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Vedmedyk [2.9K]
3 years ago
5

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Mathematics
2 answers:
Leni [432]3 years ago
4 0

Answer:

616 square centimeters

Step-by-step explanation:

Diameter of circle = 28 centimeters

π = 22/7

Area of a circle, A = π \frac{D^{2} }{4}

A =  \frac{22}{7} * \frac{28^{2} }{4}

A =  \frac{22}{7^{1} } * \frac{(4 * 7)^{2} }{4}

A =  \frac{22}{7^{1} } *  \frac{4^{2} *7^{2}   }{4}

A = 22 * 28

A = 616 square centimeters

kow [346]3 years ago
3 0

Answer:

616 cm²

Step-by-step explanation:

To find the area of a circle you use the formula A = π · r²

So we know that the diameter is 28 cm, to find the radius we would divide this in half, because d = 2r, giving us 14. Now we can do 14² which is 196, and then times that by pi or in this case 22/7.

196 × (22/7) = 616

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A metal ring hole barrels together has a radius of 3 ft find the circumference and area
irina1246 [14]
Circumference = 2*pi*radius = 2*3.14*3 = 18.84 ft

Area = pi*radius^2 = 3.14*3*3= 28.26 ft^2
7 0
3 years ago
The length of a rectangle is measured as 370mm correct to 2 significant figures.
olga nikolaevna [1]

Answer:

UB: 375

Step-by-step explanation:

370mm to 2 sig figs..

UB: 375

LB:365

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5 0
3 years ago
In August, 85% of the middle school students voted in a school election. The number of students who voted was 544. How many stud
Maksim231197 [3]

Answer:

640 students

Step-by-step explanation:

544 divided by 85%= 640

5 0
3 years ago
What is the velocity of a car that is traveling north 290 kilometers in 5 hours?
Maksim231197 [3]

Answer:

58

Step-by-step Explanation: 290 / 5 = 58

3 0
3 years ago
2. Consider the circle x^2−4x+y^2+10y+13=0. There are two lines tangent to this circle having a slope of 2/3.
likoan [24]

Answer:

a) The coordinates are (0.431, -2.646) and (3.568,-7.354)

b) The tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

Step-by-step explanation:

First, lets complete squares, by taking for each cordinate the square of a linear expression

0= x²−4x+y²+10y+13 = (x-2)²+ 4  + (y+5)²-25+13 = (x-2)²+(y+5)² - 8

Hence (x-2)² + (y+5)² = 8

Lets put y in function of x. We should obtain 2 functions f and g that represent the circle.

(y+5)² = 8 - (x-2)² = -x² + 4x + 4

y = ^+_- \sqrt{-x^2+4x+4} -5

Thus

f(x) = \sqrt{-x^2+4x+4} - 5

g(x) = -\sqrt{-x^2+4x+4} - 5

Lets find the derivate of each function and the points in which they reach the value 2/3. In those points the tangent line will have a slope of 2/3.

We may just find the values of x which the derivate of f is either 2/3 or -2/3.

\frac{-x+2}{\sqrt{-x^2+4x+4}} = ^+_-\frac{2}{3} \Leftrightarrow \frac{x^2-4x+4}{-x^2+4x+4} = \frac{4}{9} \Leftrightarrow 9(x^2-4x+4) = 4(-x^2+4x+4) \\\Leftrightarrow 13x^2-52x+20 = 0

The quadratic has roots

\frac{52 ^+_-\sqrt{1664}}{26}

one root is 3.568, which corresponds with g, and the other root is 0.431, corresponding to f.

Also g(3.568) = - 7.354 and f(0.431) = -2.646

This means that the coordinates are (0.431 , -2.646), (3.568 , -7.354) and the tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

5 0
3 years ago
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