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3 years ago

What is the slope of y-intercept of this line? y=-6x+2

Mathematics

1 answer:

matrenka [14]3 years ago

4 0

The slope is -6
The y-intercept is 2
Y=mx+b
M= slope
B= y-intercept

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A spherical block of ice melts so that its surface area decreases at a constant rate: ds/dt = - 8 pi cm^2/s. calculate how fast

sveticcg [70]

The rate a which the surface area, S, decreases is
$\frac{dS}{dt} =-8 \pi \, cm^{2}/s$

The surface area is
S = 4πr²
where r = the radius at time t.

Therefore
$\frac{dS}{dt} = \frac{dS}{dr} \frac{dr}{dt} =8 \pi r \frac{dr}{dt} \\\\ -8 \pi = 8 \pi r \frac{dr}{dt} \\\\ \frac{dr}{dt} =- \frac{1}{r}$

When r = 3 cm, obtain
$\frac{dr}{dt}]_{r=3} = - \frac{1}{3} \, cm/s$

Answer: -1/3 cm/s (or -0.333 cm/s)

5 0

3 years ago

A 18,000 gallon swimming pool contains 7,000 gallons of water when a hose is placed into the pool and begins adding water at a r

SOVA2 [1]

In 3 hours it will be 10,300 gallons of water because add 7000 + 3300 equals 10,300

7 0

3 years ago

Question 1

Effectus [21]

Answer:

Step-by-step explanation:

Substitute 3 in for m and solve

4m - 1 = 4(3) - 1 = 11

5m - 4 = 5(3) - 4 = 11

4 0

2 years ago

Read 2 more answers

A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1863 mailboxes t

forsale [732]

Answer:

3433 m²

Step-by-step explanation:

From the image, we have a rectangular box without cover and half a cylinder on top.

Formula for surface area of rectangular box with top is;

S = 2(lh + wh + lw)

From the image,

l = 0.6 m

w = 0.4 m

h = 0.55 m

Thus;

S = 2((0.6 × 0.55) + (0.4 × 0.55) + (0.6 × 0.4))

S = 1.58 m²

Now, since the top is not included for this figure, then;

Surface area of this rectangular box is;

S1 = 1.58 - (lw) = 1.58 - (0.4 × 0.6) = 1.34 m²

Surface area of a cylinder is;

S = 2πr² + 2πrh

r is radius and in this case = 0.4/2 = 0.2 m

h = 0.6

S = 2π(0.2² + (0.2 × 0.6))

S = 1.005 m²

Since it is half cylinder, then we have;

S2 = 1.005/2

S2 = 0.5025 m²

Total surface area; S_t = S1 + S2

S_t = 1.34 + 0.5025

S_t = 1.8425 m²

This is the surface area of one mail box.

Thus, for 1863 mailboxes, total surface area is;

S = 1863 × 1.8425 = 3432.5775 m²

Approximating to the nearest Sq.m gives;

S = 3433 m²

6 0

3 years ago

Differentiate f and find the domain of f. (enter the domain in interval notation.)f(x) = ln(x2 − 12x)derivative f '(x) = 2x−12x2

guajiro [1.7K]

F(x) = ln(x² - 12x)
The derivative is
$f'(x)= \frac{2x-12}{x^{2}-12x}$

f(x) is undefined when x² - 12x = x(x - 12) = 0
That is, when x = 0 or x = 12.
Therefore the domain is (-∞, 0)∪(0,12)∪(12, ∞)

Answer:
The derivative is
$f'(x) = \frac{2x-12}{x^{2}-12x}$
The domain is
(-∞, 0)∪(0, 12)∪(12,∞)

3 0

3 years ago