ}, the outcome is:

z'(x) = \frac{1}{2}  + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

8 0
3 years ago
Factor completely:
maw [93]

Answer:

d

Step-by-step explanation:

Given

12x^{5} + 6x³ + 8x² ← factor out 2x² from each term

= 2x²(6x³ + 3x + 4) → d

7 0
3 years ago
What is the following product? 3^sqr4 * sqr3​
Nina [5.8K]

Answer:

9sqrt3

Step-by-step explanation:

This is an order of operations question.

First, simply the exponent, which gives you 3^2*sqrt3

Next, 3^2=9, giving the final answer of 9sqrt3.

3 0
3 years ago
Choose all the factors of 12. (Check all that apply.) multiple choice
ira [324]

Answer:

Hey!!!!

the answers are 2, 6, 3, 12, 4, 1

Please read the explanation... it always helps..

Step-by-step explanation:

Alrighty... let's begin....

A factor is any number that you can multiply by another number to get a product

So choose the numbers you can mutiply by another number to get twelve... which are...  2, 6, 3, 12, 4, 1

if you are wondering why twelve well... 12 x 1 = 12

i hope this helps!!!!

7 0
2 years ago
Read 2 more answers
Q. If A is a square matrix such that A² = A, then write the value of 7 A −(I + A)³, where I is an identity matrix.​
andriy [413]

Answer:

7A−(I + A)³

=7A−(1³ + A³ +3.I.A² +3.1².A)

=7A−(I+ A².A+3A² +34)

= 7A-(I+A.A+3A+34) (*: A² = A)

=7A-(I+ A² +6A)

= 7A-(I+A+64)

=7A-(1+7A)

=7A-I-7A

=-1

6 0
2 years ago
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