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3 years ago

How do you do this problem?

Mathematics

1 answer:

zhenek [66]3 years ago

5 0

Answer:

A) g is increasing, and the graph of g is concave up.

Step-by-step explanation:

g'(x) = ∫₀ˣ e^(-t³) dt

Since e^(-t³) is always positive, ∫₀ˣ e^(-t³) dt is positive when x > 0. So the function is increasing.

Find g"(x) by taking the derivative using second fundamental theorem of calculus:

g"(x) = e^(-x³)

g"(x) is always positive, so the function is always concave up.

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I have completed the first three parts of this question, but now need help to finish...I need to calculate the ratios of the 4 l

galben [10]

At first, we will find the lengths of LK, Lm, ON, OP, then use them to find the ratios between them

The rule of the distance is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

For LK

Since L = (3, 6), K = (1,5.33), then

$\begin{gathered} LK=\sqrt{(3-1)^2+(6-5.33)^2} \\ LK=\sqrt{4+0.4489} \\ LK=\sqrt{4.4489} \end{gathered}$

For LM

Since L = (3, 6), M = (5, 6.67), then

$\begin{gathered} LM=\sqrt{(3-5)^2+(6-6.67)^2} \\ LM=\sqrt{4+0.4489} \\ LM=\sqrt{4.4489} \end{gathered}$

For ON

Since O = (3, 2.59) and N = (5, 4.2), then

$\begin{gathered} ON=\sqrt{(3-5)^2+(2.59-4.2)} \\ ON=\sqrt{4+2.5921} \\ ON=\sqrt{6.5921} \end{gathered}$

For OP

Since O = (3, 2.59), P = (1, 0.99), then

$\begin{gathered} OP=\sqrt{(3-1)^2+(2.59-0.99)^2} \\ OP=\sqrt{4+2.56} \\ OP=\sqrt{6.56} \end{gathered}$

Now let us find the ratios between them

$\begin{gathered} \frac{KL}{LM}=\frac{\sqrt{4.4489}}{\sqrt{4.4489}}=1 \\ \frac{PO}{ON}=\frac{\sqrt{6.56}}{\sqrt{6.5921}}=0.9975\approx1 \\ \frac{KL}{LM}=\frac{PO}{ON}=1 \end{gathered}$

That means, Parallel lines intercept equal parts

By joining MP

We will have Triangle KPM

Since KL = LM ------- Proved using the distance formula

Since LQ // KP ------ Given

Then MQ = QP ------- Using the theorem down

The theorem

If a line is drawn from a midpoint of one side of a triangle parallel to the opposite side, then it will intersect the 3rd side in its midpoint (Q is the midpoint of MP)

Parallel lines intercept equal parts

7 0

1 year ago

Re-write the quadratic function below in Standard Form<br> y =4(x + 5)2 – 3

Alenkasestr [34]

Answer:

I love algebra anyways

The ans is in the picture with the steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation: