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3 years ago

What is the equation of a line parallel to the line y = 4x + 7 and passes through the point (3, 0)?

1 answer:

5 0

Two lines to be parallel their slopes have to be equal.

so m1 = m = 4

y = mx + b ( Slope intercept form)

y = 4x + b

(3,0) is on the line:

0 = 12 + b

b = -12

y = 4x - 12

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What is the surface area of the shape?

Sladkaya [172]

Answer:

Step-by-step explanation:

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3 years ago

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Among all right circular cones with a slant height of 24, what are the dimensions (radius and height) that maximize the volum

aleksklad [387]

Answer:

5571.99

Step-by-step explanation:

We need to use the Pythagorean theorem to solve the problem.

The theorem indicates that,

$r^2+h^2=24^2 \\r^2+h^2=576\\r^2=576-h^2$

Once this is defined, we proceed to define the volume of a cone,

$v=\frac{1}{3}\pi r^2 h$

Substituting,

$v=\frac{1}{3} \pi (576-h^2)h\\v=\frac{1}{3} \pi (576h-h^3)$

We need to find the maximum height, so we proceed to calculate h, by means of its derivative and equalizing 0,

$\frac{dv}{dh} = \frac{1}{3} \pi (576-3h^2)$

$\frac{dv}{dh} = 0$ then $\rightarrow \frac{1}{3}\pi(576-3h^2)=0$

$h_1=-8\sqrt{3}\\h_2=8\sqrt{3}$

<em>We select the positiv value.</em>

We have then,

$r^2 = 576-(8\sqrt3)^2 = 384\\r=\sqrt{384}$

We can now calculate the maximum volume,

$V_{max}= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (\sqrt{384})^2 (8\sqrt{3}) = 5571.99$

4 0

3 years ago

Please help!!

valkas [14]

A calculator can show you the answer to these very quickly.

$\dfrac{7.488\cdot 10^{-8}}{3.12\cdot 10^{2}}=\dfrac{7.488}{3.12}\times 10^{(-8-2)}\\\\=2.4\cdot 10^{-10}$

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3 years ago

Benjamin traveled at an average speed of 65 miles per hour for 4.5 hours and then traveled at an average speed of 70 miles per h

shusha [124]

Answer:

542.5

Step-by-step explanation: tRUST ME ON THIS

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3 years ago

150 grams of fertilizer is required for a land area of 6 square meters.

Dahasolnce [82]

If 150g of fertilizer can cover 6 sq m of land then, 25 g of fertilizer can cover 1 sq m of land;
a)
For 13 sq m of land we need 25g*13
325g
b)
850g/25g=amount of land
34 sq m

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3 years ago