Evaluate the expression

Since both cot(θ) and cos(θ) are positive, it follows that sin(θ) is also positive:

cot(θ) = cos(θ)/sin(θ) > 0   ===>   sin(θ) > 0

Recall the Pythagorean identity:

sin²(θ) + cos²(θ) = 1

Multiplying both sides by 1/sin²(θ) yields another form of the identity,

sin²(θ)/sin²(θ) + cos²(θ)/sin²(θ) = 1/sin²(θ)

1 + cot²(θ) = csc²(θ)

so that

csc(θ) = + √(1 + cot²(θ))

csc(θ) = √(1 + (3/2)²)

csc(θ) = √13/2

By definition of cosecant, we have

csc(θ) = 1/sin(θ)

so that

sin(θ) = 2/√13

Then using the Pythagorean identity once more, we have

cos(θ) = + √(1 - sin²(θ))

cos(θ) = √(1 - (2/√13)²)

cos(θ) = 3/√13

so that, by definition of secant,

sec(θ) = 1/cos(θ)

sec(θ) = √13/3

Answer:false true

Step-by-step explanation:

Answer:

your numbers are -5 and 9, since 9 * -5 = -45 but 9 + (-5) = 9 - 5 = 4

Answer:

The numbers are 9 and -5

Step-by-step explanation:

9×-5= -45

9-5 = 4

Step-by-step explanation:

[tex]1) \: \: - x + 2y + 2z = - 4 \\ 2z = - 4 + x - 2y \\ z = \frac{ - 4 + x - 2y}{2} \\ \\ 2) \: \: 4x + y - 3z = 13 \\ - 3z = 13 - 4x - y \\ z = \frac{13 - 4x - y}{ - 3} \\ \\ 3) \: \: x - 5y + z = - 23 \\ z = - 23 - x + 5y \\ [/tex]

Answer:

d

Step-by-step explanation:

(explanation attached)

19+80=180

99=180

180_99

81

The acceptable and realistic ways to to change the confidence interval to contain zero are;

Reasons:

The confidence interval is given by the following formula;

[tex]CI=\bar{x}\pm t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex]

When the mean, [tex]\overline x[/tex], is positive and large, both values, [tex]\bar{x}+ t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and [tex]\bar{x} -t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], will be positive.

Therefore, Martha has to either intervene to reduce the mean also known as x-bar

Increasing the confidence level will increase the allowable error such that [tex]\bar{x} < t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and the interval will contain zero

Therefore;

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How much greater is [tex]8.9*10^8[/tex] than [tex]1.6*10^6[/tex]? Express your answer using either standard notation or scientific notation.

[tex]8.9*10^8 - 1.6*10^6[/tex]

[tex]890,000,000-1,600,000[/tex]    Convert to standard notation

[tex]888,400,000[/tex]    Standard Notation

[tex]8.884*10^8[/tex]     Scientific Notation

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The value of the numerical expression −3[−15 − 2(−9)]² will be negative 27.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

The expression is given below.

⇒ −3[−15 − 2(−9)]²

Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To answer the problem properly and accurately, this rule must be followed.

⇒ −3[−15 − 2(−9)]²

⇒ −3[−15 + 18]²

⇒ −3[3]²

⇒ −3 × 9

⇒ −27

The value of the numerical expression −3[−15 − 2(−9)]² will be negative 27.

More about the value of the expression link is given below.

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The amount of quarts which will be made in 36 hours and the production rate per day is :

Given the Parameters :

Time taken to make 170 quarts = 36 hours

Number of quarts made in 36 hours using the proportional relationship :

170 = 5

p = 36

Cross multiply :

5p = 170 × 36

5p = 6120

p = 6120 / 5

p = 1224 quarts

The production rate per day :

Number of hours in a day = 24 hours

170 = 5

p = 24

Cross multiply

5p = 170 × 24

5p = 4080

p = 4080/5

p = 816

Therefore, the production rate per day is 816 quarts

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Answer:

7,000

Step-by-step explanation:

Answer:

thank youuuuuu

Step-by-step explanation:

Answer:

thank

Step-by-step explanation:

Answer:

-0.8     GL HEHHEHHEHEHEHEHEHEHEHHEHEHEHHEHEH

Answer:

see explanation

Step-by-step explanation:

The reciprocal of a number n is [tex]\frac{1}{n}[/tex]

(a)

1 [tex]\frac{6}{7}[/tex] ← change to an improper fraction

= [tex]\frac{13}{7}[/tex]

Then its reciprocal is [tex]\frac{1}{\frac{13}{7} }[/tex] = [tex]\frac{7}{13}[/tex]

(b)

The reciprocal of [tex]\frac{7}{13}[/tex] is [tex]\frac{1}{\frac{7}{13} }[/tex] = [tex]\frac{13}{7}[/tex] = 1 [tex]\frac{6}{7}[/tex]

(c)

Each is the reciprocal of the other

Yes, It is an improper fraction

answer

The side

b

is

4√2

unit.

Explanation:

in right triangle

C=900,a=2,c=6c

is

the side opposite to the right angle, so it is hypotenuse,

a

and

b

are the adjacent sides of the right angle .

We know in right triangle

,a2+b2=

c2∴22+b2=62

or

b2=36−4=32∴

b=√32

or

b=4√2

unit. The side

b is 4√2

unit [Ans]

Answer:

Step-by-step explanation:

300/100 = 3 = 1%

if 3 = 1% then 3/2 or 1.5 = 0.5%

5 x 3 = 15 = 5%

15 + 1.5 = 16.5 = 5.5%

Answer:

a) 9000 gam

Step-by-step explanation:

Answer:

a) 9000 grams

Step-by-step explanation:

1 kg=1000 g

9*1000=9000

i took this exam and the answer is c.25,200

Answer:

162kph (i think, sorry if im wrong)

Which means 486km in 3 hours....

Step-by-step explanation:

Hope this helps!

Answer:

• From trigonometry ratios:

[tex]{ \boxed{ \rm{ \sin(A) = \frac{opposite}{hypotenuse} }}} \\ [/tex]

[tex]{ \rm{ \sin(A) = \frac{28}{35} }} \\ \\ { \boxed{ \boxed{ \rm{ \: \sin(A) = \frac{4}{5} \: }}}}[/tex]

Answer:

0.049

Step-by-step explanation:

17÷1=17

17÷12=1.42

1.42÷29=0.049

Answer: 183.77

Step-by-step explanation:

23*7.99 =183.77

Answer:

I believe its 288 I might be wrong but it's worth a shot

Answer:

The top of the ladder is sliding down at a rate of -1.25 ft/s.

Step-by-step explanation:

From the Pythagorean Theorem:

[tex]\displaystyle a^2 + b^2 = c^2[/tex]

(Where a is the height, b is the distance between the bottom of the ladder and the wall, and c is the length of the ladder itself.)

Note that the hypotenuse c is a constant value at 26 feet. Substitute:

[tex]\displaystyle a^2 + b^2 = (26\text{ ft})^2 = 676 \text{ ft}^2[/tex]

We want to determine how fast the top of the ladder is sliding down the wall at the instant of time when the bottom of the ladder is 10 feet from the wall and sliding away from the wall at the rate of 3 ft/s.

In other words, we want to find da/dt given that b = 10 ft, and db/dt = 3 ft/s.

First, we can differentiate both sides with respect to t, where a and b are both functions of t:

[tex]\displaystyle \frac{d}{dt}\left[ a^2 + b^2\right ] = \frac{d}{dt}\left [ 676 \text{ feet}^2\right ][/tex]

Implicit differentiation yields:

[tex]\displaystyle 2a \frac{da}{dt} + 2b \frac{db}{dt} = 0[/tex]

Next, since we know that b = 10 ft, we can find a:

[tex]\displaystyle \begin{aligned} a^2 + b^2 & = 676\text{ ft}^2 \\ \\ a^2 +(10 \text{ ft})^2 & = 676\text{ ft}^2 \\ \\ a & = 24\text{ ft} \end{aligned}[/tex]

Substitute and solve for da/dt:

[tex]\displaystyle \begin{aligned} 2a \frac{da}{dt} + 2b\frac{db}{dt} & = 0 \\ \\ 2(24 \text{ ft}) \frac{da}{dt} + 2(10 \text{ ft})(3 \text{ ft/s}) & = 0 \\ \\ 48 \text{ ft} \cdot \frac{da}{dt} & = -60 \text{ ft$^2$/s} \\ \\ \frac{da}{dt} & = -1.25 \text{ ft/s} \end{aligned}[/tex]

Since the ladder is sliding down the wall, da/dt is expected to be negative.

In conclusion, the top of the ladder is sliding down at a rate of -1.25 ft/s.