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3 years ago

The terminal side of an angle in standard position passes through P(–3, –4). What is the value of tan(theta)?

Mathematics

2 answers:

Mkey [24]3 years ago

8 0

If the point is at (-3, -4), it is located in the third quadrant. You can find the tangent of an angle by finding the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side of the angle is the vertical line with a length of 4 units, while the adjacent side of the angle is the horizontal line with a length of 3 units. <em>Thus, tan θ = 4/3.</em>

natali 33 [55]3 years ago

3 0

Answer:

Ans tan θ = 4/3

Step-by-step explanation:

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A hole is poked in a balloon so that every minute the balloon loses 3/10ft 3 of air. What is the total change in the number of c

GaryK [48]

5/9 minutes

amount lost=times times amout lost per unit of time
amount lost=5/9 times 3/10
amount lost=15/90
amount lost=5/30
amount lost=1/6

answer is 1/6 ft³ of air

6 0

3 years ago

The volume V of an ice cream cone is given by V = 2 3 πR3 + 1 3 πR2h where R is the common radius of the spherical cap and the c

Nuetrik [128]

Answer:

The change in volume is estimated to be 17.20 $\rm{in^3}$

Step-by-step explanation:

The linearization or linear approximation of a function $f(x)$ is given by:

$f(x_0+dx) \approx f(x_0) + df(x)|_{x_0}$ where $df$ is the total differential of the function evaluated in the given point.

For the given function, the linearization is:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh$

Taking $R_0=1.5$ inches and $h=3$ inches and evaluating the partial derivatives we obtain:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh\\V(R, h) = V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh$

substituting the values and taking $dx=0.1$ and $dh=0.3$ inches we have:

$V(R_0+dR, h_0+dh) =V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh\\V(1.5+0.1, 3+0.3) =V(1.5, 3) + (\frac{2 \cdot 3 \pi \cdot 1.5}{3} + 2 \pi 1.5^2)\cdot 0.1 + (\frac{\pi 1.5^2}{3} )\cdot 0.3\\V(1.5+0.1, 3+0.3) = 17.2002\\\boxed{V(1.5+0.1, 3+0.3) \approx 17.20}$

Therefore the change in volume is estimated to be 17.20 $\rm{in^3}$

4 0

3 years ago

a mechanical engineer designs a robotic rm to be used in an assembly line. one portion of the arm is 5/12 yard long, and the len

Amanda [17]

Answer:

8/12 yard or 2/3 yard

Step-by-step explanation:

The sum of the two lengths is ...

5/12 yd + 3/12 yd = (5+3)/12 yd = 8/12 yd

This fraction can be reduced by removing a factor of 4 from numerator and denominator.

8/12 yd = 2/3 yd

If the arm portions are end-to-end, the total length is 2/3 yard.

4 0

3 years ago

What is the landing strip’s area ?

attashe74 [19]

Answer:

Step-by-step explanation:

The perimeter P of a rectangle is calculated as

P = 2l + 2w ( l is the length and w the width ) , then

2l + 2(9) = 5364

2l + 18 = 5364 ( subtract 18 from both sides )

2l = 5346 ( divide both sides by 2 )

l = 2673

Then

A = lw = 2673 × 9 = 24057 m² → D

5 0

3 years ago

How do you factor 1/4(-16x+8)?

Nikitich [7]

We know that we can take 4 out of (-16x + 8) [ we know this because we can divide 16 by 4 ( to get 4 ) and we can divide 8 by 4 ( to get 2 ) ]

we can factor out a 4 then from the parentheses to get 4(-4x + 2), but since we are multiplying by 1/4 we get

1/4(4)(-4x + 2), and since 1/4 * 4 = 1, our final answer is

-4x + 2

3 0

2 years ago

Read 2 more answers