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1 year ago

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The quantities xxx and yyy are proportional. xxx yyy 5.85.85, point, 8 5.85.85, point, 8 7.57.57, point, 5 7.57.57, point, 5 11.

211.211, point, 2 11.211.211, point, 2 Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x. r =r=r, equals

2 answers:

Paul [167]1 year ago

5 0

Question:

The quantities x and y are proportional.

x y

5.8 7.5

11.2

Find the constant of proportionality (r) in the equation y=rx

Answer:

The constant of proportionality is 75/58 or 1.29

Step-by-step explanation:

Given

The table above

Required

Find the constant of proportionality

The question has an incomplete table but it can still be solved because x and y are proportional.

Given that

y = rx

Make r the subject of formula

Divide through by x

y/x = rx

y/x = r

r = y/x

When y = 7.5, x = 5.8

Substitute these values

r = y/x becomes

r = 7.5/5.8

Multiply denominator and numerator by 10

r = (7.5 * 10)/(5.8 * 10)

r = 75/58

In this case, it's best to leave the answer in fraction.

However, it can be solved further.

r = 75/58

r = 1.29 (Approximated)

Hence, the constant of proportionality is 75/58 or 1.29

QveST [7]1 year ago

5 0

Answer:

the correct answer is 1

hope this helps :D

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Kristin is swimming in the ocean and notices a coral reef below her. The angle of depression is 35∘ and the depth of the ocean,

LenaWriter [7]

Answer:

Distance: 435.9 ft

Step-by-step explanation:

This is a right triangle shown in the picture.

To solve for $x$ , we can use trigonometry.

The 35° angle's opposite side is 250 ft and the hypotenuse of the triangle is $x$ (what we are seeking to find).

The ratio that relates opposite and hypotenuse is sine.

<em>We know that,</em>

$sin(angle)=\frac{opposite}{hypotenuse}$

<em>Thus we can write:</em>

$sin(35)=\frac{250}{x}$

<em>Cross multiplying and solving for $x$ gives us:</em>

$sin(35)=\frac{250}{x}\\x=\frac{250}{sin(35)}\\x=435.9$

Second answer choice is right: 435.9 ft

6 0

2 years ago

A jet flies 425 km from Ottawa to Québec at rate v + 60. On the return flight, the

Marina CMI [18]

Answer:

a. $\frac{- 42,500}{(v + 60)(v - 40)}$

Step-by-step Explanation:

Given:

Distance Ottawa to Québec = 425 km

Initial flight rate = v + 60

Return flight rate = v - 40

$t = \frac{d}{r}$

Required:

Flight times difference of the initial and return flights

Solution:

=>Flight time of the initial flight:

$t = \frac{d}{r}$

$t = \frac{425}{v + 60}$

=>Flight time of the return flight:

$t = \frac{425}{v - 40}$

=>Difference in flight times:

$\frac{425}{v + 60} - \frac{425}{v - 40}$

$\frac{425(v - 40) -425(v + 60)}{(v + 60)(v - 40)}$

$\frac{425(v) - 425(40) -425(v) -425(+60)}{(v + 60)(v - 40)}$

$\frac{425v - 17000 -425v - 25500}{(v + 60)(v - 40)}$

$\frac{425v - 425v - 17000 - 25500}{(v + 60)(v - 40)}$

$\frac{- 42,500}{(v + 60)(v - 40)}$

3 0

2 years ago

What is the sum of the polynomials? 1.3t3 + t2 – 42t + 8 1.3t3 + t2 – 6t + 8 1.9t3 + 8.4t2 – 42t 1.9t2 – 42t + 8

Aleksandr-060686 [28]

(1)1.3t^3 +t^2 -42t +8
(2)1.3t^3 + t^2 -6t +8
(3)1.9 t^3.+ 8.4^t^2 -42t
(4)1.9t^2 -42t + 8

I hope I got that right!!
okay, now they are all separated in columns, add the ones with the same powers (e.g (1)_ 1.3t^3 + (2) 1.3t^3 + (3) 1.9 t^3 = 4.5t^3.

3 0

2 years ago

Read 2 more answers

storchak [24]

The value of d is -2

Step-by-step explanation:

The nth term of the arithmetic sequence is $u_{n}=u_{1}+(n-1)d$ , where

$u_{1}$ is the first term
d is the common difference between each 2 consecutive terms

The nth term of the geometric sequence is $u_{n}=u_{1}r^{n-1}$ , where

$u_{1}$ is the first term
r is the common ratio between each two consecutive terms $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∵ $u_{1}$ of an arithmetic sequence is 1

∵ The common difference is d, where d ≠ 0

∵ $u_{2}$ , $u_{3}$ , $u_{6}$ are the first 3 terms of a geometric sequence

∵ $u_{2}$ = 1 + (2 - 1)d

∴ $u_{2}$ = 1 + d

∵ $u_{3}$ = 1 + (3 - 1)d

∴ $u_{2}$ = 1 + 2d

∵ $u_{6}$ = 1 + (6 - 1)d

∴ $u_{2}$ = 1 + 5d

∴ The first 3 terms of the geometric sequence are (1 + d) , (1 + 2d) ,

(1 + 5d)

∵ The common ratio in the geometric sequence is $r=\frac{u_{2}}{u_{1}}=\frac{u_{3}}{u_{2}}$

∴ $r=\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

- Use cross multiplication with the equal fractions

∵ $\frac{1+2d}{1+d}=\frac{1+5d}{1+2d}$

∴ (1 + 2d)(1 + 2d) = (1 + d)(1 + 5d)

∴ 1 + 2d + 2d + 4d² = 1 + 5d + d + 5d²

- Add like terms in each side

∴ 1 + 4d + 4d² = 1 + 6d + 5d²

- Subtract 1 from both sides

∴ 4d + 4d² = 6d + 5d²

- Subtract 4d from both sides

∴ 4d² = 2d + 5d²

- Subtract 4d² from each side

∴ 0 = 2d + d²

- Take d as a common factor

∴ 0 = d(2 + d)

- Equate each factor by 0

∴ d = 0 but we will reject it because d ≠ 0

∴ 2 + d = 0

- Subtract 2 from both sides

∴ d = -2

The value of d is -2

Learn more:

You can learn more about the sequence in brainly.com/question/1522572

#LearnwithBrainly

7 0

2 years ago

The sum of an infinite geometric sequence is seven times the value of its first term.

Radda [10]

Answer:

a). r = $\frac{6}{7}$

b). At least 5 terms should be added.

Step-by-step explanation:

Formula representing sum of infinite geometric sequence is,

$S_{\inf}=\frac{a}{1-r}$

Where a = first term of the sequence

r = common ratio

a). If the sum is seven times the value of its first term.

$7a=\frac{a}{1-r}$

$7=\frac{1}{1-r}$

7(1 - r) = 1

7 - 7r = 1

7r = 7 - 1

7r = 6

r = $\frac{6}{7}$

b). Since sum of n terms of the geometric sequence is given by,

$S_{n}=\frac{a(1-r^{n})}{1-r}$

If the sum of n terms of this sequence is more than half the value of the infinite sum.

$\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}$ > $\frac{7a}{2}$

$\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}$

$\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}$

$1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}$

$1-(\frac{6}{7})^{n}> \frac{1}{2}$

$-(\frac{6}{7})^{n}> -\frac{1}{2}$

$(\frac{6}{7})^{n}< \frac{1}{2}$

$(0.85714)^{n}< (0.5)$

n[log(0.85714)] < log(0.5)

-n(0.06695) < -0.30102

n > $\frac{0.30102}{0.06695}$

n > 4.496

n > 4.5

Therefore, at least 5 terms of the sequence should be added.

8 0

2 years ago