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marissa [1.9K]
3 years ago
6

Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travel

s 4 miles east to the gas station. Then, from the gas station, she travels 5 miles to return home. The entire trip forms a triangle. What was the smallest angle made in her trip?
It is at the gas station.
It is at Lucy’s home.
It is at the post office.
It depends on the direction Lucy is traveling.
Mathematics
1 answer:
Gwar [14]3 years ago
3 0

Answer:

A. It is at the gas station

Step-by-step explanation:

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Help pls look at question, I'm confused so yeah.
lions [1.4K]

Answer

225 ml

Step-by-step explanation:

90 ml =2 parts

1 part=45

5 parts= 225

5 0
3 years ago
Find the absolute maximum and minimum values of f(x,y)=xy−4x in the region bounded by the x-axis and the parabola y=16−x2.
skad [1K]

Answer:

The absolute maximum and minimum is 20\; \text{and} -20.

Step-by-step explanation:

We first check the critical points on the interior of the domain using the

first derivative test.

f_x=y-4=0

f_y=x=0

The only solution to this system of equations is the point (0, 4), which lies in the domain.

f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1

\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1

\therefore (0,4) is a saddle point.

Boundary points -  (4,0),  (-4,0), (0,16)

Along boundary  y=16-x^2

   f=x(16-x^2)-4x

=16x-x^3-4x

\Rightarrow f^'=16-3x^2-4=0

\Rightarrow 3x^2=12

\Rightarrow x=\pm2,\;\;y=14

Values of f(x) at these points.

\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}

Therefore, the absolute maximum and minimum is 20\; \text{and} -20.

6 0
3 years ago
What is the range of possible values for x?
Talja [164]
The minimum value for 2x is 0 
<span>the maximum value is achieved when A, D and C are collinear and the quadrilateral ABCD becomes an isosceles triangle ABC </span>
<span>base AB = 52 and vertical angle 2x + 34° </span>

<span>For the sine law </span>
<span>(sin 2x)/22 = (sin ADB)/AB </span>
<span>(sin 34°)/30 = (sin BDC)/BC </span>

<span>is given that AB = BC, and sin ADC = sin BDC because they are supplementary, so from </span>
<span>(sin ADC)/AB = (sin BDC)/BC </span>

<span>it follows </span>
<span>(sin 2x)/22 = (sin 34°)/30 </span>

<span>sin 2x = 22 (sin 34°)/30 </span>

<span>2x = asin(22 (sin 34°)/30) ≈ 24.2° </span>

<span>x = 0.5 asin(22 (sin 34°)/30) ≈ 12.1° </span>

<span>0 < x < 12.1°</span>
7 0
3 years ago
Solve, leaving in terms of a logarithm, with steps please! 160(0.4^x) +1=321
ludmilkaskok [199]

Answer:

321

Step-by-step explanation:

4 0
3 years ago
Half of a set of the parts are manufactured by machine A and half by machine B. Ten percent of all the parts are defective. Six
baherus [9]

Answer:

The probability that a part was manufactured on machine A is 0.3

Step-by-step explanation:

Consider the provided information.

It is given that Half of a set of parts are manufactured by machine A and half by machine B.  

P(A)=0.5

Let d represents the probability that part is defective.

Ten percent of all the parts are defective.

P(d) = 0.10

Six percent of the parts manufactured on machine A are defective.

P(d|A)=0.06

Now we need to find the probability that a part was manufactured on machine A, and given that the part is defective :

P(A|d) =\frac{P(A \cap d)}{P(d)}

P(A|d) =\frac{P(d|A)\times P(A)}{P(d)}\\P(A|d)= \frac{0.06\times 0.5}{0.10}

P(A|d)= 0.3

Hence, the probability that a part was manufactured on machine A is 0.3

8 0
3 years ago
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