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3 years ago

This famous clock tower has a clock face with a diameter of 23 feet. What is the approximate area of this clock face

Mathematics

1 answer:

pashok25 [27]3 years ago

7 0

Answer:

Therefore the approximate area of this clock face is 415.3 feet².

Step-by-step explanation:

Given:

Clock is of Circular Shape,

Diameter = 23 feet

$Radius =r =\dfrac{diameter}{2}=\dfrac{23}{2}=11.5\ feet$

To Find :

Area of Clock Face = ?

Solution:

Area of Circle having Radius 'r' is given as,

$\textrm{Area of Circle}=\pi r^{2}$

Substituting the values we get

$\textrm{Area of Clock Face}=3.14\times (11.5)^{2}=415.265=415.3\ feet^{2}$

Therefore the approximate area of this clock face is 415.3 feet².

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Are the two triangles below similar??

kodGreya [7K]

Answer:

Yes

Step-by-step explanation:

If you find the value of all the angles, you'll find that both triangles' angles are 50, 35, and 90 degrees.

(all the angles in a triangle add up to 180)

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2 years ago

A line includes the points (4,1) and (8, 2). What is its equation in slope-intercept form?

Alisiya [41]

Answer:

$y = \frac{1}{4} x$

Step-by-step explanation:

1) First, find the slope of the equation. Use the slope formula $m= \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(2)-(1)}{(8)-(4)} \\m = \frac{2-1}{8-4}\\m = \frac{1}{4}$

Thus, the slope is $\frac{1}{4}$ .

2) Now, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation in point-slope form (from there we can convert it to slope-intercept). Substitute values for $m$ , $x_1$ , and $y_1$ .

Since $m$ represents the slope, substitute $\frac{1}{4}$ for it. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, the end result will be the same) and substitute its x and y values into the formula as well. (I chose (4,1), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the answer.

$y-(1) = \frac{1}{4} (x-4)\\y-1 = \frac{1}{4} x-1\\y = \frac{1}{4} x+0\\y=\frac{1}{4}x$

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2 years ago

A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the

Alexus [3.1K]

4x+6y=56 and y=4x can be used to determine the number of small cars rented and the number of large cars rented, where x represents number of small cars and y represents number of large cars.

Step-by-step explanation:

Number of people hold by small cars = 4

Number of people hold by large cars = 6

Let,

Number of small cars = x

Number of large cars = y

The students rented 4 times as many large cars as small cars,

y = 4x Eqn 1

which altogether can hold 56 people.

4x+6y=56 Eqn 2

4x+6y=56 and y=4x can be used to determine the number of small cars rented and the number of large cars rented, where x represents number of small cars and y represents number of large cars.

Keywords: linear equations, addition

Learn more about linear equations at:

#LearnwithBrainly

6 0

3 years ago

Two girls scout troops are completing a wilderness campouts. The blue troops hikes 2/3 mile every 1/2 hour. The yellow troop hik

sergejj [24]

Answer:

Yellow troop will complete the hike faster than blue troop

Blue troop hikes 1.33 miles in 1 hour

Yellow troop hikes 2.25 miles in 1 hour

Missing portion:

Since the final statement is missing, so we will find how much distance can the troops travels in 1 hour and which troop can complete the hike faster.

Step-by-step explanation:

As given in the statement:

Blue troops travels $\frac{2}{3}$ miles ever $\frac{1}{2}$ hour:

$\frac{1}{2}$ hr = $\frac{2}{3}$ miles

1 hr = $\frac{(2)2}{3}$

1 hr= $\frac{4}{3}$ miles = 1.33 miles

Blue troop hikes 1.33 miles in 1 hour

Yellow troops travels $\frac{3}{4}$ miles ever $\frac{1}{3}$ hour:

$\frac{1}{3}$ hr= $\frac{3}{4}$ miles

1 hr = $\frac{(3) 3}{4}$ miles

1 hr = $\frac{9}{4}$ miles =2.25 miles

Yellow troop hikes 2.25 miles in 1 hour

Yellow troop will complete the hike faster than blue troop

7 0

3 years ago

A circle has the equation 2x²+12x+2y²−16y−150=0.

KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

$(x-h)^{2} +(y-k)^{2}=r^{2}$ (1)

Where $(h,k)$ are the coordinates of the center and $r$ is the radius.

Now, we are given the equation of this circle as follows:

$2x^{2}+12x+2y^{2}-16y-150=0$ (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

$2(x^{2}+6x+y^{2}-8y-75)=0$ (3)

Rearranging the equation:

$x^{2}+6x+y^{2}-8y=75$ (4)

$(x^{2}+6x)+(y^{2}-8y)=75$ (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :