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3 years ago

Suppose that a point moves along some unknown curve y = f(x) in such a way that, at

Mathematics

1 answer:

spayn [35]3 years ago

8 0

Answer:

f(x) = x³/3 - 5/3

Step-by-step explanation:

To get the equation of the curve, integrate the slope

f(x) = integral of x²

= (x^(2+1))/3 + c

f(x) = x³/3 + c

To find c, use the given point

1 = 2³/3 + c

c = 1 - 8/3 = -5/3

f(x) = x³/3 - 5/3

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The amount of sales tax on a new car is directly proportional to the purchase price of the car. Victor bought a new car for $30,

Airida [17]

Answer:

Rita paid 47,500 dollars for the purchase price.

Step-by-step explanation:

We are given the sales tax on a new car is directly proportional to the purchase price of the car which means there is is something k such that

when you multiply it to the sales tax you get the purchase price.

Let's set this equation:

y=kx

Let y represent the purchase price and x the sales tax.

The second sentence tells us that (x,y)=(1500,30000).

We can plug this into y=kx to find the constant k. (Constant means it stays the same no matter what the input and output is).

So we have:

30000=k(1500)

300 =k(15) I went ahead and divided previous equation by 100.

Now divide both sides by 15:

300/15=k

Simplify:

20=k

So the equation to use the answer the question is

y=20x

where y is purchase price and x is sales tax.

So we want to know the purchase price on a car if the sales tax is 2375.

So replace x with 2375:

y=20(2375)

y=47500

3 0

3 years ago

Read 2 more answers

Ashlyn had some Barbie dolls. Joslyn has 78 barbies. Rounded to the nearest ten, together they have 140 Barbie dolls. How many d

azamat

ashlyn has 60 barbie dolls

6 0

3 years ago

Read 2 more answers

What is the answer to the qustion 0.3h+1.2=0.1h-2.6

andreev551 [17]

Answer:

-19

Step-by-step explanation:

0.3h+1.2=0.1h-2.6

.2h+1.2=-2.6

.2h=-3.8

h=-19

7 0

3 years ago

Molly measured the diameter of her bike tire and found that it was 2 feet across. She estimated that for every turn of the tire,

natulia [17]

Answer:

Molly's estimation was approximately correct.

Step-by-step explanation:

Given:

Diameter of bike tire = 2 feet

Also Given:

She estimated that for every turn of the tire, the bike traveled about 6 feet.

Estimated Distance traveled = 6 feet

We need to find that whether her estimation reasonable.

Solution:

Now we know that Distance traveled is equal to Circumference of tire.

Since Tire is in circular shape.

We can say that;

Circumference of the tire will be π times diameter.

framing in equation form we get;

Circumference of the tire = $\pi \times 2 = 6.28 \ feet$

Now The actual distance traveled is 6.28 feet and Molly estimated as 6 feet.

Hence we can say that Molly's estimation was approximately correct.

5 0

3 years ago

WILL MARK BRAINIEST, QUESTION IS HARD, Ann works for a city’s parks and recreation department. She is looking for some commercia

MrRa [10]

Answer:

$x =320$

Step-by-step explanation:

Given

$x^2 + 200x = 166400$

Required

Find x

We have:

$x^2 + 200x = 166400$

Rewrite as:

$x^2 + 200x - 166400 = 0$

Expand

$x^2 + 520x - 320x - 166400 = 0$

Factorize

$x(x + 520) - 320(x + 520)= 0$

Factor out x + 520

$(x - 320) (x + 520)= 0$

Split

$x - 320 = 0\ or\ x + 520= 0$

Solve

$x = 320\ or\ x =- 520$

Side length must be positive;

So:

$x = 320$

4 0

2 years ago