Find the greatest common factor of 60y^8, 40y^4, 20y^5 and 80y^5.

The area of the circular sector is equal to 49π / 10 square units.

In this problem we find the case of a circular sector, whose area (A) must be found by means of the following formula:

A = (α / 360°) · π · r²

Where:

If we know that r = 6 and α = 49°, then the area of the circular sector is:

A = (49° / 360°) · π · 6²

A = 49π / 10

The circular sector has an area of 49π / 10 square units.

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Answer:

{-3, -1, 1}

Step-by-step explanation:

Zeros refer to x-intercepts. X-intercepts are x values when y = 0. You can tell where they are by looking at where the line passes the x-axis.

Therefore, {-3, -1, 1} are the zeros.

Answer:

-i,2i

Step-by-step explanation:

zeros(2,i,-2i {5th degree}

then the conjugate zeroes are,

I,2i {conjugate zeros}

so the answer is i, 2i

Answer:

Step-by-step explanation:

148 people

Answer:

Distribute 4 to a and -5.

Step-by-step explanation:

Multiplication goes first.

The size of the angle between AH and the plane ABCD is approximately 74.4°, rounded to one decimal place.

To find the size of the angle between AH and the plane ABCD in the given cuboid, we can use the concept of three-dimensional geometry.

First, let's consider the right triangle BCA. The given angle BCA is 48°, and we know that the length of AB is 7.3 cm. Using trigonometric functions, we can find the length of BC:

BC = AB * sin(BCA)

BC = 7.3 * sin(48°)

BC ≈ 5.429 cm

Now, let's look at the right triangle BAH. The length of AH is given as 8.1 cm. We can find the length of BH by subtracting BC from AB:

BH = AB - BC

BH ≈ 7.3 - 5.429

BH ≈ 1.871 cm

Next, let's consider the right triangle ABH. We want to find the angle BAH, which is the complement of the angle between AH and the plane ABCD. We can use the cosine function to find the angle BAH:

cos(BAH) = BH / AH

cos(BAH) ≈ 1.871 / 8.1

BAH ≈ arccos(1.871 / 8.1)

BAH ≈ 74.4°

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Answer:

Albert invested $21,000

John invested $49,000

Step-by-step explanation:

First add 3 and 7

3+7=10

Now divide 70,000 by 10

70,000/10=7000

Now multiply 7000 by 3 and 7

7000x3=21,000

7000x7=49,000

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Answer:

1/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

x+3 1/2=9

x=9-7/2

x=(18-7)/2=11/2

x=5 1/2

Answer:

3 1/2 + 5 1/2= 9.

Step-by-step explanation:

Hope this helps? im sorry if it doesn't :)

Answer:

7\(\sqrt{7}\)

Step-by-step explanation:

Take 9 out of \(\sqrt{63}\)

You get 3\(\sqrt{7}\)

Take 4 out of \(\sqrt{28}\)

You get 2\(\sqrt{7}\)

So, 3(3\(\sqrt{7}\)) - 2\(\sqrt{7}\)

= 9  \(\sqrt{7}\) - 2\(\sqrt{7}\)

=7\(\sqrt{7}\)

British sterling silver =    321.1   grams

Copper =  8.9   grams

========================================================

Work Shown:

The two amounts add to 330 grams total. The x is some number in the interval 0 < x < 330.

We want to end up with 330 grams of 10% copper, so we want 0.10*330 = 33 grams of pure copper after mixing the two metals.

Set the 33 equal to the expression -0.925x+330 and solve for x.

-----------

-0.925x+330 = 33

-0.925x = 33-330

-0.925x = -297

x = -297/(-0.925)

x = 321.081 approximately

x = 321.1 when rounding to one decimal place

330-x = 330-321.1 = 8.9

-----------

We'll need  321.1   grams of British sterling silver.

We'll also need  8.9   grams of pure copper.

Answer:

b = 39

Step-by-step explanation:

The sum of the angles in a triangle are 180 degrees

b+ 2b+ b+24 = 180

Combine like terms

4b +24 =180

Subtract 24 from each side

4b+24-24 =180-24

4b = 156

Divide each side by 4

4b/4 =156/4

b =39

Answer:

\( b = 39 \: \: degrees \\ \)

Step-by-step explanation:

Sum of the angles in a triangle is 180 degrees.

\(b + 2b + b + 24 = 180 \\ 4b + 24 = 180 \\ 4b = 180 - 24 \\ 4b =1 56 \\ \frac{4b}{4} = \frac{156}{4} \\ b = 39 \: \: degrees\)

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Answer:

2x+3y=1470

Step-by-step explanation:

Answer:

whatt????/

Step-by-step explanation:

Answer:

It is not valid because some peoples birthday may be late so they will be 12 in 8th grade or some peoples birthday are early so they will be 14 in 8th grade.

Step-by-step explanation:

Answer:

This gives us the value of $x$ as 3. Hence the answer is 3.

Step-by-step explanation:

Step-by-step explanation:

if you would arrange it in order and solve you will get 3

Since our assumption holds for all values between 6 and k, and we have shown it also holds for k+1, we can conclude by strong induction that it is possible to cut a square into n smaller squares for any n ≥ 6.

To prove this using strong induction, we will first establish a base case and then prove that if the statement holds true for any value k, then it also holds true for k+1.
Base Case: n = 6
Divide the square into four equal smaller squares by drawing two lines, one vertical and one horizontal, each passing through the center.

Then, divide one of these smaller squares into two equal rectangles by drawing a line parallel to the side.

We have now divided the original square into 6 smaller squares.
Inductive Step:
Assume the statement is true for all values n = 6, 7, ..., k,

where k ≥ 6.

We want to prove that the statement is true for n = k+1.
Consider a square that is divided into k smaller squares.

We will show that it is possible to divide this square into k+1 smaller squares.

Choose one of the k squares and label it S.

If S is a rectangle, divide it into two smaller squares by drawing a line parallel to the shorter side.

If S is a square, divide it into two equal rectangles by drawing a line through the center parallel to a side.
In either case, we have replaced one of the original k squares with two smaller squares, resulting in a total of k+1 squares.

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The general solution to the given differential equation is:

y = (x/12) - (1/288)

How to solve the Differential Equation?

We want to solve the differential equation given as: y' - 24xy = -2x

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -24x. Therefore, the integrating factor is e^(-24x).

Multiplying the entire equation by the integrating factor, we get:

e^(-24x)y' - 24xe^(-24x)y = -2xe^(-24x)

The left side of the equation is the derivative of (e^(-24x)y) with respect to x:

(d/dx)(e^(-24x)y) = -2xe^(-24x)

Integrating both sides with respect to x, we have:

e^(-24x)y = ∫(-2xe^(-24x))dx

Integrating the right side, we get:

e^(-24x)y = -∫(2xe^(-24x))dx

To evaluate the integral on the right side, we can use integration by parts. Let's differentiate -2x and integrate e^(-24x):

u = -2x (differential of u = -2dx)

dv = e^(-24x) (integral of dv = -1/24e^(-24x)dx)

Using the integration by parts formula:

∫uv dx = uv - ∫v du

We can compute the integral as follows:

-∫(2xe^(-24x))dx = -[(-2x)(-1/24e^(-24x)) - ∫(-1/24e^(-24x))(-2dx)]

= -[x/12e^(-24x) + 1/12∫e^(-24x)dx]

= -[x/12e^(-24x) + 1/12(-1/24)e^(-24x)]

= -[x/12e^(-24x) - 1/(12*24)e^(-24x)]

= -[x/12e^(-24x) - 1/(288e^(-24x))]

= -[x/12 - 1/288]e^(-24x)

Substituting this back into the previous equation, we have:

e^(-24x)y = -[-(x/12 - 1/288)e^(-24x)]

Simplifying further:

e^(-24x)y = (x/12 - 1/288)e^(-24x)

Canceling out e^(-24x) on both sides:

y = x/12 - 1/288

Therefore, the general solution to the given differential equation is:

y = x/12 - 1/288

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ac is congruent to pr because those sides correspond

Answer:

Ok, in this problem we first need to define the components parallel and perpendicular to the plane of the inclined plane, so we can project the gravitational component in each one of these. (see the image below to see the change in coordinates)

The perpendicular component will be defined by -cos(pi/12) (because the weight vector points down) and the parallel one is defined by sin(pi/12).

Now, the gravitational force will be, in magnitude, F =  g*w

where g is the gravitational acceleration: g = 9.8m/s^2

Now, the perpendicular projection is:

Pe = -W*9.8m/s^2*cos(3.14/12) = W*9.799 m/s^2 (this component is canceled due to the normal force of the inclined plane)

The parallel projection will be:

Pa = W*9.8m/s^2*sin(3.14/12) = W*0.045 m/s^2

Now, we know that the car is still, then the tension on the cable must be equal in magnitude to this force (but in the opposite direction)

Then the module of the tension of the cable is:

ITI = W*0.045 m/s^2

or

T = -W*0.045 m/s^2 in the parallel axis.

b) The force that the pavement is applying on the car will be the normal force, that is equal to the perpendicular projection of the gravitational force (But again, in opposite direction).

Then the magnitude will be:

INI =  W*9.799 m/s^2

The fraction in its lowest terms for 7 1/2 percent is 3/40.

To express the mixed number 7 1/2 percent as a fraction in its lowest terms, we need to convert it to a fraction and simplify.

First, we convert the mixed number to an improper fraction:

7 1/2 percent = 7 1/2 / 100

To simplify this fraction, we find the least common multiple (LCM) of the denominator (2) and the percent denominator (100), which is 200.

Now, we can rewrite the fraction with the common denominator:

7 1/2 / 100 = (7 * 2 + 1) / 200 = 15/200

To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 200 is 5.

15/200 = (15 ÷ 5) / (200 ÷ 5) = 3/40

Therefore, the fraction in its lowest terms for 7 1/2 percent is 3/40.

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Answer:

p + 30 = 20

Step-by-step explanation:

we can add 30 to both sides to make this an addition equation:

p - 20 = -30 (now add 30 to both sides)

p - 20 + 30 = 0 (then, add 20 to both sides)

p + 30 = 20 (this would be the addition equation)

Answer:

Brand A

Step-by-step explanation:

Brand A has a box of 25 forks for 1.99

Take the price per fork

1.99 /25 = .0796

              .08 per fork

Brand B has a box of 42 totals for 3.89

3.89 / 42

.092319048

.09 per fork