All categories

3 years ago

Find the Inverse of the Function y= 10x^2 - 4

1 answer:

3 0

Hello.

1. Switch y and x.
x = 10y^2 - 4
2. Isolate y.
x + 4 = 10y^2
(x + 4)/(10) = y^2
y = sqrt[(x + 4)/(10)]
3. Replace y with f^-1(x)
f^-1(x) = sqrt[(x + 4)/(10)]

Good luck to you!

You might be interested in

Kristen can run at 9kmh-1 and walk at 3kmh-1. She completed a 42km marathon in 6 hours. What distance did Kristen run during the

Hatshy [7]

Kristen completed 42 km. We will imagine that she ran all 6 hours. => 9 * 6 =54 km which is more than she actually completed. So we will find a 9 Multiple less than 42 km and that will be 36 km. (9 * 4 = 36 km completed by running) and the rest until 42 were completed by walking (3 * 2 = 6; 6 + 36 =42).

6 0

3 years ago

N+4-9 - 5n when simplifying

natita [175]

Answer:

-4n - 5

Step-by-step explanation:

4 - 9

= -5

-5n + n

Combine like terms

= -4n

-4n - 5

7 0

3 years ago

This is the pond in a shape of a prism, it is completely full of water. Colin uses a pump to empty the pond. The level goes down

AnnZ [28]

Answer:

150 minutes

Step-by-step explanation:

P.S - The exact question is -

Given - This is the pond in a shape of a prism, it is completely full of

water. Colin uses a pump to empty the pond. The level goes

down by 20 cm in the first 30 min.

To find - Work put how many minutes Colin has to wait for the pond

to completely empty.

Proof -

Given that,

Height of prism = 1 m

Also,

Base of the prism is trapezium and

Sides of the trapezium are 0.6 m and 1.4 m

Height of trapezium is 2 m

We know that,

Area of trapezium = $\frac{1}{2}$ × (sum of sides)× height

= $\frac{1}{2}$ × (0.6 + 1.4)× 2

= $\frac{1}{2}$ × (2)× 2

= 2 m²

⇒Area of trapezium = 2 m²

Now,

Volume of prism = Area of trapezium × height of prism

= 2 m² × 1 m

= 2 m³

⇒Volume of prism = 2 m³

Now,

Given that the level goes down by 20 cm in the first 30 min

We know

100 cm = 1 m

⇒1 cm = $\frac{1}{100} m$ = 0.01 m

⇒20 cm = 20×0.01 m = 0.2 m

⇒The level goes down by 0.2 m in the first 30 min.

Also,

we know that height of water = height of prism = 1 m

So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m

Also,

Volume of Remaining water = Area of trapezium × height

= 2 m² × 0.8 m

= 1.6 m³

⇒Volume of Remaining water = 1.6 m³

Now,

Volume of emptied water = Total Volume - Volume of Remaining water

= 2 m³ - 1.6 m³

= 0.4 m³

⇒Volume of emptied water = 0.4 m³

Now,

0.4 m³ water will be empty in 30 minutes

⇒ 1 m³ water will be empty in $\frac{30}{0.4}$ = 75 minutes

⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes

∴ we get

The remaining water is empty in 120 minutes

So,

Total pond is empty in 120 + 30 minutes

⇒Total pond is empty in 150 minutes

5 0

3 years ago

Rewrite in simplest terms: -0.2t - 5 (-8t + 5)

SVETLANKA909090 [29]

Answer: 40.2t - 25

Step-by-step explanation:

-0.2t - 5 (-8t + 5)

-0.2t + 40t -25

39.8t - 25

6 0

3 years ago

10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!

Lilit [14]

After a little manipulation, the given diff'l equation will look like this:

e^y * dy = (2x + 1) * dx.
x^2
Integrating both sides, we get e^y = 2------- + x + c, or e^y = x^2 + x + c
2

Now let x=0 and y = 1, o find c:

e^1 = 0^2 + 0 + c. So, c = e, and the solution is e^y = x^2 + x + e.

4 0

3 years ago