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3 years ago

Find the y-intercept of the graph of the linear equation. 3/4 x + y = 10

Mathematics

1 answer:

zalisa [80]3 years ago

4 0

Answer:

Step-by-step explanation:

slope intercept form is y=mx+b

in this case b is 10

y=-3/4x+10

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Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

Using first principle, this gives:

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

Hence, the smallest sum is 2

3 0

3 years ago

How to Rewrite 8 + 36 as a product of their GCF and the sum of two factors

siniylev [52]

Answer:

4 (2 + 9)

Step-by-step explanation:

Given expression:

8 + 36

The greatest common factor is the highest number that divides a number:

8 and 36 ;

Factors of 8 : 1,2,4, 8

36 : 1, 2, 3, 4, 9, 18, 36

The highest common factor is 4;

8 + 36 = 4 (2 + 9)

7 0

3 years ago

What is the volume of this cone?

olchik [2.2K]

Answer:

The volume of the cone is approximately 453.0 cm³

Step-by-step explanation:

The volume of a cone is one third that of a cylinder with the same height and radius. That gives us 1/3 πr²h, where r is radius and h is height.

However, we are not given the height of the cone, but the side length. We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length. You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:

$a^2 = b^2 + c^2$

So we can find the height of the cone with that:

$10.8^2 = 7.4^2 + h^2\\h^2 = 10.8^2 - 7.4^2\\h^2 = 116.64 - 54.76\\h^2 = 61.88\\h = \sqrt{61.88}\\h \approx 7.9$

Now that we have the cone's height, we can solve for its volume:

$v = \frac{1}{3} \pi r^2 h\\v = \frac{1}{3} \pi \times 7.4^2 \times 7.9\\v = \frac{1}{3} \pi \times 54.76 \times 7.9\\v = \frac{1}{3} \pi \times 432.6\\v = \pi \times 144.2\\v \approx 453.0 cm^3$

5 0

3 years ago

Read 2 more answers

Calculate the length of the side BC. Using pythagoras

o-na [289]

Answer:

10m

Step-by-step explanation:

A^2+B^2=C^2

6^2+8^2=C^2

36+64=C^2

100=C^2

10=C

3 0

3 years ago

Read 2 more answers

Find the percent of increase or decrease? 2.5y to 1.5y

horsena [70]

Answer:

From 2.5 y to 1.5 y there is a 40 % DECREASE in the value.

Step-by-step explanation:

Here, the initial value = 2.5 y

The final value of 1.5 y

Now,as Final Value < Initial Value

So, there is a DECREASE IN THE VALUE.

Now, decrease in the value = Initial value - Final Value

= 2.5 y = 1.5 y = 1 y

or, there is a decrease of ( 1 y) in the given value.

Now, Percentage decrease in the value is given as:

$\textrm{Percentage Decrease} = \frac{\textrm{The decrease in the value}}{\textrm{The initial Value}} \times 100\\ = \frac{1 y}{2.5 y} \times 100 = 40$

or, Percentage Decrease = 40%

Hence, from 2.5y to 1.5y there is a 40 % DECREASE in the value.

4 0

3 years ago