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3 years ago

Help me solve this please

Mathematics

2 answers:

coldgirl [10]3 years ago

5 0

"Simple interest" means the interest goes into a separate bucket, and
it just waits there for you to come and get it. It doesn't get added to the
amount in the account, so next year, you don't get interest on the interest.

4 percent of $2000 is (0.04 x 2000) = $80 .

That's how much interest you get each year.

At the end of 4 years, you have (4 x $80) = $320 in the interest bucket.
(And of course, you still have the original $2000 in the account.)

klemol [59]3 years ago

4 0

2339.71712 is the whole amount but rounding up to the nearest hundred its 2339.72 for 4years. 339.72 is the answer you was looking for.

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Determine the open intervals on which the graph of f(x) = x - 4cos x is concave upward or concave downward

bazaltina [42]

The graph of the function $f(x)$ is

concave upward, when $f''(x)>0;$
concave downward, when $f''(x)$

Find $f''(x):$

$f'(x)=(x-4\cos x)'=1+4\sin x;$

$f''(x)=4\cos x.$

Now:

1. when $4\cos x>0,$ the graph of the function is concave upward and this is for

$x\in \left(-\dfrac{\pi}{2}+2\pi k,\dfrac{\pi}{2}+2\pi k\right), \text{ where } k\in Z.$

2. when $4\cos x$ the graph of the function is concave downward and this is for

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2 years ago

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

lara [203]

Answer:

$y=7x$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

we have the points (2,14) and (4,28)

Find out the constant of proportionality k

$k=y/x$

For (2,14) ----> $k=14/2=7$

For (4,28) ----> $k=28/4=7$

the value of $k=7$

therefore

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$y=7x$

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3 years ago

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Answer:

7. 183 in^2

8. 192.42 m^2

9. 239.4 ft^2

Step-by-step explanation:

7. The figure seems most easily seen as a trapezoid with a triangle removed. The trapezoid has bases of 26 and 14, and a height of 15. So, its area is ...

A = (1/2)(b1 +b2)(h) = (1/2)(26+14)(15) = 300 . . . . . . square inches

The triangle has a base of 26 and a height of 9, so an area of ...

A = (1/2)bh = (1/2)(26)(9) = 117 . . . . . . square inches

Then the shaded area is ...

300 in^2 -117 in^2 = 183 in^2

8. The area of the donut can be found different ways. One way is to multiply the width of the shaded area (3.5 m) by the circumference of its centerline.

The centerline diameter is 21 m - 3.5 m = 17.5 m, so the circumference of that circle is ...

C = πd = π(17.5 m) = 17.5π m

Then the area of the shaded part is ...

(3.5 m)(17.5π m) = 61.25π m^2 ≈ 192.42 m^2

9. As in problem 7, this can be treated as a parallelogram less a triangle. Here, we need to do a little work to find the area of the triangle.

The triangle of interest is a right triangle with hypotenuse 23.8 ft and one leg 21 ft. The Pythagorean theorem can be used to find the other leg:

h = √(23.8^2 -21^2) = √125.44 = 11.2

Then the area of the triangle is ...

A = (1/2)bh = (1/2)(21)(11.2) = 117.6 . . . ft^2

The area of the parallelogram (including the triangle) is ...

A = bh = (23.8 ft)(15 ft) = 357 ft^2

So, the shaded area is the difference ...

357 ft^2 -117.6 ft^2 = 239.4 ft^2

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Comment on significant digits

The area in problem 8 may be considered to be 192.325 m^2 if you are required to use 3.14 as the value for pi. Since that value is only good to 3 significant digits, it is quite pointless to report the answer to 6 significant digits when using that value. It is quite reasonable to use 192 m^2 for the answer, especially if you're required to round to whole numbers.

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