Can anyone help me with trig identities?

Answer:

36

Step-by-step explanation:

Total students un the contest = 84

Number of students who gave their speech yesterday:-

[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]

so 21 students gave their speech yesterday

= 63

Number of students who gave their speech today:-

[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]

Number of students who have given their speech:-

= 21 + 27

= 48

Number of students who still haven't given their speech :-

= total - 48

= 84 - 48

= 36

Answer:

t2 = 2.5 hours.

Step-by-step explanation:

The distance is the same.

d = r * t

The rates and times are different so

t1 = 3 hours

t2 = X

r1 = 50 mph

r2 = 60 mph

r1 * t1 = r2*t2

50 * 3 = 60 * t2

150 = 60 * t2

150 / 60 = t2

t2 = 2.5

Answer:

Answer: Travel Time is 2 hours & 30 minutes

Step-by-step explanation:

Original Journey Time is 3 hours, Speed is 50 mph, Distance is 150 miles

Original Distance is 150 miles, New Speed is 60 mph.

Also Combined Distance was 300 miles, Combined Time was 5 hours & 30 minutes. therefore: Average Speed for complete round trip is 54. 54 mph

Answer:

y=−3x+21

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula

Answer:

B

Step-by-step explanation:

To solve this use a unit circle (see pic)

Go to the 300 degree

Then look at the y coordinate (y coordinate because it's cosine)

Which matches with answer choice B

Answer:

100 % or 1

Step-by-step explanation:

There are two dice

Each dice has a possible roll of 1,2,3,4,5,6

The possible sums are 2,3,4,5,6,7,8,9,10,11,12

The probability of getting a sum greater than 1 is 100 % or 1 since the outcomes are all greater than 1

Answer:

The car will depreciate at a rate of 21.14% per year.

Step-by-step explanation:

Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:

13,500 x (1 + X) ^ 1x3 = 24,000

13,500 x (1 + 0.2114) ^ 3 = 24,000

X = 21.14%

Therefore, the car will depreciate at a rate of 21.14% per year.

Hi there!

[tex]\large\boxed{x = 60^o}[/tex]

We know:

∠AGB ≅ ∠DGC because they are vertical angles. They both are 90°.

∠AGE ≅ FGC because they are vertical angles, equal 30°.

∠BGF ≅ ∠DGE are vertical angles, both equal x.

All angles sum up to 360°, so:

360° = 90° + 90° + 30° + 30° + x + x

Simplify:

360° = 240° + 2x

Subtract:

120°  = 2x

x = 60°

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Answer:

  A)  (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it

Step-by-step explanation:

We want ...

  C(x)/x < 100

  (20x +160)/x < 100

  20 +160/x < 100 . . . . . separate the terms on the left

  160/x < 80 . . . . . . . subtract 20

  160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0

  x > 2 . . . . . . simplify

In interval notation this is (2, ∞).   matches choice A

__

Technically (mathematically), we also have ...

  160/80 > x . . . . and x < 0

which simplifies to x < 0, or the interval (-∞, 0).

If we include this solution, then choice C is the correct one.

_____

Comment on the solution

Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.

Answer: 90° counterclockwise

Step-by-step explanation:

Answer:

d=10.45t

Step-by-step explanation:

The last one is the answer.

Hope this helps!

--Applepi101

Answer:

D) d=10.45t

Step-by-step explanation:

His distance(d) was 100. And his time(t) was 9.58 seconds.

So 100=9.58x

x≈10.44

The answer is D, because 10.45 is greater than 10.44.

I hope this helps!

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Answer:

  $562,500 per hour

Step-by-step explanation:

The cost will be a minimum where C'(x) = 0.

 C'(x) = 0.56x -0.7 = 0

  x = 0.7/0.56 = 1.25

The cost at that production point is ...

  C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625

The minimum production cost is $562,500 per hour for production of 1250 items per hour.

_____

Additional comment

This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.

Answer:

[tex]1/16[/tex]

Step-by-step explanation:

The formula for the sequence [tex]a_n=\frac{1}{2}^n[/tex] is used to find the [tex]n[/tex]th term of the sequence.

To find the fourth term, substitute [tex]n=4[/tex]:

[tex]a_4=\left(\frac{1}{2})\right ^4,\\a_4=\frac{1^4}{2^4}=\boxed{\frac{1}{16}}[/tex]

Answer:

1/16

Step-by-step explanation:

the nth term is

[tex]a_{n} = (\frac{1}{2} )^{n}[/tex]

the 4th term is found by substituting n=4

[tex]a_{4} =(\frac{1}{2} )^{4} = \frac{1^{4} }{2^{4} } = \frac{1}{16}[/tex]

Answer:

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.

Answer:

[tex]f(x)=\sqrt[3]{x}[/tex]  [tex]3~units\: down[/tex]

[tex]f(x)=\sqrt[3]{x} -3[/tex] [tex]8 \: units \: left[/tex]

[tex]f(x+8)=\sqrt[3]{(x+8)} -3[/tex]

----------------------------

Hope it helps..

Have a great day!!

Answer:

its not B that what i put and i missed it

Step-by-step explanation:

Answer:

C) the length of DG and JL

Answer:

4*12*2

Step-by-step explanation:

it will be the right answer

Answer:

There are 6 boys in group.

Step-by-step explanation:

Since we have given that

Number of arrangement of 4 boys = 12 times the number of arrangement of 2 boys.

So, Let the number of boys in the group be 'x'.

So, Number of boys in the group will be

\begin{gathered}x=\frac{12\times 2}{4}\\\\x=\frac{24}{4}\\\\x=6\end{gathered}

x=

4

12×2

x=

4

24

x=6

Hence, there are 6 boys in the group.

hope it helps you a follow would be appreciated

Answer:

R1 = 150 in = 12.5 ft

R2 = 170 in = 14.167 ft

H = 220 in = 18.333 ft

Volume of solid cylinder = Pi * R^2 * H

So the volume of a hollow cylinder must be V = Pi * H * (R2^2 - R1^2)

V = 3.142 * 18.33 * (14.17^2 - 12.5^2) = 2565 ft^3

.

Answer:

n = 2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 30 = n / 2 sqrt(3)

2 sqrt(3) tan 30 = n

2 sqrt(3) * sqrt(3)/3 = n

2 = n

We have to find,

The required value of n.

Now we can,

Use the trigonometric functions.

→ tan(θ) = opp/adj

Let's find the required value of n,

→ tan (θ) = opp/adj

→ tan (30) = n/2√3

→ n = 2√3 × tan (30)

→ n = 2√3 × √3/3

→ n = 2√3 × 1/√3

→ [n = 2]

Thus, the value of n is 2.

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Answer:

  3

Step-by-step explanation:

AB is 1 unit long.

A'B' is 3 units long.

The scale factor is the ratio of these lengths:

  scale factor = A'B'/AB = 3/1 = 3

ABC is dilated by a factor of 3 to get A'B'C'.

Answer:

Kindly check explanation

Step-by-step explanation:

Since the triangle is right angled ; we can solve for x using Pythagoras :

x = hypotenus ; hence ;

x² = opposite² + adjacent²

x² = 15² + 8²

x² = 225 + 64

x² = 289

x = √289

x = 17

Using Trigonometry :

Sin D = side opposite D / hypotenus = 8/17

Cos D = side Adjacent D / hypotenus = 15 / 17

Tan D = side opposite D / Adjacent side = 8/15

Sin F = side opposite F / hypotenus = 15/17

Cos F = side Adjacent F / hypotenus = 8 / 17

Tan F = side opposite F / Adjacent side = 15/8

Answer:

[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = x^2[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

(a) 129600 J

(b) 81000 J

Step-by-step explanation:

The work done is given by the product of force and the displacement in the direction of force.

Force, F = 500 N

distance, d = 324 m

(a) friction force, f = 100 N

The work done is

W = (F - f) x d

W = (500 - 100) x 324

W = 129600 J

(b) Friction, f = 250 N

The work done is

W = (F - f) d

W = (500 - 250) x 324

W = 81000 J

Answer:

x = 105/16

Step-by-step explanation:

2/3x - 1 = 27/8

Add 1 to each side

2/3x - 1+1 = 27/8+1

2/3x = 27/8 + 8/8

2/3x = 35/8

Multiply each side by 3/2

3/2 * 2/3x = 35/8 *3/2

x = 105/16

Answer:

XW = 78

Step-by-step explanation:

Both triangles are similar, therefore based on triangle similarity theorem we have the following:

XW/XZ = VW/YZ

Substitute

XW/6 = 104/8

XW/6 = 13

Cross multiply

XW = 13*6

XW = 78

Answer:

= 1296x √ xy

Step-by-step explanation:

Apply exponent rule: a^b . a^c = a^b + c    3 . 3 = 3^ 1 + 1

= x . 3^1+1 √648x . 4y . 8

Add the numbers: 1 + 1 = 2

= x . 3^2 √648x . 4y . 8

= 3^2 . 144x √ xy

Refine

= 1296x √ xy

Answer:

The answer is A: 6√2 - 2√30 + 6 - 2√15

Believe me it right.

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Explanation:

  [tex]\sin^2(\theta)\times\left(1+\dfrac{1}{\tan^2(\theta)}\right)=\\\\\sin^2(\theta)\times\left(1+\dfrac{\cos^2(\theta)}{\sin^2(\theta)}\right)=\\\\\dfrac{\sin^2(\theta)\cdot(\cos^2(\theta)+\sin^2(\theta))}{\sin^2(\theta)}=\\\\\cos^2(\theta)+\sin^2(\theta)=1\qquad\text{Q.E.D.}[/tex]