Answer:
The interest rate is 7.58%
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
A = P
, where
- A is the future value of the investment, including interest
- P is the principal investment amount (the initial amount)
- r is the interest rate in decimal
- t is the time the money is invested for
∵ Angus has $3,000 he want to invest
∴ P = 3000
∵ The interest rate is compounded continuously
∵ Angus has $5,500 in 8 years
∴ A = 5500
∴ t = 8
→ Substitute them in the rule above to find r
∵ 5500 = 3000
→ Divide both sides by 3000
∴ 
=
→ Insert ㏑ in both sides
∵ ㏑( ) = ㏑()
→ Remember ㏑(
) = n
∴ ㏑( ) = 8r
→ Divide both sides by 8
∴ 0.07576697545 = r
→ Multiply it by 100% to change it to a percentage
∴ r = 0.07576697545 × 100%
∴ r = 7.576697545 %
→ Round it to the nearest hundredth
∴ r ≅ 7.58
∴ The interest rate is 7.58%
Answer:
x=−5+√29 or x=−5−√29
Step
Let's solve your equation step-by-step.
x2+10x+10=14
Step 1: Subtract 14 from both sides.
x2+10x+10−14=14−14
x2+10x−4=0
For this equation: a=1, b=10, c=-4
1x2+10x+−4=0
Step 2: Use quadratic formula with a=1, b=10, c=-4.
x=
−b±√b2−4ac
2a
x=
−(10)±√(10)2−4(1)(−4)
2(1)
x=
−10±√116
2
x=−5+√29 or x=−5−√29
answer:The width of the deck is 22.8 feet.
Step-by-step explanation:
Since we have given that
Area of the deck = 752.4 square feet
Length of deck = 33 feet
Let width of deck be 'x'.
Since Deck is in the shape of rectangle.
As we know the formula for "Area of rectangle ":
\begin{gathered}Area=Length\times width\\\\752.4=33\times x\\\\\dfrac{752.4}{33}=x\\\\22.8=x\end{gathered}
Area=Length×width
752.4=33×x
33
752.4
=x
22.8=x
Hence, the width of the deck is 22.8 feet.
Determine<span> whether a triangle with the given </span>lengths<span> is a </span>right triangle<span> or not. </span>Find<span> the </span>missing side<span> in each of the following </span>right triangles<span>. 2.</span>8 cm<span>, ') = 7 </span>cm<span> (</span><span>b) $% = 6 </span>cm<span>, %& = </span>8 cm<span>, $& = 10 </span>cm<span> (c) 34 = 17 </span>cm<span>, 45 = </span>8 cm<span>, 35 = </span>15 cm<span> 3.
</span>Use the Pythagorean Theorem to find<span> each </span>missing<span> measure. 1. 2. Example 1A</span>: Calculating theLength<span> of a </span>Side<span> of a </span>Right Triangle<span>. 12 </span>cm<span> , </span>82<span> + </span>152<span> = 17</span>2<span>.
</span>8.6.7, 8<span>.EE.2. When viewed from the </span>side<span>, the shape of some wooden waterskiing ramps is a, So, the hypotenuse is </span>15<span> inches long. Check: 02 + Write an equation you could use to </span>find<span> the length of the </span>missing side<span> of 20 </span>cm<span>. 18 yd lf the </span>sides<span> of a </span>triangle<span> have </span>lengths<span> 0,13, and c units such that 02 + is)2 = C 2</span>
