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schepotkina [342]
3 years ago
9

How do I solve this problem?

Mathematics
2 answers:
bulgar [2K]3 years ago
6 0

Answer:

3\frac{4}{8} cups

Step-by-step explanation:

<u>To subtract two fractions with different denominators easily, you can find the LCM of the denominators to make a simple subtraction problem.</u>

LCM - <em>Lowest Common Multiple</em>

<u>To find the LCM of two numbers, write down each numbers' times tables until they have a common number:</u>

4 - 4, 8, 12, 16, 20,....

8 - 8, 16, 24, 32, 40,....

Because 8 is the first number to be in both numbers' multiples, it is the LCM of 4 and 8.

<u>Now that the LCM has been determined, you need both denominators to be 8. This is an easy process as it is simple multiplication:</u>

3 \frac{1}{4} → \frac{1}{4} × \frac{2}{2} = \frac{2}{8}

6 \frac{6}{8} → no multiplication needed.

<u>Now to subtract:</u>

6 \frac{6}{8} - 3 \frac{2}{8} = 3 \frac{4}{8}

Because the question does not want a simplified fraction, the final answer is 3 \frac{4}{8} cups.

romanna [79]3 years ago
3 0

Answer:

It will be 3 4/8 or 3 1/2

<u><em>PLS MARK BRAINLIEST</em></u>

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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

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