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Zinaida [17]
3 years ago
8

What is the area of the regular polygon

Mathematics
2 answers:
fgiga [73]3 years ago
7 0
To find the area<span> of a</span>regular polygon<span>, you use an apothem — a segment that joins the </span>polygon's<span> center to the midpoint of any side and that is perpendicular to that side</span>
dalvyx [7]3 years ago
3 0
A regular polygon<span> is equilateral (it has equal sides) and equiangular (it has equal angles). To find the </span>area<span> of a regular </span>polygon<span>, you use an apothem — a segment that joins the </span>polygon's<span> center to the midpoint of any side and that is perpendicular to that side (segment HM in the following figure is an apothem).</span>
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A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by ℎ = −16푡 ଶ+103푡+5 w
Liono4ka [1.6K]

Question:

A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by h(t)=-16t^2+80t+5, where t is measured in seconds.  Write an equation to determine how long it will take for the ball to reach the ground.

Answer:

t = 5.0625

Step-by-step explanation:

Given

h(t)=-16t^2+80t+5

Required

Find t when the ball hits the ground

This implies that h(t) = 0

So, we have:

0=-16t^2+80t+5

Reorder

-16t^2+80t+5 = 0

Using quadratic formula, we have:

t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}

Where

a = -16      b =80      c = 5

So, we have:

t = \frac{-80\±\sqrt{80^2 - 4*-16*5}}{2*-16}

t = \frac{-80\±\sqrt{6400 +320}}{-32}

t = \frac{-80\±\sqrt{6720}}{-32}

t = \frac{-80\±82.0}{-32}

This gives:

t = \frac{-80+82.0}{-32} or t = \frac{-80-82.0}{-32}

t = \frac{2}{-32} or t = \frac{-162}{-32}

t = -\frac{2}{32} or t = \frac{162}{32}

But time can not be negative.

So, we have:

t = \frac{162}{32}

t = 5.0625

<em>Hence, time to hit the ground is 5.0625 seconds</em>

3 0
3 years ago
11. Twyla and Tony have a 30/5 balloon mortgage for $389,900 with a rate of 4.85%. How much will they pay in interest over the l
kykrilka [37]

Answer:

Explanation:

Twyla and Tony with a balloon mortgage of 30/5 will make constant payments over the space of 5 years and then complete the bulk balloon payment for 25 years remaining.

Given mortgage loan value of $389900

Interest rate of 4.85%

We are asked to calculate the interest over the life of the loan.

We will calculate interest by calculating constant payments over the period of 5 years before balloon payment is due and adding them together then subtracting the mortgage loan given $389900

Formula for constant payments :

A= P×r×r(1+r)^n/(1+r)^n-1

Where A= constant/monthly payments

r= interest rate on the mortgage loan

n= number of payments = 30×12= 360

P= mortgage loan given

A= $389900×0.0485×0.0485(1+0.0485)^360/(1+0.0485)^360-1

=$389900×0.0485×1231340.79/25388468.94

=$389900×0.0485×0.04850

A= $917.142

Payment for five years(with interest)= $917.142×60= $55028.52

Calculate balloon payment:

FV= PV(1+r)^n - P((1+r)^n-1/r)

Where FV= future value of balloon payment

PV= initial loan given

r= interest rate on loan

n= number of payments

P= monthly payments

Substitute:

FV= $389900(1+0.0485/12)^60-917.142((1+0.0485/12)^60-1/0.0485/12)

=$389900×1.2738-917.142(0.2738/0.004041)

=$389900×1.2738-917.142×67.756

= 496654.62-62141.87

FV = $434512.75

Therefore total payment made with interest over the life of the loan= balloon payment+ constant payments for five years= $434512.75+$55028.52

=

6 0
3 years ago
Find the measure of b, given m∠A = 38°, m∠B = 74°, and a = 31.
tatyana61 [14]
Answer:
b = 48.4017

Explanation:
For this question, we will use the sine rule to get the missing side b. The sine rule is shown in the attached image.
We are given that:
a = 31
measure angle A = 38°
measure angle B = 74°

Substitute in the relation as follows:
sinA/a = sinB/b
sin(38) / 31 = sin(74) / b
b = [sin(74)] / [sin(38) / 31]
b = 48.4017

Hope this helps :)

5 0
3 years ago
A farmer had 63 sheep.<br> She sold 1/7 of them.<br> How many sheep had she left?
kykrilka [37]
63 dives by 7 is 9 so 63-9 is 54
Answer 54
3 0
3 years ago
How do you solve this <br> It’s called multi step equations plz help me
dangina [55]

Step-by-step explanation:

Add 8n to both sides to get

8n-67 = 5

then add 67

8n = 5+67 = 72

divide by 8

n = 9

5 0
3 years ago
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