Find the general solution of the differential equation dby day +14 = 0. dxb +49 dr4 O A. None of these. OB. y=x+(C, +C_x) cos( V7x)+(C3+ C4) sin(-V7x) OC. y = (C, + C2x) cos(17x)+(C3 +Cq2) sin(17x) D.

It is to be noted that the blanks can only be filled with f(x), range, and domain.

The domain of a function is the set of all input values, or x-values, for which the function is defined.

The range of a function is the set of all output values, or y-values, for which the function is defined.

To write the equation y = ax + b in function notation, substitute f(x) for y.

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Answer:

A.quadratic

Step-by-step explanation:

3x+x^2+4

Put in order from largest to smallest power of x

x^2 +3x+4

The highest power is 2

A.quadratic   highest power 2

B. quartic   highest power 4

C. linear  highest power 1

D. cubic highest power 3

Answer:

121

Step-by-step explanation:

It's a series of odd numbers. Let

\(S _{11} = 1+3+5+7+9+11+13+15+17+19+21 \)

As a rule of thumb, the sum of n numbers of odd numbers is equal to n². There're 11 numbers in this series. Hence The sum is 11² =121

Answer:

121

Step-by-step explanation:

1 + 3 + 5 + 7 + 9 + 11 +  13 + 15 + 17 + 19 + 21 is a sum of first 11 odd numbers.

   \(\sf \boxed{\text{\bf Sum of first n odd numbers = $n^2$}}\)

Here, n is the number of terms.

In this sequence, there are 11 terms.

Sum of first 11 odd numbers = 11²

                                              = 11 *11

                                              = 121

When U = 10, the value of n is 112.604.

We are given that the number n is the algebraic sum of two terms:

Term 1 varies directly as u.

Term 2 varies inversely as U².

Let's denote the first term as k1 u, where k1 is the constant of proportionality.

And let's denote the second term as k2/U², where k2 is another constant of proportionality.

We have,

When U = 2, n = 22.

When U = 8, n = 56.5.

So, Equation 1: n = k1u + k2/U²

Equation 2: 22 = k1(2) + k2/(2)²

Equation 3: 56.5 = k1(8) + k2/(8)²

Let's solve these equations to find the values of k1 and k2.

Equation 2 becomes: 22 = 2k1 + k2/4

Equation 3 becomes: 56.5 = 8k1 + k2/64

To eliminate k2, let's multiply Equation 2 by 64:

1408 = 128k1 + k2

Now we have two equations with two variables:

128k1 + k2 = 1408

8k1 + k2/64 = 56.5

Let's subtract Equation

120k1 = 1351.5

k1 = 1351.5 / 120

k1 = 11.2625

Substituting the value of k1 back into Equation 2:

22 = 2(11.2625) + k2/4

22 = 22.525 + k2/4

k2/4 = 22 - 22.525

k2/4 = -0.525

k2 = -2.1

Now we have the values of k1 and k2:

k1 = 11.2625

k2 = -2.1

Finally, we can find the value of n when U = 10 by substituting these values into Equation 1:

n = k1u + k2/U²

n = 11.2625(10) - 2.1/(10)²

n = 112.625 - 2.1/100

n = 112.625 - 0.021

n ≈ 112.604

Therefore, when U = 10, the value of n is 112.604.

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Answer:

15 x 30

Step-by-step explanation:

Distribute -5 to each variable in the parenthesis.

-5 x -3 = 15

-5 x -6 = 30

15 x 30

Answer:

4 liters for £3.20

Step-by-step explanation:

we want to maximize quantity for each unit of money spent. if we use mL and p, we want to maximize mL/p

500 mL = 60 p

divide both sides by 60p to get a mL/p value

500 mL/60 p = 50/6 p ≈ 8.3 mL per pence

4 L = £3.20

note:

1000 mL = 1L

divide both sides by 1 L/ 1000 mL

1000 mL / 1 L = 1

1 L / 1000 mL = 1

100 p = £1

divide both sides by 100p / £1

100p / £1 = 1 = £1 / 100p

convert everything to the same units (mL and p) to accurately compare

4 L = £3.20

4L  = 4L * 1 = 4L * 1000 mL / 1 L = 4000 mL. Note that we have two options to choose from -- 1000 mL / 1 L and 1 L / 1000 mL. We choose the first one here because we want the 4L to cancel out with the 1 L

£3.20 = £3.20 * 1 = £3.20  * 100p / £1 = 320 p. note we put the £1 on the bottom so the euros cancel out.

thus,

4 L = £3.20

= 4000 mL = 320p

divide both sides by 320p to get a mL / p value

4000 mL / 320 p = 12.5 mL/p

8.3 mL per pence in the first one

12.5 mL per pence in the second one

the second one has a higher mL per pence, so that is a better value

Answer: y-intercept

Step-by-step explanation:

Answer:

rational

Step-by-step explanation:

I'm smart uhujjjjjhbbjjhh

Answer: rational number

Step-by-step explanation: branilest please

Answer:

It would require 40 teaspoons

Step-by-step explanation:

Given that;

A cookie recipe requires 3 teaspoons of baking soda for 36 cookies

The amount of teaspoons of baking soda required per cookie is;

r = 3/36 teaspoons per cookie

So, for 480 cookies i would require;

N = r × 480 cookies

Substituting r, we have;

N = 3/36 teaspoons per cookie × 480 cookies

N = 40 teaspoons

It would require 40 teaspoons

The required measure of the segment CF in the given triangle is 7.5 units.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.

Here,

The median of the triangle is the line joining the midpoint of the side to the opposite vertex, so if f is the midpoint then,
CF = EC/2
CF = 15 / 2
CF  = 7.5 units

Thus, the required measure of the segment CF in the given triangle is 7.5 units.

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The reason two different antiderivatives of a function differ by a constant is due to the additive constant of integration. When finding an antiderivative of a function, we are essentially looking for a function whose derivative is the given function. However, there are infinitely many functions whose derivative is the same given function, and these functions are related by a constant value.

For example, suppose we are given the function f(x) = x². One antiderivative of this function is F(x) = (1/3)x³, because the derivative of F(x) with respect to x is f(x).

However, we can also add a constant value, say C, to F(x) to obtain another antiderivative, G(x) = (1/3)x³ + C, which also has a derivative equal to f(x). The value of C can be any constant, and it arises because when we take the derivative of a constant value, it is always zero. Therefore, any two antiderivatives of a given function must differ by a constant value.

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A situation in which conclusions based upon aggregated crosstabulation are different from unaggregated crosstabulation is known as Simpson's paradox.

Simpson’s Paradox is an example of statistics that can be wrong. The paradox is defined as averages that can be silly and misleading. Sometimes they can be just plain baffling.

It is also called the Yule-Simpson effect which is an effect that occurs when the marginal association between two categorical variables is qualitatively different from the partial association between the same two variables after controlling for one or more other variables.

This result is often encountered in social science and medical science statistics and is particularly problematic when frequency data are unduly given causal interpretations.

It is a statistical phenomenon where an association between two variables in a population emerges or reverses when the population is divided into subpopulations.

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Answer:

She started with 50 stamps

Step-by-step explanation:

Hi! For these types of problems we always result to going backwards. So, she now has 30 right? So, to reverse into the problem, we do the opposite of what it says. "She then bought five more" 30 - 5 = 25. Then it says she sold half of them. 25 x 2 = 50. If we recheck by going back, she sold half of them (50 / 2 = 25) and she bought five more (25 + 5 = 30).

Hope this helps!

The triengle ABC and XZY are proved to be congruent by SAS.

Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.

By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)

Here in he given triangle,

BC=YZ

AC=XZ

∠ACB=∠XZY

By SAS ΔABC≅ΔXYZ

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Main Answer:The correct answer is "equality of three or more population means."

Supporting Question and Answer:

What is the purpose of the one-way analysis of variance (ANOVA) test?

ANOVA helps to assess whether these differences are statistically significant by comparing the variation between the groups to the variation within the groups.

Body of the Solution:The one-way analysis of variance (ANOVA) is used to test for" the equality of three or more population means". ANOVA compares the variation between the groups (due to differences in means) to the variation within the groups (due to individual differences within each group) to assess whether the observed differences in means are statistically significant. Therefore, the correct answer is:

"equality of three or more population means."

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To calculate the angle of elevation required to hit an object 160 meters away with a muzzle speed of 80 meters per second and neglecting air resistance, we can use the kinematic equations of motion.

Let's consider the motion in the vertical and horizontal directions separately. In the horizontal direction, the object travels a distance of 160 meters.

We can use the equation for horizontal motion, which states that distance equals velocity multiplied by time (d = v * t).

Since the horizontal velocity remains constant, the time of flight (t) is given by the distance divided by the horizontal velocity, which is 160/80 = 2 seconds.

In the vertical direction, we can use the equation for projectile motion, which relates the vertical displacement, initial vertical velocity, time, and acceleration due to gravity.

The vertical displacement is given by the equation:

d = v₀ * t + (1/2) * g * t², where v₀ is the initial vertical velocity and g is the acceleration due to gravity.

The initial vertical velocity can be calculated using the vertical component of the muzzle velocity, which is v₀ = v * sin(θ), where θ is the angle of elevation.

Plugging in the known values, we have

2 = (80 * sin(θ)) * t + (1/2) * 9.8 * t².

Substituting t = 2, we can solve this equation for θ.

Simplifying the equation, we get 0 = 156.8 * sin(θ) + 19.6. Rearranging, we have sin(θ) = -19.6/156.8 = -0.125.

Taking the inverse sine (\(sin^{-1}\)) of both sides,

we find that θ ≈ -7.18 degrees.

Therefore, an angle of elevation of approximately 7.18 degrees should be used to hit the object 160 meters away with a muzzle speed of 80 meters per second, neglecting air resistance and using g = 9.8 m/s² as the acceleration due to gravity.

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Answer:

The answer is

Step-by-step explanation:

To factor the expression

2x² - 4x - 30

First factor 2 out of the expression

That's

2( x² - 2x - 15)

Next write - 2x as a difference

2( x² + 3x - 5x - 15)

Factor out x from the expression

That's

2 [ x( x + 3) - 5x - 15 ]

Factor out -5 from the expression

2 [ x ( x + 3) - 5( x + 3) ]

Factor out x+3 from the expression

We have the final answer as

Hope this helps you

Answer:

C. 2(x - 5) (x + 3)

Step-by-step explanation:

I took the test

Answer:

angle 9 measures 105 degrees

Step-by-step explanation:

measure of angle 8 is congruent to measure of angle 11 (alternate-interior angles are congruent)

measure of angle 11 is congruent to measure of angle 9 (corresponding angles are congruent)

therefore, measure of angle 8 = measure of angle 9

Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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Hello !

c = the cost

n boxes = 66,12n

c = 66,12n

Answer:

9.05

Step-by-step explanation:

20% of 45.25 is $9.p5. Got it from g o o g l e

Answer:

y = -4x - 2

Step-by-step explanation:

y = mx + b where

m = slope, and b = y-intercept

slope = -4 = m

y-intercept = -2 = b

y = mx + b

y = -4x - 2

Answer: y = -4x - 2

Given that the equation of the line in the diagram is `y = 5 - x`. The line cuts the y-axis at P. So, the coordinates of point P are (0,5) and the gradient of the line is `-1`.

The equation of the line can be written as `y = -1x + 5`.Therefore, the y-intercept of the line is 5. Therefore, the coordinates of point P are (0,5).

To find the gradient of the line, we have to write the equation of the line in the form of `y = mx + c`.

We can rewrite `y = -1x + 5` as `y = (-1)x + 5`.From the above form of the equation, we can see that the gradient `m` is `-1`.Therefore, the gradient of line 1 is `-1`.Hence, the required answer is: Coordinates of point P is `(0,5)`.The gradient of the line is `-1`.

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Hi there!

\(\large\boxed{x = 9}\)

Both bases have an angle measure of 55°, so the triangle is isosceles.

An isosceles triangle has a different base while the remaining two side-lengths are equal, therefore:

x + 18 = 3x

Subtract x from both sides:

18 = 2x

Divide both sides by 2:

9 = x

Therefore, x = 9.

Answer:

\(y=-\displaystyle\frac{4}{5}x+\displaystyle\frac{3}{5}\)

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: \(y=mx+b\) where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis).

1) Determine the slope (m)

\(m=\displaystyle\frac{y_2-y_1}{x_2-x_1}\) where two points that fall on the line are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the given points (2, -1) and (-3, 3):

\(m=\displaystyle\frac{-1-3}{2-(-3)}\\\\m=\displaystyle\frac{-4}{2+3}\\\\m=-\displaystyle\frac{4}{5}\)

Therefore, the slope of the line is \(-\displaystyle\frac{4}{5}\). Plug this into \(y=mx+b\):

\(y=-\displaystyle\frac{4}{5}x+b\)

2) Determine the y-intercept (b)

\(y=-\displaystyle\frac{4}{5}x+b\)

Plug in one of the given points and solve for b:

\(-1=-\displaystyle\frac{4}{5}(2)+b\\\\-1=-\displaystyle\frac{8}{5}+b\\\\b=\displaystyle\frac{3}{5}\)

Therefore, the y-intercept is \(\displaystyle\frac{3}{5}\). Plug this back into \(y=-\displaystyle\frac{4}{5}x+b\):

\(y=-\displaystyle\frac{4}{5}x+\displaystyle\frac{3}{5}\)

I hope this helps!

Answer:

y= -0.8x + 0.6

Step-by-step explanation:

The ways that the exercise can be expressed such that for every 6 squares there are 3 circles include:

This question is asked in Spanish on an English site so the answer will be provided in English for better learning by other students.

The ratio of squares to circles is 6:3 or simplified, 2:1. This means for every 2 squares, there is 1 circle.

You could also use a proportional statement such that the number of squares is twice the number of circles. For every 6 squares, there are 3 circles.

There is also equation form where we can say, if S is the number of squares and C is the number of circles, the relationship could be expressed as S = 2C. This means the number of squares is twice the number of circles.

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The translated question is:

How to express this exercise for every 6 squares there are 3 circles.

Answer:

Its A. Just had this question

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

6^-14

Step-by-step explanation:

Using laws of indices you'll add the denominators power to account for multiplication

then substract it from the numerators power to get an answer which is 6×10^-14