Express the product as a sum containing only sines or cosines. 64) sin (5θ) cos (2θ)

Answer:

Step-by-step explanation:

Answer:

125 grams.

Step-by-step explanation:

We have been given an equation , which models the mass of a mammal’s brain, in grams, where x is the mass of the mammal, in kilograms.

To find the approximate mass of a mammal's brain with a body that has a mass of 60 kg, we will substitute  in our given equation.

Therefore, the mass of the mammal's brain is approximately 125 grams.

Step-by-step explanation:

you don't give us information about the runner

Answer:

.A.The volume of a gas varies directly with its temperature at constant pressure.

Step-by-step explanation:

This law is expressed mathematically as;

V₁ /T₁ =V₂/T₂ where

V₁=initial volume

T₁=initial absolute temperature

V₂=final volume

T₂=final absolute temperature

The temperature is converted to Kelvin when doing calculations where;

0°c = 273 K

An application of this law in real world examples could be  when a ball is left outside overnight it the cold, the ball shrinks a little in its volume due to decreased temperatures.

Answer:

A is the answer for sure i got it right after working it out.

Answer:

y = x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (- 4, - 5)

m = [tex]\frac{-5-4}{-4-5}[/tex] = [tex]\frac{-9}{-9}[/tex] = 1, thus

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (5, 4), then

4 = 5 + c ⇒ c = 4 - 5 = - 1

y = x - 1 ← equation in slope- intercept form

The final equation is y = x - 1.

To find the equation of the line in slope-intercept form, which is y = mx + b, we need two pieces of information: the slope (m) and the y-intercept (b). First, let's calculate the slope using the two given points (5,4) and (-4,-5).

The formula for slope is:

m = (y2 - y1) / (x2 - x1)

Therefore:

m = (-5 - 4) / (-4 - 5) = (-9) / (-9) = 1

Now that we have the slope, we use one of the points to solve for the y-intercept. By substituting the slope and the coordinates of one of the points into the equation, we get:

4 = (1)(5) + b

4 = 5 + b

b = 4 - 5 = -1

Finally, the equation of the line in slope-intercept form is:

y = x - 1

Answer:

actually ASA and SAA is the same ASA stands for angle side angle while SAA stands for side angle angle .lets prove

Step-by-step explanation:

first name the triangle as i told earlier like ABC and PQR then

first side:AB=PQ,angleA=angleP,angleB=angleQ

Answer:

Option D) 64

Step-by-step explanation:  

see the attached figure with letters to better understand the problem

In the right triangle BCD find BC

Applying the Pythagoras Theorem

[tex]BC^{2}=48^{2}+36^{2}\\BC^{2}=3,600\\BC=60\ units[/tex]

In the right triangle ABC

[tex]cos(C)=BC/AC[/tex]

substitute the values  

[tex]cos(C)=60/(x+36)[/tex] -------> equation A

In the right triangle BDC

[tex]cos(C)=CD/BC[/tex]

substitute the values

[tex]cos(C)=36/60[/tex] -------> equation B

equate equation A and equation B

[tex]60/(x+36)=36/60\\ \\(x+36)*36=60*60\\ \\36x+1,296=3,600\\ \\36x=3,600-1,296\\ \\36x=2,304\\ \\x=64\ units[/tex]

To find the missing length, use the Pythagorean theorem by setting up an equation with the given lengths in a right triangle. Solve for the missing length using the equation and determine the correct answer.

To find the missing length, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Let's assume the missing length is represented by 'x'. Using the theorem, we can set up the equation as follows:

We can solve for 'x' by substituting the given lengths into the equation and solving for 'x'.

x2 = a2 + b2

x2 = 162 + 302

x2 = 256 + 900

x2 = 1156

x = √1156

x = 34

Therefore, the missing length indicated is 34. Option B) 36 is not the correct answer.

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Answer:

C

Step-by-step explanation:

A function is even if:

f(x) = f(-x)

In other words, the function is symmetrical about the y-axis.

Function f is symmetrical, but it's not centered on the y-axis.

Function g is both symmetrical and centered on the y-axis.

So only g is an even function.  Answer C.

Answer:

Step-by-step explanation:

You multiply 27.50 with 5 and then divise by 100 (5%).It is around $1.37 to &1.38

To calculate the sales tax on a $27.50 purchase at 5%, convert 5% to decimal form (0.05) and multiply by the purchase amount. This results in a tax of $1.38, and the total cost with tax is $28.88.

To find the amount of sales tax due on a purchase of $27.50 with a 5% tax rate, you should first convert the percentage to a decimal. To do this, you divide by 100 or simply move the decimal point two places to the left. Thus, 5% becomes 0.05 as a decimal. Then, multiply this decimal by the total cost of the purchase to calculate the sales tax.

This calculation is as follows: $27.50 \ imes 0.05 = $1.375.

Since you generally do not pay fractions of a cent, you would round this number to the nearest cent, making the sales tax $1.38. The total cost with tax would then be the sum of the original cost plus the sales tax: $27.50 + $1.38 = $28.88.

To solve the equation

, you can use the numerical method such as the Newton-Raphson method to approximate the solutions. The solutions are approximately x ≈ 0.84185 and x ≈ 2.725.

To solve the equation

, we first rearrange it as

. Then, we can use a numerical method such as the Newton-Raphson method to approximate the solutions. Starting with an initial guess, we can iteratively apply the formula

until we reach an accurate solution. In this case, the solutions are approximately x ≈ 0.84185 and x ≈ 2.725.

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The solutions to the systems of equations graphically are (2, -2) and (1.52, -1.42)

From the question, we have the following parameters that can be used in our computation:

x³ - 3x + 2 = 0.1 - x

When splitted, we have

y = x³ - 3x² + 2

y = 0.1 - x

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

These points are located at (2, -2) and (1.52, -1.42)

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11 school days are left.

In the attached picture of a calendar, I marked the days the person has left. There are 11.

Answer:

6n

Step-by-step explanation:

Answer:

Carpenter = 12 hours

Blacksmith = 18 hours

Step-by-step explanation:

Look at attachment:

Hope this helps! :)

Giselle worked as a carpenter for hours and as a blacksmith for hours, last week will be 18 hours and 12 hours, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Giselle works as a carpenter and as a blacksmith. She earns $20 per hour as a carpenter and $25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 30 hours and earned a total of $690.

Let 'x' be the number of hours of a blacksmith and 'y' be the number of hours of a carpenter. Then the equations are given as,

x + y = 30                         ...1

20x + 25y = 690             ...2

From equations 1 and 2, then we have

20(30 - y) + 25y = 690

600 - 20y + 25y = 690

5y = 90

y = 18

Then the value of 'x' is given as,

x + 18 = 30

x = 30 - 18

x = 12

Giselle worked as a carpenter for hours and as a blacksmith for hours, last week will be 18 hours and 12 hours, respectively.

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Answer:

4

Step-by-step explanation:

In a 30-60-90 triangle, the short leg is half the length of the hypotenuse.

B.y i think I’m not smart

Answer:

29

Step-by-step explanation:

50 - 20 = 30

7 - 8 = -1

30 - 1 = 29

It would take 12 hours.

the equation would be 2/5=1/30x where x would equal the amount of hours it would take

Answer:

  A.  96π in³

Step-by-step explanation:

The formula you can use to find the volume of a cone is ...

  V = (π/3)r²·h . . . . where r is the radius and h is the height

Put the given numbers into the formula and do the arithmetic.

  V = (π/3)(6 in)²(8 in) = 96π in³

Answer:

The answer is 96 pi cu in

Step-by-step explanation:

The magnitude of the net force on the box is 100 Newtons to the left.

A force is the result of the interaction between two things and can be either a push or a pull. Due to the fact that it is a vector quantity, it possesses both magnitude and direction. The object's state of motion, direction, size, and form might all change as a result.

Given, the box is being pushed to the right with a force of 300 newtons, and to the left with a force of 400 newtons.

Here,

400 newtons > 300 newtons

400 newtons is much more than 300 newtons,

The net force on the box will be the sum of F₁ and F₂.

Let the forces F₁ and F₂ act on the table in opposite direction,

F₁ is the greater than F₂,

the F net = F₁-F₂

And the magnitude of the net force on the box,

400 -300 = 100 newtons.

Therefore, net force on the box is 100 Newtons to the left.

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The complete question is:

A box is being pushed to the right with a force of 300 Newtons', and to the left with a force of 400 Newtons'. What is the magnitude of the net force on the box?

if the rectangular coordiante is (x,y) and the polar coordinate is (R,t), then they are related as follows:

R^2=x^2+y^2

tant=y/x

1.(pi,pi/4)

here, R=

[tex] \sqrt{ {\pi}^{2} + { (\frac{\pi}{4} })^{2} } = \sqrt{ \frac{17 {\pi}^{2} }{16} } = \frac{\pi}{4} \sqrt{17} \\tant = \frac{ \frac{\pi}{4} }{4} \\ t = {tan}^{ - 1} \pi = 89.682[/tex]

therefore the polar form of Q.1 is

(pi sq. root 17/4,89.682°)

you can do 2 in similar way.

Answer:

10.125 feet

Step-by-step explanation:

h(t) = -2t² + 3t + 9

The maximum height is at the vertex of the parabola.  For a parabola ax² + bx + c, the vertex is at x = -b/(2a).

t = -3 / (2×-2)

t = 3/4

h(3/4) = -2(3/4)² + 3(3/4) + 9

h(3/4) = -9/8 + 9/4 + 9

h(3/4) = 81/8

h(3/4) = 10.125 feet

Answer:

0.125

Step-by-step explanation:

This is a standard calculus question. If you search out L'Hopital's Rule you will find that there are only Calculus examples present. If you use calculus, the answer comes to 1/8. The only way I can think of doing this without the use of Calculus is to let x = something very small -- say x = 0.0001 That approaches 0, but it is not quite = to 0.

So let's try it.

16 + 0.00001  = 16.00001

sqrt(16.0001) = 4.00000125

Now subtract 4

4.00000125 - 4

0.00000125

Now divide by 0.00001

0.12499998

which is close to 0.125.

If someone else can give you an answer that is "purer" than this one, take it.

Answer:

C

Step-by-step explanation:

C:  7 spaces to the right and 5 spaces up

this point is in Quadrant I.

Answer:

7  spaces to the right and 5 spaces up

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

we know that

Applying the law of sines

24/sin(92°)=7/sin(Z°)

sin(Z)=7*sin(92°)/24

sin(Z)=0.291489

Z=arcsin(0.291489)=16.9°

Answer:

$7500

Step-by-step explanation:

$5000 was deposited

5% annual interest of the $5000 is $250

so in ten years the interest will be 10 ×$250 =$2500

so the total sum that will be in the account is $5000 + $2500 =$7500

Answer:

One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero. Does this mean that when you analyze a body in equilibrium

Step-by-step explanation:

One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero. Does this mean that when you analyze a body in equilibrium

There are 2 conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of equilibrium).

Torque is the expression of a rotational or twisting force. The engines in vehicles rotate about an axis, thus creating torque.

One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero.

When a body or a system is in equilibrium, there is no net tendency to change.

In mechanics, equilibrium has to do with the forces acting on a body. When no force is acting to make a body move in a line, the body is in translational equilibrium; when no force is acting to make the body turn, the body is in rotational equilibrium.

There are 2 conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of equilibrium).

These two conditions must be simultaneously satisfied in equilibrium.

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Answer: Option D.

Step-by-step explanation:

You can calculate the surface area of this right prism by adding the area of its faces.

You can observe that the faces of the right prism are:  Three different rectangles and two equal triangles.

The formula for calculate the  area of a rectangle is:

[tex]A=lw[/tex]

 Where "l" is the lenght and "w" is the width.

The formula for calculate the  area of a triangle is:

[tex]A=\frac{bh}{2}[/tex]

Where "b" is the base and "h" is the height.

You can observe that the hypotenuse of the each triangle is the width of one of the larger rectangle, then , you can find its value with the Pythagorean Theorem:

[tex]a=\sqrt{b^2+c^2}[/tex]

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Then, this is:

[tex]a=\sqrt{(8units)^2+(15units)^2}=17units[/tex]

Therefore, you can add the areas of the faces to find the surface area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:

[tex]SA=(10units)(8units)+(15units)(10units)+(17units)(10units)+2(\frac{(15units)(8units)}{2})\\\\SA=520units^2[/tex]

Answer:

520 units^2

Step-by-step explanation:

Answer:

You should order 66 short sleeve mediums.

hope this helps

Answer:

The coordinates of point s are (-3 , 3)

Step-by-step explanation:

* Lets revise some transformation

- If the point (x , y) translated horizontally to the right by h units

 then the new point  = (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then the new point  = (x - h , y)

- If the point (x , y) translated vertically up by k units

 then the new point  = (x  , y + k)

- If the point (x , y) translated vertically down by k units

 then the new point  = (x  , y - k)

* Now lets solve the problem

∵ The vertices of triangle cde are c (-3 , 1) , d (-1 , 4) , e (-6 , 4)

∵ The new coordinates of two vertices are q (-1 , 6) , r (-6 , 6)

- The image of point d is q and the image of point e is r

∵ Point d = (-1 , 4) and point q = (-1 , 6)

∵ Point e = (-6 , 4) and point r = (-6 , 6)

- The x-coordinate has no change but the y-coordinate added by 2

∴ The triangle cde translated vertically up by 2 units to create the

  congruent triangle sqr

- Lets translate point c two units up to find the coordinates of point s

∵ Point c = (-3 , 1)

∴ Poin s = (-3 , 1 + 2) = -3 , 3)

* The coordinates of point s are (-3 , 3)

Answer:

(x + 1) (3x - 1)

Step-by-step explanation:

Using the AC method, here a = 3, b = 2, and c = -1.

ac = 3 * -1 = -3

Factors of -3 that add up to +2 are +3 and -1.

Divide by a: +3/3, -1/3

Reduce: +1/1, -1/3

So the factors are x + 1 and 3x - 1.

3x² + 2x - 1 = (x + 1) (3x - 1)

Answer:

x = 1/3 or x = -1

Step-by-step explanation:

    3x^2 + 2x - 1

=>  3x^2 + 3x - 1x - 1                                         product = -3     sum = 2

=>   3x( x + 1 ) - 1(x + 1 )

=>    (3x - 1) (x + 1)

       3x = 1  

    =>x=1/3  or x = -1  

HOPE THIS HELPS YOU ~