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crimeas [40]
3 years ago
13

$10,000 at an annual rate of 7%, compounded semi-annually, for 2 years

Mathematics
1 answer:
forsale [732]3 years ago
8 0

Answer:

\$13,107.96

Step-by-step explanation:

Since interest is compounded semi-annually (half a year or 6 months), in a spawn of 2 years, the interest will have been compounded 4 times. As given in the problem, each time the interest is compounded, the new balance will be 107% or 1.07 times the amount of the old balance.

Therefore, we can set up the following equation to find the new balance after 2 years:

\text{New balanace}=10,000\text{ (old balance)}\cdot 1.07\cdot 1.07\cdot 1.07\cdot 1.07,\\\text{New balanace}=10,000\cdot 1.07^4=\boxed{\$13,107.96}

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What are the answers to these angle questions?​
mafiozo [28]

Step-by-step explanation:

Firstly, we have to find m∠J.

Since all the angles of a Δ equal 180°, angles J, L, and K should have a sum of 180°.

So,

m∠J + m∠L + m∠K = 180°

The diagram shows us that ∠L = 49° and ∠K = 90°, so we plug in those numbers in the equation.

m∠J + 49° + 90° = 180°

Then we simplify

m∠J + 139° = 180°

Subtract 139° to both sides

∠J = 41

Now the other angles.

Since ΔJKL ~ ΔRST, then ∠J ≅ ∠R, ∠K ≅ ∠S, and ∠L ≅ ∠T

Meaning, m∠J = m∠R, m∠K = m∠S, and m∠L = m∠T

Since we know m∠J = 41°, m∠K = 90°, and m∠L = 49° we could plug those in so...

41° = m∠R , 90° = m∠S , and 49° = m∠T

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We want to find the zeros of this polynomial <br> Graph the zeros
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Match the following equation to the correct situation.
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3 years ago
Amelia launched her science fair rocket, and then backed away. The path of the rocket is given by the equation below, where y is
Mamont248 [21]

Answer:

1)The rocket hit the ground at     x = \frac{5}{4}

2)The maximum height of the rocket = 12.468 feet

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given equation  

                y = -2 x² + 5 x + 7 ...(i)

Differentiating equation (i) with respective to 'x' , we get

             \frac{dy}{dx} = -2( 2x) +5(1) =  -4x +5

Equating zero

            \frac{dy}{dx} = 0

⇒      -4 x +5 =0

⇒      -4 x = -5

⇒          x = \frac{5}{4}

<em> The rocket hit the ground at     </em>x = \frac{5}{4}<em></em>

<u><em>Step(ii):</em></u>-

    \frac{dy}{dx}  =  -4x +5  ...(ii)

Again differentiating equation (ii) with respective to 'x' , we get

 \frac{d^{2} y}{dx^{2} }  = - 4(1)

The maximum height at x = \frac{-5}{4}

  y = -2 x² + 5 x + 7

 y = -2 (\frac{5}{4})^{2}  + 5 (\frac{5}{4} )  + 7

y = \frac{-2(25)+ 25 (16)+7(64)}{64}

y = \frac{798}{64} = 12.468 feet

<em>The maximum height of the rocket = 12.468 feet</em>

       

4 0
3 years ago
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