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2 months ago

Find all points on the circle (x^2) + (y^2) = 676 where the slope is 5/12

1 answer:

8 0

Implicit differentiation: remember that dy/dx y = dy/dx, so take the derivative of both sides. To solve for the derivative, subtract 2x from both sides, then divide by 2y. When considering the slope, solve for it and determine where the circle intersects with the line. Substitute for y and proceed by multiplying both sides. Take the square root of both sides, accounting for both positive and negative roots, leading to x = ±10. Thus, the points located are (10,-24) and (-10,24).

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Simplify the given expression, using only positive exponents. Then complete the statements that follow. [ (x2y3)−1 (x−2y2z)2 ] 2

AnnZ [12381]

Answer: y²z⁴ / x¹²

The exponent for x is 12

The exponent for y is 2

The exponent for z is 4

Explanation:

1) The expression to simplify:

$((x^2y^3)^{-1}(x^{-2}y^2z)^2)^2$

2) Rule: power of a power:

$(x^{-4}y^{-6})(x^{-8}y^8z^4)$

3) Rule: product of powers with identical bases

$x^{(-2-8)}y^{(-6+8)}z^4$

4) Add up the exponents

$x^{-12}y^2z^4$

5) Transfer the negative exponent to the denominator:

$\frac{y^2z^4}{x^{12}}$

The exponent attached to x is 12, for y it is 2, and for z it is 4.

4 0

2 months ago

Read 2 more answers

We flip a fair coin five times. For every heads you pay me $1 and for every tails I pay you $1. Let X denote the my net winning

AnnZ [12381]

The probability mass function of X equals 0.03. To clarify:
Assuming the requirement for winning is one side as heads and the opposing side as tails, the likelihood of both outcomes is 1/2 or 0.5. Thus, we can construct a graph to calculate all probabilities related to achieving heads. In this context, X indicates the dollar amounts won during the coin flips, while the probability of heads reflects the likelihood of each outcome and the potential winnings. The chances of winning decrease as the winning amount rises.

8 0

2 months ago

Stackable polystyrene cups have a height h1=12.5 cm. Two stacked cups have a height of h2=14 cm. Three stacked cups have a heigh

AnnZ [12381]

Answer:

Approximately 59 stacked cups.

Step-by-step explanation:

We have the following measurements:

Height of one cup = 12.5 cm,

Height of two cups stacked = 14 cm,

Height of three cups stacked = 15.5 cm,

...and so on.

This situation can be described by an arithmetic sequence,

12.5, 14, 15.5,....

The first term is defined as a = 12.5,

with a common difference of d = 1.5 cm.

Thus, the height of x stacked cups is given by

$h(x) = a+(x-1)d = 12.5 + (x-1)1.5 = 1.5x + 11$

As per the problem,

h(x) = 200

⇒ 1.5x + 11 = 200

⇒ 1.5x = 189

⇒ x = 59.3333333333 ≈ 59.

Therefore, you will need approximately 59 stacked cups.

3 0

3 months ago

Read 2 more answers

a falling object travels a distance given by the formula d=5t + 16t^2 ft, where t is measured in seconds. how long will it take

zzz [12365]

It is provided that

$d=5t+16t^{2}$

We need to determine t when d equals 74

Thus, $74=5t+16t^{2}$ or

$16t^{2}+5t-74 = 0$

$16t^{2}+37t-32t-74 = 0$

t(16t + 37) - 2(16t + 37) = 0

(t - 2)(16t + 37) = 0

t - 2 = 0 or 16t + 37 = 0

t cannot be negative.

Thus, t equals 2

Therefore, it will require 2 seconds for the object to cover 74 feet.

8 0

3 months ago

Read 2 more answers

The Freeman family is barbecuing veggie burgers, corn cobs, and mushroom caps in their local park. If 3/8 of the items barbecued

AnnZ [12381]

Answer:

7/24

Step-by-step explanation:

All the items being grilled collectively equal 1.

Each item represents a fractional portion of 1.

Combine 3/8 and 1/3, then subtract that sum from 1.

3/8 + 1/3 = 9/24 + 8/24 = 17/24

This means that veggie burgers and corn contribute to 17/24 of the total.

To determine the fraction accounted for by mushrooms, we take 1 and subtract 17/24.

1 - 17/24 = 24/24 - 17/24 = 7/24.

Final answer: 7/24

8 0

3 months ago