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3 years ago

A is true but f(x) is wrong need help

Mathematics

1 answer:

MrRissso [65]3 years ago

3 0

Answer:

f(x)=-18x^2

Step-by-step explanation:

Given:

1+Integral(f(t)/t^6, t=a..x)=6x^-3

Let's get rid of integral by differentiating both sides.

Using fundamental of calculus and power rule(integration):

0+f(x)/x^6=-18x^-4

Additive Identity property applied:

f(x)/x^6=-18x^-4

Multiply both sides by x^6:

f(x)=-18x^-4×x^6

Power rule (exponents) applied"

f(x)=-18x^2

Check:

1+Integral(-18t^2/t^6, t=a..x)=6x^-3

1+Integral(-18t^-4, t=a..x)=6x^-3

1+(-18t^-3/-3, t=a..x)=6x^-3

1+(6t^-3, t=a..x)=6x^-3

That looks great since those powers are the same on both side after integration.

Plug in limits:

1+(6x^-3-6a^-3)=6x^-3

We need 1-6a^-3=0 so that the equation holds true for all x.

Subtract 1 on both sides:

-6a^-3=-1

Divide both sides by-6:

a^-3=1/6

Raise both sides to -1/3 power:

a=(1/6)^(-1/3)

Negative exponent just refers to reciprocal of our base:

a=6^(1/3)

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write an equation of a line that passes through the following tow points (4, -6) and (2, 8) show work

stiks02 [169]

Answer:

$y = -7x + 22$

Step-by-step explanation:

Given

$(x_1,y_1) = (4,-6)$

$(x_2,y_2) = (2,8)$

Required

Determine the line equation

This question will be answered using linear interpolation.

This is represented as thus:

$\frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute values for x1,x2,y1 and y2

$\frac{y - (-6)}{x - 4} = \frac{8 - (-6)}{2 - 4}$

$\frac{y +6}{x - 4} = \frac{8 +6}{2 - 4}$

$\frac{y +6}{x - 4} = \frac{14}{-2}$

$\frac{y +6}{x - 4} =-7$

Cross Multiply

$y + 6 = -7(x - 4)$

$y + 6 = -7x + 28$

Make y the subject

$y = -7x + 28-6$

$y = -7x + 22$

7 0

3 years ago

Why is probability limited to numbers between 0 and 1

jok3333 [9.3K]

Answer:

Probability by definition is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.

Since number of elements in the set of favourable cases is less than or equal to the number of elements in the set of whole number of cases, their ratio would always end up being 1 or less than one.

Probability equals one when favourable number of cases are same as that of the whole number of cases and probability equals zero when there is no favourable case

3 0

3 years ago

Angle between 0 and 360 coterminal to 444 degrees

ycow [4]

Answer:

444 is coterminal to 84

Step-by-step explanation:

Just subtract 360 from 444 and you have your answer

444 - 360 = 84

4 0

2 years ago

A rectangular field is 75 yards wide and 105 yards long

nika2105 [10]

Answer:

width = 72 yards

length = 108 yards

Step-by-step explanation:

Given:

Width = 75 yards
Length = 105 yards

Area of the field with the given values:

$\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\& = \sf 75 \times 105\\& = \sf 7875\:\: yd^2\end{aligned}$

To maintain the same perimeter, but change the area, either:

decrease the width and increase the length by the same amount, or
increase the width and decrease the length by the same amount.

In geometry, length pertains to the longest side of the rectangle while width is the shorter side. Therefore, we should choose:

decrease the width and increase the length by the same amount.

Define the variables:

Let x = the amount by which to decrease/increase the width and length.

Therefore:

$\implies \sf width \times length < 7875\:\:yd^2$

$\implies (75-x)(105+x) < 7875$

Solve the inequality:

$\begin{aligned}(75-x)(105+x) & < 7875\\7875-30x-x^2 & < 7875\\-x^2-30x & < 0\\-x(x+30) & < 0\\x(x+30) & > 0\\\implies x & > 0 \:\: \textsf{ or }\:\:x < - 30\end{aligned}$

Therefore, as distance is positive only and the maximum width is 75 yd (since we are subtracting from the original width):

$\begin{cases}\textsf{width} = 75 - x\\\textsf{length} = 105 + x\end{cases}$

$\textsf{where } 0 < x < 75$

Therefore, to find the width and length of another rectangular field that has the same perimeter but a smaller area than the first field, simply substitute a value of x from the restricted interval into the found expressions for width and length:

Example 1:

Let x = 3

⇒ Width = 75 - 3 = 72 yd

⇒ Length = 105 + 3 = 108 yd

⇒ Perimeter = 2(72 + 108) = 360 yd

⇒ Area = 72 × 108 = 7776 yd²

Example 2:

Let x = 74

⇒ Width = 75 - 74 = 1 yd

⇒ Length = 105 + 74 = 179 yd

⇒ Perimeter = 2(1 + 179) = 360 yd

⇒ Area = 1 × 179 = 179 yd²

4 0

1 year ago

Read 2 more answers

A highway curve has a radius of 118.0 m. At what angle should the road be banked so that a car traveling at 25.90 m/s has no ten

dimaraw [331]

Answer:

0.51 degrees

Step-by-step explanation:

6 0

3 years ago