Ask question

Ask question

All categories

3 years ago

5

If a,b,c,d are in continuous proportion then prove that (c+a) (c+d) = (b+c) (b+d)

1 answer:

sesenic [268]3 years ago

8 0

Answer:

We must prove that (c+a)(c+d) = (b+c)(b+d)

Let us use principles from mathematical induction
$\frac{a}{b} = \frac{b}{c} = \frac{c}{d} = x$
a=bx , b=cx, c=dx
a+c = b + c
c +d = b + d
Such that (a+c)(c+d)=(b+c)(b+d)

Rate positively and give brainlist

You might be interested in

2+2 can u plz help me

Elza [17]

Answer: 4

Step-by-step explanation:

(1 + 1) + (1 + 1)

2 + 2 = 4

4 0

3 years ago

Read 2 more answers

Which of the following ordered pairs is a solution of 3x+2y=-19

34kurt

We need the ordered pairs to choose an answer, but if you want to do it yourself you plug in the x and y values (x,y) and test to see if the equation is true, and equals -19.

8 0

3 years ago

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equatio

AnnZ [28]

The motion of the hour hand of a clock is a periodic motion that repeats every 12 hours.

The equation that can be used to models the height as a function of time, based on the given options, is presented as follows; $\displaystyle \underline{ H = 0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}$

Reasons:

The given parameters are;

The variation of the height of the tip of the hour hand = 9 feet to 10 feet

At t = 0, the time = 12.00 a.m.

Required: The equation that can be used to model the height as a function of time.

Solution:

The general form of the cosine function is presented as follows;

y = a·cos(b·x - c) + d

The amplitude = a

$\displaystyle a = \mathbf{ \frac{Maximum \ value -Minimum \ value}{2}}$

Therefore;

$\displaystyle a = \frac{10 -9}{2} = 0.5$

b = The cycle speed

The period, T, is given as follows;

$\displaystyle T = \mathbf{ \frac{2 \cdot \pi}{b}}$

The period of a block, T = 12 hours

Therefore;

$\displaystyle b = \frac{2 \cdot \pi}{T}$

$\displaystyle b = \frac{2 \cdot \pi}{12} = \mathbf{ \frac{ \pi}{6}}$

$\displaystyle d = \mathbf{ \frac{Maximum \ value +Minimum \ value}{2} = \frac{10 + 9 }{2}} = 9.5$

At t = 0, H = The highest point = 10 ft.

Which gives;

$\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \times 0 -c\right) + 9.5} = 10$

$\displaystyle cos \left( -c\right) = \frac{0.5}{0.5} = 1$

-c = arcos(1) = 0

-c = 0

c = 0

The equation is therefore;

$\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}$

The above equation is the same as; <u>H = 0.5cosine (StartFraction pi Over 6 EndFraction t) + 9.5</u>

Learn more about the cosine function here:

brainly.com/question/4458343

brainly.com/question/24368105

4 0

3 years ago

Read 2 more answers

The distribution of the values of a population is shown below, and a simple Random sample is drawn from the population. Based on

posledela

Answer: C

Step-by-step explanation:

Yes, because the population values appear to be normally distributed

6 0

3 years ago

Profit is always calculated as revenue minus expenses. If a company's expenses were $10 million, write an equation that expresse

Usimov [2.4K]

Answer:

c. P=R-10; 35 million

Step-by-step explanation:

P=R-10, just read what the text says, namely profit = revenue - expenses

P=25, 25=R-10 <=> R=35

3 0

3 years ago

Read 2 more answers