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Darina [25.2K]
3 years ago
11

A diver descended 45.98 feet in 12.1 minutes. What was the diver's average change in elevation per minute?

Mathematics
1 answer:
Kruka [31]3 years ago
6 0
The answer should be 3.8

You can find this by dividing the total descent by the minutes the descent took
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Solve please!<br> 2(3√2)2(5+√2)
Dahasolnce [82]
2\cdot3\sqer2\cdot2(5+\sqrt2)=(2\cdot3\cdot2)\sqrt2(5+\sqrt2)=12\sqrt2(5+\sqrt2)\\\\=60\sqrt2+12\sqrt{2^2}=60\sqrt2+12\cdot2=60\sqrt2+24
3 0
3 years ago
4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail
Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

h^{-1}(x)=\sqrt{\frac{x+1}{3}} ⇒ answer D

Step-by-step explanation:

* <em>Lets explain how to find the inverse of a function</em>

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = f^{-1}(x)

* <em>Lets use these steps to solve the problems</em>

∵ f(x)=\sqrt{x-3}

∵ f(x) = y

∴ y=\sqrt{x-3}

- Exchange x and y

∴ x=\sqrt{y-3}

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by f^{-1}(x)

∴ f^{-1}(x)=x^{2}+3

∵ g(x) = x² + 3

∴ f^{-1}(x)=g(x)

∴ <u><em>The functions are inverses to each other</em></u>

* <em>Now lets find f(g(x))</em>

- To find f(g(x)) substitute x in f(x) by g(x)

∵ f(x)=\sqrt{x-3}

∵ g(x) = x² + 3

∴ f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x

∴ <u><em>f(g(x)) = x</em></u>

∴ The functions are inverses; f(g(x)) = x

* <em>Lets find the inverse of h(x)</em>

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ \frac{x + 1}{3}=y^{2}

- Take √ for both sides

∴ ± \sqrt{\frac{x+1}{3}}=y

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ \sqrt{\frac{x+1}{3}}=y

- replace y by h^{-1}(x)

∴ h^{-1}(x)=\sqrt{\frac{x+1}{3}}

4 0
3 years ago
Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B a
evablogger [386]

Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1=\frac{1}{2} *PQ*RM

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2=\frac{1}{2} *SR*PN

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1=\frac{1}{2}*PQ*h

S2=\frac{1}{2}*SR*h

Adding them together, we get the area of the whole trapezoid:

S=S1+S2=\frac{1}{2} (PQ+SR)h,

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}

Simplifying, we have

=>A= \frac{ah+2b_{1+C} }{2}

Factoring we have,

=> A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2}  \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}

 But, a+ b_{1} + c  is equal to b_{2}, the longer base of our trapezoid.

Hence, A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}

We have discussed two ways by which we can derive area of a trapezoid.

Read to know more about Trapezoid

brainly.com/question/4758162?referrer=searchResults

#SPJ10

5 0
2 years ago
What is distributive property
fomenos
The Distributive Property<span> is an algebra </span>property<span> which is used to multiply a single term and two or more terms inside a set of parentheses. Take a look at the problem below. 2(3 + 6)</span>
8 0
3 years ago
Read 2 more answers
Alissa emptied her piggy bank for disney world. She had $7.70. if she had 10 pennies, twice as many times as quarters, and 1/2 a
Tju [1.3M]

Answer:

She has 20 quarters.

Step-by-step explanation:

Alissa emptied her piggy bank for Disney world. She had $7.70.

If she had 10 pennies and twice as many times as quarters, then we can write the equation as

Q = 2P {Where, Q represents the number of quarters and P for pennies}

⇒ Q = 10 × 2

⇒ Q = 20

So, she has 20 quarters.

Therefore, she has 20 quarters. (Answer)

3 0
3 years ago
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