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3 years ago

Write the direct variation function given that y varies directly with x, and y = 1.5 when x = 5.

Mathematics

1 answer:

Cloud [144]3 years ago

4 0

Answer:

y=0.3x

Step-by-step explanation:

Formula = $K=\frac{y}{x}$

y α x

y = kx

Where k is the constant of proportionality.

When y = 1.5; x = 5;

We substitute these known values in the equation,

y = kx

1.5 = k5

Dividing both sides of the equation by 5 to find the value for k, we have

1.5/5= k0.3/5

Therefore,

K = 0.3

Having found the value of k,

We substitute this value into the relationship

y = kx

Therefore we have,

y = 0.3x.

The direct variation function is therefore,

y = 0.3x.

[RevyBreeze]

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A sailboat depreciates at 15% of its original value each year. If the sailboat was $9500 at its time of purchase, what is the va

eimsori [14]

Answer: After 7 years, the value of the sailboat is $3045.49.

Step-by-step explanation:

Since we have given that

Original value of the sailboat = $9500

Depreciation rate = 15%

Number of years = 7

As we know the formula for "Compound Interest "i.e

$A=P(1-\frac{r}{100})^n$

where,

A denotes Amount

P denotes original value

r denotes rate of depreciation,

n denotes number of years.

So, our equation becomes ,

$A=9500(1-\frac{15}{100})^7\\\\A=9500(1-0.15)^7\\\\A=9500(0.85)^7\\\\A=\$3045.49$

Hence, after 7 years, the value of the sailboat is $3045.49.

6 0

3 years ago

Read 2 more answers

2 [32-(4-1) power of 3

REY [17]

2(32-3)^3
= 2(29) ^3
=78 ^ 3
= 78 times 78 times 78
= 42,588

5 0

3 years ago

What's the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m? Round your answer to

yuradex [85]

Hello!

The Correct Answer to this would be 100%:

Option "85.4".

(Work Below)

Given:
height = 6m
chord = 20 m

We need to find the radius of the circle.

20 m = 2 √ [ 6m( 2 x radius - 6 m ) ]
20 m / 2 = 2 √[ 6m( 2 x radius - 6 m ) ] / 2
10 m = √ [ 6m( 2 x radius - 6 m ) ]
(10 m)² = √[ 6m( 2 x radius - 6 m ) ] ²
100 m² = 6 m( 2 x radius - 6 m )
100 m² = 12 m x radius - 36 sq m
100 m² + 36 m² = 12 m x radius - 36 m² + 36 m²
136 m² = 12 m x radius
136 m² / 12 m = 12 m x radius / 12 m
11.333 m = radius

the area beneath an arc:

Area = r² x arc cosine [ ( r - h ) / r ] - ( r - h ) x √( 2 x r x h - h² ).

r² = (11.333 m)² = 128.444 m²
r - h= 11.333 m - 6 m = 5.333 m
r * h = 11.333 m x 6 m = 68 m²

Area = 128.444 m² x arc cosine [ 5.333 m / 11.333 m ] - 5.333 m x √[ 2 x 68 m² - 36 m² ]

Area = 128.444 m² x arc cosine [ 0.4706 ] - 5.333 m x √ [ 100m² ]

Area = 128.444 m² x 1.0808 radians - 5.333 m x 10 m

Area = 138.828 m² - 53.333 m²

Area = 85.4 m²


Hope this Helps! Have A Wonderful Day! :)

And as Always...

7 0

3 years ago

After a tropical storm in a certain state, news reports indicated that 19 percent of households in the state lost power during t

olya-2409 [2.1K]

Answer:

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Step-by-step explanation:

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3 years ago

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professor190 [17]

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8 0

3 years ago