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3 years ago

Someone please solve this!! show work:))

Mathematics

2 answers:

sergij07 [2.7K]3 years ago

6 0

the final answer is n=6 1/4

Dimas [21]3 years ago

6 0

N = 6 1/4 that is your answer

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A bicycle company has designed and built a new model of sports bicycle. They have determined that the profit for the sale of the

ycow [4]

The answer would be c)$120

4 0

3 years ago

What is the answer to -9(4x-10)+24

Fantom [35]

Answer:

-36x+114

Step-by-step explanation:

5 0

3 years ago

An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base

kirill115 [55]

Answer:

the original volume is lesser than the new volume by 242.47 in³

Step-by-step explanation:

Volume of a cone is;

V = ⅓πr²h

Where;

r is radius

h is height

For the original chamber;

r = 5.7/2 = 2.85 inches

h = 12 inches

Volume of this original chamber is;

V_orig = ⅓ × π × 2.85² × 12

V_orig = 102.02 in³

In the new design, the chamber is scaled by a factor of 1.5.

Thus;

r_new = 2.85 × 1.5 = 4.275 inches

h_new = 12 × 1.5 = 18 inches

V_new = ⅓ × π × 4.275² × 18

V_new = 344.49 inch³

V_new - V_orig = 344.49 - 102.02 =

Thus, the original volume is lesser than the new volume by 242.47 in³

6 0

3 years ago

$1500 is invested at a rate of 3% compounded monthly. Write a compound interest function to model this situation. Then find the

Marianna [84]

Answer:

Equation: $F=1500(1.0025)^{12t}$

The balance after 5 years is: $1742.43

Step-by-step explanation:

This is a compound growth problem . THe formula is:

$F=P(1+\frac{r}{n})^{nt}$

Where

F is future amount

P is present amount

r is rate of interest, annually

n is the number of compounding per year

t is the time in years

Given:

P = 1500

r = 0.03

n = 12 (compounded monthly means 12 times a year)

The compound interest formula modelled by the variables is:

$F=1500(1+\frac{0.03}{12})^{12t}\\F=1500(1.0025)^{12t}$

Now, we want balance after 5 years, so t = 5, substituting, we get:

$F=1500(1.0025)^{12t}\\F=1500(1.0025)^{12*5}\\F=1500(1.0025)^{60}\\F=1742.43$

The balance after 5 years is: $1742.43

3 0

3 years ago

Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4

arsen [322]

we are given

$R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k$

now, we can find x , y and z components

$x=cos(8t),y=sin(8t),z=8ln(cos(t))$

Arc length calculation:

we can use formula

$L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt$

$x'=-8sin(8t),y=8cos(8t),z=-8tan(t)$

now, we can plug these values

$L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt$

now, we can simplify it

$L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8sec(t) dt$

now, we can solve integral

$\int \:8\sec \left(t\right)dt$

$=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|$

now, we can plug bounds

and we get

$=8\ln \left(\sqrt{2}+1\right)-0$

so,

$L=8\ln \left(1+\sqrt{2}\right)$ ..............Answer

5 0

3 years ago