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3 years ago

What is the exponential form of log5 9 = x? x^9 = 5 5^x = 9 x^5 = 9 9^x = 5

Mathematics

1 answer:

Harrizon [31]3 years ago

8 0

Answer:

Step-by-step explanation:

Using the rule of logarithms

$log_{b}$ x = n ⇔ x = $b^{n}$

Hence

$log_{5}$ 9 = x ⇒ 9 = $5^{x}$ → B

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Two opposite sides of a rectangle are each of length x. If the perimeter of the rectangle is 12, then the area, as a function of

Reil [10]

Answer: $x(6-x)$

Step-by-step explanation:

Given : Two opposite sides of a rectangle are each of length x.

Let the other adjacent side be y.

The perimeter of the rectangle is 12 units.

Perimeter of rectangle is given by :-

$P=2(\text{Sum of adjacent sides})\\\\\Rightarrow\ 12=2(x+y)\\\\\Rightarrow\ x+y=\dfrac{12}{2}=6\\\\\Rightarriow\ y=6-x$

The area of rectangle is given by :-

$A=\text{product of two adjacent sides}\\\\\Rightarrow\ A=xy=x(6-x)$

Hence, the area as a function x = $x(6-x)$

7 0

3 years ago

Read 2 more answers

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Genrish500 [490]

Answer:

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2 years ago

The given line passes through the points and (-4, -3) and (4, 1).

Debora [2.8K]

Answer:

The equation of the line is y - 3 = -2(x + 4)

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line which passes through the points (x1 , y1) and

(x2 , y2) is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The product of the slopes of the perpendicular lines = -1

- That means if the slope of a line is m then the slope of the

perpendicular line to this line is -1/m

- The point-slope of the equation is $y - y_{1}=m(x - x_{1})$

* lets solve the problem

∵ A given line passes through points (-4 , -3) and (4 , 1)

∴ x1 = -4 , x2 = 4 and y1 = -3 , y2 = 1

∴ The slope of the line $m=\frac{1-(-3)}{4-(-4)}=\frac{1+3}{4+4}=\frac{4}{8}=\frac{1}{2}$

- The slope of the line perpendicular to this line is -1/m

∵ m = 1/2

∴ The slope of the perpendicular line is -2

- Lets find the equation of the line whose slope is -2 and passes

through point (-4 , 3)

∵ x1 = -4 , y1 = 3

∵ m = -2

∵ y - y1 = m(x - x1)

∴ y - 3 = -2(x - (-4))

∴ y - 3 = -2(x + 4)

* The equation of the line is y - 3 = -2(x + 4)

4 0

3 years ago

Electric utility poles in the form of right cylinders are made out of wood that costs

olga_2 [115]

The cost of a utility pole with a diameter of 1.5 ft and a height of 40 ft is $782.1

<h3>How to calculate the cost of a utility pole with a diameter of 1.5 ft and a height of 40 ft?</h3>

The given parameters are:

Cost per cubic foot = $11.07 per cubic foot

Height = 40 feet

Diameter = 1.5 feet

Shape = Cylinder

The volume of the cylinder is calculated as:

V = πr^2h

Where

r = Diameter/2

So, we have

r = 1.5/2

Evaluate

r = 0.75

The volume of the cylinder becomes

V = 3.14 * 0.75^2 * 40

Evaluate

V = 70.65

The cost per cubic foot is $11.07 per cubic foot.

So, the cost of a utility pole is

Cost = $11.07 * 70.65

Evaluate

Cost = $782.1

Hence, the cost of a utility pole with a diameter of 1.5 ft and a height of 40 ft is $782.1