Graph the linear equation using intercepts. Use a graphing calculator to check your graph.

dalvyx [7]

The answer to the question is 70.6179775281. which also can be converted to 71.

7 0

3 years ago

A line tangent to the curve f(x)=1/(2^2x) at the point (a, f(a)) has a slope of -1. What is the x-intercept of this tangent?

kirza4 [7]

Answer:

x-intercept = 0.956

Step-by-step explanation:

You have the function f(x) given by:

$f(x)=\frac{1}{2^{2x}}$ (1)

Furthermore you have that at the point (a,f(a)) the tangent line to that point has a slope of -1.

You first derivative the function f(x):

$\frac{df}{dx}=\frac{d}{dx}[\frac{1}{2^{2x}}]$ (2)

To solve this derivative you use the following derivative formula:

$\frac{d}{dx}b^u=b^ulnb\frac{du}{dx}$

For the derivative in (2) you have that b=2 and u=2x. You use the last expression in (2) and you obtain:

$\frac{d}{dx}[2^{-2x}]=2^{-2x}(ln2)(-2)$

You equal the last result to the value of the slope of the tangent line, because the derivative of a function is also its slope.

$-2(ln2)2^{-2x}=-1$

Next, from the last equation you can calculate the value of "a", by doing x=a. Furhtermore, by applying properties of logarithms you obtain:

$-2(ln2)2^{-2a}=-1 \\\\2^{2a}=2(ln2)=1.386\\\\log_22^{2a}=log_2(1.386)\\\\2a=\frac{log(1.386)}{log(2)}\\\\a=0.235$

With this value you calculate f(a):

$f(a)=\frac{1}{2^{2(0.235)}}=0.721$

Next, you use the general equation of line:

$y-y_o=m(x-x_o)$

for xo = a = 0.235 and yo = f(a) = 0.721:

$y-0.721=(-1)(x-0.235)\\\\y=-x+0.956$

The last is the equation of the tangent line at the point (a,f(a)).

Finally, to find the x-intercept you equal the function y to zero and calculate x:

$0=-x+0.956\\\\x=0.956$

hence, the x-intercept of the tangent line is 0.956

5 0

3 years ago

1. LeAnn has 20 coins in her piggy bank. All the coins are either pennies or dimes. The total value of the coins is 83 cents. H

mafiozo [28]

There is 7 dimes and 13 pennies

8 0

3 years ago

Footlocker in the mall is having a 25% off sale on all tennis shoes. Joe paid $67.50 for his

marta [7]

Answer:

The original price of the shoes was $90.

Step-by-step explanation:

25% off means the price Joe paid for it is 75% of the original price.

Set up an equation:

75/100 = 67.50/x

Cross multiply

75 × x = 100 × 67.50

75x = 6750

x = 90

Check our work:

First solve for 25% off of 90 (our answer).

25% = 0.25

90 × 0.25 = 22.50

Next, subtract the discount from 90.

90 - 22.50 = 67.50

67.50 was what Joe paid so this is correct.

8 0

3 years ago

Two kilos of taronges and three kilos of mandarins cost 11.50 euros. Three kilos of taronges and two of mandarins cost 11 euros.

Illusion [34]

Answer:

Hence the pricing for each product will be taronges with 2 euros and mandarins with 2.5 euros.

Step-by-step explanation:

Given:

2 kg of taronges and 3 kg mandarins cost 11.5 euros

3kg taronges and 2 kg mandarins cost 11 euros

To Find:

Price for each product

Solution:

Consider 

Taronges =x euros

Mandarins=y euros

So by given condition,

$2x+3y=11.5$ ....................equation(1)

and $3x+2y=11 ...$ ...........equation (2)

So , using substitution method,

$3x=11-2y$

$x=11-2y/3$ .......equation (3)

Using above value in equation(1) we get ,

$2(11-2y)/3+3y=11.5$

$y=(11.5*3-22)/5$ )

y=2.5 euros

Using above value in equation(3) we get ,

$x=(11-2y)/3$

$x=(11-2*2.5)/3$

$x=(11-5)/3$

x=2 euros

5 0

3 years ago