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Doss [256]
3 years ago
13

In a right triangle, <A and <B are acute. Find the value of sin A, when tan A = 8/15​

Mathematics
1 answer:
finlep [7]3 years ago
3 0

Answer:sinA=8/17

Step-by-step explanation:

Using Pythagoras principle

x=√(15^2+8^2)

x=√(15x15+8x8)

x=√(225+64)

x=√(289)

x=17

SinA=opposite/hypothenus

SinA=8/17

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Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software,
vichka [17]

Answer:

A(-1,0) is a local maximum point.

B(-1,0)  is a saddle point

C(3,0)  is a saddle point

D(3,2) is a local minimum point.

Step-by-step explanation:

The given function is  

f(x,y)=x^3+y^3-3x^2-3y^2-9x

The first partial derivative with respect to x is  

f_x=3x^2-6x-9

The first partial derivative with respect to y is  

f_y=3y^2-6y

We now set each equation to zero to obtain the system of equations;

3x^2-6x-9=0

3y^2-6y=0

Solving the two equations simultaneously, gives;

x=-1,x=3  and y=0,y=2

The critical points are

A(-1,0), B(-1,2),C(3,0),and D(3,2).

Now, we need to calculate the discriminant,

D=f_{xx}(x,y)f_{yy}(x,y)-(f_{xy}(x,y))^2

But, we would have to calculate the second partial derivatives first.

f_{xx}=6x-6

f_{yy}=6y-6

f_{xy}=0

\Rightarrow D=(6x-6)(6y-6)-0^2

\Rightarrow D=(6x-6)(6y-6)

At A(-1,0),

D=(6(-1)-6)(6(0)-6)=72\:>\:0 and f_{xx}=6(-1)-6=-18\:

Hence A(-1,0) is a local maximum point.

See graph

At B(-1,2);

D=(6(-1)-6)(6(2)-6)=-72\:

Hence, B(-1,0) is neither a local maximum or a local minimum point.

This is a saddle point.

At C(3,0)

D=(6(3)-6)(6(0)-6)=-72\:

Hence, C(3,0) is neither a local minimum or maximum point. It is a saddle point.

At D(3,2),

D=(6(3)-6)(6(2)-6)=72\:>\:0 and f_{xx}=6(3)-6=12\:>\:0

Hence D(3,2) is a local minimum point.

See graph in attachment.

3 0
3 years ago
Joey father stops at the gas station to buy gas the car has a 16 gallon tank and the. Fuel gauge says there is 3/8 of a tank of
Alex777 [14]

Answer:

\frac{3}{8} *16=6 gallons

Step-by-step explanation:


3 0
3 years ago
The formula is not giving me the answer I want ​
il63 [147K]

so is this the formula you trying to get an an see for?

4 0
3 years ago
A man shares a $1,200,00 inheritance between his 3 sons in ratio 1: 3: 6. Calculate the difference between the largest share and
soldi70 [24.7K]

A man's inheritance money = $1200

Given :

He shared his inheritance between his 3 sons in the ratio 1:3:6

Then, the money the first son got :

= \tt \frac{1}{10}  \: of  \: 1200

=\tt  \frac{1}{10}  \times 1200

=\tt  \frac{1 \times 120}{10}

= \tt \frac{1200}{10}

\color{plum} =\tt\$ \: 120

▪︎Thus, the first son inherited $120.

Money the second son got :

= \tt \frac{3}{10}  \: of  \: 1200

= \tt \frac{3}{10}  \times 1200

=\tt  \frac{3 \times 1200}{10}

= \tt \frac{3600}{10}

\color{plum} =\tt \$360

▪︎Thus, the second son inherited $360.

Money the third son got :

=\tt  \frac{6}{10}  \: of  \: 1200

=\tt  \frac{6}{10}  \times 1200

= \tt \frac{6 \times 1200}{10}

= \tt \frac{7200}{10}

\color{plum} = \tt\$720

▪︎Thus, the third son inherited $720.

We know that :

The largest share = $720

The smallest share = $120

Difference between the largest and smallest share :

= \tt720 - 120

\color{hotpink}\tt = 600

<h3> ●=> Therefore :</h3>

▪︎<em>The difference between the largest and smallest share = 600</em>

7 0
3 years ago
In an ice cream shop there is some money in a drawer. After 6 ice creams were sold, there were 70 euros left in the drawer. Afte
Verizon [17]

Answer: There were 40 euros in the drawer at the beginning.

Step-by-step explanation:

When we subtract 6 from 16, we get 10 more ice-creams were sold.

Similarly, we subtract 70 from 120, we get 50 euros was the total selling price of 10 ice-creams.

i.e. Selling price of 1 ice-cream = (50)÷10 =5 euros

Selling price of 6 ice-creams = 6 x 5 = 30 euros

Money in the drawer at the beginning = 70-30 = 40 euros

Hence, there were 40 euros in the drawer at the beginning.

7 0
3 years ago
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