Rewrite with only sin x and cos x. cos 3x

Answers

Answer 1

[tex]\cos (3x)=4\cos^3 x-3\cos x[/tex]

Related Questions

222+203 is rounded up to what?

Answers

[tex]222: 220 \\ 203 = 200 \\ \\ 222 + 203 = 425 \\ 220 + 200 = 420 \\ \\ \\ \\ Good \\ luck \\ on \\ your \\ assignment \\ \\ enjoy \\ your \\ day \\ \\ \\ MeIsKaitlyn :)[/tex]

[tex]Remember [/tex]↓

[tex]1-5[/tex] would rounded [tex]downward [/tex]
[tex]6-9[/tex] would be rounded [tex]upward [/tex]

A total of 504 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?

Answers

a + s = 504
s = a + 54

a + (a + 54) = 504
2a + 54 = 504
2a = 504 - 54
2a = 450
a = 450/2
a = 225 <=== adults

a + s = 504
225 + s = 504
s = 504 - 225
s = 279 <=== students

Final answer:

Using algebra, we find that 225 adult tickets were sold out of a total of 504 tickets.

Explanation:

Let's denote the number of adult tickets as x. Since there were 54 more student tickets sold than adult tickets, we can represent the number of student tickets as x + 54. The total number of tickets sold is 504, so we set up the equation x + (x + 54) = 504.

Combining like terms, we get 2x + 54 = 504. Subtracting 54 from both sides gives us 2x = 450. Finally, dividing both sides by 2 gives us x = 225.

Therefore, 225 adult tickets were sold.

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A cold front moved in last weekend. In eight hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour ?

Answers

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ \begin{cases} x_1=0\\ x_2=8 \end{cases}\implies \cfrac{f(8)-f(0)}{8-0}\implies \cfrac{14-(-10)}{8-0}\implies \cfrac{14+10}{8}\implies \cfrac{3^o}{1hr}[/tex]

Bill's Roast Beef sells 5 times as many sandwiches as Pete's Deli. The difference between their sales is 360 sandwiches. How Many did each sell ?

Answers

b - p = 360
b = 5p

5p - p = 360
4p = 360
p = 360/4
p = 90 <== Pete's deli

b = 5p
b = 5(90)
b = 450 <== Bill's Roast Beef

Answer:

5y-y =360

4y =360

y= 90 sandwiches by Pete's deli

x= 5(90) = 450 sandwiches by Bills Roast Beef

Step-by-step explanation:

Suppose Q and R are independent events. Find P(Q and R) if P(Q) =4/5 and P(R) =4/11

Answers

Since Q and R are independent, this means P(Q and R) = P(Q)*P(R)

P(Q and R) = P(Q)*P(R)
P(Q and R) = (4/5)*(4/11)
P(Q and R) = (4*4)/(5*11)
P(Q and R) = 16/55

Tina wants to save money for school. Tina invests 400$ in an account that pays interest rate of 8%. How many years will it take if her goal is 5500$

Answers

To determine the number of years it would take for money to reach a certain amount, we need to know the type of interest of the problem. As a general rule, when it is not stated clearly in the problem, we assume that it is a simple interest problem since it is the basic type of interest. We use the formula for the future value for simple interest rate. It is expressed as:

F = P (1 + i )^n where F is the future value, P is the present value, i is the interest rate, and n is the number of years

We calculate as follows:
5500 = 400 (1 + .08 )^n
55/4 = (1 + .08)^n
n = 34.06 years

5. Simplify (15x2 – 24x + 9) ÷ (3x – 3) = ?

Answers

The likelihood is that because we've been told to divide the quadratic by a linear expression, it may perfectly factorize and the linear expression is, in fact, one of the two factors so we can use it to find the other factor by inspection:
3x would have to multiply by 5x to get the 15x² term in the quadratic.
-3 would have to multiply by -3 to get the 9 term in the quadratic.
The second factor would, therefore, be (5x - 3) if the linear divisor is actually a factor. In this case, it is, which we can confirm by expanding.
15x² - 24x + 9 = (3x - 3)(5x - 3)
So:
(15x2 – 24x + 9) ÷ (3x – 3) = 5x - 3

In the middle of the page draw a equilateral triangle with 2 inch sides and the bottom parallel to the of the page

Answers

The sum of the angle of a triangle is 180 degrees. If you are to draw a pattern of equilateral triangles then you know that an equilateral triangle has three equal sides. Also, its angles are the same, having 60 degrees at each corner of the triangle. A triangle cannot qualify as an equilateral triangle if it is greater than 180 degrees or less than 180 degrees as a total angle. Also if a triangle that has no two right angles, then it is called a scalene triangle. If the triangle has two right angles, it is called isosceles triangle. A triangle with equal sides is called an equilateral triangle.

A total of 487 tickets were sold for the school play. They were either adult tickets or student tickets. There were 63 fewer student tickets sold than adult tickets. How many adult tickets were sold?

Answers

s=a-63

s+a=487, using s from above in this equation you get:

a-63+a=487 combining like terms

2a-63=487 adding 63 to both sides

2a=550 dividing both sides by 2

a=275

So there were 275 adult tickets sold.

Final answer:

To determine the number of adult tickets sold for the school play, a system of equations is set up and solved, revealing that 275 adult tickets were sold.

Explanation:

To find the number of adult tickets sold for the school play, we need to set up a system of equations based on the information given. Let x represent the number of adult tickets and y represent the number of student tickets. According to the problem, the following two statements are true:

The total number of tickets sold is 487: x + y = 487

There were 63 fewer student tickets sold than adult tickets: y = x - 63

We can substitute the second equation into the first to find the value of x:

x + (x - 63) = 487

2x - 63 = 487

2x = 487 + 63

2x = 550

x = 275

Therefore, 275 adult tickets were sold.

A company made 4 million in the second quarter this is 1/3 more then it made in the first quarter and 4/5 of what it made in the third quarter how much did the company make in all 3/4 combined

Answers

In this problem, you have to find the total profit the company made in the three quarters which makes up 3/4 of the whole. In the second quarter, the profit is 4 million. Let x be the profit in the first quarter. Following the description,

4 = (1+1/3)x
x = 3 million

Thus, the second quarter made 5.33 million profit.

For the third quarter, let's assign it to the y variable. Following the description,

4 = (4/5)(y)
y = 5 million

Thus, the total profit is 4 + 3 + 5 = 12 million

How Do You Sell More Walnuts In A Perfectly Competitive Market?
If the equilibrium price in a perfectly competitive market for walnuts
is $4.99 per pound,then an individual firm in this market can

A. Not sell additional walnuts unless the firm lowers its price.
B. Not sell additional walnuts at any price because the market is at equilibrium.
C. Sell an additional pound of walnuts at $4.99.
D. Sell more only by increasing its advertising budget.
the subject is Economics.

Answers

C I'm pretty sure is the answer.

A company that creates model cars uses a 1.5 foot : 1 inch ration when creating the models. If a real car is 12 feet long, how long will the model car be?

Answers

I believe the answer would be 8 inches.

richerd works at an ice cream shop. regular cones get two scopes of ice cream and large cones get three scoops. One hot saturday richard scooped 234 regular cones and 156 large cones one scoop of ice cream is 3 ounces a tub of ice cream is 10 pounds how many tubs of ice cream did richerd use to make the cones?

Answers

234 x 2 = 468 scoops

156 x 3 = 468 scoops

468 + 468 = 936 total scoops

936 x 3 = 2808 ounces

16 ounces = 1 pound

2808/16 = 175.5 pounds

175.5/10 = 17.55 tubs

round answer as needed

What is the slope of a line that passes through the following points (-3,8) and (2,1)

Answers

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 8}})\quad % (c,d) &({{ 2}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-8}{2-(-3)}\implies \cfrac{1-8}{2+3}\implies \cfrac{-7}{5}[/tex]

Hello!

Step-by-step explanation:

Slope: [tex]\frac{Y^2-Y^1}{X^2-X^1}=\frac{rise}{run}[/tex]

[tex]\frac{1-8=-7}{2-(-3)=2+3=5}=\frac{-7}{5}=-\frac{7}{5}[/tex]

Slope is -7/5

Answer is -7/5

Hope this helps!

Thanks!

-Charlie

Find an approximation of the area of the region R under the graph of the function f on the interval [-1, 2]. Use n = 6 subintervals. Choose the representative points to be the left endpoints of the subintervals. f(x) = 7 - x2

Answers

The approximation of the area of the region R under the graph of the function is 18.625 square units.

In this question we must calculate the approximate area ([tex]A[/tex]) below the curve by means of Riemann sums with left endpoints, whose expression is described below:

[tex]A = \Delta x \cdot \Sigma\limits^{n-1}_{i=0} f(a + i\cdot \Delta x)[/tex], for [tex]x \in [a,b][/tex] (1)

[tex]\Delta x = \frac{b-a}{n}[/tex] (2)

Where:

[tex]a[/tex] - Lower bound[tex]b[/tex] - Upper bound[tex]n[/tex] - Number of subintervals[tex]i[/tex] - Index

If we know that [tex]a = -1[/tex], [tex]b = 2[/tex], [tex]n = 6[/tex] and [tex]f(x) = 7 - x^{2}[/tex], then the approximate area is:

[tex]\Delta x = \frac{2-(-1)}{6}[/tex]

[tex]\Delta x = 0.5[/tex]

[tex]A = 0.5\cdot [f(-1) + f(-0.5)+f(0)+f(0.5)+f(1)+f(1.5)][/tex]

[tex]A = 0.5\cdot (6+6.75+7+6.75+6+4.75)[/tex]

[tex]A = 18.625[/tex]

The approximation of the area of the region R under the graph of the function is 18.625 square units.

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Three counters are used for a board game.If the counters are tossed,how many ways can at least one counter with Side A occur?

Answers

We use the equation for repeated trials written below:

Probability = n!/r!(n-r)! * p^(n-r) * q^r

The p is the probability of getting a side A in one toss. Since a counter has only two side, p = 0.5. The q is the probability of not getting side A in one toss, which is also q = 0.5. Now, r is the number of success per n trials. There are 3 tosses so, n=3. The question is getting "at least 1" counter. So, r=1, r=2 and r=3.

Probability for r=1: 3!/1!(3-1)! * (0.5)^(3-1) * (0.5)^1= 0.375
Probability for r=2: 3!/2!(3-2)! * (0.5)^(3-2) * (0.5)^2= 0.375
Probability for r=1: 3!/3!(3-3)! * (0.5)^(3-3) * (0.5)^3= 0.125

Total probability = 0.375 + 0.375 + 0.125 = 0.875

What's the average of 200 and 300

Answers

To find the average, add both of the numbers and divide by the amount of numbers. For this, it is 200+300=500. Then, 500/2=250. The average is 250. Hope this helps! ;)

The average should be at least 250 because if you add 200+300 that will 500 so it has to be between that amount so the average 250

a patient requires 30% decrease in the dosage of the medication her current dosage is 340 MGS what will the dosage be after the decrease

Answers

a 30 % decrease means u r giving 70%
0.70(340) = 238 MGS

Answer:

The dosage will be 238 MGS after decrease.

Step-by-step explanation:

The current dosage of the medication of the patient = 340 MGS

patient requires 30% decrease in the dosage of the medication.

Now her new dosage after decrease = 340 -(30% × 340)

= 340 -(0.30 × 340)

= 340 - 102

= 238 MGS

The dosage will be 238 MGS after decrease.

The sales tax in Bill's state is 6%. Bill bought a Scion having a sales tax of $820. What was the cost of the car, rounded to the nearest dollar.

Answers

I'm not sure how you're supposed to do it, but that how I did it.

Change 6% to a decimal. So, $.06.
Then divide .06 by the actual tax. 820/$.06= 13666.66666666666666666666666666.... Round $13666.67.
To check, multiply the answer by the tax which is
$.06, to get $820.

A figure has a vertex at (5, 2). If the figure has line symmetry about the y-axis, what are the coordinates of another vertex of the figure?

Answers

The answer will be (-5, 2)

Answer:

[tex](-5,2)[/tex]

Step-by-step explanation:

We have been given that a figure has a vertex at (5,2). The figure has line symmetry about the y-axis.

We know that if a figure is symmetric about y-axis, then its x-coordinate changes to opposite sign and y-coordinate remains same.

We can see that x-coordinate of our given point is 5, so x-coordinate of another vertex of the figure would be -5.

Therefore, the point [tex](-5,2)[/tex] is symmetric about y-axis for our given point.

Find the arc length of the curve on the given interval. (round your answer to three decimal places.) parametric equations interval x = 6t + 5, y = 7 − 7t −1 ≤ t ≤ 3

Answers

[tex]\displaystyle\int_{-1}^3\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

[tex]x=6t+5\implies\dfrac{\mathrm dx}{\mathrm dt}=6[/tex]
[tex]y=7-7t\implies\dfrac{\mathrm dy}{\mathrm dt}=-7[/tex]

[tex]\displaystyle\int_{-1}^3\sqrt{36+49}\,\mathrm dt=\sqrt{85}(3-(-1))=4\sqrt{85}[/tex]

The arc length of the curve on the given interval −1 ≤ t ≤ 3 with parametric equation x = 6t + 5 and y = 7 − 7t −1 is 4√85.

What is integration?

It is the reverse of differentiation.

The arc length of the curve on the given interval.

Parametric equations interval

x = 6t + 5, −1 ≤ t ≤ 3

y = 7 − 7t, −1 ≤ t ≤ 3

We know that the parametric form of the arc length will be given as

[tex]\rm \int _{-1}^3 \sqrt{(\dfrac{dx}{dt})^2 + (\dfrac{dy}{dt})^2} \ dt[/tex]

Then we have

[tex]\rm \dfrac{dx}{dt} = 6\\\\\dfrac{dy}{dt} = -7[/tex]

Then the arc length will be

[tex]\rightarrow \rm \int _{-1}^3 \sqrt{(3)^2 + (-7)^2} \ dt\\\\\rightarrow \sqrt{85} [t]_{-1}^3 \\\\\rightarrow 4 \sqrt{85}[/tex]

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Mick and LaToya have some shirts. The ratio of the number of shirts Mick has to the number of shirts LaToya has is 3:8. If they have a total of "k" shirts, how many fewer shirts does Mick have than LaToya?

Answers

This is the concept of algebra, given that Latoya and Mick have shirts that total up to k shirts, and the ratio of shirts that Mick has to Latoya is 3:8, then to solve our question we proceed as follows;
total ratio is :
3+8=11
thus the number of shirts Mick has is:
3/11*k=3/11k
The number of shirts Latoya has is:
8/11k
To calculate how many more shirts Latoya has compared to Mick we proceed as follows;
8/11k-3/11k
=5/11k
The answer is 5/11k

Sara must plant 340 trees. In the past 6 days Sara planted 204 trees. If she continues at this rate, how many more days will it take her to plant all the trees?

Answers

204/6 = 34 trees a day. 340-204 =136 trees left to plant. 136/34 = 4 4 days

A bird feeder is in the shape of a cylinder. It has a volume of about 100 cubic inches. It has a radius of 2 inches. What is the approximate height of the bird feeder? Use 3.14 for pi

Answers

volume = pi x r^2x h

100 = 3.14 x 2^2 x h

100 =3.14 x 4 x h

100 = 12.56 x h

h = 100/12.56 = 7.9617

the height is approximately 8 inches tall

Simplify the expression. 33 • 32 + 12 ÷ 4

Answers

Final answer:

The expression 33 • 32 + 12 ÷ 4 simplifies to 1059.

Explanation:

To simplify the expression 33 • 32 + 12 ÷ 4, we follow the order of operations - performing multiplication and division before addition.

Multiply 33 and 32 to get 1056.Divide 12 by 4 to get 3.

Now we can add the results: 1056 + 3 = 1059.

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A chemist is using 353 millimeters of a solution of acid and water. If 16.5% of the solution is acid, how many millimeters of acid are there? Round your answer to the nearest tenth.

Answers

16.3%=0.163

353(0.163)=57.539

57.539 is rounded to 57.5

There are 57.5 millimeters of acid. Hope this helps!

In how many different ways can you make exactly 0.75 using only nickles dimes and quarters if you have at least one of each coin?

Answers

There are 18 different ways to make 75 cents

18 different ways to make 75 cents

which number produces a rational number when added to 0.5

Answers

Let, the number be x

Therefore, x +0.5= p/q where q is non zero and (p, q) co-prime.

Then, x= -0.5 + (p/q)

now you can substitute any value of p and q to get x.

Answer:

Any rational number.

Step-by-step explanation:

∴ [tex]x+0.5[/tex] is rational if and only if x is rational.

To proveL: we proceed as follows:

Suppose that [tex]x+0.5[/tex] is rational.

Then there are some integers p , q with [tex]q\neq 0[/tex] such that

[tex]x+\frac{1}{2}=\frac{p}{q}[/tex]

Subtract both sides by [tex]\frac{1}{2}[/tex], we get

[tex]x=\frac{p}{q}-\frac{1}{2}=\frac{2p-q}{2q}[/tex] which is rational.

Conversely, if x is rational, then there are integers a,b with b>0 such that [tex]x=\frac{a}{b}[/tex] then we have,

[tex]x+\frac{1}{2}=\frac{a}{b}+\frac{1}{2}=\frac{2a+b}{2b}[/tex] which is also a rational.

What is the volume of an oblique cone with radius 9 cm and height 12 cm?

972π cm3

486π cm3

648π cm3

324π cm3

Answers

the correct answer is the fourth one 324\pi cm3

[tex]V = \frac{1}{3}\pi \cdot r^{2}h[/tex]
[tex] = \frac{1}{3}\pi \cdot 81\cdot 12[/tex]
[tex] = \frac{972\pi}{3}[/tex]
[tex] = 324\pi (cm)^{3}[/tex]

What is the arc measure of an arc with length 4.189 cm and radius equal to 3 cm.'?

Answers

Given that the arc length is 4.189 cm and the radius is 3 cm, the size of the arc will found as follows;
C=theta/360 πd
suppose:
size of arc=theta=x
d=3*2=6 cm
hence;
4.189=x/360*π*6
4.189=0.0524x
x=4.189/0.0524
x=80.004°
The size of the arc length is 80.004°

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