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3 years ago

Simplify cos(θ) − sec(θ) / sin(θ)

1 answer:

7 0

<span>Replace tan θ with sin θ/cos θ

= sin²θ/cos θ + cos θ

Now multiply the right-hand side by cos θ/cos θ to get the same denominator:

= sin²θ/cos θ + cos²θ/cos θ
= (sin²θ + cos²θ)/cos θ

The numerator is equivalent to 1:

= 1 / cos θ
= sec θ</span>

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Ok so I’m using most of my points on this so fake answers will be reported understand ok good

Arada [10]

<h2>○=> <u>Correct answer</u> :</h2><h2> $\color{plum} = \tt\bold{30 \: cubic \: inches}$ </h2><h3>○=> <u>Steps to derive correct answer</u> :</h3>

Given :

Base area of Ms. Jones decorative pyramid = 6 inches²

Height of the decorative pyramid = 15 inches

We know that :

$\color{hotpink}\tt \: volume \: of \: a \: triangular \: pyramid\color{plum} \tt \: = \frac{1}{3}Bh$

Volume of the decorative pyramid :

$=\tt \frac{1}{3} \times 15 \times 6$

$=\tt \frac{15 \times 6}{3}$

$=\tt \frac{90}{3}$

$\color{plum} =\tt 30 \: {inches}^{3}$

Therefore, the volume of the decorative pyramid with Ms. Jones = 30 inches³

6 0

3 years ago

A new building that costs $1,000,000 has a useful life of 10 years and a scrap value of $200,000. Using straight-line depreciati

vazorg [7]

Answer:

V = -80,000*t + 1,000,000

Step-by-step explanation:

Given:

- The original cost V_i = $1,000,000

- Scrap Value V_f = $200,000

- Total number of years n = 10

Find:

Using straight-line depreciation, find the equation for the value V in terms of t, where t is in years.

Solution:

- The straight line depreciation method means their is a linear relationship between the value of building and time elapsed till useful life. The linear relationship takes a form:

V = m*t + C

Where,

V: It is the current value of the building

m: The rate at which value increase or decrease with time t

C: The initial value of the building

- We will compute constants m and C as follows:

m = (V_f - V_i) / ( 10 - 0 )

m = (200,000 - 1,000,000) / 10

m = - $80,000/year

C = V_i = $1,000,000

- Plug the values of the constants evaluated above in the linear expression:

V = -80,000*t + 1,000,000

8 0

4 years ago

Tim is 4 years older than one-third of Juan's age. In 10 years, Juan will be 6 years older than twice as old as Tim is now. How

olga55 [171]

Answer:

Juan's current age = 12

Tim's current age = 8

Step-by-step explanation:

Let x= Juan's current age; x+10=Juan's age in 10 years

Then (1/3)x+4=Tim's current age;

Now we are told that:

x+10=2{(1/3)x+4}+6 eliminate brackets

x+10=(2/3)x+8+6 =(2/3)x+14 multiply both sides by 3

3x+30=2x+42 subtract 30 and 2x from both side s

3x-2x+30-30=2x-2x+42-30 collect like terms

Juan's current age: x=12

Tim's current age: (1/3)x+4=(1/3)*12+4=8

4 years older than 1/3 of Juan's age=(1/3)*12+4=8

8=8

In 10 years, Juan will be 6 years older than twice as old as Tim is now.

12+10=22

2*8+6=22

22=22

3 0

4 years ago

Read 2 more answers

What is the volume of the space filled with tissue paper in the packaging box? 81.84 cubic centimeters 105.84 cubic centimeters

Svetllana [295]

The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

Let l,b,h be the dimensions of small gift box V1 = Volume = l*b*h

= 24cm^3

Dimension of Large box are 2.1l , 2.1b,2.1h

Volume of large box = 2.1 l*2.1b*2.1h

= (2.1)^3*lbh

= (2.1)^3*24

V2 =222.264

Volume filled with tissue paper is V2-V1

222.264 - 24

= 198.264cm^3

Hence The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

The complete question is shown below

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters.What is the volume of the tissue paper in the packaging box?

Learn more about the volume here

brainly.com/question/1972490

#SPJ1

6 0

2 years ago

Hey:) can you please help me posted picture of question

oee [108]

Answer:
x² + 10x + 25

Explanation:
Before we begin, remember the following:
(a + b)(a + b) = (a + b)² = a² + 2ab + b²

Now, for the given we have:
(x + 5)(x + 5)
We can note that the two brackets are identical.
Therefore, we can apply the above rule as follows:
(x + 5)(x + 5) = (x + 5)²
= (x)² + 2(x)(5) + (5)²
= x² + 10x + 25

Hope this helps :)

8 0

3 years ago