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Inga [223]
2 years ago
10

Please help as soon as possible

Mathematics
1 answer:
patriot [66]2 years ago
3 0
17.5

5 is the og length. Scale factor is 3.5. So

5(3.5)=17.5
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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
2 years ago
The prism's base area is 8 square units and its height is 16 units. What is the volume of the pyramid?
bija089 [108]

Answer:

Step-by-step explanation:

Its about 42.67

4 0
3 years ago
If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in cm/min) at which the diameter d
grin007 [14]

Answer:

The diameter decreases at a rate of 0.053 cm/min.

Step-by-step explanation:

Surface area of an snowball

The surface area of an snowball has the following equation:

S_{a} = \pi d^2

In which d is the diameter.

Implicit differentiation:

To solve this question, we differentiate the equation for the surface area implictly, in function of t. So

\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}

Surface area decreases at a rate of 3 cm2/min

This means that \frac{dS_{a}}{dt} = -3

Tind the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm.

This is \frac{dd}{dt} when d = 9. So

\frac{dS_{a}}{dt} = 2d\pi\frac{dd}{dt}

-3 = 2*9\pi\frac{dd}{dt}

\frac{dd}{dt} = -\frac{3}{18\pi}

\frac{dd}{dt} = -0.053

The diameter decreases at a rate of 0.053 cm/min.

7 0
2 years ago
Order these numbers from least to greatest. 9.4061 , 9.07 , 9.007 , 9.4
klio [65]
9.4061,
9.07,
9.007,
9.4
Because ones are equal for all numbers, we are going to begin to compare from the second digits (tenths).
Greater :
9.4061 and 9.4.
Greatest is this group is 9.4061, then will go  9.4.

Smaller :
9.07 and 9.007
Greatest in this group is 9.07, and then will go 9.007.

So, from greatest to smallest : 9.4061 , 9.4 , 9.07 , 9.007.

From least to greatest :
9.007, 9.07, 9.4, 9.4061.
3 0
3 years ago
Given a matrix where every cell has some number of coins. count number of ways to reach bottom right from top left with exactly
boyakko [2]
Yes that is very true cause we ballin
8 0
2 years ago
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