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3 years ago

What is the value of sinθ given that (−3, 4) is a point on the terminal side of θ ?

Mathematics

1 answer:

Luba_88 [7]3 years ago

5 0

Answer:

sinθ = 4/5

Step-by-step explanation:

The given point is (-3,4). This point lies in the second quadrant.

In second quadrant, sinθ is positive.

Now, please see the attached image.

The point (-3,4) is at A. The hypotenuse OA can be found by using the Pythagorean theorem.

$OA=\sqrt{4^2+3^2}\\\\OA=\sqrt{16+9}\\\\OA=\sqrt{25}\\\\OA=5$

Now, in triangle AOB,

$\sin\theta=\frac{AB}{OA}\\\\\sin\theta=\frac{4}{5}$

Thus, we have

sinθ = 4/5

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Rewrite the following equation in slope-intercept form. 3x − 11y = 19

Law Incorporation [45]

Answer:

y = 3/11(x) - 19/11

Step-by-step explanation:

Step 1: Subtract 3x from both sides.

$3x-11y-3x=19-3x$
$-11y=-3x+19$

Step 2: Divide both sides by -11.

$-11y/-11=(-3x+19)/-11$
$y=\frac{3}{11}x-\frac{19}{11}$

Therefore, the answer is y = 3/11(x) - 19/11.

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2 years ago

The diversity of algal species in a lake is calculated for a coastal area before and after an oil spill.

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3 years ago

What is the answer to the q

Anton [14]

Answer:

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Step-by-step explanation:

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6 0

3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

Using the volume formula of a cylinder

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

$V = \frac{4}{3}\pi r^3$

Divide both sides by r

$\frac{V}{r} = \frac{4}{3r}\pi r^3$

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

4 0

3 years ago

Read 2 more answers

An excavating company charges $300 an hour for the use of a backhoe and $500 an hour for the use of a bulldozer. (part of an hou

Fed [463]

We have that

Cost use of a backhoe----------------------$300 an hour

Estimate for equipment rental each week---------------------$18,400

Total hours operator per week--------------------------------------40

40*300=$12000---------------------it is the cost per week to use a backhoe

$12000<$18400 is ok

The maximum of hours that I can rent a backhoe are 40 hours, since it is the limit of the operator and it do not overcome the total budget

4 0

3 years ago