The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after 6 seconds can be described by the function#(6) f(theta)= 2cos(theta) + sqrt(3).Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)Part B: If the angle was doubled, that is theta became 2theta what are the solutions in the interval [0, 211)? How do these compare to the original function? (5 points)Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g(8) = 1-

Answer:

...

Step-by-step explanation:

To find the number of calories Davis burns while running for 30 minutes, we can use the information that he burns 1080 calories running for 2.5 hours.

We know that 30 minutes is 1/120 of 2.5 hours. So, we can divide the total number of calories by 120 and we get the calorie burn for 30 minutes:

1080 calories / 120 = 9 calories

The number of calories Davis burns while swimming for 30 minutes can be determined by using the equation y = 266x, where x represents the number of hours he swims. We know that he swims for 30 minutes, or 1/120 hours, so we can plug that value into the equation:

y = 266(1/120) = 2.216 calories

So, Davis burns 7 calories more running for 30 minutes than swimming for 30 minutes, assuming the rates remain constant.

If x = 2, y = 6, and z = 4, which expression is equivalent to 4? à 54+0-3+2=4. D Xtra 4 ... A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby.

The percentage change will be 25%.

According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.

Using these estimates, we can calculate the per cent decrease in the time spent driving as follows:

The initial time spent driving was 0.5 hours.

The final time spent driving was 0.375 hours.

The decrease in time spent driving was 0.5 - 0.375 = 0.125 hours.

The per cent decrease in time spent driving is,

P = (0.125/0.5) x  100%

P  = 25%.

Therefore, we can estimate that the per cent decrease in the time Jack spent driving his car is 25%.

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The equations that represent the largest number of x desks, y coffee tables, and z corner tables that can be made are

50x + 30y + 5z = 690

40x + 15y + 5z = 620

45x + 10y + 5z = 510

From the question, we are to determine the three equations that are needed to find the largest number of x desks, y coffee tables, and z corner tables that can be made

From the given information,

Desks use 50 units of wood, 40 units of fabrics, and 45 units of stuffing

Coffee tables use 30 units of wood, 15 units of fabrics, and 10 units of stuffing

Corner tables use 5 units of wood, 5 units of fabrics, and 5 units of stuffing

Also,

There are 690 units of wood, 620 units of fabric and 510 units of stuffing available to make the items

Thus,

The equations that represent the largest number of x desks, y coffee tables, and z corner tables that can be made are

50x + 30y + 5z = 690

40x + 15y + 5z = 620

45x + 10y + 5z = 510

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We want to find where the two lines intersect

Solution

We will subtitute equation 1 into equation 2 ( since y is already made the subject)

From (1)

Put into (2), from (2)

We substitute the value of x into (1)

From (1)

Therefore, the point is intersection is (2, -3) or the line intersect at x = 2 and y = -3

The graph below further show this claim

The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

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

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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Answer:

(L-6)(L+2)

Step-by-step explanation:

Let L be the length of the flower garden.

Then the width will be L-4.

The area of the flower garden = L*(L-4) =L²-4L

The area of the birdbath is 3*4 = 12 ft²

The area of the remaining space for planting is

= Area of flower garden - area of birdbath

We can factor the expression as follows:

taking common frome each two terms

Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.

Answer:

c6 i guess

Step-by-step explanation:

Answer:

x-2y =6

x-2y =6

= 6-2y=x=4

Answer:

\(\$498.75\)

Step-by-step explanation:

Let \(x\) be the original price of the item. We can set up the following equation:

\(x\cdot (1-0.2)=399\).

Solving for \(x\), we get:

\(x\cdot 0.8=399,\\x=\frac{399}{0.8},\\x=\fbox{$\$498.75$}\).

The surface area of the base ball to the nearest whole number is 26 in²

A sphere is defined as the set of all points in three-dimensional Euclidean space that are located at a distance.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a sphere is expressed as;

SA = 4πr²

where r is the radius and it's calculated as;

C = 2πr

9 = 2πr

r = 4.5/π =

SA = 4 π × (4.5/π)²

SA = 81/π

SA = 26 in²( nearest whole number)

Therefore the surface area of the sphere is 26 in²

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Answer:

21

Step-by-step explanation:

6 times 8 = 48-12=36 divided by 3 =12+9=21

Answer: x=24

Step-by-step explanation:

Answer:

$7.50

Step-by-step explanation:

10/4=2.5

10-2.5=7.5

Answer:

$2.50 will be saved

Step-by-step explanation:

Just took the test!

Answer:

what do you mean by land ?

The intensity of sound is proportional to the square of its amplitude.

Thus, if I9 and I8 are the intensities of sounds at 9 decibels and 8 decibels respectively, then:

I9/I8 = (10^(9/10))/(10^(8/10))

I9/I8 = 10^(0.1)

I9/I8 = 1.2589

Therefore, the relative intensity of 9 decibels is approximately 1.26 times higher than that of 8 decibels.

May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!

Answer:

S(a) = 27,5036  squared units

Step-by-step explanation:

Shaded area is :

S(a)  =  Area of the circle  - area of the regular pentagon      (1)

A(c) = area of the circle

A(c) = π*(r)²    ⇒  A(c) =  π*(6)²     ⇒   A(c) =  36*π   ⇒ A(c) = 113,0976 squared units

Area of a regular pentagon:

a) If we draw a straight line between the center and each vertex we get  5 triangles, and if we draw the apothem for each side, we get 10 triangles. We will calculate the area of one  of these triangles

The first 5 triangles has a central angle equal to 72⁰ according to:

360/5  =  72

When we divide these triangles in two triangles by means of the apothem, each central angle will be of 36⁰, then

sin 36⁰  =  0,58778  and cos 36⁰ = 0,809017    and   sin 36⁰ =  x/6      here x is half of the side of the regular pentagon. Then

0,58778  =  x/6

x = 6*0,58778

x =  3,52668 units of length  

and cos 36⁰ = a/6      where a is the apothem, then

0,809017  = a / 6     ⇒   a  = 6*0,809017

a =  4,8541 units of length

Now we are in conditon to calculate area of the triangles as:

A(t) = (1/2)*b*h

A(t) = (1/2)*x*a     ⇒ A(t) = 0,5* 3,52668*4,8541

A(t) = 8,5594 squared units

Finally we have 10 of these triangles, then

Area of regular pentagon is : 10*A(t) squared units

A(p) = 85,594 squared units

Now plugging these values in equation (1) we get the shaded area

S(a) =  113,0976 - 85,594

S(a) = 27,5036  squared units

7880.6 ft cubed

Since it is a cube, we know the side lengths are all the same, and the equation for volume is V = \((sidelength)^{3}\). Therefore we can set up an equation:

V = \((19.9)^{3}\) = 7880.6

Answer:

Answer: LCM of 20,35 and 50 is 1400

Step-by-step explanation:

Answer:

câu này là 500 nhen

Answer:

A. \(h(x)=\sqrt{x-3}\)

Step-by-step explanation:

The parent function of \(\sqrt{x}\) is translated to the left when \(h\) is positive in the transformation \(\sqrt{x+h}\).

If \(h\) is negative, the graph translates towards the left with the distance equal to the value of \(h\).

Here the graph moved 3 units towards the right. This means that \(h\) is negative and has the value of 3.

So, plugging that into the parent function for translation, the function becomes:

\(h(x)=\sqrt{x-3}\)

Check the picture below.

Answer:

steps attached

Step-by-step explanation:

Answer:

Step-by-step explanation

Ab = 29

373+68=7

You have some missing symbols, so I'm guessing that the integral reads

\(\displaystyle \int_C (x-9y) \, dx - x^2 \, dy\)

where C is composed of the two line segments,

• C₁ = {(9t, t) : 0 ≤ t ≤ 1}

• C₂ = {(9 + t, 1 - t) : 0 ≤ t ≤ 1}

The integrals over each path are

\(\displaystyle \int_{C_1} (x-9y) \, dx - x^2 \, dy = \int_0^1 (9t - 9\cdot t) (9 \, dt) - (9t)^2 \, dt\)

\(\displaystyle \cdots = -81 \int_0^1 t^2 \, dt\)

\(\displaystyle \cdots = -\frac{81}3 (1^3 - 0^3) = -27\)

and

\(\displaystyle \int_{C_2} (x-9y) \, dx - x^2 \, dy = \int_0^1 ((9 + t) - 9(1 - t)) \, dt - (9 + t)^2 (-dt)\)

\(\displaystyle \cdots = \int_0^1 (81 + 28t + t^2) \, dt\)

\(\displaystyle \cdots = 81 (1 - 0) + 14 (1^2 - 0^2) + \frac13 (1^3 - 0^3) = \frac{286}3\)

Then the overall line integral has a value of

\(\displaystyle \int_C (x-9y) \, dx - x^2 \, dy = -27 + \frac{286}3 = \boxed{\frac{205}3}\)

The solution to the variables are x = 7 and y = 4

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

Shape = Triangle

The marks on the triangles imply that

So, we have the following representation

3x - 5 = 5y - 4

3x - 5 = y + 12

Substitute 3x - 5 = y + 12 in 3x - 5 = 5y - 4

y + 12 = 5y - 4

Evaluate the like terms

4y = 16

So, we have

y = 4

Substitute y = 4 in 3x - 5 = y + 12

3x - 5 = 4 + 12

So, we have

3x = 21

This gives

x = 7

Hence, the values are x = 7 and y = 4

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Answer:

-1<0 then 9x+5

f(-1)=9*-1+5

f(-1)=-9+5= -4

f(0)=9x+10

f(0)=10

f(2)=9x+5=28

Answer:

114.8 degrees

Step-by-step explanation:

supplementary angles basically means angles equal to 180 degrees

Answer:

C. 50%

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

They told him that is was either a waffle cone or a sundae

Two options, one of which is a sundae

So 1/2 = 0.5 = 50% probability he will get a sundae, and the answer is given by option C

The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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Rounding to the nearest hundredth, the area is approximately 151.976 cm².

The formula for the area of a sector is:

A = (θ/360) x πr²

where θ is the central angle in degrees, r is the radius, and π is pi (3.14).

Plugging in the given values, we get:

A = (144/360) x 3.14 x 11^2

A = 0.4 x 3.14 x 121

A = 151.976

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