y varies directly as x and inversely as the square of z. y = 65 when x = 80 and z=4. Find y when x= 18 and z=3.

Answer: y

=

18

Explanation:

As

y

varies directly as

x

, we have

y

∝

x

. Also it varies inversely as square of

z

, which means

y

∝

1

z

2

.

Hence,

y

∝

x

z

2

or

y

=

k

×

x

z

2

, where

k

is a constant.

Now when

x

=

80

and

z

=

4

,

y

=

10

, so

10

=

k

×

80

4

2

=

k

×

80

16

=

5

k

Hence

k

=

10

5

=

2

and

y

=

2

x

z

2

.

So when

x

=

36

and

z

=

2

,

y

=

2

×

36

2

2

=

72

4

=

18

Step-by-step explanation:

The measure of angle R is 3 degrees less than twice the measure of angle S. If the sum of the measures of the two angles is 72 degrees, find the measure of each angle.

Hi it ravens home 1
Student’s Answer Key Ch.2 Grammar Advantage Eric Nelson & George Yule © 2019 Student’s Answer Key, Chapter 2, Sentence structure, Grammar Advantage
For most exercises, this key does not include even-numbered items.
■ Exercise 1 Read the passage. Based on what you already know, underline the verbs.
The Marshmallow Experiment
Imagine that you are seven years old. You are participating in an experiment. A researcher greets you and shows you into a small room. In the room there is a marshmallow. The marshmallow is for you, but here is the interesting part: The researcher tells you that he is going to leave you alone in the room for a while. You can eat the marshmallow right away, or you can wait until he gets back. If you wait until he gets back, you will get a second marshmallow.
What do you do? Do you eat the marshmallow right away?
An experiment like this, known informally as the marshmallow experiment, was conducted decades ago at Stanford University. It turned out that some children ate the marshmallow right away, while others were able to wait. In other words, some sought instant self-gratification, and some delayed it.
Years later, the researchers followed up on the participants. They found that the children who delayed self-gratification were in general more successful than those who ate the marshmallow right away. By a variety of measures, including SAT scores, they appeared to be more competent.
Common sense tells us that the ability to delay self-gratification is a mark of maturity. The marshmallow experiment provides evidence that it may also correlate with success in life.
Notes:
- Many of these verb phrases consist of an auxiliary verb and a main verb. So, for example, “are participating” and “do...eat” are considered verb phrases.
- “is going to leave”: If we consder “is going to” a kind of auxiliary verb, then this is a verb phrase, just like “will leave.”
- “known as...”: If you underlined “known,” that’s fine. It is a verb. It is a nonfinite verb, unlike the other underlined verbs and verb phrases. (See Chapter 4.)
■ Exercise 2 Underline the complete subjects in the sentences below, and double- underline the verbs that go with them. Identifying the subject means identifying the main word of the subject and the parts that modify it. (In the first sentence, the main word is in boldface.) When you underline the verb, include both auxiliary verbs and main verbs (as in the first sentence, with was...used).
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