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3 years ago

Find the value of g(7) for the function below.

Mathematics

1 answer:

algol [13]3 years ago

4 0

To get this you substitute 7 for the x.

7/8(7)-1/2

49/8-1/2

49/8-4/8

45/8 is the value.

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Fill in the blank with the correct response. The slope of the graph of y= x is___

motikmotik

Answer:

Step-by-step explanation:

y=mx+c

m is the gradient/slope

y=1x

hence m=1

5 0

3 years ago

Find the mass at time t=0. ANSWER HAS TO BE IN GRAMS

777dan777 [17]

For part (a) the answer is 400 grams for part (b) 198.63 grams and for part (c) 20 years.

<h3>What is exponential decay?</h3>

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an equation for radioactive decay:

$\rm m(t) = 400e^{-0.035t}$

a) Plug t = 0

$\rm m(0) = 400e^{-0.035\times 0}$

m(0) = 400 grams

b) plug t = 20 years

$\rm m(20) = 400e^{-0.035\times 20}$

After solving:

m(20) = 198.63 grams

c) Plug m(t) = m(0)/2 = 400/2 = 200 grams

$\rm 200 = 400e^{-0.035t}$

x = 19.80 years ≈ 20 years

Thus, for part (a) the answer is 400 grams for part (b) 198.63 grams and for part (c) 20 years.

Learn more about the exponential decay here:

brainly.com/question/14355665

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3 0

2 years ago

Find the measure of the arc or angle indicated

mr_godi [17]

Answer:

Step-by-step explanation:

6 0

3 years ago

The number a point corresponds to on a number line is called it's

cestrela7 [59]

It's called a coordinate

8 0

3 years ago

Find the? inverse, if it? exists, for the given matrix.<br><br> [4 3]<br><br> [3 6]

True [87]

Answer:

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Step-by-step explanation:

The inverse of a square matrix $A$ is $A^{-1}$ such that

$A A^{-1}=I$ where I is the identity matrix.

Consider, $A = \left[\begin{array}{ccc}4&3\\3&6\end{array}\right]$

$\mathrm{Matrix\:can\:only\:be\:inverted\:if\:it\:is\:non-singular,\:that\:is:}$

$\det \begin{pmatrix}4&3 \\3&6\end{pmatrix}\ne 0$

$\mathrm{Find\:2x2\:matrix\:inverse\:according\:to\:the\:formula}:\quad \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$

$=\frac{1}{\det \begin{pmatrix}4&3\\ 3&6\end{pmatrix}}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc$

$4\cdot \:6-3\cdot \:3=15$

$=\frac{1}{15}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}$

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

Therefore, the inverse of given matrix is

$=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}$

4 0

3 years ago