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3 years ago

In a parallelogram, consecutive angles are

Mathematics

1 answer:

goldenfox [79]3 years ago

5 0

Answer:

Consecutive angles will always some to 180 degrees, that makes consecutive angles in a parallelogram supplementary

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A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along

mina [271]

Answer:

The tip of the man shadow moves at the rate of $\frac{20}{3} ft.sec$

Step-by-step explanation:

Let's draw a figure that describes the given situation.

Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.

Here it forms two similar triangles.

Let's find the distance "y" using proportion.

From the figure, we can form a proportion.

$\frac{y - x}{y} = \frac{6}{15}$

Cross multiplying, we get

15(y -x) = 6y

15y - 15x = 6y

15y - 6y = 15x

9y = 15x

y = $\frac{15x}{9\\} y = \frac{5x}{3}$

We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).

$\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt}$ ----(1)

We are given $\frac{dx}{dt} = 4 ft/sec$ . Plug in the equation (1), we get

$\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec$

Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.

7 0

3 years ago

For fun question

ZanzabumX [31]

Consider the function $f(x)=x^{1/3}$ , which has derivative $f'(x)=\dfrac13x^{-2/3}$ .

The linear approximation of $f(x)$ for some value $x$ within a neighborhood of $x=c$ is given by

$f(x)\approx f'(c)(x-c)+f(c)$

Let $c=64$ . Then $(63.97)^{1/3}$ can be estimated to be

$f(63.97)\approxf'(64)(63.97-64)+f(64)$
$\sqrt[3]{63.97}\approx4-\dfrac{0.03}{48}=3.999375$

Since $f'(x)>0$ for $x>0$ , it follows that $f(x)$ must be strictly increasing over that part of its domain, which means the linear approximation lies strictly above the function $f(x)$ . This means the estimated value is an overestimation.

Indeed, the actual value is closer to the number 3.999374902...

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3 years ago

elise gets a free tax allowance of $6000 and pays tax at 25% on the next $20 000. she pays tax at a raye of 30% on the rest. if

Likurg_2 [28]

Answer:

Step-by-step explanation:

i know because im not g.a.y like u guys

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3 years ago

What is the scale factor of ABC to A DEF?

vampirchik [111]

Answer:

Step-by-step explanation:

All sides of triangle EFD have x6 of BAC.

E.g.: BA = 2. ED = 2 x 6 = 12

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3 years ago

Solve:

Alex Ar [27]

Answer:

Step-by-step explanation:

8 0

3 years ago

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