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4 years ago

6

Landon used a semicircle, a rectangle, and a right triangle to form the figure below. Which is the best estimate of the area of

the figure in square centimeters?

2 answers:

Nuetrik [128]4 years ago

6 0

Let’s start with the rectangle. 6(4) = 24 cm^2.
The triangle is 1/2(bh).
We know the bottom of the triangle is 4 because 10-6=4.
4(4) = 16
16/2 = 8
We’re at 32 square cm so far.
Now the semi circle.
The diameter is 4, so the radius is 2.
A = (pi)r^2
A = (pi)4
A= 4pi
Best estimate could be expressed as 32 + 4pi cm^2, or substituting 3.14 for pi, 44.56 cm^2

Damm [24]4 years ago

4 0

Answer:

38.28cm^2

Step-by-step explanation:

Area of rectangle = 24cm^2

Area of rectangle = 8cm^2

Area of semicircle = 6.28cm^2

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What is the amount of interest earned with a deposit of 7,000 at 6.5% for 120 days

aev [14]

The interest figure always means the interest for a year.

120 days is 1/3 of a year, so you'll only earn 1/3 of 6.5% .

6.5% = 0.065

1/3 of that is 0.02167 .

(0.02167) x (7,000) = 151.67

3 0

3 years ago

Read 2 more answers

Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is

olganol [36]

<h2><u>Answer</u>:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2><u>Step-by-step explanation:</u></h2>

<em>The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;</em>

(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ------------------(i)

<em>From the question:</em>

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

<em>Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;</em>

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25 ------------------(ii)

<em>Open the brackets and have the following:</em>

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0 [<em>equation has already been normalized since the coefficient of x² is 1</em>]

<em>Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:</em>

x² + y² + z² + 18(x - y + z) + 218 = 0

(2) To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25 [<em>subtract 25 from both sides</em>]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

6 0

4 years ago

Marta_Voda [28]

Answer:

a) 50 meters

b) 2354 meters

c) 12 seconds

d) 24.13 seconds

Step-by-step explanation:

Hello!

<h3>a) How far is Lincoln above the ground when he shoots the gun?</h3>

We need to really understand what the variables represent in this question. Given that t is time, and h is height, the time at which he shoots the bullet will be 0, as the bullet hasn't started traveling yet. This means that we can solve for the original height of the bullet by plugging in 0 for time in the equation.

Equation: $h = -16t^2 + 384t + 50$

Plug in 0 for t:

$h = -16t^2 + 384t + 50$
$h = -16(0)^2 + 384(0) + 50$
$h = 50$

The height at which Lincoln shot the bullet is 50 meters.

We can also look at this graphically. The height of origin will simply be when the x-value (in this case t-value) is 0. That means it is the point at which the graph intersects the y-axis, known as the y-intercept.

Standard form of a Parabola: $y = ax^2 + bx + c$

The y-intercept is the "c" value.

Given our equation: $h = -16t^2 + 384t + 50$

The c-value is 50. This proves that the y-intercept is 50.

<h3 /><h3>b)How high does the bullet travel vertically relative to the ground?</h3>

We want to find the highest point of the graph. To do that, we can find the vertex.

We can utilize the Axis of Symmetry (AOS) to find the Vertex.

First, find the AOS using the formula: $AOS = -\frac{b}{2a}$

a = -16
b = 384

Plug it into the formula:

$AOS = -\frac{b}{2a}$
$AOS = -\frac{384}{2(-16)}$
$AOS = \frac{384}{32}$
$AOS = 12$

Plug in 12 for t in the equation:

$h = -16t^2 + 384t + 50$
$h = -16(12)^2 + 384(12) + 50$
$h = -2304 + 4608 + 50$
$h = 2304+50$
$h = 2354$

Therefore, the highest point of the bullet is 2354 meters.

<h3>c)How long does it take the bullet to reach its greatest height?</h3>

We answered this in the last question. The t-value when h is at its highest is 12.

<h3>d)After how many seconds (round to nearest 100th) does the bullet hit the ground?</h3>

We have to solve for the values of t when h is 0 (when it touches the ground).

Set the equation to 0, and solve using the quadratic formula.

Quadratic formula: $x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$
$x = \frac{-384\pm\sqrt{384^2 - 4(-16)(50)}}{2(-16)}$
$x = \frac{-384\pm\sqrt{147456 +3200}}{-32}$
$x = \frac{-384\pm\sqrt{150656}}{-32}$
$x = \frac{-384\pm388.14}{-32}$
$x = -\frac{4.14}{32}, x = \frac{772.14}{32}$

We are only going to take the positive solution, as we can't have a negative time. The solution that doesn't work is called an extraneous solution.

$x = \frac{772.14}{32}$
$x = 24.13$

It takes approximately 24.13 seconds for the bullet to hit the ground.

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3 years ago

Janice's mother gave her a $10 bill to buy 5 pounds each of bananas and apples at the grocery store when she got there she find

Katarina [22]

No, Janice's mom didn't give her enough money.

5 0

3 years ago

Read 2 more answers

The volume of a sphere is decreasing at a constant rate of 116 cubic centimeters per second. At the instant when the volume of t

nirvana33 [79]

Answer:

$\frac{dr}{dt} = -1.325 \ cm/s$

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

<u>Calculus</u>

Derivatives

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Taking Derivatives with respect to time

Step-by-step explanation:

<u>Step 1: Define</u>

Given:

<u /> $V = \frac{4}{3} \pi r^3$ <u />

<u /> $\frac{dV}{dt} = -116 \ cm^3/s$ <u />

<u /> $V = 77 \ cm^3$ <u />

<u />

<u>Step 2: Solve for </u><em><u>r</u></em>

Substitute: $77 = \frac{4}{3} \pi r^3$
Isolate <em>r</em> term: $\frac{77}{\frac{4}{3} \pi} = r^3$
Isolate <em>r</em>: $\sqrt[3]{\frac{77}{\frac{4}{3} \pi}} = r$
Evaluate: $2.63917 = r$
Rewrite: $r = 2.63917 \ cm$

<u>Step 3: Differentiate</u>

<em>Differentiate the Volume Formula with respect to time t.</em>

Define: $V = \frac{4}{3} \pi r^3$
Differentiate [Basic Power Rule]: $\frac{dV}{dt} = \frac{4}{3} \pi \cdot 3 \cdot r^{3-1} \cdot \frac{dr}{dt}$
Simplify: $\frac{dV}{dt} = 4 \pi r^2 \cdot \frac{dr}{dt}$

<u>Step 4: Find radius rate</u>

Substitute in variables: $-116 \ cm^3/sec = 4 \pi (2.63917 \ cm)^2 \cdot \frac{dr}{dt}$
Isolate dr/dt rate: $\frac{-116 \ cm^3/s}{4 \pi (2.63917 \ cm)^2} = \frac{dr}{dt}$
Evaluate: $-1.3253 \ cm/s = \frac{dr}{dt}$
Rewrite: $\frac{dr}{dt} = -1.3253 \ cm/s$
Round: $\frac{dr}{dt} = -1.325 \ cm/s$

Our radius is decreasing at a rate of -1.325 cm per second.

6 0

3 years ago