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2 years ago

I need help with this question.

Mathematics

1 answer:

Strike441 [17]2 years ago

8 0

Answer:

Step-by-step explanation:

30/x = 25/100

cross multiply

3,000=25x

3,000/25=25x/25

3,000/25=120

60% of 120 = 60/100*120

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Find all values of x (if any) where the tangent line to the graph of the given equation is horizontal. HINT [The tangent line is

Nostrana [21]

By "y = −9x2 − 2x" I assume you meant y = −9x^2 − 2x (the "^" symbol represents exponentiation).

Let's find the first derivative of y with respect to x: dy/dx = -18x - 2. This is equivalent to the slope of the tangent line to the (parabolic) curve. Now let this derivative (slope) = 0 and solve for the critical value: -18x - 2 = 0, or
-18x = 2. Solving for x, x = -2/18, or x = -1/9.

When x = -1/9, y = -9(-1/9)^2 - 2(-1/9). This simplifies to y = -9/9 + 2/9, or
y = -7/9.

The only point at which the tangent to the curve is horiz. is (-1/9,-7/9).

6 0

3 years ago

A competitive knitter is knitting a circular place mat. The radius of the mat is given by the formula

Ilia_Sergeevich [38]

Answer: A. $A'(t)=\frac{4356\pi}{(t+11)^{3}}-\frac{527076\pi}{(t+11)^{5}}$

B. A'(5) = 1.76 cm/s

Step-by-step explanation: Rate of change measures the slope of a curve at a certain instant, therefore, rate is the derivative.

A. Area of a circle is given by

$A=\pi.r^{2}$

So to find the rate of the area:

$\frac{dA}{dt}=\frac{dA}{dr}.\frac{dr}{dt}$

$\frac{dA}{dr} =2.\pi.r$

Using $r(t)=3-\frac{363}{(t+11)^{2}}$

$\frac{dr}{dt}=\frac{726}{(t+11)^{3}}$

Then

$\frac{dA}{dt}=2.\pi.r.[\frac{726}{(t+11)^{3}}]$

$\frac{dA}{dt}=2.\pi.[3-\frac{363}{(t+11)^{2}}].\frac{726}{(t+11)^{3}}$

Multipying and simplifying:

$\frac{dA}{dt}=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$

The rate at which the area is increasing is given by expression $A'(t)=\frac{4356\pi}{(t+11)^{3}} -\frac{527076\pi}{(t+11)^{5}}$ .

B. At t = 5, rate is:

$A'(5)=\frac{4356\pi}{(5+11)^{3}} -\frac{527076\pi}{(5+11)^{5}}$

$A'(5)=\frac{4356\pi}{4096} -\frac{527076\pi}{1048576}$

$A'(5)=\frac{2408693760\pi}{4294967296}$

$A'(5)=1.76268$

At 5 seconds, the area is expanded at a rate of 1.76 cm/s.

5 0

3 years ago

5-7:

garri49 [273]

The 3 panes would cost $7.65.

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3 years ago

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Chinese checkers is a game in which players move their pieces across a board using single moves or jumps like the traditional ga

DENIUS [597]

A. it is a hexagon (there are 6 sides) B. using the equation (n-2)180 (where n is the number of sides we get (6-2)180=4*180=720. divide 720 by 6 to get 120 for each angle of the hexagon. (it has no irregularities in it's shape so that number will be correct for them all.) C. to get that just divide 39 by 6 to get 6.5 in per side. Hope that helps:)

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4 years ago

Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this

Anastasy [175]

Answer:

Step-by-step explanation:

Let X be average interest paid monthly by a bank's Visa cardholders

Given that X is N(28, 8)

In the following to find out probability we convert X to z score and use std normal distribution table

Z = $\frac{x-28}{8}$

Probability being less than 1 is here equal to the proportion also.

A) P(X>32) = P(Z>0.5)=0.5-0.1915=0.3085

B) P(X>40) = P(Z>1)=0.5-0.3413=0.1687

C) P(X<19) = P(Z<-1.125)=0.5-0.0438=0.4562

D) We have to find 19th percentile here

Z =-0.88

$X=28-0.88(8)\\=20.96$

5 0

3 years ago