A ladder is leaning against a building. the distance from the bottom of the ladder to the building is 16 ft shorter than the length of the ladder. how high up side of the building is the top of the ladder if the distance is 8 ft less

The formula for volume of cylinder is:

V = π r^2 h

since volume is 100 cubic inches, so:

100 = π r^2 h

Rewriting in terms of h:

h = 100 / π r^2

The least amount of metal means least amount of surface area needed. The surface area of cylinder is:

A = 2 π r h + 2 π r^2

insert the value of h in terms of r:

A = 2 π r (100 / π r^2) + 2 π r^2

A = 200 r-1 + 2 π r^2

Take the 1st derivate and set to 0, dA/dr = 0:

dA/dr = - 200 r-2 + 4 π r

0 = - 200 r-2 + 4 π r

200 / r^2 = 4 π r

r^3 = 50 / π

r = 2.52 inches

So height h is:

h = 100 / π r^2

h = 100 / π (2.52)^2

h = 5.01 inches

Answers:

r = 2.52 inches

h = 5.01 inches

The required missing term of the given sequence is given as 485 and 1457.

The sequence is a pattern of placing the values in a specified manner.

here,

5 = 1 + 4
Since, [tex]b_0 = 4[/tex] and [tex]a_0 = 1[/tex]

17 = 5 + 12

So, the general term is given as

[tex]a_n = a_{n-1} + b_{n}[/tex]

Where, [tex]b_n = 3b_{n-1}[/tex]

For 6 th term

6 the term = 161 + 3(108)

6 the term   = 485

For the 7th term
7th term = 485 + 3(324)
7th term =  1457

Thus, the required missing term of the given sequence is given as 485 and 1457.

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Final answer:

Belinda's total expenses for the week are the sum of her bus fare, lunch out, hair cut, and movie rental, which adds up to d. $38.00.

Explanation:

To calculate the total of Belinda's expenses for the week, we should add up each of the expenses mentioned. This includes the bus fare, lunch out, hair cut, and movie rental. Here's how we do it step-by-step:

Now, let's add them up:

$8.70 (Bus fare) + $7.35 (Lunch out) + $16.00 (Hair cut) + $5.95 (Movie rental)

When we sum these amounts, we get $8.70 + $7.35 + $16.00 + $5.95 = $38.00.

Therefore, the total of Belinda's expenses for the week is $38.00, which corresponds to option D.

I can tell you for sure that the answer to the first one is

C) 63,475

and the second is

A) 22,149

The attendance at the movie theater in seven years will be 63,476. Then option C is correct. And the number of customers that visit the business in 10 years will be 22,149. Then option A is correct.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The yearly participation at a neighborhood movie theater is 42,000 and develops ceaselessly at a pace of 5.9% every year. Then the attendance at the movie theater in seven years will be given as,

[tex]\rm y = 42,000 \times (e)^{0.059\times 7}\\\\y = 42,000 \times (e)^{0.413}[/tex]

Simplify the equation further, then we have

y = 42,000 × 1.5113

y = 63,476

The quantity of clients that visit a neighborhood private venture is 29,600 and has been persistently declining at a pace of 2.9% every year.

Then the number of customers that visit the business in 10 years will be given as,

[tex]\rm y = 29,600\times (e)^{-0.029\times 10}\\\\y = 29,600 \times (e)^{-0.29}\\[/tex]

Simplify the equation further, then we have

y = 29,600 × 0.748

y = 22,149

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Answer:

[tex]2\frac{7}{40}[/tex] pounds

Step-by-step explanation:

Given information:

Weight on the left side = [tex]3\frac{3}{8}[/tex] pounds

Weight on the right side = [tex]1\frac{1}{5}[/tex] pounds

We need to balance both sides.

Let x be the weight which is added to the right side to balance the scale.

[tex]3\frac{3}{8}=1\frac{1}{5}+x[/tex]

[tex]\frac{24+3}{8}=\frac{5+1}{5}+x[/tex]

[tex]\frac{27}{8}=\frac{6}{5}+x[/tex]

Subtract 6/5 from both sides.

[tex]\frac{27}{8}-\frac{6}{5}=x[/tex]

[tex]\frac{135-48}{40}=x[/tex]

[tex]\frac{87}{40}=x[/tex]

[tex]2\frac{7}{40}=x[/tex]

Therefore, [tex]2\frac{7}{40}[/tex] pounds weight is added to the right side to balance the scale.

For the first image, the median range would be 88. In order to find the median, you'll place all your numbers in numerical order (smallest to largest). If there are an odd amount of numbers, find the one directly in the middle. If there is an even amount, you'll take the two most central ones and find the mean, that will tell you the median. Therefore, B (88)  would be the answer to your first one.

The second one would be C (20.4). It's asking for the mean. In order to find the mean of a set of numbers, you'll simply add up all of the numbers and divide by how many numbers are in your number set. That gives you the mean.

Answer:

Triangle 4

Step-by-step explanation:

Congruent triangles are identical in all aspects. They have identical sides and angles.

The ASA the Angle Side Angle criterion.

Congruent triangles should be able to "close up" on each other if one triangle is placed on top of the other. Let's look at the triangle in question.

The triangle ABC is made distinct by the lines on it.

The lines mark the different angles on the triangle.

By looking at the triangle and comparing, Triangle satisfies the ASA criterion

c^2 = a^2+b^2       now subtract a^2 from both sides

c^2 - a^2 = b^2       Now take the square root of both sides

b = +- sqrt(c^2-a^2)

Final answer:

To solve for B in the equation C = sqrt(A^2 + B^2), you square both sides of the equation, subtract A^2 from both sides, and then take the square root of the result to find B = sqrt(C^2 - A^2).

Explanation:

The equation C = sqrt(A^2 + B^2) is representative of the Pythagorean theorem, which is used in mathematics to relate the sides of a right triangle. To solve for B, we must isolate B on one side of the equation. Here's how you can do it:

This gives us the magnitude of B in terms of A and C.

The probability of selecting 22 red balls is  [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

A bag contains 44 red balls and 55 blue balls

The total number of balls=44+55=99

22 balls are selected at random from bag.

We need to find the probability of selecting 22 red balls.

The probability of selecting 22 red balls from 44 balls

[tex]^{44} C_{22}[/tex]

2,104,098,963,720

and [tex]^{99} C_{22}[/tex] is 5.7190121704386E+21

So probability of selecting 22 red balls is

[tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]

Hence, the probability of selecting 22 red balls is  [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]

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We want to create a system of equations that allows us to find the values of two supplementary angles.

We will find that the larger angle measures 140° and the smaller one measures 40°.

------------------------

Two angles A and B are supplementary if their measures add up to 180°, so we have:

A + B = 180°.

Let's assume that B is the larger one, we also do know that:

"The larger is 20° less than 4 times the smaller"

Then we can write:

B = 4*A - 20°.

Then our system of equations is:

A + B = 180°.

B = 4*A - 20°.

To solve it we need to isolate one variable in one of the equations and replace it on the other equation. Here we can see that B is already isolated on the second equation, so we can replace it in the first one to get:

A + B = 180°.

A + (4*A - 20°) = 180°

Now we can solve this for A:

A + (4*A - 20°) = 180°

5*A - 20° = 180°

5*A = 180° + 20° = 200°

A = 200°/5 = 40°

Now that we know the value of A we can get the value of B:

B = 4*A - 20° = 4*40° - 20° = 140°

Then the larger angle measures 140° and the smaller measures 40°

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Answer:

answer is 1440,ok

Step-by-step explanation:

Final Answer:

The maximum value of f(x) = xa(7 - x)b on the interval 0 ≤ x ≤ 7 occurs when x = 7/2 for a > 0 and b > 0.

Explanation:

To find the maximum value of f(x) on the interval 0 ≤ x ≤ 7, we'll use calculus. First, take the derivative of f(x) with respect to x.

f'(x) = a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a

Setting f'(x) = 0 to find critical points:

a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a = 0

Solving for x gives x = 7/2. To determine if this point is a maximum, minimum, or inflection point, we'll use the second derivative test.

f''(x) = a * (7 - x)^(b-1) * x^(a-2) * ((a - 1) * x - 7) - b * a * (7 - x)^(b-2) * x^(a-1) * ((b - 1) * x - 7)

When x = 7/2, f''(7/2) > 0, indicating a concave-up shape and confirming it as a local minimum. Therefore, the maximum value of f(x) occurs at the endpoints of the interval, x = 0 and x = 7, or potentially at x = 7/2 if it surpasses these values.

For a > 0 and b > 0, plugging in x = 7/2 into f(x) = xa(7 - x)b yields the maximum value of the function within the given interval.

Understanding the critical points through derivatives helps identify where the maximum or minimum points occur in the function. In this case, x = 7/2 stands as the point of maximum value within the interval 0 ≤ x ≤ 7 when a and b are both positive.