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3 years ago

Could someone pls help me

Mathematics

2 answers:

babunello [35]3 years ago

4 0

Answer: y = 90 x = 29

Step-by-step explanation:

xenn [34]3 years ago

4 0

Y=90 x=29
a straight is 180

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The velocity function, in feet per second, is given for a particle moving along a straight line. Find (a) the displacement and (

AveGali [126]

Answer:

(a) 2 feet.

(b) 2 feet.

Step-by-step explanation:

We have been given that the velocity function $v(t)=\frac{1}{\sqrt{t}}$ in feet per second, is given for a particle moving along a straight line.

(a) We are asked to find the displacement over the interval $1\leq t\leq 4$ .

Since velocity is derivative of position function , so to find the displacement (position shift) from the velocity function, we need to integrate the velocity function.

$\int\limits^b_a {v(t)} \, dt$

$\int\limits^4_1 {\frac{1}{\sqrt{t}}} \, dt$

$\int\limits^4_1 {\frac{1}{t^{\frac{1}{2}}} \, dt$

$\int\limits^4_1 t^{-\frac{1}{2}} \, dt$

Using power rule, we will get:

$\left[\frac{t^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}}\right] ^4_1$

$\left[\frac{t^{\frac{1}{2}}}{\frac{1}{2}}}\right] ^4_1$

$\left[2t^{\frac{1}{2}}\right] ^4_1$

$2(4)^{\frac{1}{2}}-2(1)^{\frac{1}{2}}=2(2)-2=4-2=2$

Therefore, the total displacement on the interval $1\leq t\leq 4$ would be 2 feet.

(b). For distance we need to integrate the absolute value of the velocity function.

$\int\limits^b_a |{v(t)|} \, dt$

$\int\limits^4_1 |{\frac{1}{\sqrt{t}}}| \, dt$

Since square root is not defined for negative numbers, so our integral would be $\int\limits^4_1 {\frac{1}{\sqrt{t}}} \, dt$ .

We already figured out that the value of $\int\limits^4_1 {\frac{1}{\sqrt{t}}} \, dt$ is 2 feet, therefore, the total distance over the interval $1\leq t\leq 4$ would be 2 feet.

7 0

3 years ago

Flying against the wind, an airplane travels 3360 kilometers in hours. Flying with the wind, the same plane travels 7560 kilomet

Lerok [7]

Answer:

606.6 and 233.3 respectively

Step-by-step explanation:

Let the speed of plane in still air be x and the speed of wind be y.

ATQ, (x+y)*9=7560 and (x-y)*9=3360. Solving it, we get x=606.6 and y=233.3

6 0

3 years ago

What three simpler multiplications can you use to find 8*242

Jlenok [28]

$242=200+40+2\\\\8\cdot242=8\cdot200+8\cdot40+8\cdot2=1600+320+16=1936$

6 0

4 years ago

A box (with no top) will be made by cutting squares of equal size out of the corners of a 2626 inch by 4343 inch rectangular p

Troyanec [42]

If x represents the side length of the square cut from each corner, then the dimensions of the base of the box are 26-2x by 43-2x. The volume of the box is

... V = x(26-2x)(43-2x)

where x is restricted to the domain 0 ≤ x ≤ 13.

Plotting this equation using a graphing calculator shows the maximum volume to be 2644.7 in³.

_____

The analytical solution can be found by setting the derivative of V to zero.

... V = 4x³ - 138x² +1118x

... dV/dx = 0 = 12x² -276x +1118

This has solutions given by the quadratic formula, where a=12, b=-276, c=1118:

... x = (-b±√(b²-4ac))/(2a)

The plus sign will give a solution that is not in the allowed domain of x, so the only viable solution is the one where the radical is subtracted.

... x = (276 - √(76176--53664))/24 = (23/2) - √(469/12) ≈ 5.2483 . . . inches

Then the corresponding maximum volume is found from the equation for V.

... V ≈ (5.2483)(26 - 2·5.2483)(43 - 2·5.2483) ≈ 2644.6877 in³ . . . . as above

5 0

3 years ago

What is 150 in simplified radical form? A.75/3 B.25/6 C.5/6 D.5/2

Gemiola [76]

Your answer is b .25/6

4 0

3 years ago