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2 years ago

23:

Mathematics

2 answers:

irina [24]2 years ago

8 0

Answer:

$(-\frac{3}{7}, 0)$ -- x intercept

$(0,3)$ -- y intercept

Step-by-step explanation:

Given

$y = 7x + 3$

Required

Determine the x and y intercept

For x intercept.

Set $y = 0$

So, we have:

$y = 7x + 3$

$0 = 7x + 3$

Collect Like Terms

$7x = -3$

Make x the subject

$x = -\frac{3}{7}$

Hence, the x intercept is: $(-\frac{3}{7}, 0)$

For the y intercept;

Set $x = 0$

So, we have:

$y = 7x + 3$

$y = 7*0 + 3$

$y = 0 + 3$

$y = 3$

Hence, the y intercept is: $(0,3)$

RUDIKE [14]2 years ago

6 0

AnswerB

Step-by-step explanation:

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The percent of concentration of a certain drug in the bloodstream x hours after the drug is administered is given by K(x) 5x/x^2

Olegator [25]

Given :

The percent of concentration of a certain drug in the bloodstream x hours after the drug is administered is given by $K(x) = \dfrac{5x}{x^2+9}$ .

To Find :

Find the time at which the concentration is a maximum. b. Find the maximum concentration.

Solution :

For maximum value of x, K'(x) = 0.

$K'(x) = \dfrac{5(x^2+9)- 5x(2x)}{(x^2+9)^2}=0\\\\5x^2+45-10x^2=0\\\\5x^2 = 45\\\\x = \pm 3$

Since, time cannot be negative, so ignoring x = -3 .

Putting value of x = 3, we get, K(3) = 15/( 9 + 9) = 5/6

Therefore, maximum value drug in bloodstream is 5/6 at time x = 3 units.

Hence, this is the required solution.

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2 years ago

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igomit [66]

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3 years ago

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Shkiper50 [21]

answer: (-6,6) that's youre answer

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2 years ago

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Over the interval [0,2pi), what are the solutions to cos(2x) = cos(x)? check all that apply

kykrilka [37]

$\cos(2x) = \cos(x)$

Solution (1)

$2x = x + 2k\pi$

$2x - x = 2k\pi$

$x = 2k\pi$

for k=0 / for k=1 / for k=-1

x=0 / x=2π / x=-2π

acc / acc / rej

solution (2)

$2x = - x + 2k\pi$

$2x + x = 2k\pi$

$3x = 2k\pi$

$x = \frac{2k\pi}{3}$

for k=0 / for k=1 / for k=-1

x=0 / x=2π/3 / x=-2π/3

acc / acc / rej

Note that i'm trying values of K which make the answer belong to our interval;

So our solution which i will represent as a set is;

S € {0,2π/3,2π}

6 0

2 years ago

The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of

Goryan [66]

ANSWER

The length of a Diameter is 3.714

EXPLANATION

The circumscribed triangle is shown in the attachment.

We use the cosine ratio to find the altitude of the isosceles triangle.

$\cos(60 \degree) = \frac{altitude}{hypotenuse}$

$\cos(60 \degree) = \frac{altitude}{8}$

Altitude =8cos(60°)

Altitude=4cm

Let the upper half of the altitude be y cm.

Then the radius of the circle is (y-4)cm

The upper radius meets the tangent at right angles.

From the smaller right triangle,

$\sin(60 \degree) = \frac{4 - y}{y}$

$y\sin(60 \degree) = 4 - y$

$y\sin(60 \degree) + y= 4$

$(\sin(60 \degree) + 1)y= 4$

$y= \frac{4}{\sin(60 \degree) + 1}$

$y = 16 - 8 \sqrt{3}$

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The diameter is 2y

$d = 32 - 16 \sqrt{3}$

=2(1.875)

The length of a Diameter is 3.714

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2 years ago

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