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Bingel [31]
3 years ago
13

Michael invested 5,000 in an account that has a 5.5% annual interest rate. What equation best describes investment after T years

?
Mathematics
1 answer:
ivolga24 [154]3 years ago
5 0

Answer:

V = 5000 +  275*T   for simple annual interest

or:   A = 5000 * (1.055)^T   for an annual compound interest

Step-by-step explanation:

I assume this is a simple interest rate.  If not I will give the one for compound interest.

V = 5000 + 5000* 0.055 * T      (Value of account after T years)

V = 5000 +  275*T   for simple annual interest

or:   A = 5000 * (1.055)^T   for an annual compound interest

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Consider the region bounded by the curves y=|x^2+x-12|,x=-5,and x=5 and the x-axis
Tasya [4]
Ooh, fun

what I would do is to make it a piecewise function where the absolute value becomse 0

because if you graphed y=x^2+x-12, some part of the garph would be under the line
with y=|x^2+x-12|, that part under the line is flipped up

so we need to find that flipping point which is at y=0
solve x^2+x-12=0
(x-3)(x+4)=0
at x=-4 and x=3 are the flipping points

we have 2 functions, the regular and flipped one
the regular, we will call f(x), it is f(x)=x^2+x-12
the flipped one, we call g(x), it is g(x)=-(x^2+x-12) or -x^2-x+12
so we do the integeral of f(x) from x=5 to x=-4, plus the integral of g(x) from x=-4 to x=3, plus the integral of f(x) from x=3 to x=5


A.
\int\limits^{-5}_{-4} {x^2+x-12} \, dx + \int\limits^{-4}_3 {-x^2-x+12} \, dx + \int\limits^3_5 {x^2+x-12} \, dx

B.
sepearte the integrals
\int\limits^{-5}_{-4} {x^2+x-12} \, dx = [\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-5}_{-4}=(\frac{-125}{3}+\frac{25}{2}+60)-(\frac{64}{3}+8+48)=\frac{23}{6}

next one
\int\limits^{-4}_3 {-x^2-x+12} \, dx=-1[\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-4}_{3}=-1((-64/3)+8+48)-(9+(9/2)-36))=\frac{343}{6}

the last one you can do yourself, it is \frac{50}{3}
the sum is \frac{23}{6}+\frac{343}{6}+\frac{50}{3}=\frac{233}{3}


so the area under the curve is \frac{233}{3}
6 0
3 years ago
The next number in the arithmetic sequence 15, 22, 29, is: <br><br>A) 34<br>B) 35<br>C) 36<br>D) 37​
harkovskaia [24]
ANSWER: C) 36
EXPLANATION: +7 is the sequence
4 0
2 years ago
Compare 2.3 and 2.03
Andru [333]
2.3= 2.03 so there for it is equal
8 0
3 years ago
Factor the trinomial<br><br> x^2-9x+4x
8090 [49]

Answer:


Step-by-step explanation:

Simplifying

x2 + -9x = 4x + -4

Reorder the terms:

-9x + x2 = 4x + -4

Reorder the terms:

-9x + x2 = -4 + 4x

Solving

-9x + x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:

4 + -9x + -4x + x2 = -4 + 4x + 4 + -4x

Combine like terms: -9x + -4x = -13x

4 + -13x + x2 = -4 + 4x + 4 + -4x

Reorder the terms:

4 + -13x + x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0

4 + -13x + x2 = 0 + 4x + -4x

4 + -13x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0

4 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.

4 + -13x + -4 + x2 = 0 + -4

Reorder the terms:

4 + -4 + -13x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0

0 + -13x + x2 = 0 + -4

-13x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4

-13x + x2 = -4

The x term is -13x.  Take half its coefficient (-6.5).

Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.

-13x + 42.25 + x2 = -4 + 42.25

Reorder the terms:

42.25 + -13x + x2 = -4 + 42.25

Combine like terms: -4 + 42.25 = 38.25

42.25 + -13x + x2 = 38.25

Factor a perfect square on the left side:

(x + -6.5)(x + -6.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting  

(x + -6.5) equal to 6.184658438 and -6.184658438.


8 0
2 years ago
Read 2 more answers
A subtending arc on a circle with a radius of 4.5 centimeters has an arc length of 8π. The measure of the angle subtended by the
dem82 [27]

Answer: 320°

Step-by-step explanation:

This is a circle geometry.

The arc length of the circle is given to be 8πcm and the radius is 4.5cm.

Now the length of an arc of a circle is

Arc length = πr0°/180° or 2πr0°/360°

To find the angle 0° subtend at the center we equate the arc length with the formula and solve for 0°.Now we go

πr0°/180 = 8π, convert to a simple linear equal and solve for the angle.

πr0° = 8π × 180

0°. = 8π × 180

-----------

π × r

= 8 × 180. 8 × 180

-------- or ---------

9/2. 4.5

= 8 × 180 × 2

------------

9

= 8 × 20 × 2

= 320°

or 8 × 180/4.5

= 1440/4.5

= 320°

4 0
3 years ago
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