A man is walking away from a lamppost with a light source h = 4 m above the ground. The man is m = 2 m tall. How long is the man's shadow when he is d = 15 m from the lamppost? [Hint: Use similar triangles.]

Cross product of a and b : a x b = (3 - t, t - t^2, t^3 - 3t^2)

To find the cross product a x b for a = (t, 3, 1/t) and b = (t^2, t^2, 1), follow these steps:

Write out the components of vectors a and b:

a = (t, 3, 1/t)
b = (t^2, t^2, 1)

Use the cross product formula:

a x b = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1)

Calculate the components of the cross product:

a x b = (3(1) - (1/t)(t^2), (1/t)(t^2) - t(1), t(t^2) - 3(t^2))

Simplify the expression:

a x b = (3 - t, t^2/t - t, t^3 - 3t^2)

Write the final cross product:

a x b = (3 - t, t - t^2, t^3 - 3t^2)

To verify that the cross product is orthogonal to both a and b, we need to check if the dot product of a x b with a and b is zero.

Calculate the dot product of a x b with a:

(3 - t)(t) + (t - t^2)(3) + (t^3 - 3t^2)(1/t)

Simplify the expression:

3t - t^2 + 3t - 3t^2 + t^2 - 3t = 0

Calculate the dot product of a x b with b:

(3 - t)(t^2) + (t - t^2)(t^2) + (t^3 - 3t^2)(1)

Simplify the expression:

3t^2 - t^3 + t^3 - t^4 + t^3 - 3t^2 = 0

Since both dot products are equal to zero, the cross product a x b = (3 - t, t - t^2, t^3 - 3t^2) is orthogonal to both vectors a and b.

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Answer:

What technology devices do you use everyday?

Step-by-step explanation:

Christian is trying to see which technology device is the most popular. The first question doesn't ask about different types of technology devices, but rather the amount of time spent on them. The second asks what they are used for and the third asks if you have a technology device. Neither of these questions answers which device is the most popular, except for the fourth or last option. Which technology devices are used everyday can help him see which one is the most popular.

Answer:

What technology devices do you use everyday?

Step-by-step explanation:

Christian is trying to see which technology device is the most popular. The first question doesn't ask about different types of technology devices, but rather the amount of time spent on them. The second asks what they are used for and the third asks if you have a technology device. Neither of these questions answers which device is the most popular, except for the fourth or last option. Which technology devices are used everyday can help him see which one is the most popular.

To show that the given equations represent trigonometric identity statements, we will simplify each equation and demonstrate that both sides of the equation are equal.

Starting with sec²θ(1 - cos²θ):

Using the Pythagorean identity sin²θ + cos²θ = 1, we can rewrite sec²θ as 1 + tan²θ. Substituting this into the equation, we get:

(1 + tan²θ)(1 - cos²θ)

= 1 - cos²θ + tan²θ - cos²θtan²θ

= 1 - cos²θ(1 - tan²θ)

= sin²θ

Thus, the equation simplifies to sin²θ, which is a trigonometric identity.

For cosx(secx - cosx) = sin²x:

Using the reciprocal identities secx = 1/cosx and tanx = sinx/cosx, we can rewrite the equation as:

cosx(1/cosx - cosx)

= cosx/cosx - cos²x

= 1 - cos²x

= sin²x

Hence, the equation simplifies to sin²x, which is a trigonometric identity.

Considering cosθ + sinθtanθ = secθ:

Dividing both sides of the equation by cosθ, we obtain:

1 + sinθ/cosθ = 1/cosθ

Using the identity tanθ = sinθ/cosθ, the equation becomes:

1 + tanθ = secθ

This is a well-known trigonometric identity, where the left side is equal to the reciprocal of the right side.

Simplifying (1 - cos∝)(cosec∝ + cot∝):

Expanding the expression, we have:

cosec∝ - cos∝cosec∝ + cot∝ - cos∝cot∝

= cot∝ - cos∝cot∝ + cosec∝ - cos∝cosec∝

= cot∝(1 - cos∝) + cosec∝(1 - cos∝)

= cot∝tan∝ + cosec∝sec∝

= 1 + 1

= 2

Thus, the equation simplifies to 2, which is a constant value.

In summary, we have analytically shown that the given equations represent trigonometric identity statements by simplifying each equation and demonstrating that both sides are equal.

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Answer:

a^2 +b^2=c^2

Given vertices of the triangle are A(4,4),B(3,5) and C(−1,−1)

We know that slope of line passing through the points (x 1,y 1) and (x 2,y 2

) is given by m= x 2−x 1

y

2

​

−y

1

​

​

,x

2

​



=x

1

​

Slope of AB i.e.m

1

​

=

3−4

5−4

​

=−1

Slope of BC i.e.m

2

​

=

−1−3

−1−5

​

=

−4

−6

​

=

2

3

​

Slope of CA i.e. m

3

​

=

4+1

4+1

​

=

5

5

​

=1

Clearly, m

1

​

m

3

​

=−1

⇒ line segments AB and CA are perpendicular to each other i.e; the given triangle is right angled at A(4,4).

Thus the points (4,4),(3,5) and (1,1) are the vertices of a right angled triangle.

Step-by-step explanation:

2

Step-by-step explanation:

-2 -2/ -3+1 = -4/-2 = 2

you just have to use the slope formula

Answer:

C. 2

The slope is 4/2 which is simplified to 2

The data analyst should a)investigate the outlier to determine if it can lead to any important observations and b)use a filter to highlight the outlier, as it is more important than the rest of the data.

When analyzing data, it is important to look at outliers as they can provide valuable information. Outliers can point to an unexpected correlation or reveal a hidden trend that could be missed if they were removed. By investigating the outlier, a data analyst can look for any important observations the outlier might reveal.

Additionally, using a filter to highlight the outlier allows the analyst to focus on the outlier and compare it to the other data points. This can help the analyst to understand how the outlier differs from the rest of the data and draw any relevant conclusions.

Removing the outlier should be avoided as it can lead to data bias and remove important information from the analysis.

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Answer: y = 3x+9

Step-by-step explanation:

points are -2,3 and -1,6

6-3/-1-(-2) = 3

y-int is 9 since its given

Answer: The number is 2

Step-by-step explanation: Suzie says that \(\frac{1}{2}\), which is half of a whole, is equal to only \(\frac{1}{4}\) of the unknown number. This means that to find the value of the unknown number, you need to multiply \(\frac{1}{2}\) by 4 so that it equals to \(\frac{4}{4}\) of the mystery number.

Simply put, multiply \(\frac{1}{2}\) by 4. Then reduce for the answer, and this gives us these equations.

\(x=4(\frac{1}{2} )\)

\(x=\frac{4}{2}\)

\(x=2\)

Hope that this helps!

Answer:

lesser x = -4/3

greater x = -1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

its 20

Step-by-step explanation:

These descriptors can be classified as a geographic distribution, expressed mathematically as a percentage of the total population living within a certain radius or certain counties.

These descriptors can best be classified as a geographic distribution. Specifically, the 70% of season ticket holders within 30 miles of the stadium can be expressed mathematically as a percentage of the total population living within that radius. The equation for this would be:

P = (70/100) * T

Where P is the percentage of the total population living within 30 miles of the stadium, and T is the total population within that radius.

The 40% of season ticket holders living within three different counties can also be expressed mathematically as a percentage of the total population living within those counties. The equation for this would be:

P = (40/100) * T

Where P is the percentage of the total population living within the three counties, and T is the total population within those counties.

Therefore, these descriptors can be classified as a geographic distribution, expressed mathematically as a percentage of the total population living within a certain radius or certain counties.

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72 = 3x + 6 equation represents if each pie was then cut into six pieces and sold. There were a total of 72 pieces to sell.

In mathematics, an equation is an expression or a statement that consists of two algebraic expressions that have the same value and are separated from one another by the equal symbol. It is an otherwise stated proposition that has been mathematically quantified. There are numerous possible equation types. To equate two expressions, we employ equations.

Given,

The Cooking Club made some pies to sell during lunch to raise money for a field trip. The cafeteria helped by donating three pies to the club.

Each pie was then cut into six pieces and sold.

There were a total of 72 pieces to sell.

Equation representing this equation is:

72 = 3x + 6

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m(MLK)=130

m(MLK)=m(ZLK)+m(MLZ)

-> x+86+x+66=130

  2x+152=130

2x = -22

x = -11

m(ZLK)=86-11=75

Answer:

cos = 4/5

Step-by-step explanation:

having sides 3 and 5, means that this is a right triangle with sides 3,4, and 5

cos = adjacent side/ hypotenuse

sin= opposite side/ hypotenuse

since 5 is the biggest number it will be the hypotenuse since that is the longest side, so it will stay on the bottom.

hope this helps! if you have any more questions just ask

Answer:

3?

Step-by-step explanation:

First I added 20 dollars to 2.50 and I got 22.50 than  I divided 67.50 / 22.50 which gave me 3, so I guess the answer is 3. Hope this helped!

Answer:

3 friends ( unless u mean 3/4 instead of 34 then its 2 friends)

Step-by-step explanation:

Tripling the rotor radius (increasing it three times) results in a 9-fold increase in power.

The relationship between the rotor radius and power can be described by the equation P ∝ r^3, where P represents power and r represents the rotor radius. According to the given scenario, when the rotor radius is tripled (increased three times), we can calculate the power increase by substituting the new radius into the equation.

Let's assume the original power is P0 and the original rotor radius is r0. When the rotor radius is tripled, the new radius becomes 3r0. To find the new power, we substitute the new radius into the equation:

P_new ∝ (3r0)^3

P_new ∝ 27r0^3

Therefore, the new power is 27 times the original power. This means that tripling the rotor radius results in a 27-fold increase in power, which corresponds to a 9-fold increase (27 divided by 3). So, tripling the rotor radius results in a 9-fold increase in power.

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Hyperkalemia is a medical condition that refers to an elevated level of potassium in the blood.

This condition can be caused by several factors, including kidney disease, certain medications, and hormone imbalances. Symptoms of hyperkalemia can range from mild to severe, depending on the level of potassium in the blood.

In a 60-year-old female diagnosed with hyperkalemia, the most likely symptom that would be observed is muscle weakness. This is because high levels of potassium can interfere with the normal functioning of muscles, leading to weakness, fatigue, and even paralysis in severe cases.

Other symptoms that may be observed in hyperkalemia include nausea, vomiting, irregular heartbeat, and numbness or tingling in the extremities. Treatment of hyperkalemia typically involves addressing the underlying cause of the condition, as well as managing symptoms through medication and lifestyle changes.

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The possible number of pizza special is (7 x 11 x 6 x 3 x 2 = 2772 variations.

As per the problem statement, there is a linear relation,  between de whole earnings of Jada,  and her working time.

Solution:

y = 240 + 6×t

A Linear relation  is of the form:

y = ax + b

If we call total earnings´Jada "y",  and "t" the whole quantity of worked hours per week,  we get:

a fixed amount working 40 hours      12×40 = 480 $

and the quantity over 40 hours as   ( t - 40 ) × 6.

Then  y = fixed quantity + overtime

y = 480 + ( t - 40 ) × 6       reordering this expression

y = 480 + 6×t - 240

y = 240 + 6×t

Just for checking,  if this equation satisfies, the conditions of the problem

if t = 40 h    that means she did´nt do any overtime,

she earns    y = 240 + 6×(40)   ⇒  y = 480 $

if t = 50 h  meaning 10 hours of overtime, she earns:

y = 240 + (50)×6   ⇒  y = 540 $

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Answer:

I hope that is useful for you :)

If it right tell me in the comments plz thanks alot

Answer:

the two numbers are 36 and 25 sum=61

Step-by-step explanation:

√900=30

closest square numbers to 30=25 and 36

to make sure multiply 36 by 25=900

We were given that:

For P

The solution of the given initial value problem is y(t) = sin(t) + H(t-2π)cos(t-2π), where H(t) is the Heaviside step function.

To solve the initial value problem, we start by finding the complementary solution, which satisfies the homogeneous differential equation y'' + y = 0. The complementary solution is given by y_c(t) = A sin(t) + B cos(t), where A and B are constants to be determined.

Next, we find the particular solution for the given non-homogeneous term δ(t-2π)cos(t). Since the forcing term is a Dirac delta function at t = 2π, we can write the particular solution as y_p(t) = K(t-2π)cos(t-2π), where K is a constant to be determined.

Applying the initial conditions y(0) = 0 and y'(0) = 1, we can solve for the constants A, B, and K. Plugging in these initial conditions into the general solution, we find A = 0, B = 1, and K = 1.

Therefore, the solution of the initial value problem is y(t) = sin(t) + H(t-2π)cos(t-2π), where H(t) is the Heaviside step function.

The initial value problem with the given conditions is solved by finding the complementary solution and the particular solution. The solution is y(t) = sin(t) + H(t-2π)cos(t-2π), where H(t) is the Heaviside step function. This solution satisfies the given initial conditions y(0) = 0 and y'(0) = 1.

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$2816.80 is the raise

21 is 30% of 70

Answer:

6869

Step-by-step explanation:

Answer:

B. irrational

Step-by-step explanation:

-13/12 = −1.083333333