All categories

2 years ago

What is the degree of the polynomial 5a6bc2+8d5+7e6f2−10g4h7 ? Enter your answer in the box.+

Mathematics

1 answer:

Leni [432]2 years ago

8 0

Answer:

Step-by-step explanation:

The degree of a polynomial is he highest of the degrees of its monomials (individual terms) with non-zero coefficients.

You are given the polynomial

$5a^6bc^2+8d^5+7e^6f^2-10g^4h^7$

It consists of 4 terms:

$5a^6bc^2$
$8d^5$
$7e^6f^2$
$-10g^4h^7$

The degrees are:

of the first term is $6+1+2=9$
of the second term is $5$
of the third term is $6+2=8$
of the fourth term is $4+7=11$

The greatest degree is 11.

You might be interested in

Jane wishes to bake an apple pie for dessert. The baking instructions say that she should bake the pie in an oven at a constant

Viktor [21]

Answer:

Therefore $k= \frac{ln2 }{18}$ , A=184

Step-by-step explanation:

Given function is

$T(t)=230 -e^{-kt}$

where T(t) is the temperature in °C and t is time in minute and A and k are constants.

She noticed that after 18 minutes the temperature of the pie is 138°C

Putting T(t) =138°C and t= 18 minutes

$138=230 -Ae^{-k\times 18}$

$\Rightarrow -Ae^{-18k}=138-230$

$\Rightarrow Ae^{-18k}=92$ .....(1)

Again after 36 minutes it is 184°C

Putting T(t) =184°C and t= 36 minutes

$184=230-Ae^{-k\times 36}$

$\Rightarrow Ae^{-36k}=230-184$

$\Rightarrow Ae^{-36k}=46$ .......(2)

Dividing (2) by (1)

$\frac{Ae^{-36k}}{Ae^{-18k}}=\frac{46}{92}$

$\Rightarrow e^{-18k}=\frac{46}{92}$

Taking ln both sides

$ln e^{-18k}=ln\frac{46}{92}$

$\Rightarrow -18k =ln (\frac12)$

$\Rightarrow -18k= ln1-ln2$

$\Rightarrow k= \frac{ln2 }{18}$

Putting the value k in equation (1)

$Ae^{-18\frac{ln2}{18}}=92$

$\Rightarrow A e^{ln2^{-1}}=92$

$\Rightarrow A.2^{-1}=92$

$\Rightarrow \frac{A}{2}=92$

$\Rightarrow A= 92 \times 2$

⇒A= 184.

Therefore $k= \frac{ln2 }{18}$ , A=184

7 0

2 years ago

Laila wants to create a data display to clearly show the median salary, the highest salary,

deff fn [24]

Answer:

a box plot

Step-by-step explanation:

Given the number of employees at her company is 685

If she chooses to create a dot plot, it means that she need to draw a lot, the total number of dots is 685 and even a wide domain of the number of data values on the x-axis.

If she chooses the box lot, which means that she wants to displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.

=> So it is the best fit for her choice.

If she chooses histogram, it means that she wants to group numbers into ranges to identify the underlying frequency distribution (shape) of a set of continuous data

Hope it will find you well

7 0

2 years ago

Read 2 more answers

A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto

Gre4nikov [31]

$\begin{cases}y=2x-2\\y=2x+2\end{cases}\implies\begin{cases}-2x+y=-2\\-2x+y=2\end{cases}$

For these lines, let $u=-2x+y$ .

$\begin{cases}y=2-x\\y=4-x\end{cases}\implies\begin{cases}x+y=2\\x+y=4\end{cases}$

And for these, let $v=x+y$ .

Now,

$\begin{cases}u=-2x+y\\v=x+y\end{cases}\implies \begin{bmatrix}u\\v\end{bmatrix}=\underbrace{\begin{bmatrix}-2&1\\1&1\end{bmatrix}}_{\mathbf T}\begin{bmatrix}x\\y\end{bmatrix}$

The vertices of $S$ in the x-y plane are (0, 2), (2/3, 10/3), (2, 2), and (4/3, 2/3). Applying $\mathbf T$ to each of these yields, respectively, (2, 2), (2, 4), (-2, 4), and (-2, 2), which are the vertices of a rectangle whose sides are parallel to the u-v plane.

6 0

2 years ago

Which of the following notations correctly describe the end behavior of the polynomial graphed below

Irina18 [472]

The answer is B
To visualize this, think of the first line as saying "As x approaches negative infinity, f(x) (or just y) approaches __". As the graph goes left, it goes up: so, as x approaches negative infinity, f(x) approaches infinity. As the graph goes right, it goes down: so, as x approaches infinity, f(x) approaches negative infinity.

5 0

2 years ago

Read 2 more answers

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with dia

Sav [38]

Answer:

10.12 $m^{3}$