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3 years ago

3 sinx + 4 cosx = 5

1 answer:

7 0

3sinx+4cosx=5
=> 3/5 sinx +4/5 cosx = 1
let cosA=3/5 => sinA=4/5
=> cosAsinx + sinAcosx = 1
=> sin(x+A) = 1
Now,
4sinx - 3cosx
= 5(4/5sinx - 3/5 cosx) [multipying numerator and denominator by 5]
= 5(sinAsinx - cosAcosx)
= -5{cos(x+A)} = -5[root{1-(sin(x+A)^2)}] = -5 x 0 = 0 Ans 0

TRICK: if asinx+bcosx is given then multiply numerator and denominator by root(a^2 +b^2)
this method is useful in many questions

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A spinner has 10 equal-sized sections. Two of the sections are red.

hichkok12 [17]

Answer:

a. Probability of landing on red = $\frac{1}{5}$

b. See Explanation

Step-by-step explanation:

Given

A Spinner

Number of section = 10 (equal sized)

Number of red section = 2

Required

- Probability of landing on red

- Describe the probability in words

Calculating the probability of landing on red

The formula used in calculating probability is as follows

Probability = Number of required outcomes / Number of possible outcomes

In this case, the number of required outcomes is the number of red section.

Hence, number of required outcomes = 2

And the number of possible outcomes is the total section of the spinner

Hence, Number of possible outcomes = 10

By Substitution

Probability of landing on red = $\frac{2}{10}$

Probability of landing on red = $\frac{1}{5}$

Describe the probability in words

From (a) above, we have that the probability of the spinner landing on color red is $\frac{1}{5}$

This means that, for every five times, you spin the spinner, it's likely that one of the outcomes will be red.

8 0

4 years ago

Andre and Elena are each saving money. Andre starts with $100 in his savings account and adds $5 per week. Elena starts with $10

Tomtit [17]

Answer:

Andre have more money after 4 weeks and after 6 week they have same amount of money.

Step-by-step explanation:

When Andre =100 then Elena =10.

After 4 week,

Andre = 100+(5*4)=100+20=120

In this time Elena = 10+(20*4) =10+80 = 90

After more 2months Andre have more 5+5=10

Then his total balance will be 120+10=130.

Than Elena after 2 week have 20+20=40.

Then her total balance will be 90+40=130.

That's mean 4 weeks+ extra 2 weeks total 6 weeks

6 0

3 years ago

Read 2 more answers

The sum of a number and 2 times its reciprocal is -3

Marysya12 [62]

Answer:

(-2,-1)

Step-by-step explanation:

let the number=x

its reciprocal=1/x

x+2(1/x)=-3

x+2/x=-3

x²+2=-3x

x²+3x+2=0

(x+2)(x+1)=0

x=-2,-1

6 0

3 years ago

Evaluate the following expression In e^e. A) e^2 B) 1 C) 0 D) e

saw5 [17]

Answer:

D) e

Step-by-step explanation:

ln e^e

We know that ln x^a is the same as a ln x

e ln (e)

we know that ln e =1

e (1)

5 0

4 years ago

Read 2 more answers

john surveyed a random sample of 10 students in 7th grade seven of them they would vote for tammy as class president if there ar

dmitriy555 [2]

7 out of 10 would vote for Tammy so what value (x) would vote for her out of 230. Set up a proportion comparing the two.

x= # of people who vote Tammy

7 out of 10= x out of 230
7/10= x/230
cross multiply

(7*230)= (10*x)
1610= 10x
divide both sides by 10

161= x

ANSWER: 161 people in 7th grade would vote for Tammy.

Hope this helps! :)

6 0

3 years ago