What is the following sum? Assume x20 and 20.
√√x²y³ +2√√x³y² + xy √√y

Answer:

(0,-41)

Step-by-step explanation:

You can see that for each 9 units that x goes up, y goes up by 19. If we continue this pattern, it will take 2 more jumps of 9 units for the x value to be 0 or to reach the y intercept. Adding 19 twice to -79 gives -41. Hope this helps!

Answer:

Answer Is A

Step-by-step explanation:

Just trust me

The value of C is acos(±√(1/10)). In spherical coordinates, the cone 9z^2=x^2+y^2 has the equation phi = c, where phi represents the angle between the positive z-axis and the line connecting the origin to a point on the cone.

To find c, we can use the relationship between Cartesian and spherical coordinates:

x = rho sin(phi) cos(theta)
y = rho sin(phi) sin(theta)
z = rho cos(phi)

Substituting x^2+y^2=9z^2 into the Cartesian coordinates, we get:

rho^2 sin^2(phi) cos^2(theta) + rho^2 sin^2(phi) sin^2(theta) = 9rho^2 cos^2(phi)

Simplifying this equation, we get:

tan^2(phi) = 1/9

Taking the square root of both sides, we get:

tan(phi) = 1/3

Since we know that phi = c, we can solve for c:

c = arctan(1/3)

Therefore, the equation of the cone 9z^2=x^2+y^2 in spherical coordinates is phi = arctan(1/3).

In spherical coordinates, the cone 9z^2 = x^2 + y^2 can be represented by the equation φ = c. To find the constant c, we first need to convert the given equation from Cartesian coordinates to spherical coordinates.

Recall the conversions:
x = r sin(φ) cos(θ)
y = r sin(φ) sin(θ)
z = r cos(φ)

Now, substitute these conversions into the given equation:

9(r cos(φ))^2 = (r sin(φ) cos(θ))^2 + (r sin(φ) sin(θ))^2

Simplify the equation:

9r^2 cos^2(φ) = r^2 sin^2(φ)(cos^2(θ) + sin^2(θ))

Since cos^2(θ) + sin^2(θ) = 1, the equation becomes:

9r^2 cos^2(φ) = r^2 sin^2(φ)

Divide both sides by r^2 (r ≠ 0):

9 cos^2(φ) = sin^2(φ)

Now, use the trigonometric identity sin^2(φ) + cos^2(φ) = 1 to express sin^2(φ) in terms of cos^2(φ):

sin^2(φ) = 1 - cos^2(φ)

Substitute this back into the equation:

9 cos^2(φ) = 1 - cos^2(φ)

Combine terms:

10 cos^2(φ) = 1

Now, solve for cos(φ):

cos(φ) = ±√(1/10)

Finally, to find the constant c, we can calculate the angle φ:

φ = c = acos(±√(1/10))

So the cone equation in spherical coordinates is φ = c, where c = acos(±√(1/10)).

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The values of trigonometric-ratios in the given triangle whose legs are 4 and \(4\sqrt{3}\) are:

a)sinθ=0.5

b)cosθ=0.866

c)tanθ=0.577

What is trigonometric-ratios ?

A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are their respective acronyms. These ratios show the ratio of various sides depending on the angle selected.

Given sides of triangle: 4 and \(4\sqrt{3}\)

hypotenuse=\(\sqrt{perpendicular^{2}+base^{2} }\)

                  =\(\sqrt{4^{2}+\((4\sqrt{3}) ^{2} }\)

                  =\(\sqrt{16+48}\)

                  =8

a)Sin θ=\(\frac{side opposite to the given angle}{hypotenuse}\)

Sin θ=\(\frac{4 }{8}\)

Sin θ=\(\frac{1}{2}\)

Sin θ=0.5

b)Cos θ=\(\frac{side adjacent to the given angle}{hypotenuse}\)

            =\(\frac{4\sqrt{3} }{8}\)

            =\(\frac{\sqrt{3} }{2}\)

            =\(\frac{1.732}{2}\)

Cos θ=0.866

c)tan θ=\(\frac{side opposite to the given angle}{side adjacent to the given angle}\)

            =\(\frac{4}{4\sqrt{3} }\)

            =\(\frac{1}{\sqrt{3} }\)

tan θ=0.577

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Answer:

Answer A

Step-by-step explanation:

Slope formula is y2-y1/x2-x1

2-6/3-5

-4/-2

Slope = 2

Plug into the equation with either (5,6) or (3,2)

6 = 2(5) + b

6 = 10 + b

b = -4

y = 2x - 4

Answer:

the slope is 2, so 2x+b=y

substitute the values into the equation

6+b=2

the y-intercept (b) is -4

y=2x-4

It's on the picture

It's on the picture

Answer:

ok

Step-by-step explanation:

35

Answer:

12

Step-by-step explanation:

192/16=12

Her 32 kg playmate have to sit at a distance of 1.2 m from the pivot point on the other side for the seesaw to be in equilibrium.

According to the given information,

A 35 kg child is at a distance of 1.1 m from the pivot point (or fulcrum).

Let the distance from the pivot point for the 32 kg playmate be d.

To make the seesaw balance, the clockwise and anticlockwise moments should be equal.

Clockwise moment = 35 kg × 1.1 m = 38.5 Nm

Anticlockwise moment = 32 kg × d = 32d Nm

Since the seesaw is in equilibrium,

38.5 = 32d

⇒d = 38.5/32

= 1.203125m

≈ 1.2 m

Therefore, her 32 kg playmate have to sit at a distance of 1.2 m from the pivot point on the other side for the seesaw to be in equilibrium.

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From the graph, let's write the equations for f(x) and g(x).

Apply the slope-intercept form of linear equations:

y = mx + b

Where m is the slope and b is the y-intercept.

• For f(x):

To find the slope apply the slope formula:

Take two points on the line of f(x):

(x1, y1) ==> (0, -1)

(x2, y2) ==> (-2, 0)

Thus, we have:

The y-intercept (b), is the point the line crosses the y-axis.

Therefore, the y-intercept for f(x) is at b = -1

Therefore, the equation for f(x) is:

• For g(x):

Take two points on the line of g(x).

(x1, y1) ==> (-2, 0)

(x2, y2) ==> (2, 2)

Apply the slope formula to find the slope:

The y-intercept of g(x) is: b = 1

Therefore, the equation for g(x) is:

To determine the reflection that transforms f(x) to g(x):

From the graph, we can see the red line represents f(x) while the blue line is that of g(x).

Apply the transformation rules for functions.

When f(x) becomes -f(x), there is a reflection over the x-axis.

Here, the parent function f(x) becomes -f(x) = g(x)

Therefore, there was a reflection over the x-axis that transforms the grah f(x) to g(x).

ANSWER:

• f(x) = -½x - 1

• g(x) = ½x + 1

• Reflection over the x-axis.

Answer:

Step-by-step explanation:

The number of sick birds grew by a factor of 4 each week.  In other words, the number of sick birds quadrupled each week.

The correct answer is 475 and 525. To find the range of values that 95% of the observations lie between.

We can use the empirical rule, which states that for a normal distribution with mean μ and standard deviation σ, about 95% of the observations will fall within 2 standard deviations of the mean.

In this case, the mean is 500 and the standard deviation is 10. So, 2 standard deviations below the mean is 500 - 2(10) = 480, and 2 standard deviations above the mean is 500 + 2(10) = 520.

Therefore, about 95% of the observations lie between 480 and 520, or approximately between 475 and 525.

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Step-by-step explanation:

\(at \:x = 0 \: y = 5 \\ at \:x = 1 \: y = 20 \\ y = mx + b \\ b = 5 \\ 20 = m + 5 \\ m = 15 \\ y = 15x + 5\)

Answer:

your range is -9 to positive 5

Step-by-step explanation:

range is how many numbers are in a squence for example i have 1 2 3 so my range is 1-3

The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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The area occupied by the colony when first observed is 1/9 square centimeter and the doubling time for the colony is approximately 5.57 hours.

Let's start by finding out how many times the colony tripled in the first 12 hours. Since the colony triples every 4 hours, it will have gone through 3 cycles of tripling in 12 hours.

Therefore, the area occupied by the colony when first observed is (3)^2 = 9 times the original area.

Let A be the original area occupied by the colony. Then we have

9A = 1 square centimeter

Solving for A, we get

A = 1/9 square centimeter

The doubling time is the time it takes for the colony to double its area. Let's call this time t. We know that the colony triples every 4 hours, so in t hours it will have tripled twice, or multiplied by a factor of 9. Therefore, we can write

A(0) * 9 = A(0) * 2^(t/d)

where A(0) is the initial area occupied by the colony and d is the doubling time. Solving for d, we get

d = t/log(9/2)

We know that after 12 hours the colony occupies 1 square centimeter, so we can use this information to solve for the doubling time

1/9 * 2^(12/d) = 1

Solving for d, we get

d = 4*log(3) ≈ 5.57 hours

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Answer:

x = \(\frac{1}{4}\)

Step-by-step explanation:

Given

\(\frac{x}{7}\) + x - \(\frac{2}{14}\) = \(\frac{1}{7}\)

Multiply through by 14 to clear the fractions

2x + 14x - 2 = 2 ( add 2 to both sides )

16x = 4 ( divide both sides by 16 )

x = \(\frac{4}{16}\) = \(\frac{1}{4}\)

Answer:

1. y=1/4x+3

2. y=2x

3. y=-1/4x+9/2

4. I cannot solve 4 because there is not two point to solve fir slope intercept form

The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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Answer:

Step-by-step explanation:

let the first angle be 5x

second be 4x

and third be 1x

as we know that by adding all the sides of triangle we get 180°

therefore  ,

5x+4x+1x=180°

10x=180°

hence ,  

x=18°

first angle - 18*5 = 90°

second angle - 18*4=72°

third angle - 18°

HOPE THIS HELPS YOU !!!

Answer:

18°, 72°, 90°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

sum the parts of the ratio, 5 + 4 + 1 = 10 parts

divide to find the value of one part of the ratio

180° ÷ 10 = 18° ← value of 1 part of the ratio , thus

5 parts = 5 × 18° = 90°

4 parts = 4 × 18° = 72°

Thus the angles of the triangle are 18°, 72° and 90°

Answer: NO

Step-by-step explanation:

The line that separates the two part is a dashed line which means that the point on the lines are not in the solution

EXTRA: ONLY IF IT IS A SOLID LINE, THE POINTS WILL BE A SOLUTION

(-2,0) is on the dashed line, so it is not a solution

Answer:

Fdssawweerttyyyhjiokmnbvvffffdeewwsstttggytrf

Step-by-step explanation:

Yttfffrdeesdcxfftggvbred

To find the percent of something, turn the percent into a decimal and multiply (move the decimal place 2 places left, e.g. 53% = .53)

Answer:

Yes, the lines on the graph at 3 and -3 a part  of the solution,

Step-by-step explanation:

The inequality \(|y| \leq 3\) contains all the values of \(y\) 3 units from the origin including the values 3 and -3.

Thus, the lines on the graph y =-3 and y = 3 are the part of the solution.

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Answer:

±5 is your answer

Step-by-step explanation:

x²-25=0

comparing above equation with ax²+bx+c

we get

a=1

b=0

c=-25

by using quadratic equation

x=(-b±√(b²-4ac))/2a=(-0±√(0²-4×1×-25))/2×1

=±{√(100)}/2=±(√10²)/2=±10/2=±5

Answer:

5, - 5

Step-by-step explanation:

x^2 = 25

x = ± √25

= ± 5

x = 5, - 5

Answer:

93,500,000

Step-by-step explanation:

Rounding rule:

1) If the digit directly next to the one you are finding is 5 or greater, round up.

2) If the digit is 4 or less, round down.

Note the hundred thousands place value (underlined and bolded):

93,487,991

Look at the digit value directly next to the place value you are looking for. The value of the digit is 8. Because 8 is greater then 5, round up:

93,487,991 rounded to the nearest hundred thousand is 93,500,000.

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A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising

At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.

During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.

Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.

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