John asked 60 people to name their favourite fruit here are his results

Which algebraic expressions are polynomials

ivolga24 [154]

Answer:

2,3,5,6

Step-by-step explanation:

4 0

2 years ago

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true or false? the circumcenter of a triangle is the center of the only circle that can be inscribed about it

MissTica

Answer:

TRUE

Step-by-step explanation:

The circumcenter of a triangle is the center of the only circle that can be circumscribed about it

6 0

3 years ago

(x - 6) (X - 4) =<br> How do I solve this?

Vedmedyk [2.9K]

Answer: x^2 -10x + 24

Step-by-step explanation:

(x-6) (x-4)

= x^2 - 6x - 4x + 24

= x^2 -10x + 24

5 0

2 years ago

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200 σ j=1 2j( j 3) describe the steps to evaluate the summation. what is the sum?

ziro4ka [17]

The sum of the equation is = 5494000.

<h3>What does summation mean in math?</h3>

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.

<h3>Briefing:</h3>

Distribute 2j to (j+3).

Rewrite the summation as the sum of two individual summations.

Evaluate each summation using properties or formulas from the lesson.

The lower index is 1, so any properties can be used.

The sum is 5,494,000.

<h3>Calculation according to the statement:</h3>

$\sum_{j=1}^{200} 2 j(j+3)$

simplifying them we get:

$\sum_{j=1}^{200} 2 j^{2}+6 j$

Split the summation into smaller summations that fit the summation rules.

$\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j$

$\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}$

The formula for the summation of a polynomial with degree 2

is:

$\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}$

Substitute the values into the formula and make sure to multiply by the front term.

$(2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$$

we get: 5373400

Evaluating same as above : $6 \sum_{j=1}^{200} j$

we get: 120600

Add the results of the summations.

5373400 + 120600

= 5494000

The sum of the equation is = 5494000.

To know more about summations visit:

brainly.com/question/16679150

#SPJ4

6 0

1 year ago

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

inessss [21]

Answer:

The height of cone is decreasing at a rate of 0.085131 inch per second.

Step-by-step explanation:

We are given the following information in the question:

The radius of a cone is decreasing at a constant rate.

$\displaystyle\frac{dr}{dt} = -7\text{ inch per second}$

The volume is decreasing at a constant rate.

$\displaystyle\frac{dV}{dt} = -948\text{ cubic inch per second}$

Instant radius = 99 inch

Instant Volume = 525 cubic inches

We have to find the rate of change of height with respect to time.

Volume of cone =

$V = \displaystyle\frac{1}{3}\pi r^2 h$

Instant volume =

$525 = \displaystyle\frac{1}{3}\pi r^2h = \frac{1}{3}\pi (99)^2h\\\\\text{Instant heigth} = h = \frac{525\times 3}{\pi(99)^2}$

Differentiating with respect to t,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)$

Putting all the values, we get,

$\displaystyle\frac{dV}{dt} = \frac{1}{3}\pi \bigg(2r\frac{dr}{dt}h + r^2\frac{dh}{dt}\bigg)\\\\-948 = \frac{1}{3}\pi\bigg(2(99)(-7)(\frac{525\times 3}{\pi(99)^2}) + (99)(99)\frac{dh}{dt}\bigg)\\\\\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi} = (99)^2\frac{dh}{dt}\\\\\frac{1}{(99)^2}\bigg(\frac{-948\times 3}{\pi} + \frac{2\times 7\times 525\times 3}{99\times \pi}\bigg) = \frac{dh}{dt}\\\\\frac{dh}{dt} = -0.085131$

Thus, the height of cone is decreasing at a rate of 0.085131 inch per second.

3 0

2 years ago