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melomori [17]
3 years ago
8

Matthew invested $5,300 in an account paying an interest rate of 2.1% compounded annually. Assuming no deposits or withdrawals a

re made, how long would it take, to the nearest year, for the value of the account to reach $6,020?
Mathematics
2 answers:
Mariulka [41]3 years ago
6 0

Answer: it would be 6

Step-by-step explanation

Delta math

kvv77 [185]3 years ago
4 0

Answer:  

6  

Step-by-step explanation:

I got it right  

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HELP ME PLEASE! I am not good at math
Diano4ka-milaya [45]
First you subtract 1/3 from both sides, that leaves you with 5/12, then you multiply the reciprocal of 1/2 by both sides, which is 2, which gives you 5/6. Therefore, K>5/6
4 0
3 years ago
Calculus Problem
Roman55 [17]

The two parabolas intersect for

8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2

and so the base of each solid is the set

B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, |x^2-(8-x^2)| = 2|x^2-4|. But since -2 ≤ x ≤ 2, this reduces to 2(x^2-4).

a. Square cross sections will contribute a volume of

\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x

where ∆x is the thickness of the section. Then the volume would be

\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x

We end up with the same integral as before except for the leading constant:

\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx

Using the result of part (a), the volume is

\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x

and using the result of part (a) again, the volume is

\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}

7 0
2 years ago
In an effort to determine the most effective way to teach safety principles to a group of employees, four different methods were
musickatia [10]

Answer:

critical value = 5.29

Step-by-step explanation:

Given that they are divided into 4 groups and a sample of 5 test was selected

N = 5 * 4 = 20

k = 4

∝ = 0.01

Df for numerator ( SS group )= k - 1 = 3

Df for denominator ( SSE group )  = N - k = 20 - 4 = 16

DF ( degree of freedom )

Next we will use the F table to determine the critical value

Critical value =   F_{16,3,0.01} = 5.29

5 0
3 years ago
Help me plzzzzz i give u<br> BRAINLIEST
poizon [28]
The answer is most likely 32 I’m the best at math
5 0
3 years ago
What is the square root of 2x plus the square root of 2x
WITCHER [35]

Answer:

i just took the test, so its b. 84

i dont know hwy

6 0
3 years ago
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