The height of a stuntperson jumping off a building that is 20 m high is modeled by the equation h = 20 – 5t2, where t is the time in seconds. a high-speed camera is ready to film the person between 15 m and 10 m above the ground. for which interval of time should the camera film the person?

Answer:

A

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle, thus

x = 64° + 45° = 109° → A

Answer:

A

Step-by-step explanation:

64+45=109

180-109=71

180-71=109 *

*This step is only if you want to check your work!

Answer:

sorry I don't know about this Question

We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

The particular solution to the given differential equation is y^2 = x^2 + y0^2, where y0 is the initial value of y at x = 0.

The given differential equation is dy/dx = x/y, where y cannot equal 0. It is a separable differential equation that can be solved by rearranging terms and integrating both sides.

To solve the differential equation dy/dx = x/y, we can begin by rearranging the equation to separate the variables. Multiplying both sides by y and dx, we get y dy = x dx. Now, we can integrate both sides:

∫y dy = ∫x dx

Integrating, we obtain (1/2)y^2 = (1/2)x^2 + C, where C is the constant of integration. Simplifying this equation, we have y^2 = x^2 + C.

To find the particular solution, we need an initial condition. Let's assume that at x = 0, y = y0. Substituting these values into the equation, we get y0^2 = 0^2 + C, which gives C = y0^2.

Therefore, the particular solution to the given differential equation is y^2 = x^2 + y0^2, where y0 is the initial value of y at x = 0.

It's important to note that the solution is valid as long as y ≠ 0, as division by zero is undefined.

Learn more about differential equation here:

https://brainly.com/question/31492438

#SPJ11

Answer:

the answer should be A

Step-by-step explanation:

hope it helps, have a good day :)

Answer:

P(A or B) = 0.88

Step-by-step explanation:

P(A or B) = P(A) + P(B) = 15/40 + 20/40 = 35/40 = 7/8 ≈ 0.88

Answer: 17%

Step-by-step explanation:

15.47 over 91 = x over 100

cross multiply and reduce to find 17.

Answer:

The ratios must be 88% of grade A sugar and 12% of grade B sugar.

Step-by-step explanation:

On the grade A every kg costs £75, while on the grade B every kg costs  £50. The final mixture we want to make needs to cost  £72 per kg. We will sum a certain mass of grade A, "x", with a certain mass of grade B, "y". The sum of these masses must be equal to 1 kg. So we have:

\(x + y = 1\)

Since we want the final mixture to cost  £72, we need to satisfy:

\(75*x+ 50*y = 72\)

Solving the system of equation will reveal the ration that must be used.

\(\left \{ {{x + y=1} \atop {75*x + 50*y=72}} \right.\\ \left \{ {{-50*x + -50*y=-50} \atop {75*x + 50*y=72}} \right.\\25*x = 22\\x = \frac{22}{25} = 0.88\\y + x = 1\\y = 1 - x \\y = 1 - 0.88 = 0.12\)

The ratios must be 88% of grade A sugar and 12% of grade B sugar.

Answer:

3+9=7 to the sqaure root of nine

Step-by-step explanation:

your welcome

Answer:

33 square meters per hour

Step-by-step explanation:

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The required equation is ~

\( \boxed{ \sf{y = \frac{x}{2} + 2 }}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

Let's find the slope of given line ~

comparing it with general slope - intercept form of line (y = mx + c) we get, m = -2 (that is slope of the line)

let the slope of the required line be n

And, now since the required line Is perpendicular to the given line. the product of their slopes is -1

that is ~

slope of required line is ~ 1/2

now, let's use the point - slope form of line to find the equation of required (perpendicular) line (using point (0 , 2) ~

that is ~

here, m = slope ~

I hope it helps ~

(a) The outcomes are 8

(b) Values of X are : 0, 1, 2, 3

(a) To determine the number of outcomes in the sample space, we need to consider all the possible combinations of the switches.

Since each switch can either fail (F) or not fail (NF), there are two possible outcomes for each switch. Therefore, the total number of outcomes in the sample space can be calculated as 2 × 2 × 2 = 8.

(b) Let X represent the number of switches that fail. We can define the values of X as 0, 1, 2, or 3, depending on the number of switches that fail. The probability of each outcome can be calculated using the binomial distribution formula.

Learn more about function

brainly.com/question/30721594

#SPJ11

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

Using linear functions, the costs are given as follows:

For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.

A linear function is modeled by:

y = mx + b

In which:

For Company A, we have two points on the column: (2, 33), (3, 49). Hence for one additional hour, the cost increased by $16, hence the slope is of 16 and:

A(x) = 16x + b.

When x = 2, A(x) = 33, hence we use it to find b as follows:

33 = 16(2) + b

b = 1.

Hence:

A(x) = 16x + 1.

Companies B and C have intercepts of 0, while the slopes are hourly costs, hence:

For 4 hours, the costs are given as follows:

The difference is:

72 - 57 = 15.

For 4 hours, the difference is costs between the company that charges the most and the one that charges the least is of $15.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

false

Step-by-step explanation:

We need to calculate the definite integral of the function over the interval and divide it by the width of the interval. The average value of the function cos(x) over the interval [0, 2] is approximately 0.909

In summary, to find the average value of the function f(x) = cos(x) over the interval [0, 2], we calculate the definite integral of the function over the interval and divide it by the width of the interval.

To find the definite integral of cos(x) over the interval [0, 2], we can integrate the function:

∫cos(x) dx = sin(x) + C

Evaluating the integral from 0 to 2 gives us:

∫[0 to 2] cos(x) dx = sin(2) - sin(0)

Since sin(0) = 0, we have:

∫[0 to 2] cos(x) dx = sin(2)

To find the average value, we divide this result by the width of the interval:

Average value = (1/2 - 0) * sin(2)

Rounded to three decimal places, the average value of the function cos(x) over the interval [0, 2] is approximately 0.909.

To learn more about cos(x) click here, brainly.com/question/28892265

#SPJ11

The option that depicts the correct statement is that B. 0.75 inches of snow melted daily.

The expression given is

T= −0.75x+5,

where, T represents the total snowfall.

x represents the daily change in the amount of snow.

It should be noted that the negative sign beside 0.75x implies that the snow was melting. In a situation whereby the snow was increasing, a plus sign will have been put in there.

In conclusion, 0.75 inches of snow melted daily

Read related link on:

https://brainly.com/question/24937587

Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true

The final values of the angles are:

C0 = A0 = 2

C1 = B1 = -7

theta1 = 0 degrees

C2 = B2 = -7

theta2 = 0 degrees

Here, we have,

To determine the values of C0, C1, theta1 (in degrees), C2, and theta2 (in degrees), we need to match the given expressions for x(t) with the given values for A0, A1, B1, A2, B2, and w.

Comparing the expressions:

x(t) = C0 + C1sin(wt+theta1) + C2sin(2wt+theta2)

x(t) = A0 + A1cos(wt) + B1sin(wt) + A2cos(2wt) + B2sin(2w*t)

We can match the constant terms:

C0 = A0 = 2

For the terms involving sin(wt):

C1sin(wt+theta1) = B1sin(w*t)

We can equate the coefficients:

C1 = B1 = -7

For the terms involving sin(2wt):

C2sin(2wt+theta2) = B2sin(2wt)

Again, equating the coefficients:

C2 = B2 = -7

Now let's determine the angles theta1 and theta2 in degrees.

For the term C1sin(wt+theta1), we know that C1 = -7. Comparing this with the given expression, we have:

C1sin(wt+theta1) = -7sin(wt)

Since the coefficients match, we can equate the arguments inside the sin functions:

wt + theta1 = wt

This implies that theta1 = 0.

Similarly, for the term C2sin(2wt+theta2), we have C2 = -7. Comparing this with the given expression, we have:

C2sin(2wt+theta2) = -7sin(2w*t)

Again, equating the arguments inside the sin functions:

2wt + theta2 = 2wt

This implies that theta2 = 0.

Therefore, the final values are:

C0 = A0 = 2

C1 = B1 = -7

theta1 = 0 degrees

C2 = B2 = -7

theta2 = 0 degrees

To learn more on angle click:

brainly.com/question/28451077

#SPJ4

The indefinite integral of cos14 x sin x dx= -cos 14x cos x + 14 sin x + C, Where C is the constant of integration.

We can solve the given problem by using the substitution method.

Using the formula:

∫u'v = uv - ∫uv' dx

Consider,

cos 14x as u' and sin x dx as v

Now we find v' as derivative of

v.∫ cos14 x sin x dx = ∫ u'v

Now,

v' = sin x

Therefore, v = -cos x

Now we have:

∫ cos 14x sin x dx

= ∫ u'v∫ cos 14x sin x dx

= -cos 14x cos x + ∫ cos x * 14 * sin x dx

Now we apply the formula again. We get:

∫ cos14 x sin x dx = -cos 14x cos x + 14 ∫ cos x sin x dx

Now we apply the same substitution again. We get:

∫ cos14 x sin x dx = -cos 14x cos x + 14 ∫ cos x sin x dx

u' = cos xv = sin x dxv' = cos x

Therefore, the solution is:

∫ cos14 x sin x dx

= -cos 14x cos x + 14 ∫ cos x sin x dx

= -cos 14x cos x + 14 sin x + C, Where C is the constant of integration.

To know more about indefinite integral, visit:

https://brainly.com/question/32465992

#SPJ11

Answer:inequality form  x  ≤  -1

for 3x + 9  ≤ 6

Step-by-step explanation:isolate the variable by dividing eash side by factors that dont contain the variable

Answer:

Answer Varies

Step-by-step explanation:

For the 1st equation, there are a lot of numbers that could fit x, such as any negative number, such as -1,-2,-3, etc. For the 2nd equation, 9 and below would work. Please correct me if I am wrong because everybody makes mistakes.

Answer:

decision-making

Step-by-step explanation:

The ladder slipped down the wall by approximately 296 cm to the nearest 1 cm.

We can use the Pythagorean theorem to solve this problem.

Let the distance the ladder slips down the wall be represented by x (in cm).

Then, at the start of the day, we have a right triangle formed by the wall, the ground, and the ladder, with the ladder being the hypotenuse.

The length of the ladder is 3m = 300cm, and the distance from the foot of the ladder to the wall is 50cm.

Therefore, we have:

(300)² = x² + (50)²

Simplifying this equation, we get:

90000 = x² + 2500

Subtracting 2500 from both sides, we get:

87500 = x²

Taking the square root of both sides, we get:

x = √87500

x = 295.8 cm

x ≈ 296 cm

Learn more about slipping of ladder here: https://brainly.com/question/13652193

#SPJ1

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

for more seach question surveying

https://brainly.com/question/17365081

#SPJ8

Answer:

166.5

Step-by-step explanation:

Answer:

3 times.

Step-by-step explanation:

She has 1 1/2 hour to spend in the gym.

1 hr = 60 minutes.
1/2 of an hour= 1/2 * 60= 30 minutes.

In total, she spends 90 minutes in the gym.

If 1/3 of an hour is meant in running, it translates into: 1/3 * 60 = 20 minutes.

If 1/6 of an hour is spent in weight-lifting, it translates into: 1/6 * 60 = 10 minutes.

In total, she spends, 20 minutes + 10 minutes = 30 minutes for both activities.

To obtain the number of times she would perform both activities, we divide the total amount of time spent in the gym by the amount of time spent for both activities.

 90 minutes/30 minutes= 3 times for each cycle.

The statement is true and the function f(x) = ln(x)/x is a solution of the differential equation x^2y' + xy = 1.

To determine whether the statement is true or false, we need to check whether the function f(x) = ln(x)/x satisfies the differential equation x^2y' + xy = 1.
Differentiating f(x) with respect to x, we get:
f'(x) = (1 - ln(x))/x^2
Substituting y = f(x) and y' = f'(x) into the differential equation, we get:
x^2f'(x) + xf(x) = 1
Substituting the expression for f'(x) we derived earlier, we get:
x^2[(1 - ln(x))/x^2] + x[ln(x)/x] = 1
Simplifying, we get:
1 - ln(x) + ln(x) = 1
The equation simplifies to 1 = 1, which is always true.
Therefore, the statement is true and the function f(x) = ln(x)/x is a solution of the differential equation x^2y' + xy = 1.
In conclusion, we have verified that the given function satisfies the differential equation. The importance of checking whether a given function satisfies a differential equation lies in its applications, as it enables us to model various physical and natural phenomena.

To know more about function visit :

https://brainly.com/question/30594198

#SPJ11

Answer:

It's not very high

Step-by-step explanation:

The angle that the string and the ground maje, is acute, because it's smaller than a right angle. So, since it is an acute angle, it's not very high. It is about 30cm high.

The equation for C, in terms of t, representing the number of chocolates remaining in the box t days after Violet's birthday is C = 24 - 4t

Number of chocolate violet eats each night = 4

Number of chocolate originally in the box = 24

Number of chocolate remaining = C

Number of days after violet birthday = t

Number of chocolate remaining = Number of chocolate originally in the box - (Number of chocolate violet eats each night × Number of days after violet birthday)

C = 24 - (4 × t)

C = 24 - 4t

In conclusion, the equation which represents violet's remaining chocolate after her birthday is C = 24 - 4t

Read more on system of equation:

https://brainly.com/question/13729904

#SPJ1

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

To know more about Number visit:

brainly.com/question/3589540

#SPJ11