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antiseptic1488 [7]

3 years ago

12

1. tan a = cot(a + 10°)

1 answer:

Temka [501]3 years ago

7 0

Answer:

$a=40+90n$

Step-by-step explanation:

Use a cofunction identity on the right hand side or left hand side...

So $\tan(a)=\cot(90-a)$ .

We have the equation:

$\tan(a)=\cot(a+10)$

Make the above replacement:

$\cot(90-a)=\cot(a+10)$

Since cotangent has period 180 degrees, we can also write this as:

$\cot(90-a+180n)=\cot(a+10)$

So solving the following will give us a set of solutions for $a$ :

$90-a+180n=a+10$

Add $a$ on both sides:

$90+180n=2a+10$

Subtract 10 on both sides:

$80+180n=2a$

Divide both sides by 2:

$40+90n=a$

Symmetric property:

$a=40+90n$

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Let Q(x, y) be the predicate "If x < y then x2 < y2," with domain for both x and y being R, the set of all real numbers.

Levart [38]

Answer:

a) Q(-2,1) is false

b) Q(-5,2) is false

c)Q(3,8) is true

d)Q(9,10) is true

Step-by-step explanation:

Given data is $Q(x,y)$ is predicate that $x$ then $x^{2}$ . where $x,y$ are rational numbers.

a)

when $x=-2, y=1$

Here $-2$ that is $x$ satisfied. Then

$(-2)^{2}$

$4$ this is wrong. since $4>1$

That is $x^{2}$ $>y^{2}$ Thus $Q(x,y)$ $=Q(-2,1)$ is false.

b)

Assume $Q(x,y)=Q(-5,2)$ .

That is $x=-5, y=2$

Here $-5$ that is $x$ this condition is satisfied.

Then

$(-5)^{2}$

$25$ this is not true. since $25>4$ .

This is similar to the truth value of part (a).

Since in both $x$ satisfied and $x^{2} >y^{2}$ for both the points.

c)

if $Q(x,y)=Q(3,8)$ that is $x=3$ and $y=8$

Here $3$ this satisfies the condition $x$ .

Then $3^{2}$

$9$ This also satisfies the condition $x^{2}$ .

Hence $Q(3,8)$ exists and it is true.

d)

Assume $Q(x,y)=Q(9,10)$

Here $9$ satisfies the condition $x$

Then $9^{2}$

$81$ satisfies the condition $x^{2}$ .

Thus, $Q(9,10)$ point exists and it is true. This satisfies the same values as in part (c)

6 0

3 years ago

Jill has a photograph that is 4 inches wide by 6 inches high. If she enlarges it so that the width is 12

Nadya [2.5K]

Answer:

The inches in height will be 18 inches.

Step-by-step explanation:

Okay so we know that the original width is 4 inches and she enlarged that to 12 inches

So what we first have to do is find out how much did the photograph "grow" per se. To find this we have to divide 12 by 4. 12 divided by 4 = 3.

So, the width of the photograph grew "times 3" inches

Now whatever you do to the width you have to do to the height. In this case, what is "3 times" 6 (which is the height). 3 times 6 = 18 inches

So in simpler words 12 divided 4 = 3 x 6 = 18 inches

The inches in height will be 18 inches.

Jill has a square with a width of 12 inches, and a height of 18 inches.

Have a wonderful day!

5 0

3 years ago

A scrapbooking store is selling rubber stamps for four dollarsand $4.95 each. The total sales F(n) is a function of the number o

just olya [345]

A. Independent variable: number of rubber stamps n sold. Dependent variable: F(n), the total sales.

B. Only whole numbers. It is impossible to have negative and/or fractional stamps.

C. F(n) = $4.95n, which is 4.95 times n.

So, plugin 5 for n

$f(5)= \$4.95(5)$

F(n) = $24.75

6 0

3 years ago

Read 2 more answers

Please help me this is urgent! Both need an answer.

dolphi86 [110]

My answer is B and A that's my answer

3 0

3 years ago

CAN SOMEONE PLEASE HELP ME ANSWER THIS

iren [92.7K]

Answer:

The answer to this question is 40

8 0

3 years ago

Read 2 more answers