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2 years ago

T

Mathematics

1 answer:

weqwewe [10]2 years ago

4 0

Answer:

Step-by-step explanation:

140 - 56 = 84 bottles

5 - 2 = 3 minutes

84 / 3 = 28 bottles per minute

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Answer the questions about the following function.

balandron [24]

Answer:

Step-by-step explanation:

(a) The function ...

$f(x)=\dfrac{16x^{2}}{x^{4}+64}$

can be evaluated for x=-2√2 to get ...

$\displaystylef(-2\sqrt{2})=\frac{16(-2\sqrt{2})^{2}}{(-2\sqrt{2})^4+64}=\frac{128}{64+64}=1$

The point (-2√2, 1) is on the graph of f(x).

(b) Likewise, we can evaluate for x=2:

$f(2)=\dfrac{16\cdot 2^2}{2^4+64}=\dfrac{64}{80}=0.8$

The point on the graph is (2, 0.8).

(c) From part (a), we know that f(-2√2) = 1. Since the function is even, this means that f(2√2) = 1. The graph is a maximum at those points, so there are no other values for which f(x) = 1.

The points (±2√2, 1) are on the graph.

(d) There are no values of x for which f(x) is undefined. The domain is all real numbers.

(e) The only x-intercept is at the origin, (0, 0). The x-axis is a horizontal asymptote.

(f) The only y-intercept is at the origin, (0, 0).

8 0

3 years ago

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Lydia earned $9.75 per hour last summer. She worked 25 hours a week. About how much did she earn in 8 weeks.

Kay [80]

Lydia earned $1,950 in 8weeks

5 0

4 years ago

(Q7) Determine the graph of the polar equation r = 12/6+4 cos theta.

masya89 [10]

ANSWER

b.

EXPLANATION

The given polar equation is,

$r = \frac{12}{6 + 4 \cos( \theta) }$

Cross multiply to get,

$r(6 + 4 \cos( \theta) ) = 12$

$6r + 4r\cos( \theta) ) = 12$

Substitute,

$r\cos( \theta) = x$

and

$r = \sqrt{ {x}^{2} + {y}^{2} }$

$6 \sqrt{ {x}^{2} + {y}^{2} } + 4x = 12$

$3\sqrt{ {x}^{2} + {y}^{2} } + 2x = 6$

$3\sqrt{ {x}^{2} + {y}^{2} } = 4 - 2x$

$9({x}^{2} + {y}^{2}) =( 4 - 2x ) ^{2}$

$9{x}^{2} + 9 {y}^{2} =16 - 16x + 4x ^{2}$

$5{x}^{2} + 9 {y}^{2} + 16x = 16$

This is an ellipse whose center is shifted to the left with orientation on the x-axis

The correct choice is B.

8 0

4 years ago

What is the square root of 3

KiRa [710]

Answer: 1.73205080757

Step-by-step explanation: The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is more precisely called the principal square root of 3, to distinguish it from the negative number with the same property. It is denoted by √3. The square root of 3 is an irrational number.

8 0

3 years ago

The diameter of a lake is 20 meters. I swim half way around the lake. How far did I swim?

MrRa [10]

Swimming half way around implies half of the circumference.

Circumference = pi x diameter

C = pi x 20

C = 20pi

20pi / 2 = 10pi

You swam 10pi meters = 31.42 meters.

Hope this helps!! :)

7 0

3 years ago

Read 2 more answers