All categories

3 years ago

Find the measure of the indicated angle to the nearest degree

Mathematics

1 answer:

polet [3.4K]3 years ago

5 0

9514 1404 393

Answer:

25°

Step-by-step explanation:

The relevant trig relation is ...

Sin = Opposite/Hypotenuse

sin(?) = 25/60

? = arcsin(25/60) ≈ 24.62°

The indicated angle is about 25°.

You might be interested in

Mike has 57 action figures. Alex has 186 action figures. Which is the best estimate of the number of action figures together?

MariettaO [177]

57 rounds to 60 and 186 rounds to 190. 60+190=150

5 0

3 years ago

Read 2 more answers

40 POINTS<br> Which expression is equivalent to (3k - 4b) ^ 3 in expanded form?

GuDViN [60]

The Answer is B

I just took the test

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%24a%2Ba%20r%2Ba%20r%5E%7B2%7D%2B%5Cldots%20%5Cinfty%3D15%24%24a%5E%7B2%7D%2B%28a%20r%29%5E%7B

riadik2000 [5.3K]

Let

$S_n = \displaystyle \sum_{k=0}^n r^k = 1 + r + r^2 + \cdots + r^n$

where we assume |r| < 1. Multiplying on both sides by r gives

$r S_n = \displaystyle \sum_{k=0}^n r^{k+1} = r + r^2 + r^3 + \cdots + r^{n+1}$

and subtracting this from $S_n$ gives

$(1 - r) S_n = 1 - r^{n+1} \implies S_n = \dfrac{1 - r^{n+1}}{1 - r}$

As n → ∞, the exponential term will converge to 0, and the partial sums $S_n$ will converge to

$\displaystyle \lim_{n\to\infty} S_n = \dfrac1{1-r}$

Now, we're given

$a + ar + ar^2 + \cdots = 15 \implies 1 + r + r^2 + \cdots = \dfrac{15}a$

$a^2 + a^2r^2 + a^2r^4 + \cdots = 150 \implies 1 + r^2 + r^4 + \cdots = \dfrac{150}{a^2}$

We must have |r| < 1 since both sums converge, so

$\dfrac{15}a = \dfrac1{1-r}$

$\dfrac{150}{a^2} = \dfrac1{1-r^2}$

Solving for r by substitution, we have

$\dfrac{15}a = \dfrac1{1-r} \implies a = 15(1-r)$

$\dfrac{150}{225(1-r)^2} = \dfrac1{1-r^2}$

Recalling the difference of squares identity, we have

$\dfrac2{3(1-r)^2} = \dfrac1{(1-r)(1+r)}$

We've already confirmed r ≠ 1, so we can simplify this to

$\dfrac2{3(1-r)} = \dfrac1{1+r} \implies \dfrac{1-r}{1+r} = \dfrac23 \implies r = \dfrac15$

It follows that

$\dfrac a{1-r} = \dfrac a{1-\frac15} = 15 \implies a = 12$

and so the sum we want is

$ar^3 + ar^4 + ar^6 + \cdots = 15 - a - ar - ar^2 = \boxed{\dfrac3{25}}$

which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?

7 0

3 years ago

In a translation, the line segments that connect each point on the preimage to the corresponding point on the image are not only

Marianna [84]

Translation doesn't change the shape, size, or orientation of anything.
It just moves things around.

So the line segments in the image are not only congruent to the ones
in the original figure. They're also parallel.

7 0

4 years ago

Read 2 more answers

how many spherical pellets of diameter 4 cm can be made out of a cube of lead for which each edge measures 27 cm ? round the ans

Harlamova29_29 [7]

Step-by-step explanation:

A lead cube of side $27\text{ cm}$ is used to make spherical pellets of diameter $4\text{ cm}$ .

As the volume of lead is conserved, the volume of raw material equals the volume of finished products.

$\text{Volume of cube} = \text{Volume of spheres produced}$

Let us assume that $n$ cubes are produced. Volume of a cube of side $s$ is $s^{3}$ . The volume of a sphere of diameter $d$ is $\dfrac{\pi d^{3}}{6}$ .

$(27\text{ cm})^{3}=n\times (\dfrac{\pi (4 cm)^{3}}{6} )\\\\19683\text{ cm}^{3}=n\times (\dfrac{32\pi \text{ cm}^{3}}{3} )\\\\n=587.37$

n is rounded off to 587.

∴ 587 spherical pellets can be made.

7 0

4 years ago