The sum of two numbers is 45. One number is 4 times as large as the other. What are the numbers?

Angle a and angle b are pairs of angles called the alternate angles. Alternate angles are pair of angles that is formed by two parallel lines. These two angles are not adjacent to each other. They are located on the opposite sides of the line that intersects the parallel lines.

To write the decimal number 0.8(repeating) as a fraction, use the concept of an infinite geometric series and convert it to an equation. Multiply both sides of the equation by 10 to eliminate the decimal point and subtract the original equation to eliminate the repeating part. Finally, divide by 9 to get the equivalent fraction form.

To write the decimal number 0.8(repeating) as a fraction, we can use the concept of an infinite geometric series. Let's assume the repeating decimal as x: x = 0.8(repeating). Now, multiply both sides of the equation by 10 to remove the decimal point: 10x = 8(repeating). Next, subtract the original equation from this new equation to eliminate the repeating part: 10x - x = 8(repeating) - 0.8(repeating). Simplifying these expressions gives us: 9x = 7.2. Finally, divide both sides of the equation by 9: x = 7.2/9. Therefore, the equivalent fraction form of 0.8(repeating) is 7.2/9.

The differential of the function v = 2y cos(xy) is found using the product rule and the chain rule, yielding dv = 2 cos(xy) dy - 2y sin(xy) (xdy + ydx), which accounts for changes with respect to both x and y.

To find the differential of the function v = 2y cos(xy), we'll need to apply the product rule and the chain rule. The product rule states that the differential of a product of two functions is d(uv) = u dv + v du. The chain rule is used when differentiating composite functions, and it implies that d/dx (f(g(x))) = f'(g(x)) * g'(x).

Applying the product rule, we get:

Combining these, the differential dv becomes:

dv = 2 cos(xy) dy - 2y sin(xy) (xdy + ydx).

This equation represents the total differential of the function v with respect to both x and y.

For implicit differentiation examples like in equation In(xy) = x2y3 or systems of differential equations, understanding and applying the product rule, chain rule, and implicit differentiation are essential to calculate derivatives and solve the equations.

The acceleration of the body at t = 3 seconds is approximately  [tex]\( -58.58785 \, \text{m/s}^2 \).[/tex]

To find the acceleration of the body at ( t = 3 ) seconds, we need to find the second derivative of the displacement function [tex]\( x(t) \)[/tex] with respect to time t.

Given that[tex]\( x(t) = a \sin(\omega t + \phi) \)[/tex] , where [tex]\( a = 5 \) m, \( \omega = 3.444 \) rad/s, and \( \phi = 1.0472 \)[/tex] rad, the acceleration a(t) is the second derivative of of x(t) with respect to t:

First, let's find the first derivative of of x(t) with respect to t:

[tex]\[ v(t) = \frac{dx}{dt} = a \omega \cos(\omega t + \phi) \][/tex]

Now, let's find the second derivative of x(t) with respect to t:

[tex]\[ a(t) = \frac{d^2x}{dt^2} = -a \omega^2 \sin(\omega t + \phi) \][/tex]

Now, substitute the given values:

[tex]\[ a(t) = -5 \times (3.444)^2 \sin(3.444 \times 3 + 1.0472) \][/tex]

Now, calculate:

[tex]\[ a(t) = -5 \times (3.444)^2 \sin(10.332 + 1.0472) \]\[ a(t) = -5 \times (3.444)^2 \sin(11.3792) \][/tex]

Now, compute:

[tex]\[ a(t) = -5 \times (11.858736) \sin(11.3792) \]\[ a(t) \approx -5 \times (11.858736) \times 0.97989 \]\[ a(t) \approx -58.58785 \, \text{m/s}^2 \][/tex]

Therefore, the acceleration of the body at t = 3 seconds is approximately  [tex]\( -58.58785 \, \text{m/s}^2 \).[/tex]

Answer:

w + 2w = 60

Step-by-step explanation:

w + 2w = 60

This equation will not give you the correct value for W because W is the siez or represents the size of the smaller side, since you have 4 sides, 2 small and 2 big, the sum of this 4 sides will be the perimeter, or the total meters of fence needed, since the total meter of fence need is 60 and in the equation you just have 2 sides, the value for W will be double than the real.

The volume of the cylinder is; 128π in3

Base area(πr^2)*height

Π = 3.14

Therefore; 3.14 * 4^2 * 8

3.14 * 128

= 401.92 in3

Answer:

A. the volleyball reached it's maximum height of 3 sec

B. The maximum height of the vollybal was 23 ft

E. The vball was served from a height of 5 ft

Step-by-step explanation:

h(t) = -2 (t-3)^2 +23

Given equation is in the form of [tex]f(x)= a(x-h)^2 + k[/tex]

(h,k) is the vertex

Now we compare f(x) with h(t)

h(t) = -2 (t-3)^2 +23

h = 3  and k = 23

Vertex is (3,23)

h=3 . this means the volleyball reaches its maximum height in 3 seconds

k = 23. this means the volleyball reaches the maximum height of 23 ft

When ball reaches the ground the height becomes 0. so plug in 0 for h(t) and solve for t

0= -2 (t-3)^2 +23

Subtract 23 on both sides

-23 = -2(t-3)^2

Divide both sides by -2

[tex]\frac{-23}{-2} = (t-3)^2[/tex]

Take square root on both sides

[tex]+-\sqrt{\frac{23}{2}}= t-3[/tex]

Add 3 on both sides

[tex]+-\sqrt{\frac{23}{2}}+3= t[/tex]

We will get two value for t

t=-0.39  and t= 6.39

So option C is not correct

Given h(t) is a quadratic function not exponential

To find initial height we plug in 0 for x and find out h(0)

h(0) = -2 (0-3)^2 +23 = -2(-3)^2 + 23= -18+ 23= 5

The volleyball was served from a height of 5 ft

Answer:

36 cm^2

Step-by-step explanation:

Answer:

A. f(x) = 3*(1/2)^x

Step-by-step explanation:

We know that, a function can be stretched or shrinked both horizontally and vertically.

Now, according to our question we are required to look at the vertical stretch of an exponential function.

The general form for a vertical stretch of a function f(x) is k*f(x) where k>1.

So, we compare this form with the options provided.

We see that in option A the exponential function is multiplied by 3 and so the function will be stretched vertically.

Hence, option A is correct.

We know that [tex] \boldsymbol{A^2}=\boldsymbol{A\times A} [/tex]

We also know that [tex] \boldsymbol{I}=\begin{bmatrix}
1 &0 \\
0&1
\end{bmatrix} [/tex]

Now, it has been given to us that [tex] \boldsymbol{A^2}=\boldsymbol{I} [/tex]

Therefore, we will have to find the correct [tex] \boldsymbol{A} [/tex] from the given options and we find that when:

[tex] \boldsymbol{A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix} [/tex]

then [tex] \boldsymbol{A^2}=\boldsymbol{A\times A}=\begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}\times \begin{bmatrix}
3 &-2 \\
4&-3
\end{bmatrix}=\begin{bmatrix}
1 & 0\\
0 & 1
\end{bmatrix} [/tex]

Therefore, from the above given options, Option C is the correct option.

Therefore, [tex] \boldsymbol{A}=\begin{bmatrix}
3 & -2\\
4 & -3
\end{bmatrix} [/tex] is the correct answer.

Answer:

C. [3, -2]

    [4, -3]

Step-by-step explanation:

PLATOOOO

Final answer:

To find the number of members for any year on the video sharing website, use the recursive rule with a base case of 20,000 initial members and apply the recursive step Mₙ = 0.75 × Mₙ₋₁ + 10,000 for each subsequent year.

Explanation:

The situation described can be modeled with a recursive rule where each year's membership is based on the previous year's membership.

To write such a rule, we'll use Mn to denote the number of members in year n, and Mn-1 to denote the number of members in the previous year.

The recursive rule is as follows:

This means that for any year n, the number of members is equal to 75% of the previous year's members plus an additional 10,000 new members.