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3 years ago

Match the vocabulary terms to their definitions.

Mathematics

1 answer:

jolli1 [7]3 years ago

7 0

The questions 1, 2, and 5 are already matched in correct order.

Step-by-step explanation:

1. Meter - standard metric unit of length.

2. hypothesis - a proposed explanation for a scientific problem.

3. mass - amount of matter in an object.

4. liter - standard unit of volume.

5. control - a quantity in an experiment that remains unchanged or constant.

6. meniscus - the curved top surface of a liquid column.

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The line plot shows the weights of all the fish caught on a fishing trip.

Natalija [7]

Answer:

B) 4 3/4

Step-by-step explanation:

We are looking for the total weight of the fish that weight more than 1 1/4 lbs

There are 2 fish that weight 1 1/2 and 1 that weights 1 3/4

2 ( 1 1/2 ) + ( 1 3/4)

Change the 1st mixed number to improper fractions

2 ( 2*1+1)/2 + (1 3/4)

2 * (3/2) + 1 3/4

3 + 1 3/4

4 3/4

7 0

3 years ago

Read 2 more answers

Solve the Anti derivative.

Alex Ar [27]

Answer:

$\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C$

General Formulas and Concepts:

Algebra I

Factoring

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Factor fraction denominator: $\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx$
[Integral] Integration Property - Multiplied Constant: $\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx$

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

$\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx$

Step 4: Integrate Pt. 2

[Integral] Substitute u-du: $\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du$
[Integral] Trig Integration: $\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C$
[Integral] Simplify: $\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C$
[integral] Multiply: $\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C$
[Integral] Back-Substitute: $\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C$