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3 years ago

0.199 to the nearest hundredth.

1 answer:

6 0

0.20 would be the answer.
The number places on a number go as follows starting at 0. and going to the right
ones, tenths, hundredth
This means that 0.00 is the hundredth place (the bolded 0). Since you round a 9 up one, this makes the 1 in the tenths place go to a 2 and the hundredth go to a 0

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Find sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B).

Reil [10]

Answer:

Part A) $sin(\alpha)=\frac{4}{7},\ cos(\beta)=\frac{4}{7}$

Part B) $tan(\alpha)=\frac{4}{\sqrt{33}},\ tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) $sec(\alpha)=\frac{7}{\sqrt{33}},\ csc(\beta)=\frac{7}{\sqrt{33}}$

Step-by-step explanation:

Part A) Find $sin(\alpha)\ and\ cos(\beta)$

we know that

If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sin(\alpha)=cos(\beta)$

Find the value of $sin(\alpha)$ in the right triangle of the figure

$sin(\alpha)=\frac{8}{14}$ ---> opposite side divided by the hypotenuse

simplify

$sin(\alpha)=\frac{4}{7}$

therefore

$sin(\alpha)=\frac{4}{7}$

$cos(\beta)=\frac{4}{7}$

Part B) Find $tan(\alpha)\ and\ cot(\beta)$

we know that

If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$tan(\alpha)=cot(\beta)$

Find the value of the length side adjacent to the angle alpha

Applying the Pythagorean Theorem

Let

x ----> length side adjacent to angle alpha

$14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132$

$x=\sqrt{132}\ units$

simplify

$x=2\sqrt{33}\ units$

Find the value of $tan(\alpha)$ in the right triangle of the figure

$tan(\alpha)=\frac{8}{2\sqrt{33}}$ ---> opposite side divided by the adjacent side angle alpha

simplify

$tan(\alpha)=\frac{4}{\sqrt{33}}$

therefore

$tan(\alpha)=\frac{4}{\sqrt{33}}$

$tan(\beta)=\frac{4}{\sqrt{33}}$

Part C) Find $sec(\alpha)\ and\ csc(\beta)$

we know that

If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle

In this problem

$\alpha+\beta=90^o$ ---> by complementary angles

$sec(\alpha)=csc(\beta)$

Find the value of $sec(\alpha)$ in the right triangle of the figure

$sec(\alpha)=\frac{1}{cos(\alpha)}$

Find the value of $cos(\alpha)$

$cos(\alpha)=\frac{2\sqrt{33}}{14}$ ---> adjacent side divided by the hypotenuse

simplify

$cos(\alpha)=\frac{\sqrt{33}}{7}$

therefore

$sec(\alpha)=\frac{7}{\sqrt{33}}$

$csc(\beta)=\frac{7}{\sqrt{33}}$

6 0

3 years ago

A cube with an edge of length s has a volume of 27 units. What is the length of s?

matrenka [14]

Answer:

s = 3

Step-by-step explanation:

The volume formula for a cube is V = s^3, where “s” is the edge length. Since we know the volume and need to find “s,” we just do the inverse operation for an exponent, which is a radical. The cubed root of 27 is 3, so there’s your answer! Hope this is helpful & accurate. Best wishes.

5 0

3 years ago

Answer to this please ??

mr_godi [17]

Answer:

31°

Step-by-step explanation:

The upper and lower triangles are similar, because their bases are parallel.

This implies that their correspondent angles have the same measure: the correspondent angle of x is the 31° angle.

7 0

3 years ago

Read 2 more answers

[6] Jessica sold one third of her records and then bought 84 more. She now has 178 records. How many records did Jessica begin w

tia_tia [17]

Answer:

141 records

Step-by-step explanation:

Let the initial number be x

Sold 1/3x, and now has:

x - 1/3x = 2/3x

Bought 84 more and now got 178:

2/3x + 84 = 178
2/3x = 94
x = 94 ÷ 2/3
x = 94 × 3/2
x = 141

Jessica had 141 records initially

7 0

3 years ago

If sally had 10 apples and then gave her friend Jeniffer 5 apples and then Jennifer's friend jane stole all the apples, how many

riadik2000 [5.3K]

Answer:

Jeniffer has 0, Sally has 0, and Jane has all the apples. This is because if Jane stole all the apples, she has every apple in the question making everyone else have zero apples.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers