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2 years ago

14

Chris used 45 meters of fencing to enclose a circular garden. What is the approximate radius of the garden,rounded to the neares

t tenth of a meter? Use 3.14 for π

2 answers:

xxMikexx [17]2 years ago

4 0

We are given the circumference of the circle. The formula for circumference of a circle is C = 2πr, where r is the radius of the circle. Since we want to find r, we can isolate it in the formula.

C = 2πr

Divide both sides of the equation by 2π to isolate the variable.

C / 2π = r

r = C / 2π

The circumference is given as 45 metres. Substitute this into the formula and solve.

r = 45 / 2π

r = 45 / 2(3.14)

r = 45 / 6.28

r = 7.2

Answer:

7.2 metres

kobusy [5.1K]2 years ago

3 0

The length of the fencing corresponds to the length of the perimeter of the garden:
$p=45 m$
We also know that the perimeter of a circle is given by:
$p=2 \pi r$
where r is the radius of the circle.

Putting together the two equations, we have
$2 \pi r = 45$
from which we can find r, the radius of the garden:
$r= \frac{45}{2 \pi}= \frac{45}{2 \cdot 3.14}=7.17 m$

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M^2 + n^2

Step 1:
Substitute in the numbers
-5^2 + 3^2

Step 2:
Square both numbers
25 + 9

Step 3:
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Answer is 34

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2 years ago

a box of cereal states that there are 72 calories in a 3/4 cup serving. What is the unit rate for calories per cup? how many cal

Leona [35]

Answer:

96 and 192 calories

Step-by-step explanation:

<u>Given</u>

72 calories in a 3/4 cup

<u>Divide both by 3/4 to find the unit rate:</u>

72:3/4 in 3/4:3/4
96 calories in 1 cup

<u>Then multiply both by 2 to get the calories for 2 cups:</u>

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7 0

2 years ago

Simplify the expression 8 + (7 + x)

baherus [9]

Answer:

15 + x

Step-by-step explanation:

6 0

1 year ago

Find the length of the segment that joins the points (-5, 4) and (6,-3).

Helen [10]

Answer:

$\boxed {\boxed {\sf d=\sqrt{170} \ or \ d\approx 13.04}}}$

Step-by-step explanation:

We are asked to find the length of a segment or the <em>distance</em> between the 2 points. The formula for distance is:

$d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:

x₁= -5
y₁= 4
x₂= 6
y₂ = -3

Substitute the values into the formula.

$d= \sqrt{(6--5)^2+(-3-4)^2$

Solve inside the parentheses.

6--5 (Back to back negative signs become a positive)= 6+5 =11
-3-4= -7

$d= \sqrt{(11)^2+(-7)^2$

Solve the exponents.

(11)²= 11*11= 121
(-7)²= -7*-7= 49

$d= \sqrt {(121)+(49)$

Add.

$d= \sqrt {170}$

$d=13.0384048104$

Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

13.03<u>8</u>4048104

$d\approx 13.04$

The length of the segment is <u>√170</u> or approximately <u>13.04. </u>

7 0

2 years ago

A ladder 16 feet long is leaning against the wall of a tall building. The base of the ladder is moving away from the wall at a r

svet-max [94.6K]

Answer:

a. 0.588

b. 0.0722

c. 4.576 sqft/sec

Step-by-step explanation:

Let b and h denote the base and height as indicated in the diagram. By pythagoras theorem, $h^2 + b^2 = 16^2 = 256 \dotsc\;(1)$ because it is a right angle triangle.

It is given that $\frac{db}{dt} = 1$

Now differentiate (1) with respect to t (time) :

$\displaystyle{2h\frac{dh}{dt} + 2b\frac{db}{dt} = 0 \implies \frac{dh}{dt} = -\frac{b}{h} \frac{db}{dt}}$

$\displaystyle{=-\frac{b}{\sqrt{256 - b^2}} \frac{db}{dt} = -\frac{8}{13.856} \times 1 = -0.588}$

The minus sign indicates that the value of h is actually decreasing. The required answer is 0.588.

b. From the diagram, infer that $16 \sin{\theta} = b$ . When b = 8, then $\theta = \arcsin{0.5} = \ang{30}$ .

Differentiate the above equation w.r.t t

$\displaystyle{16 \cos{\theta} \frac{d\theta}{dt} = \frac{db}{dt} \implies \frac{d\theta}{dt} = \frac{1}{16 \cos{\theta}} = \frac{1}{13.856} = \mathbf{0.0722}}$

c. The area of the triangle is given by $A = 0.5\times h \times b$ . Differentiating w.r.t t,

$\displatstyle{\frac{dA}{dt} = 0.5 b \frac{dh}{dt} + 0.5 h \frac{db}{dt}}$

Plugging in b = 8, h = 13.856, $\frac{dh}{dt} = -0.588$ ,

$\frac{dA}{dt} = -2.352 + 6.928 = \mathbf{4.576 ft^2/sec}$

8 0

3 years ago