All categories

3 years ago

What are the approximate values of the minimum and maximum points of

Mathematics

2 answers:

Vaselesa [24]3 years ago

4 0

Answer: The answers A

Step-by-step explanation:

Serga [27]3 years ago

3 0

Find critical points by setting derivative equal to 0.

Derivative of polynomial is found by multiplying coefficient by exponent, then subtracting 1 from exponent.

f'(x) = 5x^4 - 30x^2 + 9 = 0

This is in quadratic form, use quadratic formula to find x^2

$x^2 = \frac{15 \pm 6\sqrt{5}}{5} \\ \\ 
x = \pm\sqrt{\frac{15 \pm 6\sqrt{5}}{5}} = \pm 0.5628, \pm 2.384$

You might be interested in

Q20-23 with steps pls

just olya [345]

20: Let $x$ be the amount of money. If this amount is shared between 8 people, each person will get x/8 dollars. But there actually are 6 people, so everyone is getting x/6 dollars. We know that this difference results in 30 dollars more, so we have

$\dfrac{x}{6}=\dfrac{x}{8}+30 \iff \dfrac{x}{6}-\dfrac{x}{8}=30$

Rearrange the left hand side as

$\dfrac{4x-3x}{24}=30$

And multiply both sides by 24 to get

$x=720$

21: Let $M$ and $J$ be the number of marbles owned by Mike and Judy, respectively. At the beginning, we have

$M=3J+11$

If they both get 9 more marbles, Mike will have $M+9$ marbles, and Judy will have $J+9$ marbles. So, we have

$M+J+18=93 \iff M+J=75 \iff M=75-J$

Plug this value in the first equation and we have

$75-J=3J+11 \iff 4J=64 \iff J=16$

And we deduce

$M=16\cdot 3 + 11=59$

So, the difference is

$M-J=59-16=43$

22: Let $x,y,z$ be the number of $10, $20 and $50 coupon, respectively. We're given:

$\begin{cases}x=2y+3\\z=\frac{1}{2}y\\x+y+z=38\end{cases}
We can write the third equation by substituting the expressions for x and z:
[tex]x+y+z=(2y+3)+y+\left(\dfrac{1}{2}y\right)=38$

Rearrange as follows:

$(2y+3)+y+\left(\dfrac{1}{2}y\right)=38 \iff \dfrac{7}{2}y=35 \iff 7y=70 \iff y=10$

And now we can deduce the number of the other coupons:

$x=2\cdot 10+3=23,\quad z=\dfrac{1}{2}\cdot 10=5$

So, the total value is

$23\cdot 10+10\cdot 20+5\cdot 50=230+200+100=530$

23: a) In order to find the first three terms of the sequence, you just need to plug n=1,2,3:

$a_1=4\cdot 1+3=7,\quad a_2=4\cdot 2+3=11,\quad a_3=4\cdot 3+3=15$

b) We have

$a_r = 4r+3=71 \iff 4r=68 \iff r=\dfrac{68}{4}=17$

c) 105 is a term of the sequence if and only if there exists an integer k such that

$a_k=4k+3=105 \iff 4k = 102 \iff k=\dfrac{102}{4}=25.5$

So, 105 is not a term of the sequence.

8 0

4 years ago

Which pair of triangles can be proven congruent by SAS?

wolverine [178]

Answer:

top choice

Step-by-step explanation:

For SAS, you need a side followed by an angle followed by another side of one triangle to be congruent to the corresponding parts of another triangle.

The top choice shows side-angle-side.

The middle choice shows angle-side-angle.

The bottom choice shows side-side-side.

Answer: top choice

3 0

3 years ago

Read 2 more answers

Write a function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x).

lakkis [162]

The function that models the distance D from a point on the line y = 9 x - 8 to the point (0,0) (as a function of x) is y = 9x

Given the equation of a line in standard form as y = 9x - 8

Get the slope of the line

mx = 9x

m = 9

Since the line passes through the origin (0, 0), substitute the slope and the point in the point-slope form of the equation as shown below:

$y-y_0=m(x-x_0)$