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Ilya [14]
3 years ago
7

Help me with my math plz

Mathematics
2 answers:
sergij07 [2.7K]3 years ago
7 0
You could solve this by finding the area of the WHOLE figure and subtracting the piece that is taken out.
The area of the WHOLE rectangle is 18 * 15 = 270.
The area of the piece taken out is 9 * 10 = 90.
270 - 90 = 180 in^2
Gwar [14]3 years ago
5 0
Let's separate this shape into three parts. A smaller rectangle at the top, and one at the bottom, and a bigger rectangle in the middle.

The smaller rectangle at the top:

The equation to find the area of a rectangle is
(a = area, l = lenght, w = width)

a = l · w
Put in the values
a = 18 · 3
a = 54

Since the smaller rectangle at the bottom has the same length and width, it has the same area. 

The bigger rectangle in the middle:

a = l · w
Put in the values
a = 8 · 9
a = 72

Now add all of the areas together to get the answer!

72 + 54 + 54 = 180

The answer is 180 :)

Hopefully this helps! If you have any more questions or don't understand, feel free to DM me, and I'll get back to you ASAP! :)
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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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Jonathan purchased 30 markers for $5.40. What is the price per marker?
madreJ [45]

Answer: 0.18 is your answer

Step-by-step explanation:

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Ivahew [28]
It would take her 1 hour to earn $1, you don’t get paid by the minutes.
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Larry read a 400400400-page book. He read at a rate of 101010 pages per day for ddd days. Write an equation that could be used t
ira [324]

Answer:

From Larry's rate, the equation can be given as D = T/101010

Step-by-step explanation:

Larry's book has 400400400 pages

His reading rate is 101010 pages per day

Let D = Number of days to read the book

To get the number of days it takes fro Larry to read this book, we say

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Let Total pages = T

and Reading rate = R

Hence;

D = T / R

From Larry's rate, the equation can be given as D = T/101010.

From the question,

ddd = 400400400 (pages) / 101010 (pages/day) = 3963.9 days

Hence, it takes Larry approximately 3964 days to read the book.

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