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2 years ago

5

An amount of $24,000 is borrowed for 9 years at 6.75% interest, compounded annually. If the loan is paid in full at the end of t

hat period, how much must be
paid back?
Use the calculator provided and round your answer to the nearest dollar.

1 answer:

MA_775_DIABLO [31]2 years ago

4 0

38,580 is the full amount of what he has to pay back

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Akira receives a prize at a science fair for having the most informative project. Her trophy is in the shape of a

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This question is Incomplete because it lacks the appropriate diagram for the square pyramid. Please kindly find attached the required diagram

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Step-by-step explanation:

From the question, we are told that the foil covers the body of the trophy including the bottom, hence the formula we would be applying =

Total Surface Area of the Square pyramid = 2bs + b²

Where s = Height of the square pyramid

b = Edge length of the square pyramid

From the attached diagram, we can see that:

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b = 3 inches

Total Surface Area of the Square pyramid = 2bs + b²

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3 years ago

Find the sum of these polynomials.

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Need a little help here pls

Crank

Answer:

The statements that must be true are:

XY and JK form four right angles ⇒ B

XY ⊥ JK ⇒ C

JP = KP ⇒ E

m∠JPX = 90° ⇒ F

Step-by-step explanation:

From the given figure

∵ Line XY is the perpendicular bisector of the line segment JK

→ That means line XY is the line of symmetry of the line segment JK

∴ XY ⊥ JK ⇒ C

∵ XY ∩ JK at point P

∴ P is the midpoint of JK

∵ XY ⊥ JK

∴ ∠JPX, ∠KPX, ∠JPY, and ∠KPY are right angles

∴ XY and JK form four right angles ⇒ B

∵ The measure of the right angle is 90°

∴ m∠JPX = m∠KPX = m∠JPY = m∠KPY = 90°

∴ m∠JPX = 90° ⇒ F

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3 years ago

An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of

Helga [31]

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = $\pi r^{2} \frac{h}{3}$

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

$r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm$

We will now find the volume of the cone.

Volume of cone $\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}$

We know the density of ice is 0.93 grams per $1cm^{3}$

$1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g$ (Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = $\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}$

Volume of cone being melted = New Volume - Original volume

= $\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}$

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = $\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}$

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = $5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}$

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= $\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}$

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

4 0

2 years ago